id	sid	tid	token	lemma	pos
ap-652	1	1	ap04-bittnar2.vp	ap04-bittnar2.vp	NOUN
ap-652	1	2	1	1	NUM
ap-652	1	3	introduction	introduction	NOUN
ap-652	1	4	cellular	cellular	ADJ
ap-652	1	5	solids	solid	NOUN
ap-652	1	6	can	can	AUX
ap-652	1	7	either	either	CCONJ
ap-652	1	8	be	be	AUX
ap-652	1	9	found	find	VERB
ap-652	1	10	in	in	ADP
ap-652	1	11	nature	nature	NOUN
ap-652	1	12	or	or	CCONJ
ap-652	1	13	manufactured	manufacture	VERB
ap-652	1	14	by	by	ADP
ap-652	1	15	foaming	foaming	NOUN
ap-652	1	16	of	of	ADP
ap-652	1	17	polymers	polymer	NOUN
ap-652	1	18	,	,	PUNCT
ap-652	1	19	metals	metal	NOUN
ap-652	1	20	and	and	CCONJ
ap-652	1	21	ceramics	ceramic	NOUN
ap-652	1	22	,	,	PUNCT
ap-652	1	23	or	or	CCONJ
ap-652	1	24	by	by	ADP
ap-652	1	25	other	other	ADJ
ap-652	1	26	technologies	technology	NOUN
ap-652	1	27	,	,	PUNCT
ap-652	1	28	e.g.	e.g.	ADV
ap-652	1	29	by	by	ADP
ap-652	1	30	cvd	cvd	PROPN
ap-652	1	31	-	-	PUNCT
ap-652	1	32	chemical	chemical	ADJ
ap-652	1	33	vapor	vapor	NOUN
ap-652	1	34	deposition	deposition	NOUN
ap-652	1	35	,	,	PUNCT
ap-652	1	36	or	or	CCONJ
ap-652	1	37	dmls	dmls	VERB
ap-652	1	38	-	-	PUNCT
ap-652	1	39	direct	direct	ADJ
ap-652	1	40	metal	metal	NOUN
ap-652	1	41	laser	laser	NOUN
ap-652	1	42	sintering	sinter	VERB
ap-652	1	43	.	.	PUNCT
ap-652	2	1	they	they	PRON
ap-652	2	2	have	have	VERB
ap-652	2	3	a	a	DET
ap-652	2	4	wide	wide	ADJ
ap-652	2	5	range	range	NOUN
ap-652	2	6	of	of	ADP
ap-652	2	7	applications	application	NOUN
ap-652	2	8	namely	namely	ADV
ap-652	2	9	in	in	ADP
ap-652	2	10	absorbing	absorb	VERB
ap-652	2	11	the	the	DET
ap-652	2	12	kinetic	kinetic	ADJ
ap-652	2	13	energy	energy	NOUN
ap-652	2	14	from	from	ADP
ap-652	2	15	impacts	impact	NOUN
ap-652	2	16	,	,	PUNCT
ap-652	2	17	or	or	CCONJ
ap-652	2	18	as	as	ADP
ap-652	2	19	thermal	thermal	ADJ
ap-652	2	20	and	and	CCONJ
ap-652	2	21	electrical	electrical	ADJ
ap-652	2	22	insulators	insulator	NOUN
ap-652	2	23	.	.	PUNCT
ap-652	3	1	to	to	PART
ap-652	3	2	exploit	exploit	VERB
ap-652	3	3	these	these	DET
ap-652	3	4	properties	property	NOUN
ap-652	3	5	fully	fully	ADV
ap-652	3	6	and	and	CCONJ
ap-652	3	7	efficiently	efficiently	ADV
ap-652	3	8	,	,	PUNCT
ap-652	3	9	suitable	suitable	ADJ
ap-652	3	10	methodologies	methodology	NOUN
ap-652	3	11	allowing	allow	VERB
ap-652	3	12	a	a	DET
ap-652	3	13	detailed	detailed	ADJ
ap-652	3	14	characterization	characterization	NOUN
ap-652	3	15	of	of	ADP
ap-652	3	16	the	the	DET
ap-652	3	17	behavior	behavior	NOUN
ap-652	3	18	of	of	ADP
ap-652	3	19	the	the	DET
ap-652	3	20	cellular	cellular	ADJ
ap-652	3	21	solids	solid	NOUN
ap-652	3	22	are	be	AUX
ap-652	3	23	needed	need	VERB
ap-652	3	24	.	.	PUNCT
ap-652	4	1	in	in	ADP
ap-652	4	2	this	this	DET
ap-652	4	3	paper	paper	NOUN
ap-652	4	4	we	we	PRON
ap-652	4	5	will	will	AUX
ap-652	4	6	examine	examine	VERB
ap-652	4	7	the	the	DET
ap-652	4	8	upper	upper	ADJ
ap-652	4	9	bounds	bound	NOUN
ap-652	4	10	on	on	ADP
ap-652	4	11	homogenized	homogenized	ADJ
ap-652	4	12	linear	linear	ADJ
ap-652	4	13	elastic	elastic	ADJ
ap-652	4	14	properties	property	NOUN
ap-652	4	15	.	.	PUNCT
ap-652	5	1	a	a	DET
ap-652	5	2	cellular	cellular	ADJ
ap-652	5	3	solid	solid	ADJ
ap-652	5	4	(	(	PUNCT
ap-652	5	5	a	a	DET
ap-652	5	6	foam	foam	NOUN
ap-652	5	7	)	)	PUNCT
ap-652	5	8	is	be	AUX
ap-652	5	9	composed	compose	VERB
ap-652	5	10	of	of	ADP
ap-652	5	11	an	an	DET
ap-652	5	12	interconnected	interconnected	ADJ
ap-652	5	13	network	network	NOUN
ap-652	5	14	of	of	ADP
ap-652	5	15	solid	solid	ADJ
ap-652	5	16	beams	beam	NOUN
ap-652	5	17	and	and	CCONJ
ap-652	5	18	shell	shell	ADJ
ap-652	5	19	parts	part	NOUN
ap-652	5	20	,	,	PUNCT
ap-652	5	21	which	which	PRON
ap-652	5	22	can	can	AUX
ap-652	5	23	be	be	AUX
ap-652	5	24	assigned	assign	VERB
ap-652	5	25	to	to	ADP
ap-652	5	26	cells	cell	NOUN
ap-652	5	27	that	that	PRON
ap-652	5	28	are	be	AUX
ap-652	5	29	repeated	repeat	VERB
ap-652	5	30	in	in	ADP
ap-652	5	31	the	the	DET
ap-652	5	32	medium	medium	NOUN
ap-652	5	33	.	.	PUNCT
ap-652	6	1	two	two	NUM
ap-652	6	2	essential	essential	ADJ
ap-652	6	3	features	feature	NOUN
ap-652	6	4	characterize	characterize	VERB
ap-652	6	5	cellular	cellular	ADJ
ap-652	6	6	media	medium	NOUN
ap-652	6	7	:	:	PUNCT
ap-652	6	8	�	�	PROPN
ap-652	6	9	the	the	DET
ap-652	6	10	size	size	NOUN
ap-652	6	11	of	of	ADP
ap-652	6	12	the	the	DET
ap-652	6	13	voids	voids	NOUN
ap-652	6	14	is	be	AUX
ap-652	6	15	very	very	ADV
ap-652	6	16	small	small	ADJ
ap-652	6	17	compared	compare	VERB
ap-652	6	18	to	to	ADP
ap-652	6	19	the	the	DET
ap-652	6	20	size	size	NOUN
ap-652	6	21	of	of	ADP
ap-652	6	22	the	the	DET
ap-652	6	23	full	full	ADJ
ap-652	6	24	medium	medium	NOUN
ap-652	6	25	,	,	PUNCT
ap-652	6	26	and	and	CCONJ
ap-652	6	27	thus	thus	ADV
ap-652	6	28	homogenization	homogenization	NOUN
ap-652	6	29	techniques	technique	NOUN
ap-652	6	30	(	(	PUNCT
ap-652	6	31	see	see	VERB
ap-652	6	32	duvaut	duvaut	NOUN
ap-652	6	33	(	(	PUNCT
ap-652	6	34	1976	1976	NUM
ap-652	6	35	)	)	PUNCT
ap-652	6	36	,	,	PUNCT
ap-652	6	37	bensoussan	bensoussan	ADJ
ap-652	6	38	at	at	ADP
ap-652	6	39	al	al	PROPN
ap-652	6	40	.	.	PUNCT
ap-652	7	1	(	(	PUNCT
ap-652	7	2	1978	1978	NUM
ap-652	7	3	)	)	PUNCT
ap-652	7	4	,	,	PUNCT
ap-652	7	5	suquet	suquet	NOUN
ap-652	7	6	(	(	PUNCT
ap-652	7	7	1985	1985	NUM
ap-652	7	8	)	)	PUNCT
ap-652	7	9	,	,	PUNCT
ap-652	7	10	bakhvalov	bakhvalov	NOUN
ap-652	7	11	and	and	CCONJ
ap-652	7	12	panasenko	panasenko	PROPN
ap-652	7	13	(	(	PUNCT
ap-652	7	14	1989	1989	NUM
ap-652	7	15	)	)	PUNCT
ap-652	7	16	,	,	PUNCT
ap-652	7	17	nemat	nemat	NOUN
ap-652	7	18	-	-	PUNCT
ap-652	7	19	nasser	nasser	PROPN
ap-652	7	20	and	and	CCONJ
ap-652	7	21	hori	hori	PROPN
ap-652	7	22	(	(	PUNCT
ap-652	7	23	1993	1993	NUM
ap-652	7	24	)	)	PUNCT
ap-652	7	25	)	)	PUNCT
ap-652	7	26	can	can	AUX
ap-652	7	27	be	be	AUX
ap-652	7	28	used	use	VERB
ap-652	7	29	in	in	ADP
ap-652	7	30	determining	determine	VERB
ap-652	7	31	of	of	ADP
ap-652	7	32	the	the	DET
ap-652	7	33	effective	effective	ADJ
ap-652	7	34	properties	property	NOUN
ap-652	7	35	.	.	PUNCT
ap-652	8	1	�	�	PROPN
ap-652	8	2	the	the	DET
ap-652	8	3	relative	relative	ADJ
ap-652	8	4	density	density	NOUN
ap-652	8	5	is	be	AUX
ap-652	8	6	low	low	ADJ
ap-652	8	7	,	,	PUNCT
ap-652	8	8	usually	usually	ADV
ap-652	8	9	below	below	ADP
ap-652	8	10	0.3	0.3	NUM
ap-652	8	11	(	(	PUNCT
ap-652	8	12	gibson	gibson	PROPN
ap-652	8	13	and	and	CCONJ
ap-652	8	14	ashby	ashby	PROPN
ap-652	8	15	(	(	PUNCT
ap-652	8	16	1988	1988	NUM
ap-652	8	17	)	)	PUNCT
ap-652	8	18	)	)	PUNCT
ap-652	8	19	.	.	PUNCT
ap-652	9	1	as	as	ADP
ap-652	9	2	a	a	DET
ap-652	9	3	consequence	consequence	NOUN
ap-652	9	4	,	,	PUNCT
ap-652	9	5	at	at	ADV
ap-652	9	6	least	least	ADV
ap-652	9	7	one	one	NUM
ap-652	9	8	dimension	dimension	NOUN
ap-652	9	9	of	of	ADP
ap-652	9	10	the	the	DET
ap-652	9	11	solid	solid	ADJ
ap-652	9	12	phase	phase	NOUN
ap-652	9	13	(	(	PUNCT
ap-652	9	14	thickness	thickness	NOUN
ap-652	9	15	)	)	PUNCT
ap-652	9	16	at	at	ADP
ap-652	9	17	the	the	DET
ap-652	9	18	cell	cell	NOUN
ap-652	9	19	level	level	NOUN
ap-652	9	20	is	be	AUX
ap-652	9	21	small	small	ADJ
ap-652	9	22	compared	compare	VERB
ap-652	9	23	to	to	ADP
ap-652	9	24	the	the	DET
ap-652	9	25	characteristic	characteristic	ADJ
ap-652	9	26	cell	cell	NOUN
ap-652	9	27	size	size	NOUN
ap-652	9	28	.	.	PUNCT
ap-652	10	1	this	this	DET
ap-652	10	2	condition	condition	NOUN
ap-652	10	3	justifies	justify	VERB
ap-652	10	4	the	the	DET
ap-652	10	5	use	use	NOUN
ap-652	10	6	of	of	ADP
ap-652	10	7	structural	structural	ADJ
ap-652	10	8	theories	theory	NOUN
ap-652	10	9	in	in	ADP
ap-652	10	10	homogenization	homogenization	NOUN
ap-652	10	11	calculations	calculation	NOUN
ap-652	10	12	instead	instead	ADV
ap-652	10	13	of	of	ADP
ap-652	10	14	the	the	DET
ap-652	10	15	full	full	ADJ
ap-652	10	16	3d	3d	PROPN
ap-652	10	17	elasticity	elasticity	NOUN
ap-652	10	18	model	model	NOUN
ap-652	10	19	.	.	PUNCT
ap-652	11	1	cellular	cellular	ADJ
ap-652	11	2	solids	solid	NOUN
ap-652	11	3	may	may	AUX
ap-652	11	4	be	be	AUX
ap-652	11	5	classified	classify	VERB
ap-652	11	6	as	as	ADP
ap-652	11	7	closed	closed	ADJ
ap-652	11	8	-	-	PUNCT
ap-652	11	9	cell	cell	NOUN
ap-652	11	10	,	,	PUNCT
ap-652	11	11	partly	partly	ADV
ap-652	11	12	open	open	ADJ
ap-652	11	13	-	-	PUNCT
ap-652	11	14	cell	cell	NOUN
ap-652	11	15	and	and	CCONJ
ap-652	11	16	open	open	ADJ
ap-652	11	17	-	-	PUNCT
ap-652	11	18	cell	cell	NOUN
ap-652	11	19	foams	foam	NOUN
ap-652	11	20	.	.	PUNCT
ap-652	12	1	in	in	ADP
ap-652	12	2	this	this	DET
ap-652	12	3	work	work	NOUN
ap-652	12	4	we	we	PRON
ap-652	12	5	will	will	AUX
ap-652	12	6	restrict	restrict	VERB
ap-652	12	7	our	our	PRON
ap-652	12	8	analysis	analysis	NOUN
ap-652	12	9	to	to	ADP
ap-652	12	10	open	open	ADJ
ap-652	12	11	-	-	PUNCT
ap-652	12	12	cell	cell	NOUN
ap-652	12	13	foams	foam	NOUN
ap-652	12	14	,	,	PUNCT
ap-652	12	15	which	which	PRON
ap-652	12	16	consist	consist	VERB
ap-652	12	17	solely	solely	ADV
ap-652	12	18	of	of	ADP
ap-652	12	19	solid	solid	ADJ
ap-652	12	20	beams	beam	NOUN
ap-652	12	21	.	.	PUNCT
ap-652	13	1	then	then	ADV
ap-652	13	2	the	the	DET
ap-652	13	3	name	name	NOUN
ap-652	13	4	repetitive	repetitive	ADJ
ap-652	13	5	lattice	lattice	NOUN
ap-652	13	6	structures	structure	NOUN
ap-652	13	7	can	can	AUX
ap-652	13	8	also	also	ADV
ap-652	13	9	be	be	AUX
ap-652	13	10	adopted	adopt	VERB
ap-652	13	11	.	.	PUNCT
ap-652	14	1	several	several	ADJ
ap-652	14	2	works	work	NOUN
ap-652	14	3	deal	deal	VERB
ap-652	14	4	with	with	ADP
ap-652	14	5	the	the	DET
ap-652	14	6	effective	effective	ADJ
ap-652	14	7	elastic	elastic	ADJ
ap-652	14	8	properties	property	NOUN
ap-652	14	9	of	of	ADP
ap-652	14	10	open	open	ADJ
ap-652	14	11	-	-	PUNCT
ap-652	14	12	cell	cell	NOUN
ap-652	14	13	foams	foam	NOUN
ap-652	14	14	or	or	CCONJ
ap-652	14	15	repetitive	repetitive	ADJ
ap-652	14	16	lattice	lattice	NOUN
ap-652	14	17	structures	structure	NOUN
ap-652	14	18	,	,	PUNCT
ap-652	14	19	but	but	CCONJ
ap-652	14	20	the	the	DET
ap-652	14	21	upper	upper	ADJ
ap-652	14	22	bounds	bound	NOUN
ap-652	14	23	on	on	ADP
ap-652	14	24	them	they	PRON
ap-652	14	25	are	be	AUX
ap-652	14	26	rarely	rarely	ADV
ap-652	14	27	analyzed	analyze	VERB
ap-652	14	28	.	.	PUNCT
ap-652	15	1	the	the	DET
ap-652	15	2	main	main	ADJ
ap-652	15	3	monograph	monograph	NOUN
ap-652	15	4	on	on	ADP
ap-652	15	5	cellular	cellular	ADJ
ap-652	15	6	solids	solid	NOUN
ap-652	15	7	was	be	AUX
ap-652	15	8	published	publish	VERB
ap-652	15	9	by	by	ADP
ap-652	15	10	gibson	gibson	PROPN
ap-652	15	11	and	and	CCONJ
ap-652	15	12	ashby	ashby	PROPN
ap-652	15	13	(	(	PUNCT
ap-652	15	14	1988	1988	NUM
ap-652	15	15	)	)	PUNCT
ap-652	15	16	.	.	PUNCT
ap-652	16	1	extensive	extensive	ADJ
ap-652	16	2	work	work	NOUN
ap-652	16	3	by	by	ADP
ap-652	16	4	christensen	christensen	PROPN
ap-652	16	5	has	have	AUX
ap-652	16	6	been	be	AUX
ap-652	16	7	dedicated	dedicate	VERB
ap-652	16	8	to	to	ADP
ap-652	16	9	the	the	DET
ap-652	16	10	characterization	characterization	NOUN
ap-652	16	11	of	of	ADP
ap-652	16	12	effectively	effectively	ADV
ap-652	16	13	isotropic	isotropic	ADJ
ap-652	16	14	open	open	ADJ
ap-652	16	15	-	-	PUNCT
ap-652	16	16	cell	cell	NOUN
ap-652	16	17	microstructures	microstructure	NOUN
ap-652	16	18	,	,	PUNCT
ap-652	16	19	where	where	SCONJ
ap-652	16	20	the	the	DET
ap-652	16	21	response	response	NOUN
ap-652	16	22	is	be	AUX
ap-652	16	23	governed	govern	VERB
ap-652	16	24	by	by	ADP
ap-652	16	25	bending	bend	VERB
ap-652	16	26	or	or	CCONJ
ap-652	16	27	direct	direct	ADJ
ap-652	16	28	(	(	PUNCT
ap-652	16	29	axial	axial	ADJ
ap-652	16	30	)	)	PUNCT
ap-652	16	31	resistance	resistance	NOUN
ap-652	16	32	,	,	PUNCT
ap-652	16	33	(	(	PUNCT
ap-652	16	34	christensen	christensen	PROPN
ap-652	16	35	(	(	PUNCT
ap-652	16	36	1994	1994	NUM
ap-652	16	37	,	,	PUNCT
ap-652	16	38	1995	1995	NUM
ap-652	16	39	)	)	PUNCT
ap-652	16	40	)	)	PUNCT
ap-652	16	41	.	.	PUNCT
ap-652	17	1	in	in	ADP
ap-652	17	2	christensen	christensen	PROPN
ap-652	17	3	(	(	PUNCT
ap-652	17	4	1995	1995	NUM
ap-652	17	5	)	)	PUNCT
ap-652	17	6	the	the	DET
ap-652	17	7	values	value	NOUN
ap-652	17	8	of	of	ADP
ap-652	17	9	the	the	DET
ap-652	17	10	upper	upper	ADJ
ap-652	17	11	bound	bind	VERB
ap-652	17	12	on	on	ADP
ap-652	17	13	the	the	DET
ap-652	17	14	effective	effective	ADJ
ap-652	17	15	bulk	bulk	NOUN
ap-652	17	16	and	and	CCONJ
ap-652	17	17	shear	shear	NOUN
ap-652	17	18	modulus	modulus	NOUN
ap-652	17	19	are	be	AUX
ap-652	17	20	presented	present	VERB
ap-652	17	21	.	.	PUNCT
ap-652	18	1	the	the	DET
ap-652	18	2	value	value	NOUN
ap-652	18	3	of	of	ADP
ap-652	18	4	the	the	DET
ap-652	18	5	bulk	bulk	ADJ
ap-652	18	6	modulus	modulus	NOUN
ap-652	18	7	bound	bind	VERB
ap-652	18	8	has	have	AUX
ap-652	18	9	also	also	ADV
ap-652	18	10	been	be	AUX
ap-652	18	11	addressed	address	VERB
ap-652	18	12	in	in	ADP
ap-652	18	13	several	several	ADJ
ap-652	18	14	other	other	ADJ
ap-652	18	15	works	work	NOUN
ap-652	18	16	,	,	PUNCT
ap-652	18	17	but	but	CCONJ
ap-652	18	18	only	only	ADV
ap-652	18	19	in	in	ADP
ap-652	18	20	the	the	DET
ap-652	18	21	sense	sense	NOUN
ap-652	18	22	of	of	ADP
ap-652	18	23	an	an	DET
ap-652	18	24	effective	effective	ADJ
ap-652	18	25	property	property	NOUN
ap-652	18	26	of	of	ADP
ap-652	18	27	some	some	DET
ap-652	18	28	particular	particular	ADJ
ap-652	18	29	microstructure	microstructure	NOUN
ap-652	18	30	,	,	PUNCT
ap-652	18	31	(	(	PUNCT
ap-652	18	32	see	see	VERB
ap-652	18	33	e.g.	e.g.	ADV
ap-652	18	34	warren	warren	PROPN
ap-652	18	35	and	and	CCONJ
ap-652	18	36	kraynik	kraynik	X
ap-652	18	37	(	(	PUNCT
ap-652	18	38	1988	1988	NUM
ap-652	18	39	,	,	PUNCT
ap-652	18	40	1997	1997	NUM
ap-652	18	41	)	)	PUNCT
ap-652	18	42	,	,	PUNCT
ap-652	18	43	kraynik	kraynik	PROPN
ap-652	18	44	and	and	CCONJ
ap-652	18	45	warren	warren	PROPN
ap-652	18	46	(	(	PUNCT
ap-652	18	47	1994	1994	NUM
ap-652	18	48	)	)	PUNCT
ap-652	18	49	,	,	PUNCT
ap-652	18	50	zhu	zhu	PROPN
ap-652	18	51	et	et	PROPN
ap-652	18	52	al	al	PROPN
ap-652	18	53	.	.	PROPN
ap-652	19	1	(	(	PUNCT
ap-652	19	2	1997	1997	NUM
ap-652	19	3	)	)	PUNCT
ap-652	19	4	)	)	PUNCT
ap-652	19	5	.	.	PUNCT
ap-652	20	1	methodologies	methodology	NOUN
ap-652	20	2	for	for	ADP
ap-652	20	3	determining	determine	VERB
ap-652	20	4	effective	effective	ADJ
ap-652	20	5	properties	property	NOUN
ap-652	20	6	can	can	AUX
ap-652	20	7	be	be	AUX
ap-652	20	8	discrete	discrete	ADJ
ap-652	20	9	or	or	CCONJ
ap-652	20	10	continuous	continuous	ADJ
ap-652	20	11	.	.	PUNCT
ap-652	21	1	discrete	discrete	ADJ
ap-652	21	2	approaches	approach	NOUN
ap-652	21	3	are	be	AUX
ap-652	21	4	usually	usually	ADV
ap-652	21	5	based	base	VERB
ap-652	21	6	on	on	ADP
ap-652	21	7	micromechanics	micromechanic	NOUN
ap-652	21	8	.	.	PUNCT
ap-652	22	1	they	they	PRON
ap-652	22	2	exploit	exploit	VERB
ap-652	22	3	either	either	CCONJ
ap-652	22	4	the	the	DET
ap-652	22	5	periodicity	periodicity	NOUN
ap-652	22	6	or	or	CCONJ
ap-652	22	7	the	the	DET
ap-652	22	8	regularity	regularity	NOUN
ap-652	22	9	of	of	ADP
ap-652	22	10	the	the	DET
ap-652	22	11	medium	medium	NOUN
ap-652	22	12	under	under	ADP
ap-652	22	13	consideration	consideration	NOUN
ap-652	22	14	.	.	PUNCT
ap-652	23	1	in	in	ADP
ap-652	23	2	the	the	DET
ap-652	23	3	former	former	ADJ
ap-652	23	4	case	case	NOUN
ap-652	23	5	,	,	PUNCT
ap-652	23	6	the	the	DET
ap-652	23	7	calculations	calculation	NOUN
ap-652	23	8	are	be	AUX
ap-652	23	9	performed	perform	VERB
ap-652	23	10	on	on	ADP
ap-652	23	11	a	a	DET
ap-652	23	12	unit	unit	NOUN
ap-652	23	13	or	or	CCONJ
ap-652	23	14	a	a	DET
ap-652	23	15	basic	basic	ADJ
ap-652	23	16	cell	cell	NOUN
ap-652	23	17	,	,	PUNCT
ap-652	23	18	while	while	SCONJ
ap-652	23	19	in	in	ADP
ap-652	23	20	the	the	DET
ap-652	23	21	latter	latter	ADJ
ap-652	23	22	case	case	NOUN
ap-652	23	23	either	either	CCONJ
ap-652	23	24	a	a	DET
ap-652	23	25	representative	representative	ADJ
ap-652	23	26	volume	volume	NOUN
ap-652	23	27	element	element	NOUN
ap-652	23	28	or	or	CCONJ
ap-652	23	29	a	a	DET
ap-652	23	30	typical	typical	ADJ
ap-652	23	31	joint	joint	NOUN
ap-652	23	32	is	be	AUX
ap-652	23	33	used	use	VERB
ap-652	23	34	.	.	PUNCT
ap-652	24	1	for	for	ADP
ap-652	24	2	instance	instance	NOUN
ap-652	24	3	in	in	ADP
ap-652	24	4	kraynik	kraynik	PROPN
ap-652	24	5	and	and	CCONJ
ap-652	24	6	warren	warren	PROPN
ap-652	24	7	(	(	PUNCT
ap-652	24	8	1994	1994	NUM
ap-652	24	9	)	)	PUNCT
ap-652	24	10	and	and	CCONJ
ap-652	24	11	warren	warren	PROPN
ap-652	24	12	and	and	CCONJ
ap-652	24	13	kraynik	kraynik	X
ap-652	24	14	(	(	PUNCT
ap-652	24	15	1997	1997	NUM
ap-652	24	16	)	)	PUNCT
ap-652	24	17	the	the	DET
ap-652	24	18	effective	effective	ADJ
ap-652	24	19	properties	property	NOUN
ap-652	24	20	are	be	AUX
ap-652	24	21	determined	determine	VERB
ap-652	24	22	by	by	ADP
ap-652	24	23	considering	consider	VERB
ap-652	24	24	a	a	DET
ap-652	24	25	tetrahedral	tetrahedral	ADJ
ap-652	24	26	joint	joint	NOUN
ap-652	24	27	(	(	PUNCT
ap-652	24	28	kelvin	kelvin	PROPN
ap-652	24	29	foam	foam	PROPN
ap-652	24	30	)	)	PUNCT
ap-652	24	31	under	under	ADP
ap-652	24	32	the	the	DET
ap-652	24	33	assumption	assumption	NOUN
ap-652	24	34	of	of	ADP
ap-652	24	35	affine	affine	NOUN
ap-652	24	36	displacements	displacement	NOUN
ap-652	24	37	.	.	PUNCT
ap-652	25	1	application	application	NOUN
ap-652	25	2	of	of	ADP
ap-652	25	3	this	this	DET
ap-652	25	4	methodology	methodology	NOUN
ap-652	25	5	to	to	ADP
ap-652	25	6	a	a	DET
ap-652	25	7	medium	medium	NOUN
ap-652	25	8	with	with	ADP
ap-652	25	9	randomly	randomly	ADV
ap-652	25	10	placed	place	VERB
ap-652	25	11	basic	basic	ADJ
ap-652	25	12	cells	cell	NOUN
ap-652	25	13	of	of	ADP
ap-652	25	14	the	the	DET
ap-652	25	15	regular	regular	ADJ
ap-652	25	16	cubic	cubic	ADJ
ap-652	25	17	lattice	lattice	NOUN
ap-652	25	18	yields	yield	NOUN
ap-652	25	19	also	also	ADV
ap-652	25	20	the	the	DET
ap-652	25	21	maximum	maximum	ADJ
ap-652	25	22	shear	shear	NOUN
ap-652	25	23	response	response	NOUN
ap-652	25	24	.	.	PUNCT
ap-652	26	1	in	in	ADP
ap-652	26	2	this	this	DET
ap-652	26	3	context	context	NOUN
ap-652	26	4	,	,	PUNCT
ap-652	26	5	we	we	PRON
ap-652	26	6	can	can	AUX
ap-652	26	7	also	also	ADV
ap-652	26	8	mention	mention	VERB
ap-652	26	9	the	the	DET
ap-652	26	10	work	work	NOUN
ap-652	26	11	of	of	ADP
ap-652	26	12	dimitrovová	dimitrovová	NOUN
ap-652	26	13	(	(	PUNCT
ap-652	26	14	1999	1999	NUM
ap-652	26	15	)	)	PUNCT
ap-652	26	16	,	,	PUNCT
ap-652	26	17	where	where	SCONJ
ap-652	26	18	there	there	PRON
ap-652	26	19	is	be	VERB
ap-652	26	20	a	a	DET
ap-652	26	21	detailed	detailed	ADJ
ap-652	26	22	discussion	discussion	NOUN
ap-652	26	23	of	of	ADP
ap-652	26	24	applicability	applicability	NOUN
ap-652	26	25	of	of	ADP
ap-652	26	26	the	the	DET
ap-652	26	27	orientational	orientational	ADJ
ap-652	26	28	averaging	averaging	NOUN
ap-652	26	29	to	to	ADP
ap-652	26	30	periodic	periodic	ADJ
ap-652	26	31	cells	cell	NOUN
ap-652	26	32	.	.	PUNCT
ap-652	27	1	among	among	ADP
ap-652	27	2	other	other	ADJ
ap-652	27	3	works	work	NOUN
ap-652	27	4	,	,	PUNCT
ap-652	27	5	grenestedt	grenestedt	NOUN
ap-652	27	6	(	(	PUNCT
ap-652	27	7	1998	1998	NUM
ap-652	27	8	)	)	PUNCT
ap-652	27	9	and	and	CCONJ
ap-652	27	10	li	li	PROPN
ap-652	27	11	,	,	PUNCT
ap-652	27	12	gao	gao	PROPN
ap-652	27	13	and	and	CCONJ
ap-652	27	14	roy	roy	PROPN
ap-652	27	15	(	(	PUNCT
ap-652	27	16	2003	2003	NUM
ap-652	27	17	)	)	PUNCT
ap-652	27	18	should	should	AUX
ap-652	27	19	also	also	ADV
ap-652	27	20	be	be	AUX
ap-652	27	21	mentioned	mention	VERB
ap-652	27	22	.	.	PUNCT
ap-652	28	1	continuum	continuum	ADJ
ap-652	28	2	modeling	modeling	NOUN
ap-652	28	3	of	of	ADP
ap-652	28	4	repetitive	repetitive	ADJ
ap-652	28	5	lattice	lattice	NOUN
ap-652	28	6	structures	structure	NOUN
ap-652	28	7	is	be	AUX
ap-652	28	8	reviewed	review	VERB
ap-652	28	9	by	by	ADP
ap-652	28	10	noor	noor	PROPN
ap-652	28	11	(	(	PUNCT
ap-652	28	12	1988	1988	NUM
ap-652	28	13	)	)	PUNCT
ap-652	28	14	.	.	PUNCT
ap-652	29	1	the	the	DET
ap-652	29	2	literature	literature	PROPN
ap-652	29	3	review	review	NOUN
ap-652	29	4	in	in	ADP
ap-652	29	5	this	this	DET
ap-652	29	6	paragraph	paragraph	NOUN
ap-652	29	7	is	be	AUX
ap-652	29	8	far	far	ADV
ap-652	29	9	from	from	ADP
ap-652	29	10	complete	complete	ADJ
ap-652	29	11	,	,	PUNCT
ap-652	29	12	because	because	SCONJ
ap-652	29	13	it	it	PRON
ap-652	29	14	is	be	AUX
ap-652	29	15	not	not	PART
ap-652	29	16	the	the	DET
ap-652	29	17	aim	aim	NOUN
ap-652	29	18	of	of	ADP
ap-652	29	19	this	this	DET
ap-652	29	20	paper	paper	NOUN
ap-652	29	21	to	to	PART
ap-652	29	22	determine	determine	VERB
ap-652	29	23	homogenized	homogenized	ADJ
ap-652	29	24	properties	property	NOUN
ap-652	29	25	,	,	PUNCT
ap-652	29	26	but	but	CCONJ
ap-652	29	27	their	their	PRON
ap-652	29	28	upper	upper	ADJ
ap-652	29	29	bounds	bound	NOUN
ap-652	29	30	.	.	PUNCT
ap-652	30	1	the	the	DET
ap-652	30	2	inverse	inverse	ADJ
ap-652	30	3	problem	problem	NOUN
ap-652	30	4	of	of	ADP
ap-652	30	5	identifying	identify	VERB
ap-652	30	6	microstructures	microstructure	NOUN
ap-652	30	7	that	that	PRON
ap-652	30	8	achieve	achieve	VERB
ap-652	30	9	the	the	DET
ap-652	30	10	prescribed	prescribe	VERB
ap-652	30	11	effective	effective	ADJ
ap-652	30	12	properties	property	NOUN
ap-652	30	13	has	have	AUX
ap-652	30	14	also	also	ADV
ap-652	30	15	been	be	AUX
ap-652	30	16	extensively	extensively	ADV
ap-652	30	17	studied	study	VERB
ap-652	30	18	(	(	PUNCT
ap-652	30	19	see	see	VERB
ap-652	30	20	,	,	PUNCT
ap-652	30	21	e.g.	e.g.	ADV
ap-652	30	22	sigmund	sigmund	NOUN
ap-652	30	23	(	(	PUNCT
ap-652	30	24	1994	1994	NUM
ap-652	30	25	)	)	PUNCT
ap-652	30	26	,	,	PUNCT
ap-652	30	27	neves	neve	NOUN
ap-652	30	28	et	et	PROPN
ap-652	30	29	al	al	PROPN
ap-652	30	30	.	.	PROPN
ap-652	31	1	(	(	PUNCT
ap-652	31	2	2000	2000	NUM
ap-652	31	3	)	)	PUNCT
ap-652	31	4	,	,	PUNCT
ap-652	31	5	gibiansky	gibiansky	NOUN
ap-652	31	6	and	and	CCONJ
ap-652	31	7	sigmund	sigmund	PROPN
ap-652	31	8	(	(	PUNCT
ap-652	31	9	2000	2000	NUM
ap-652	31	10	)	)	PUNCT
ap-652	31	11	,	,	PUNCT
ap-652	31	12	guedes	guede	NOUN
ap-652	31	13	et	et	PROPN
ap-652	31	14	al	al	PROPN
ap-652	31	15	.	.	PUNCT
ap-652	32	1	(	(	PUNCT
ap-652	32	2	2003	2003	NUM
ap-652	32	3	)	)	PUNCT
ap-652	32	4	)	)	PUNCT
ap-652	32	5	.	.	PUNCT
ap-652	33	1	these	these	DET
ap-652	33	2	methods	method	NOUN
ap-652	33	3	exploit	exploit	VERB
ap-652	33	4	homogenization	homogenization	NOUN
ap-652	33	5	techniques	technique	NOUN
ap-652	33	6	,	,	PUNCT
ap-652	33	7	starting	start	VERB
ap-652	33	8	with	with	ADP
ap-652	33	9	a	a	DET
ap-652	33	10	basic	basic	ADJ
ap-652	33	11	cell	cell	NOUN
ap-652	33	12	,	,	PUNCT
ap-652	33	13	whose	whose	DET
ap-652	33	14	shape	shape	NOUN
ap-652	33	15	must	must	AUX
ap-652	33	16	be	be	AUX
ap-652	33	17	specified	specify	VERB
ap-652	33	18	in	in	ADP
ap-652	33	19	advance	advance	NOUN
ap-652	33	20	,	,	PUNCT
ap-652	33	21	and	and	CCONJ
ap-652	33	22	then	then	ADV
ap-652	33	23	the	the	DET
ap-652	33	24	available	available	ADJ
ap-652	33	25	material	material	NOUN
ap-652	33	26	is	be	AUX
ap-652	33	27	optimally	optimally	ADV
ap-652	33	28	distributed	distribute	VERB
ap-652	33	29	within	within	ADP
ap-652	33	30	it	it	PRON
ap-652	33	31	.	.	PUNCT
ap-652	34	1	©	©	PROPN
ap-652	34	2	czech	czech	PROPN
ap-652	34	3	technical	technical	PROPN
ap-652	34	4	university	university	PROPN
ap-652	34	5	publishing	publishing	NOUN
ap-652	34	6	house	house	NOUN
ap-652	34	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	34	8	171	171	NUM
ap-652	34	9	acta	acta	PROPN
ap-652	34	10	polytechnica	polytechnica	PROPN
ap-652	34	11	vol	vol	NOUN
ap-652	34	12	.	.	PROPN
ap-652	35	1	44	44	NUM
ap-652	35	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	35	3	a	a	DET
ap-652	35	4	new	new	ADJ
ap-652	35	5	methodology	methodology	NOUN
ap-652	35	6	to	to	PART
ap-652	35	7	establish	establish	VERB
ap-652	35	8	upper	upper	ADJ
ap-652	35	9	bounds	bound	NOUN
ap-652	35	10	on	on	ADP
ap-652	35	11	open	open	ADJ
ap-652	35	12	-	-	PUNCT
ap-652	35	13	cell	cell	NOUN
ap-652	35	14	foams	foam	NOUN
ap-652	35	15	homogenized	homogenize	VERB
ap-652	35	16	properties	property	NOUN
ap-652	35	17	z.	z.	PROPN
ap-652	35	18	dimitrovová	dimitrovová	PROPN
ap-652	35	19	the	the	DET
ap-652	35	20	methodology	methodology	NOUN
ap-652	35	21	for	for	ADP
ap-652	35	22	determining	determine	VERB
ap-652	35	23	the	the	DET
ap-652	35	24	upper	upper	ADJ
ap-652	35	25	bounds	bound	NOUN
ap-652	35	26	on	on	ADP
ap-652	35	27	the	the	DET
ap-652	35	28	homogenized	homogenize	VERB
ap-652	35	29	linear	linear	ADJ
ap-652	35	30	elastic	elastic	ADJ
ap-652	35	31	properties	property	NOUN
ap-652	35	32	of	of	ADP
ap-652	35	33	cellular	cellular	ADJ
ap-652	35	34	solids	solid	NOUN
ap-652	35	35	,	,	PUNCT
ap-652	35	36	described	describe	VERB
ap-652	35	37	for	for	ADP
ap-652	35	38	the	the	DET
ap-652	35	39	two	two	NUM
ap-652	35	40	-	-	PUNCT
ap-652	35	41	dimensional	dimensional	ADJ
ap-652	35	42	case	case	NOUN
ap-652	35	43	in	in	ADP
ap-652	35	44	dimitrovová	dimitrovová	NOUN
ap-652	35	45	and	and	CCONJ
ap-652	35	46	faria	faria	PROPN
ap-652	35	47	(	(	PUNCT
ap-652	35	48	1999	1999	NUM
ap-652	35	49	)	)	PUNCT
ap-652	35	50	,	,	PUNCT
ap-652	35	51	is	be	AUX
ap-652	35	52	extended	extend	VERB
ap-652	35	53	to	to	ADP
ap-652	35	54	three	three	NUM
ap-652	35	55	-	-	PUNCT
ap-652	35	56	dimensional	dimensional	ADJ
ap-652	35	57	open	open	ADJ
ap-652	35	58	-	-	PUNCT
ap-652	35	59	cell	cell	NOUN
ap-652	35	60	foams	foam	NOUN
ap-652	35	61	.	.	PUNCT
ap-652	36	1	besides	besides	SCONJ
ap-652	36	2	the	the	DET
ap-652	36	3	upper	upper	ADJ
ap-652	36	4	bounds	bound	NOUN
ap-652	36	5	,	,	PUNCT
ap-652	36	6	the	the	DET
ap-652	36	7	methodology	methodology	NOUN
ap-652	36	8	provides	provide	VERB
ap-652	36	9	necessary	necessary	ADJ
ap-652	36	10	and	and	CCONJ
ap-652	36	11	sufficient	sufficient	ADJ
ap-652	36	12	conditions	condition	NOUN
ap-652	36	13	on	on	ADP
ap-652	36	14	optimal	optimal	ADJ
ap-652	36	15	media	medium	NOUN
ap-652	36	16	.	.	PUNCT
ap-652	37	1	these	these	DET
ap-652	37	2	conditions	condition	NOUN
ap-652	37	3	are	be	AUX
ap-652	37	4	written	write	VERB
ap-652	37	5	in	in	ADP
ap-652	37	6	terms	term	NOUN
ap-652	37	7	of	of	ADP
ap-652	37	8	generalized	generalized	ADJ
ap-652	37	9	internal	internal	ADJ
ap-652	37	10	forces	force	NOUN
ap-652	37	11	and	and	CCONJ
ap-652	37	12	geometrical	geometrical	ADJ
ap-652	37	13	parameters	parameter	NOUN
ap-652	37	14	.	.	PUNCT
ap-652	38	1	in	in	ADP
ap-652	38	2	some	some	DET
ap-652	38	3	cases	case	NOUN
ap-652	38	4	dependence	dependence	NOUN
ap-652	38	5	on	on	ADP
ap-652	38	6	internal	internal	ADJ
ap-652	38	7	forces	force	NOUN
ap-652	38	8	can	can	AUX
ap-652	38	9	be	be	AUX
ap-652	38	10	replaced	replace	VERB
ap-652	38	11	by	by	ADP
ap-652	38	12	geometrical	geometrical	ADJ
ap-652	38	13	expressions	expression	NOUN
ap-652	38	14	.	.	PUNCT
ap-652	39	1	in	in	ADP
ap-652	39	2	such	such	ADJ
ap-652	39	3	cases	case	NOUN
ap-652	39	4	,	,	PUNCT
ap-652	39	5	the	the	DET
ap-652	39	6	optimality	optimality	NOUN
ap-652	39	7	of	of	ADP
ap-652	39	8	some	some	DET
ap-652	39	9	medium	medium	NOUN
ap-652	39	10	under	under	ADP
ap-652	39	11	consideration	consideration	NOUN
ap-652	39	12	can	can	AUX
ap-652	39	13	be	be	AUX
ap-652	39	14	verified	verify	VERB
ap-652	39	15	directly	directly	ADV
ap-652	39	16	from	from	ADP
ap-652	39	17	the	the	DET
ap-652	39	18	microstructure	microstructure	NOUN
ap-652	39	19	,	,	PUNCT
ap-652	39	20	without	without	ADP
ap-652	39	21	any	any	DET
ap-652	39	22	additional	additional	ADJ
ap-652	39	23	calculation	calculation	NOUN
ap-652	39	24	.	.	PUNCT
ap-652	40	1	some	some	PRON
ap-652	40	2	of	of	ADP
ap-652	40	3	the	the	DET
ap-652	40	4	bounds	bound	NOUN
ap-652	40	5	derived	derive	VERB
ap-652	40	6	in	in	ADP
ap-652	40	7	this	this	DET
ap-652	40	8	paper	paper	NOUN
ap-652	40	9	are	be	AUX
ap-652	40	10	published	publish	VERB
ap-652	40	11	for	for	ADP
ap-652	40	12	the	the	DET
ap-652	40	13	first	first	ADJ
ap-652	40	14	time	time	NOUN
ap-652	40	15	,	,	PUNCT
ap-652	40	16	along	along	ADP
ap-652	40	17	with	with	ADP
ap-652	40	18	a	a	DET
ap-652	40	19	proof	proof	NOUN
ap-652	40	20	of	of	ADP
ap-652	40	21	their	their	PRON
ap-652	40	22	optimality	optimality	NOUN
ap-652	40	23	.	.	PUNCT
ap-652	41	1	keywords	keyword	NOUN
ap-652	41	2	.	.	PUNCT
ap-652	42	1	upper	upper	ADJ
ap-652	42	2	bounds	bound	NOUN
ap-652	42	3	on	on	ADP
ap-652	42	4	effective	effective	ADJ
ap-652	42	5	properties	property	NOUN
ap-652	42	6	,	,	PUNCT
ap-652	42	7	open	open	ADJ
ap-652	42	8	-	-	PUNCT
ap-652	42	9	cell	cell	NOUN
ap-652	42	10	foams	foam	NOUN
ap-652	42	11	,	,	PUNCT
ap-652	42	12	homogenization	homogenization	NOUN
ap-652	42	13	techniques	technique	NOUN
ap-652	42	14	,	,	PUNCT
ap-652	42	15	energy	energy	NOUN
ap-652	42	16	methods	method	NOUN
ap-652	42	17	,	,	PUNCT
ap-652	42	18	optimization	optimization	NOUN
ap-652	42	19	,	,	PUNCT
ap-652	42	20	optimal	optimal	ADJ
ap-652	42	21	microstructures	microstructure	NOUN
ap-652	42	22	.	.	PUNCT
ap-652	43	1	cellular	cellular	ADJ
ap-652	43	2	solids	solid	NOUN
ap-652	43	3	can	can	AUX
ap-652	43	4	be	be	AUX
ap-652	43	5	viewed	view	VERB
ap-652	43	6	as	as	ADP
ap-652	43	7	two	two	NUM
ap-652	43	8	-	-	PUNCT
ap-652	43	9	phase	phase	NOUN
ap-652	43	10	composites	composite	NOUN
ap-652	43	11	with	with	ADP
ap-652	43	12	void	void	ADJ
ap-652	43	13	and	and	CCONJ
ap-652	43	14	solid	solid	ADJ
ap-652	43	15	(	(	PUNCT
ap-652	43	16	generally	generally	ADV
ap-652	43	17	non	non	ADJ
ap-652	43	18	-	-	ADJ
ap-652	43	19	homogeneous	homogeneous	ADJ
ap-652	43	20	)	)	PUNCT
ap-652	43	21	phases	phase	NOUN
ap-652	43	22	.	.	PUNCT
ap-652	44	1	determining	determine	VERB
ap-652	44	2	the	the	DET
ap-652	44	3	bounds	bound	NOUN
ap-652	44	4	on	on	ADP
ap-652	44	5	composite	composite	ADJ
ap-652	44	6	effective	effective	ADJ
ap-652	44	7	properties	property	NOUN
ap-652	44	8	has	have	AUX
ap-652	44	9	been	be	AUX
ap-652	44	10	the	the	DET
ap-652	44	11	subject	subject	NOUN
ap-652	44	12	of	of	ADP
ap-652	44	13	considerable	considerable	ADJ
ap-652	44	14	research	research	NOUN
ap-652	44	15	for	for	ADP
ap-652	44	16	many	many	ADJ
ap-652	44	17	years	year	NOUN
ap-652	44	18	.	.	PUNCT
ap-652	45	1	it	it	PRON
ap-652	45	2	may	may	AUX
ap-652	45	3	be	be	AUX
ap-652	45	4	argued	argue	VERB
ap-652	45	5	,	,	PUNCT
ap-652	45	6	that	that	SCONJ
ap-652	45	7	there	there	PRON
ap-652	45	8	is	be	VERB
ap-652	45	9	no	no	DET
ap-652	45	10	need	need	NOUN
ap-652	45	11	for	for	ADP
ap-652	45	12	a	a	DET
ap-652	45	13	new	new	ADJ
ap-652	45	14	methodology	methodology	NOUN
ap-652	45	15	,	,	PUNCT
ap-652	45	16	since	since	SCONJ
ap-652	45	17	the	the	DET
ap-652	45	18	bounds	bound	NOUN
ap-652	45	19	for	for	ADP
ap-652	45	20	foams	foam	NOUN
ap-652	45	21	can	can	AUX
ap-652	45	22	be	be	AUX
ap-652	45	23	obtained	obtain	VERB
ap-652	45	24	from	from	ADP
ap-652	45	25	the	the	DET
ap-652	45	26	composite	composite	ADJ
ap-652	45	27	two	two	NUM
ap-652	45	28	-	-	PUNCT
ap-652	45	29	phase	phase	NOUN
ap-652	45	30	bounds	bound	NOUN
ap-652	45	31	,	,	PUNCT
ap-652	45	32	just	just	ADV
ap-652	45	33	by	by	ADP
ap-652	45	34	introducing	introduce	VERB
ap-652	45	35	zero	zero	NUM
ap-652	45	36	void	void	ADJ
ap-652	45	37	properties	property	NOUN
ap-652	45	38	.	.	PUNCT
ap-652	46	1	this	this	PRON
ap-652	46	2	is	be	AUX
ap-652	46	3	true	true	ADJ
ap-652	46	4	in	in	ADP
ap-652	46	5	2d	2d	NOUN
ap-652	46	6	,	,	PUNCT
ap-652	46	7	but	but	CCONJ
ap-652	46	8	in	in	ADP
ap-652	46	9	3d	3d	NUM
ap-652	46	10	the	the	DET
ap-652	46	11	optimal	optimal	ADJ
ap-652	46	12	foams	foam	NOUN
ap-652	46	13	must	must	AUX
ap-652	46	14	contain	contain	VERB
ap-652	46	15	shell	shell	ADJ
ap-652	46	16	parts	part	NOUN
ap-652	46	17	in	in	ADP
ap-652	46	18	some	some	DET
ap-652	46	19	regimes	regime	NOUN
ap-652	46	20	of	of	ADP
ap-652	46	21	optimality	optimality	NOUN
ap-652	46	22	(	(	PUNCT
ap-652	46	23	allaire	allaire	PROPN
ap-652	46	24	and	and	CCONJ
ap-652	46	25	kohn	kohn	PROPN
ap-652	46	26	(	(	PUNCT
ap-652	46	27	1993	1993	NUM
ap-652	46	28	)	)	PUNCT
ap-652	46	29	)	)	PUNCT
ap-652	46	30	,	,	PUNCT
ap-652	46	31	therefore	therefore	ADV
ap-652	46	32	upper	upper	ADJ
ap-652	46	33	bounds	bound	NOUN
ap-652	46	34	on	on	ADP
ap-652	46	35	the	the	DET
ap-652	46	36	homogenized	homogenized	ADJ
ap-652	46	37	properties	property	NOUN
ap-652	46	38	of	of	ADP
ap-652	46	39	open	open	ADJ
ap-652	46	40	-	-	PUNCT
ap-652	46	41	cell	cell	NOUN
ap-652	46	42	foams	foam	NOUN
ap-652	46	43	are	be	AUX
ap-652	46	44	strictly	strictly	ADV
ap-652	46	45	lower	low	ADJ
ap-652	46	46	than	than	ADP
ap-652	46	47	those	those	PRON
ap-652	46	48	for	for	ADP
ap-652	46	49	general	general	ADJ
ap-652	46	50	foams	foam	NOUN
ap-652	46	51	,	,	PUNCT
ap-652	46	52	and	and	CCONJ
ap-652	46	53	the	the	DET
ap-652	46	54	development	development	NOUN
ap-652	46	55	of	of	ADP
ap-652	46	56	a	a	DET
ap-652	46	57	new	new	ADJ
ap-652	46	58	methodology	methodology	NOUN
ap-652	46	59	addressing	address	VERB
ap-652	46	60	this	this	DET
ap-652	46	61	issue	issue	NOUN
ap-652	46	62	is	be	AUX
ap-652	46	63	fully	fully	ADV
ap-652	46	64	justified	justify	VERB
ap-652	46	65	.	.	PUNCT
ap-652	47	1	only	only	ADV
ap-652	47	2	the	the	DET
ap-652	47	3	upper	upper	ADJ
ap-652	47	4	bounds	bound	NOUN
ap-652	47	5	on	on	ADP
ap-652	47	6	effective	effective	ADJ
ap-652	47	7	elastic	elastic	ADJ
ap-652	47	8	properties	property	NOUN
ap-652	47	9	will	will	AUX
ap-652	47	10	be	be	AUX
ap-652	47	11	examined	examine	VERB
ap-652	47	12	,	,	PUNCT
ap-652	47	13	because	because	SCONJ
ap-652	47	14	the	the	DET
ap-652	47	15	lower	low	ADJ
ap-652	47	16	bounds	bound	NOUN
ap-652	47	17	for	for	ADP
ap-652	47	18	media	medium	NOUN
ap-652	47	19	with	with	ADP
ap-652	47	20	one	one	NUM
ap-652	47	21	void	void	ADJ
ap-652	47	22	phase	phase	NOUN
ap-652	47	23	are	be	AUX
ap-652	47	24	zero	zero	NUM
ap-652	47	25	.	.	PUNCT
ap-652	48	1	without	without	ADP
ap-652	48	2	loss	loss	NOUN
ap-652	48	3	of	of	ADP
ap-652	48	4	generality	generality	NOUN
ap-652	48	5	only	only	ADV
ap-652	48	6	open	open	ADJ
ap-652	48	7	-	-	PUNCT
ap-652	48	8	cell	cell	NOUN
ap-652	48	9	foams	foam	NOUN
ap-652	48	10	with	with	ADP
ap-652	48	11	a	a	DET
ap-652	48	12	periodic	periodic	ADJ
ap-652	48	13	microstructure	microstructure	NOUN
ap-652	48	14	will	will	AUX
ap-652	48	15	be	be	AUX
ap-652	48	16	considered	consider	VERB
ap-652	48	17	,	,	PUNCT
ap-652	48	18	because	because	SCONJ
ap-652	48	19	in	in	ADP
ap-652	48	20	a	a	DET
ap-652	48	21	medium	medium	NOUN
ap-652	48	22	with	with	ADP
ap-652	48	23	a	a	DET
ap-652	48	24	random	random	ADJ
ap-652	48	25	microstructure	microstructure	NOUN
ap-652	48	26	,	,	PUNCT
ap-652	48	27	a	a	DET
ap-652	48	28	representative	representative	ADJ
ap-652	48	29	volume	volume	NOUN
ap-652	48	30	element	element	NOUN
ap-652	48	31	can	can	AUX
ap-652	48	32	be	be	AUX
ap-652	48	33	chosen	choose	VERB
ap-652	48	34	so	so	SCONJ
ap-652	48	35	that	that	SCONJ
ap-652	48	36	a	a	DET
ap-652	48	37	medium	medium	NOUN
ap-652	48	38	created	create	VERB
ap-652	48	39	by	by	ADP
ap-652	48	40	its	its	PRON
ap-652	48	41	periodic	periodic	ADJ
ap-652	48	42	repetition	repetition	NOUN
ap-652	48	43	will	will	AUX
ap-652	48	44	have	have	VERB
ap-652	48	45	the	the	DET
ap-652	48	46	same	same	ADJ
ap-652	48	47	effective	effective	ADJ
ap-652	48	48	properties	property	NOUN
ap-652	48	49	as	as	ADP
ap-652	48	50	the	the	DET
ap-652	48	51	original	original	ADJ
ap-652	48	52	random	random	ADJ
ap-652	48	53	one	one	NOUN
ap-652	48	54	.	.	PUNCT
ap-652	49	1	the	the	DET
ap-652	49	2	contribution	contribution	NOUN
ap-652	49	3	of	of	ADP
ap-652	49	4	this	this	DET
ap-652	49	5	paper	paper	NOUN
ap-652	49	6	is	be	AUX
ap-652	49	7	that	that	SCONJ
ap-652	49	8	it	it	PRON
ap-652	49	9	extends	extend	VERB
ap-652	49	10	of	of	ADP
ap-652	49	11	the	the	DET
ap-652	49	12	methodology	methodology	NOUN
ap-652	49	13	proposed	propose	VERB
ap-652	49	14	by	by	ADP
ap-652	49	15	dimitrovová	dimitrovová	PROPN
ap-652	49	16	and	and	CCONJ
ap-652	49	17	faria	faria	PROPN
ap-652	49	18	(	(	PUNCT
ap-652	49	19	1999	1999	NUM
ap-652	49	20	)	)	PUNCT
ap-652	49	21	from	from	ADP
ap-652	49	22	2d	2d	NUM
ap-652	49	23	to	to	ADP
ap-652	49	24	3d	3d	NUM
ap-652	49	25	.	.	PUNCT
ap-652	50	1	the	the	DET
ap-652	50	2	methodology	methodology	NOUN
ap-652	50	3	is	be	AUX
ap-652	50	4	based	base	VERB
ap-652	50	5	on	on	ADP
ap-652	50	6	homogenization	homogenization	NOUN
ap-652	50	7	theory	theory	NOUN
ap-652	50	8	and	and	CCONJ
ap-652	50	9	does	do	AUX
ap-652	50	10	not	not	PART
ap-652	50	11	require	require	VERB
ap-652	50	12	any	any	DET
ap-652	50	13	restriction	restriction	NOUN
ap-652	50	14	on	on	ADP
ap-652	50	15	the	the	DET
ap-652	50	16	basic	basic	ADJ
ap-652	50	17	cell	cell	NOUN
ap-652	50	18	shape	shape	NOUN
ap-652	50	19	or	or	CCONJ
ap-652	50	20	arrangement	arrangement	NOUN
ap-652	50	21	.	.	PUNCT
ap-652	51	1	the	the	DET
ap-652	51	2	influence	influence	NOUN
ap-652	51	3	of	of	ADP
ap-652	51	4	the	the	DET
ap-652	51	5	boundary	boundary	ADJ
ap-652	51	6	layer	layer	NOUN
ap-652	51	7	is	be	AUX
ap-652	51	8	not	not	PART
ap-652	51	9	accounted	account	VERB
ap-652	51	10	for	for	ADP
ap-652	51	11	and	and	CCONJ
ap-652	51	12	it	it	PRON
ap-652	51	13	is	be	AUX
ap-652	51	14	assumed	assume	VERB
ap-652	51	15	that	that	SCONJ
ap-652	51	16	the	the	DET
ap-652	51	17	basic	basic	ADJ
ap-652	51	18	cell	cell	NOUN
ap-652	51	19	contains	contain	VERB
ap-652	51	20	a	a	DET
ap-652	51	21	finite	finite	ADJ
ap-652	51	22	number	number	NOUN
ap-652	51	23	of	of	ADP
ap-652	51	24	structural	structural	ADJ
ap-652	51	25	members	member	NOUN
ap-652	51	26	,	,	PUNCT
ap-652	51	27	i.e.	i.e.	X
ap-652	51	28	beams	beam	NOUN
ap-652	51	29	or	or	CCONJ
ap-652	51	30	bars	bar	NOUN
ap-652	51	31	.	.	PUNCT
ap-652	52	1	the	the	DET
ap-652	52	2	upper	upper	ADJ
ap-652	52	3	bounds	bound	NOUN
ap-652	52	4	are	be	AUX
ap-652	52	5	derived	derive	VERB
ap-652	52	6	by	by	ADP
ap-652	52	7	a	a	DET
ap-652	52	8	bounding	bounding	NOUN
ap-652	52	9	procedure	procedure	NOUN
ap-652	52	10	using	use	VERB
ap-652	52	11	results	result	NOUN
ap-652	52	12	from	from	ADP
ap-652	52	13	linear	linear	ADJ
ap-652	52	14	algebra	algebra	NOUN
ap-652	52	15	and	and	CCONJ
ap-652	52	16	the	the	DET
ap-652	52	17	voigt	voigt	PROPN
ap-652	52	18	bound	bind	VERB
ap-652	52	19	basic	basic	ADJ
ap-652	52	20	assumption	assumption	NOUN
ap-652	52	21	(	(	PUNCT
ap-652	52	22	hill	hill	NOUN
ap-652	52	23	(	(	PUNCT
ap-652	52	24	1963	1963	NUM
ap-652	52	25	)	)	PUNCT
ap-652	52	26	)	)	PUNCT
ap-652	52	27	.	.	PUNCT
ap-652	53	1	the	the	DET
ap-652	53	2	main	main	ADJ
ap-652	53	3	advantage	advantage	NOUN
ap-652	53	4	of	of	ADP
ap-652	53	5	the	the	DET
ap-652	53	6	new	new	ADJ
ap-652	53	7	methodology	methodology	NOUN
ap-652	53	8	is	be	AUX
ap-652	53	9	that	that	SCONJ
ap-652	53	10	the	the	DET
ap-652	53	11	necessary	necessary	ADJ
ap-652	53	12	and	and	CCONJ
ap-652	53	13	sufficient	sufficient	ADJ
ap-652	53	14	conditions	condition	NOUN
ap-652	53	15	characterizing	characterize	VERB
ap-652	53	16	the	the	DET
ap-652	53	17	optimal	optimal	ADJ
ap-652	53	18	media	medium	NOUN
ap-652	53	19	will	will	AUX
ap-652	53	20	immediately	immediately	ADV
ap-652	53	21	follow	follow	VERB
ap-652	53	22	from	from	ADP
ap-652	53	23	the	the	DET
ap-652	53	24	bounding	bounding	NOUN
ap-652	53	25	procedure	procedure	NOUN
ap-652	53	26	.	.	PUNCT
ap-652	54	1	these	these	DET
ap-652	54	2	conditions	condition	NOUN
ap-652	54	3	are	be	AUX
ap-652	54	4	written	write	VERB
ap-652	54	5	in	in	ADP
ap-652	54	6	terms	term	NOUN
ap-652	54	7	of	of	ADP
ap-652	54	8	generalized	generalized	ADJ
ap-652	54	9	internal	internal	ADJ
ap-652	54	10	forces	force	NOUN
ap-652	54	11	and	and	CCONJ
ap-652	54	12	geometrical	geometrical	ADJ
ap-652	54	13	parameters	parameter	NOUN
ap-652	54	14	.	.	PUNCT
ap-652	55	1	the	the	DET
ap-652	55	2	proposed	propose	VERB
ap-652	55	3	methodology	methodology	NOUN
ap-652	55	4	recovers	recover	VERB
ap-652	55	5	the	the	DET
ap-652	55	6	well	well	ADV
ap-652	55	7	known	know	VERB
ap-652	55	8	bounds	bound	NOUN
ap-652	55	9	for	for	ADP
ap-652	55	10	effectively	effectively	ADV
ap-652	55	11	isotropic	isotropic	ADJ
ap-652	55	12	open	open	ADJ
ap-652	55	13	-	-	PUNCT
ap-652	55	14	cell	cell	NOUN
ap-652	55	15	foams	foam	NOUN
ap-652	55	16	,	,	PUNCT
ap-652	55	17	though	though	SCONJ
ap-652	55	18	with	with	ADP
ap-652	55	19	a	a	DET
ap-652	55	20	different	different	ADJ
ap-652	55	21	proof	proof	NOUN
ap-652	55	22	.	.	PUNCT
ap-652	56	1	the	the	DET
ap-652	56	2	main	main	ADJ
ap-652	56	3	contribution	contribution	NOUN
ap-652	56	4	lies	lie	VERB
ap-652	56	5	in	in	ADP
ap-652	56	6	identifying	identifying	NOUN
ap-652	56	7	of	of	ADP
ap-652	56	8	new	new	ADJ
ap-652	56	9	bounds	bound	NOUN
ap-652	56	10	on	on	ADP
ap-652	56	11	the	the	DET
ap-652	56	12	effective	effective	ADJ
ap-652	56	13	shear	shear	NOUN
ap-652	56	14	moduli	modulus	NOUN
ap-652	56	15	of	of	ADP
ap-652	56	16	open	open	ADJ
ap-652	56	17	-	-	PUNCT
ap-652	56	18	cell	cell	NOUN
ap-652	56	19	microstructures	microstructure	NOUN
ap-652	56	20	with	with	ADP
ap-652	56	21	effective	effective	ADJ
ap-652	56	22	cubic	cubic	ADJ
ap-652	56	23	symmetry	symmetry	NOUN
ap-652	56	24	.	.	PUNCT
ap-652	57	1	in	in	ADP
ap-652	57	2	such	such	ADJ
ap-652	57	3	cases	case	NOUN
ap-652	57	4	,	,	PUNCT
ap-652	57	5	dependence	dependence	NOUN
ap-652	57	6	on	on	ADP
ap-652	57	7	internal	internal	ADJ
ap-652	57	8	forces	force	NOUN
ap-652	57	9	in	in	ADP
ap-652	57	10	maximality	maximality	NOUN
ap-652	57	11	conditions	condition	NOUN
ap-652	57	12	can	can	AUX
ap-652	57	13	be	be	AUX
ap-652	57	14	replaced	replace	VERB
ap-652	57	15	by	by	ADP
ap-652	57	16	geometrical	geometrical	ADJ
ap-652	57	17	expressions	expression	NOUN
ap-652	57	18	,	,	PUNCT
ap-652	57	19	implying	imply	VERB
ap-652	57	20	that	that	SCONJ
ap-652	57	21	the	the	DET
ap-652	57	22	optimality	optimality	NOUN
ap-652	57	23	of	of	ADP
ap-652	57	24	the	the	DET
ap-652	57	25	medium	medium	NOUN
ap-652	57	26	under	under	ADP
ap-652	57	27	consideration	consideration	NOUN
ap-652	57	28	can	can	AUX
ap-652	57	29	be	be	AUX
ap-652	57	30	verified	verify	VERB
ap-652	57	31	directly	directly	ADV
ap-652	57	32	from	from	ADP
ap-652	57	33	the	the	DET
ap-652	57	34	microstructure	microstructure	NOUN
ap-652	57	35	,	,	PUNCT
ap-652	57	36	without	without	ADP
ap-652	57	37	any	any	DET
ap-652	57	38	additional	additional	ADJ
ap-652	57	39	calculation	calculation	NOUN
ap-652	57	40	.	.	PUNCT
ap-652	58	1	the	the	DET
ap-652	58	2	approximations	approximation	NOUN
ap-652	58	3	inherent	inherent	ADJ
ap-652	58	4	to	to	ADP
ap-652	58	5	the	the	DET
ap-652	58	6	methodology	methodology	NOUN
ap-652	58	7	are	be	AUX
ap-652	58	8	within	within	ADP
ap-652	58	9	the	the	DET
ap-652	58	10	structural	structural	ADJ
ap-652	58	11	simplifications	simplification	NOUN
ap-652	58	12	commonly	commonly	ADV
ap-652	58	13	used	use	VERB
ap-652	58	14	.	.	PUNCT
ap-652	59	1	the	the	DET
ap-652	59	2	limitations	limitation	NOUN
ap-652	59	3	are	be	AUX
ap-652	59	4	based	base	VERB
ap-652	59	5	on	on	ADP
ap-652	59	6	the	the	DET
ap-652	59	7	assumption	assumption	NOUN
ap-652	59	8	of	of	ADP
ap-652	59	9	a	a	DET
ap-652	59	10	finite	finite	ADJ
ap-652	59	11	number	number	NOUN
ap-652	59	12	of	of	ADP
ap-652	59	13	structural	structural	ADJ
ap-652	59	14	members	member	NOUN
ap-652	59	15	in	in	ADP
ap-652	59	16	the	the	DET
ap-652	59	17	basic	basic	ADJ
ap-652	59	18	cell	cell	NOUN
ap-652	59	19	,	,	PUNCT
ap-652	59	20	allowing	allow	VERB
ap-652	59	21	only	only	ADV
ap-652	59	22	the	the	DET
ap-652	59	23	identification	identification	NOUN
ap-652	59	24	of	of	ADP
ap-652	59	25	single	single	ADJ
ap-652	59	26	scale	scale	NOUN
ap-652	59	27	microstructures	microstructure	NOUN
ap-652	59	28	,	,	PUNCT
ap-652	59	29	which	which	PRON
ap-652	59	30	implicitly	implicitly	ADV
ap-652	59	31	excludes	exclude	VERB
ap-652	59	32	multiple	multiple	ADJ
ap-652	59	33	rank	rank	NOUN
ap-652	59	34	laminates	laminate	NOUN
ap-652	59	35	(	(	PUNCT
ap-652	59	36	see	see	VERB
ap-652	59	37	e.g.	e.g.	ADV
ap-652	59	38	allaire	allaire	PROPN
ap-652	59	39	and	and	CCONJ
ap-652	59	40	aubry	aubry	PROPN
ap-652	59	41	(	(	PUNCT
ap-652	59	42	1999	1999	NUM
ap-652	59	43	)	)	PUNCT
ap-652	59	44	)	)	PUNCT
ap-652	59	45	and	and	CCONJ
ap-652	59	46	the	the	DET
ap-652	59	47	hashin	hashin	PROPN
ap-652	59	48	spheres	sphere	NOUN
ap-652	59	49	medium	medium	ADJ
ap-652	59	50	(	(	PUNCT
ap-652	59	51	hashin	hashin	NOUN
ap-652	59	52	(	(	PUNCT
ap-652	59	53	1962	1962	NUM
ap-652	59	54	)	)	PUNCT
ap-652	59	55	)	)	PUNCT
ap-652	59	56	.	.	PUNCT
ap-652	60	1	the	the	DET
ap-652	60	2	paper	paper	NOUN
ap-652	60	3	is	be	AUX
ap-652	60	4	organized	organize	VERB
ap-652	60	5	as	as	SCONJ
ap-652	60	6	follows	follow	VERB
ap-652	60	7	.	.	PUNCT
ap-652	61	1	the	the	DET
ap-652	61	2	methodology	methodology	NOUN
ap-652	61	3	is	be	AUX
ap-652	61	4	reviewed	review	VERB
ap-652	61	5	in	in	ADP
ap-652	61	6	section	section	NOUN
ap-652	61	7	2	2	NUM
ap-652	61	8	,	,	PUNCT
ap-652	61	9	namely	namely	ADV
ap-652	61	10	in	in	ADP
ap-652	61	11	section	section	NOUN
ap-652	61	12	2.1	2.1	NUM
ap-652	61	13	simplified	simplify	VERB
ap-652	61	14	assumptions	assumption	NOUN
ap-652	61	15	and	and	CCONJ
ap-652	61	16	basic	basic	ADJ
ap-652	61	17	relations	relation	NOUN
ap-652	61	18	are	be	AUX
ap-652	61	19	introduced	introduce	VERB
ap-652	61	20	,	,	PUNCT
ap-652	61	21	in	in	ADP
ap-652	61	22	section	section	NOUN
ap-652	61	23	2.2	2.2	NUM
ap-652	61	24	it	it	PRON
ap-652	61	25	is	be	AUX
ap-652	61	26	shown	show	VERB
ap-652	61	27	that	that	SCONJ
ap-652	61	28	the	the	DET
ap-652	61	29	optimal	optimal	ADJ
ap-652	61	30	media	medium	NOUN
ap-652	61	31	can	can	AUX
ap-652	61	32	be	be	AUX
ap-652	61	33	initially	initially	ADV
ap-652	61	34	searched	search	VERB
ap-652	61	35	within	within	ADP
ap-652	61	36	a	a	DET
ap-652	61	37	specific	specific	ADJ
ap-652	61	38	class	class	NOUN
ap-652	61	39	of	of	ADP
ap-652	61	40	micro	micro	NOUN
ap-652	61	41	-	-	NOUN
ap-652	61	42	trusses	truss	NOUN
ap-652	61	43	(	(	PUNCT
ap-652	61	44	this	this	DET
ap-652	61	45	term	term	NOUN
ap-652	61	46	will	will	AUX
ap-652	61	47	be	be	AUX
ap-652	61	48	explained	explain	VERB
ap-652	61	49	later	later	ADV
ap-652	61	50	on	on	ADV
ap-652	61	51	)	)	PUNCT
ap-652	61	52	,	,	PUNCT
ap-652	61	53	and	and	CCONJ
ap-652	61	54	in	in	ADP
ap-652	61	55	section	section	NOUN
ap-652	61	56	2.3	2.3	NUM
ap-652	61	57	the	the	DET
ap-652	61	58	methodology	methodology	NOUN
ap-652	61	59	is	be	AUX
ap-652	61	60	reviewed	review	VERB
ap-652	61	61	within	within	ADP
ap-652	61	62	this	this	DET
ap-652	61	63	restricted	restricted	ADJ
ap-652	61	64	class	class	NOUN
ap-652	61	65	.	.	PUNCT
ap-652	62	1	the	the	DET
ap-652	62	2	bounds	bound	NOUN
ap-652	62	3	are	be	AUX
ap-652	62	4	proven	prove	VERB
ap-652	62	5	in	in	ADP
ap-652	62	6	section	section	NOUN
ap-652	62	7	3	3	NUM
ap-652	62	8	,	,	PUNCT
ap-652	62	9	along	along	ADP
ap-652	62	10	with	with	ADP
ap-652	62	11	a	a	DET
ap-652	62	12	specification	specification	NOUN
ap-652	62	13	of	of	ADP
ap-652	62	14	the	the	DET
ap-652	62	15	optimal	optimal	ADJ
ap-652	62	16	media	medium	NOUN
ap-652	62	17	microstructures	microstructure	NOUN
ap-652	62	18	.	.	PUNCT
ap-652	63	1	the	the	DET
ap-652	63	2	paper	paper	NOUN
ap-652	63	3	is	be	AUX
ap-652	63	4	concluded	conclude	VERB
ap-652	63	5	in	in	ADP
ap-652	63	6	section	section	NOUN
ap-652	63	7	4	4	NUM
ap-652	63	8	with	with	ADP
ap-652	63	9	a	a	DET
ap-652	63	10	discussion	discussion	NOUN
ap-652	63	11	and	and	CCONJ
ap-652	63	12	an	an	DET
ap-652	63	13	analysis	analysis	NOUN
ap-652	63	14	of	of	ADP
ap-652	63	15	the	the	DET
ap-652	63	16	developments	development	NOUN
ap-652	63	17	.	.	PUNCT
ap-652	64	1	2	2	NUM
ap-652	64	2	review	review	NOUN
ap-652	64	3	of	of	ADP
ap-652	64	4	the	the	DET
ap-652	64	5	new	new	ADJ
ap-652	64	6	methodology	methodology	NOUN
ap-652	64	7	2	2	NUM
ap-652	64	8	.	.	NOUN
ap-652	64	9	1	1	NUM
ap-652	64	10	simplifying	simplify	VERB
ap-652	64	11	assumptions	assumption	NOUN
ap-652	64	12	and	and	CCONJ
ap-652	64	13	basic	basic	ADJ
ap-652	64	14	relations	relation	NOUN
ap-652	64	15	the	the	DET
ap-652	64	16	basic	basic	ADJ
ap-652	64	17	cell	cell	NOUN
ap-652	64	18	,	,	PUNCT
ap-652	64	19	�	�	PROPN
ap-652	64	20	,	,	PUNCT
ap-652	64	21	defined	define	VERB
ap-652	64	22	as	as	ADP
ap-652	64	23	the	the	DET
ap-652	64	24	(	(	PUNCT
ap-652	64	25	smallest	small	ADJ
ap-652	64	26	)	)	PUNCT
ap-652	64	27	region	region	NOUN
ap-652	64	28	of	of	ADP
ap-652	64	29	a	a	DET
ap-652	64	30	periodic	periodic	ADJ
ap-652	64	31	medium	medium	NOUN
ap-652	64	32	that	that	PRON
ap-652	64	33	can	can	AUX
ap-652	64	34	compose	compose	VERB
ap-652	64	35	the	the	DET
ap-652	64	36	full	full	ADJ
ap-652	64	37	one	one	NUM
ap-652	64	38	by	by	ADP
ap-652	64	39	periodic	periodic	ADJ
ap-652	64	40	repetition	repetition	NOUN
ap-652	64	41	,	,	PUNCT
ap-652	64	42	will	will	AUX
ap-652	64	43	be	be	AUX
ap-652	64	44	conveniently	conveniently	ADV
ap-652	64	45	rescaled	rescale	VERB
ap-652	64	46	to	to	ADP
ap-652	64	47	v	v	NOUN
ap-652	64	48	,	,	PUNCT
ap-652	64	49	where	where	SCONJ
ap-652	64	50	the	the	DET
ap-652	64	51	spatial	spatial	ADJ
ap-652	64	52	microvariable	microvariable	ADJ
ap-652	64	53	y	y	PROPN
ap-652	64	54	is	be	AUX
ap-652	64	55	introduced	introduce	VERB
ap-652	64	56	.	.	PUNCT
ap-652	65	1	it	it	PRON
ap-652	65	2	is	be	AUX
ap-652	65	3	assumed	assume	VERB
ap-652	65	4	that	that	SCONJ
ap-652	65	5	v	v	NOUN
ap-652	65	6	contains	contain	VERB
ap-652	65	7	a	a	DET
ap-652	65	8	finite	finite	ADJ
ap-652	65	9	number	number	NOUN
ap-652	65	10	of	of	ADP
ap-652	65	11	beams	beam	NOUN
ap-652	65	12	and	and	CCONJ
ap-652	65	13	that	that	SCONJ
ap-652	65	14	the	the	DET
ap-652	65	15	solid	solid	ADJ
ap-652	65	16	phase	phase	NOUN
ap-652	65	17	is	be	AUX
ap-652	65	18	homogeneous	homogeneous	ADJ
ap-652	65	19	and	and	CCONJ
ap-652	65	20	isotropic	isotropic	NOUN
ap-652	65	21	.	.	PUNCT
ap-652	66	1	therefore	therefore	ADV
ap-652	66	2	the	the	DET
ap-652	66	3	term	term	NOUN
ap-652	66	4	material	material	NOUN
ap-652	66	5	volume	volume	NOUN
ap-652	66	6	fraction	fraction	NOUN
ap-652	66	7	can	can	AUX
ap-652	66	8	be	be	AUX
ap-652	66	9	used	use	VERB
ap-652	66	10	instead	instead	ADV
ap-652	66	11	of	of	ADP
ap-652	66	12	relative	relative	ADJ
ap-652	66	13	density	density	NOUN
ap-652	66	14	.	.	PUNCT
ap-652	67	1	there	there	PRON
ap-652	67	2	are	be	VERB
ap-652	67	3	two	two	NUM
ap-652	67	4	extreme	extreme	ADJ
ap-652	67	5	possibilities	possibility	NOUN
ap-652	67	6	for	for	ADP
ap-652	67	7	the	the	DET
ap-652	67	8	structural	structural	ADJ
ap-652	67	9	model	model	NOUN
ap-652	67	10	of	of	ADP
ap-652	67	11	a	a	DET
ap-652	67	12	joint	joint	NOUN
ap-652	67	13	between	between	ADP
ap-652	67	14	the	the	DET
ap-652	67	15	beams	beam	NOUN
ap-652	67	16	composing	compose	VERB
ap-652	67	17	the	the	DET
ap-652	67	18	foam	foam	NOUN
ap-652	67	19	:	:	PUNCT
ap-652	67	20	(	(	PUNCT
ap-652	67	21	i	i	NOUN
ap-652	67	22	)	)	PUNCT
ap-652	67	23	a	a	DET
ap-652	67	24	pin	pin	NOUN
ap-652	67	25	joint	joint	NOUN
ap-652	67	26	and	and	CCONJ
ap-652	67	27	(	(	PUNCT
ap-652	67	28	ii	ii	NOUN
ap-652	67	29	)	)	PUNCT
ap-652	67	30	a	a	DET
ap-652	67	31	rigid	rigid	ADJ
ap-652	67	32	joint	joint	NOUN
ap-652	67	33	.	.	PUNCT
ap-652	68	1	a	a	DET
ap-652	68	2	pin	pin	NOUN
ap-652	68	3	joint	joint	NOUN
ap-652	68	4	can	can	AUX
ap-652	68	5	not	not	PART
ap-652	68	6	transmit	transmit	VERB
ap-652	68	7	bending	bend	VERB
ap-652	68	8	moments	moment	NOUN
ap-652	68	9	,	,	PUNCT
ap-652	68	10	and	and	CCONJ
ap-652	68	11	therefore	therefore	ADV
ap-652	68	12	it	it	PRON
ap-652	68	13	allows	allow	VERB
ap-652	68	14	rotations	rotation	NOUN
ap-652	68	15	of	of	ADP
ap-652	68	16	the	the	DET
ap-652	68	17	structural	structural	ADJ
ap-652	68	18	members	member	NOUN
ap-652	68	19	connected	connect	VERB
ap-652	68	20	to	to	ADP
ap-652	68	21	it	it	PRON
ap-652	68	22	.	.	PUNCT
ap-652	69	1	consequently	consequently	ADV
ap-652	69	2	,	,	PUNCT
ap-652	69	3	a	a	DET
ap-652	69	4	non	non	ADJ
ap-652	69	5	-	-	ADJ
ap-652	69	6	loaded	loaded	ADJ
ap-652	69	7	structural	structural	ADJ
ap-652	69	8	member	member	NOUN
ap-652	69	9	with	with	ADP
ap-652	69	10	two	two	NUM
ap-652	69	11	pin	pin	NOUN
ap-652	69	12	joints	joint	NOUN
ap-652	69	13	can	can	AUX
ap-652	69	14	only	only	ADV
ap-652	69	15	support	support	VERB
ap-652	69	16	the	the	DET
ap-652	69	17	internal	internal	ADJ
ap-652	69	18	forces	force	NOUN
ap-652	69	19	acting	act	VERB
ap-652	69	20	in	in	ADP
ap-652	69	21	the	the	DET
ap-652	69	22	direction	direction	NOUN
ap-652	69	23	of	of	ADP
ap-652	69	24	the	the	DET
ap-652	69	25	line	line	NOUN
ap-652	69	26	connecting	connect	VERB
ap-652	69	27	the	the	DET
ap-652	69	28	joints	joint	NOUN
ap-652	69	29	.	.	PUNCT
ap-652	70	1	on	on	ADP
ap-652	70	2	the	the	DET
ap-652	70	3	other	other	ADJ
ap-652	70	4	hand	hand	NOUN
ap-652	70	5	,	,	PUNCT
ap-652	70	6	a	a	DET
ap-652	70	7	rigid	rigid	ADJ
ap-652	70	8	joint	joint	ADJ
ap-652	70	9	preserves	preserve	NOUN
ap-652	70	10	the	the	DET
ap-652	70	11	angles	angle	NOUN
ap-652	70	12	between	between	ADP
ap-652	70	13	the	the	DET
ap-652	70	14	beams	beam	NOUN
ap-652	70	15	connected	connect	VERB
ap-652	70	16	to	to	ADP
ap-652	70	17	it	it	PRON
ap-652	70	18	.	.	PUNCT
ap-652	71	1	if	if	SCONJ
ap-652	71	2	all	all	DET
ap-652	71	3	joints	joint	NOUN
ap-652	71	4	are	be	AUX
ap-652	71	5	rigid	rigid	ADJ
ap-652	71	6	,	,	PUNCT
ap-652	71	7	the	the	DET
ap-652	71	8	term	term	NOUN
ap-652	71	9	micro	micro	NOUN
ap-652	71	10	-	-	NOUN
ap-652	71	11	frame	frame	ADJ
ap-652	71	12	medium	medium	NOUN
ap-652	71	13	can	can	AUX
ap-652	71	14	be	be	AUX
ap-652	71	15	used;	used;	PROPN
ap-652	71	16	on	on	ADP
ap-652	71	17	the	the	DET
ap-652	71	18	other	other	ADJ
ap-652	71	19	hand	hand	NOUN
ap-652	71	20	not	not	PART
ap-652	71	21	necessarily	necessarily	ADV
ap-652	71	22	straight	straight	ADJ
ap-652	71	23	structural	structural	ADJ
ap-652	71	24	members	member	NOUN
ap-652	71	25	connected	connect	VERB
ap-652	71	26	by	by	ADP
ap-652	71	27	pin	pin	PROPN
ap-652	71	28	joints	joint	NOUN
ap-652	71	29	will	will	AUX
ap-652	71	30	be	be	AUX
ap-652	71	31	named	name	VERB
ap-652	71	32	as	as	ADP
ap-652	71	33	micro	micro	ADJ
ap-652	71	34	-	-	ADJ
ap-652	71	35	truss	truss	ADJ
ap-652	71	36	media	medium	NOUN
ap-652	71	37	.	.	PUNCT
ap-652	72	1	therefore	therefore	ADV
ap-652	72	2	any	any	DET
ap-652	72	3	micro	micro	ADJ
ap-652	72	4	-	-	NOUN
ap-652	72	5	frame	frame	ADJ
ap-652	72	6	medium	medium	NOUN
ap-652	72	7	has	have	VERB
ap-652	72	8	its	its	PRON
ap-652	72	9	related	relate	VERB
ap-652	72	10	micro	micro	NOUN
ap-652	72	11	-	-	NOUN
ap-652	72	12	truss	truss	ADJ
ap-652	72	13	,	,	PUNCT
ap-652	72	14	which	which	PRON
ap-652	72	15	is	be	AUX
ap-652	72	16	obtained	obtain	VERB
ap-652	72	17	by	by	ADP
ap-652	72	18	switching	switch	VERB
ap-652	72	19	the	the	DET
ap-652	72	20	behavior	behavior	NOUN
ap-652	72	21	of	of	ADP
ap-652	72	22	rigid	rigid	ADJ
ap-652	72	23	joints	joint	NOUN
ap-652	72	24	to	to	AUX
ap-652	72	25	pin	pin	VERB
ap-652	72	26	joints	joint	NOUN
ap-652	72	27	.	.	PUNCT
ap-652	73	1	in	in	ADP
ap-652	73	2	reality	reality	NOUN
ap-652	73	3	,	,	PUNCT
ap-652	73	4	joint	joint	ADJ
ap-652	73	5	behavior	behavior	NOUN
ap-652	73	6	is	be	AUX
ap-652	73	7	somewhere	somewhere	ADV
ap-652	73	8	between	between	ADP
ap-652	73	9	these	these	DET
ap-652	73	10	two	two	NUM
ap-652	73	11	extreme	extreme	ADJ
ap-652	73	12	cases	case	NOUN
ap-652	73	13	and	and	CCONJ
ap-652	73	14	should	should	AUX
ap-652	73	15	be	be	AUX
ap-652	73	16	represented	represent	VERB
ap-652	73	17	by	by	ADP
ap-652	73	18	a	a	DET
ap-652	73	19	flexible	flexible	ADJ
ap-652	73	20	joint	joint	NOUN
ap-652	73	21	.	.	PUNCT
ap-652	74	1	pin	pin	VERB
ap-652	74	2	joint	joint	ADJ
ap-652	74	3	behavior	behavior	NOUN
ap-652	74	4	can	can	AUX
ap-652	74	5	be	be	AUX
ap-652	74	6	achieved	achieve	VERB
ap-652	74	7	either	either	CCONJ
ap-652	74	8	by	by	ADP
ap-652	74	9	special	special	ADJ
ap-652	74	10	construction	construction	NOUN
ap-652	74	11	allowing	allow	VERB
ap-652	74	12	for	for	ADP
ap-652	74	13	rotations	rotation	NOUN
ap-652	74	14	of	of	ADP
ap-652	74	15	the	the	DET
ap-652	74	16	connected	connected	ADJ
ap-652	74	17	members	member	NOUN
ap-652	74	18	or	or	CCONJ
ap-652	74	19	as	as	ADP
ap-652	74	20	a	a	DET
ap-652	74	21	limit	limit	NOUN
ap-652	74	22	case	case	NOUN
ap-652	74	23	:	:	PUNCT
ap-652	74	24	if	if	SCONJ
ap-652	74	25	the	the	DET
ap-652	74	26	beams	beam	NOUN
ap-652	74	27	connected	connect	VERB
ap-652	74	28	to	to	ADP
ap-652	74	29	a	a	DET
ap-652	74	30	given	give	VERB
ap-652	74	31	joint	joint	NOUN
ap-652	74	32	have	have	VERB
ap-652	74	33	uniform	uniform	PROPN
ap-652	74	34	cross	cross	PROPN
ap-652	74	35	sectional	sectional	ADJ
ap-652	74	36	areas	area	NOUN
ap-652	74	37	and	and	CCONJ
ap-652	74	38	the	the	DET
ap-652	74	39	material	material	NOUN
ap-652	74	40	volume	volume	NOUN
ap-652	74	41	fraction	fraction	NOUN
ap-652	74	42	tends	tend	VERB
ap-652	74	43	to	to	ADP
ap-652	74	44	zero	zero	NUM
ap-652	74	45	,	,	PUNCT
ap-652	74	46	then	then	ADV
ap-652	74	47	the	the	DET
ap-652	74	48	flexible	flexible	ADJ
ap-652	74	49	joint	joint	ADJ
ap-652	74	50	approaches	approach	NOUN
ap-652	74	51	pin	pin	VERB
ap-652	74	52	joint	joint	ADJ
ap-652	74	53	behavior	behavior	NOUN
ap-652	74	54	.	.	PUNCT
ap-652	75	1	in	in	ADP
ap-652	75	2	structural	structural	ADJ
ap-652	75	3	theories	theory	NOUN
ap-652	75	4	,	,	PUNCT
ap-652	75	5	beams	beam	NOUN
ap-652	75	6	are	be	AUX
ap-652	75	7	defined	define	VERB
ap-652	75	8	by	by	ADP
ap-652	75	9	their	their	PRON
ap-652	75	10	middle	middle	ADJ
ap-652	75	11	axes	axis	NOUN
ap-652	75	12	and	and	CCONJ
ap-652	75	13	joints	joint	NOUN
ap-652	75	14	can	can	AUX
ap-652	75	15	be	be	AUX
ap-652	75	16	replaced	replace	VERB
ap-652	75	17	by	by	ADP
ap-652	75	18	single	single	ADJ
ap-652	75	19	points	point	NOUN
ap-652	75	20	(	(	PUNCT
ap-652	75	21	joint	joint	ADJ
ap-652	75	22	“	"	PUNCT
ap-652	75	23	centers	center	NOUN
ap-652	75	24	”	"	PUNCT
ap-652	75	25	)	)	PUNCT
ap-652	75	26	located	locate	VERB
ap-652	75	27	in	in	ADP
ap-652	75	28	the	the	DET
ap-652	75	29	intersection	intersection	NOUN
ap-652	75	30	of	of	ADP
ap-652	75	31	the	the	DET
ap-652	75	32	middle	middle	ADJ
ap-652	75	33	axes	axis	NOUN
ap-652	75	34	.	.	PUNCT
ap-652	76	1	the	the	DET
ap-652	76	2	term	term	NOUN
ap-652	76	3	theoretical	theoretical	ADJ
ap-652	76	4	length	length	NOUN
ap-652	76	5	will	will	AUX
ap-652	76	6	be	be	AUX
ap-652	76	7	used	use	VERB
ap-652	76	8	to	to	PART
ap-652	76	9	identify	identify	VERB
ap-652	76	10	the	the	DET
ap-652	76	11	middle	middle	ADJ
ap-652	76	12	axis	axis	NOUN
ap-652	76	13	length	length	NOUN
ap-652	76	14	between	between	ADP
ap-652	76	15	the	the	DET
ap-652	76	16	joint	joint	ADJ
ap-652	76	17	centers	center	NOUN
ap-652	76	18	,	,	PUNCT
ap-652	76	19	and	and	CCONJ
ap-652	76	20	active	active	ADJ
ap-652	76	21	length	length	NOUN
ap-652	76	22	will	will	AUX
ap-652	76	23	be	be	AUX
ap-652	76	24	usedto	usedto	PROPN
ap-652	76	25	identify	identify	VERB
ap-652	76	26	the	the	DET
ap-652	76	27	same	same	ADJ
ap-652	76	28	length	length	NOUN
ap-652	76	29	shortened	shorten	VERB
ap-652	76	30	by	by	ADP
ap-652	76	31	the	the	DET
ap-652	76	32	parts	part	NOUN
ap-652	76	33	inside	inside	ADP
ap-652	76	34	the	the	DET
ap-652	76	35	joints	joint	NOUN
ap-652	76	36	(	(	PUNCT
ap-652	76	37	fig	fig	NOUN
ap-652	76	38	.	.	PUNCT
ap-652	77	1	1	1	NUM
ap-652	77	2	)	)	PUNCT
ap-652	77	3	.	.	PUNCT
ap-652	78	1	small	small	ADJ
ap-652	78	2	discrepancies	discrepancy	NOUN
ap-652	78	3	when	when	SCONJ
ap-652	78	4	middle	middle	ADJ
ap-652	78	5	axes	axis	NOUN
ap-652	78	6	do	do	AUX
ap-652	78	7	not	not	PART
ap-652	78	8	intersect	intersect	VERB
ap-652	78	9	exactly	exactly	ADV
ap-652	78	10	at	at	ADP
ap-652	78	11	a	a	DET
ap-652	78	12	single	single	ADJ
ap-652	78	13	point	point	NOUN
ap-652	78	14	will	will	AUX
ap-652	78	15	not	not	PART
ap-652	78	16	be	be	AUX
ap-652	78	17	considered	consider	VERB
ap-652	78	18	.	.	PUNCT
ap-652	79	1	172	172	NUM
ap-652	79	2	©	©	PROPN
ap-652	79	3	czech	czech	PROPN
ap-652	79	4	technical	technical	PROPN
ap-652	79	5	university	university	PROPN
ap-652	79	6	publishing	publishing	NOUN
ap-652	79	7	house	house	NOUN
ap-652	79	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	79	9	acta	acta	PROPN
ap-652	79	10	polytechnica	polytechnica	PROPN
ap-652	79	11	vol	vol	NOUN
ap-652	79	12	.	.	PROPN
ap-652	80	1	44	44	NUM
ap-652	80	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	80	3	active	active	ADJ
ap-652	80	4	length	length	NOUN
ap-652	80	5	fig	fig	NOUN
ap-652	80	6	.	.	PUNCT
ap-652	81	1	1	1	NUM
ap-652	81	2	:	:	PUNCT
ap-652	81	3	introduction	introduction	NOUN
ap-652	81	4	of	of	ADP
ap-652	81	5	theoretical	theoretical	ADJ
ap-652	81	6	and	and	CCONJ
ap-652	81	7	active	active	ADJ
ap-652	81	8	lengths	length	NOUN
ap-652	81	9	we	we	PRON
ap-652	81	10	will	will	AUX
ap-652	81	11	address	address	VERB
ap-652	81	12	only	only	ADV
ap-652	81	13	open	open	ADJ
ap-652	81	14	-	-	PUNCT
ap-652	81	15	cell	cell	NOUN
ap-652	81	16	foams	foam	NOUN
ap-652	81	17	with	with	ADP
ap-652	81	18	effective	effective	ADJ
ap-652	81	19	isotropy	isotropy	NOUN
ap-652	81	20	or	or	CCONJ
ap-652	81	21	cubic	cubic	ADJ
ap-652	81	22	symmetry	symmetry	NOUN
ap-652	81	23	.	.	PUNCT
ap-652	82	1	the	the	DET
ap-652	82	2	tensor	tensor	NOUN
ap-652	82	3	of	of	ADP
ap-652	82	4	the	the	DET
ap-652	82	5	effective	effective	ADJ
ap-652	82	6	elastic	elastic	ADJ
ap-652	82	7	constants	constant	NOUN
ap-652	82	8	can	can	AUX
ap-652	82	9	thus	thus	ADV
ap-652	82	10	be	be	AUX
ap-652	82	11	written	write	VERB
ap-652	82	12	in	in	ADP
ap-652	82	13	dimensionless	dimensionless	NOUN
ap-652	82	14	matrix	matrix	NOUN
ap-652	82	15	form	form	NOUN
ap-652	82	16	as	as	ADP
ap-652	82	17	:	:	PUNCT
ap-652	82	18	c	c	PROPN
ap-652	82	19	c	c	NOUN
ap-652	82	20	0	0	NUM
ap-652	82	21	0	0	PUNCT
ap-652	83	1	c	c	X
ap-652	83	2	*	*	PUNCT
ap-652	84	1	*	*	PUNCT
ap-652	84	2	*	*	PUNCT
ap-652	84	3	�	�	PROPN
ap-652	84	4	�	�	PROPN
ap-652	84	5	�	�	PROPN
ap-652	84	6	�	�	PROPN
ap-652	84	7	�	�	PROPN
ap-652	84	8	�	�	PROPN
ap-652	84	9	�	�	PROPN
ap-652	84	10	�	�	PROPN
ap-652	84	11	�	�	PROPN
ap-652	84	12	1	1	NUM
ap-652	84	13	2	2	NUM
ap-652	84	14	,	,	PUNCT
ap-652	84	15	(	(	PUNCT
ap-652	84	16	1a	1a	X
ap-652	84	17	)	)	PUNCT
ap-652	84	18	where	where	SCONJ
ap-652	84	19	c	c	PROPN
ap-652	84	20	i2	i2	PROPN
ap-652	84	21	2	2	NUM
ap-652	84	22	*	*	PUNCT
ap-652	84	23	*	*	PROPN
ap-652	84	24	�	�	PROPN
ap-652	84	25	g	g	PROPN
ap-652	84	26	and	and	CCONJ
ap-652	84	27	c1	c1	PROPN
ap-652	84	28	1	1	NUM
ap-652	85	1	1	1	NUM
ap-652	85	2	1	1	NUM
ap-652	85	3	1	1	NUM
ap-652	85	4	1	1	NUM
ap-652	85	5	4	4	NUM
ap-652	85	6	3	3	NUM
ap-652	85	7	2	2	NUM
ap-652	85	8	3	3	NUM
ap-652	85	9	2	2	NUM
ap-652	85	10	3	3	NUM
ap-652	85	11	4	4	NUM
ap-652	85	12	3	3	NUM
ap-652	85	13	2	2	NUM
ap-652	85	14	3	3	NUM
ap-652	85	15	*	*	PUNCT
ap-652	85	16	*	*	PUNCT
ap-652	85	17	*	*	PUNCT
ap-652	86	1	*	*	PUNCT
ap-652	87	1	*	*	PUNCT
ap-652	88	1	*	*	PUNCT
ap-652	89	1	*	*	PUNCT
ap-652	90	1	*	*	PUNCT
ap-652	91	1	*	*	PUNCT
ap-652	91	2	*	*	PUNCT
ap-652	91	3	*	*	PUNCT
ap-652	91	4	.	.	PUNCT
ap-652	92	1	�	�	PROPN
ap-652	93	1	k	k	PROPN
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ap-652	94	1	k	k	PROPN
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ap-652	95	1	k	k	PROPN
ap-652	95	2	g	g	PROPN
ap-652	96	1	k	k	PROPN
ap-652	96	2	g	g	PROPN
ap-652	96	3	k	k	PROPN
ap-652	96	4	g	g	PROPN
ap-652	96	5	symm	symm	NOUN
ap-652	96	6	k	k	PROPN
ap-652	96	7	*	*	PUNCT
ap-652	96	8	*	*	PUNCT
ap-652	96	9	�	�	PROPN
ap-652	96	10	�	�	PROPN
ap-652	96	11	�	�	PROPN
ap-652	96	12	�	�	PROPN
ap-652	96	13	�	�	PROPN
ap-652	96	14	�	�	PROPN
ap-652	96	15	�	�	PROPN
ap-652	96	16	�	�	PROPN
ap-652	96	17	�	�	PROPN
ap-652	96	18	�	�	PROPN
ap-652	96	19	4	4	NUM
ap-652	96	20	31	31	NUM
ap-652	96	21	g	g	NOUN
ap-652	96	22	.	.	PUNCT
ap-652	97	1	(	(	PUNCT
ap-652	97	2	1b	1b	NUM
ap-652	97	3	)	)	PUNCT
ap-652	97	4	here	here	ADV
ap-652	97	5	i	i	PRON
ap-652	97	6	stands	stand	VERB
ap-652	97	7	for	for	ADP
ap-652	97	8	the	the	DET
ap-652	97	9	unit	unit	NOUN
ap-652	97	10	3	3	NUM
ap-652	97	11	by	by	ADP
ap-652	97	12	3	3	NUM
ap-652	97	13	matrix	matrix	NOUN
ap-652	97	14	and	and	CCONJ
ap-652	97	15	0	0	NUM
ap-652	97	16	for	for	ADP
ap-652	97	17	the	the	DET
ap-652	97	18	zero	zero	NUM
ap-652	97	19	3	3	NUM
ap-652	97	20	by	by	ADP
ap-652	97	21	3	3	NUM
ap-652	97	22	matrix	matrix	NOUN
ap-652	97	23	.	.	PUNCT
ap-652	98	1	effective	effective	ADJ
ap-652	98	2	engineering	engineering	NOUN
ap-652	98	3	constants	constant	NOUN
ap-652	98	4	k	k	PROPN
ap-652	98	5	,	,	PUNCT
ap-652	98	6	g1	g1	PROPN
ap-652	98	7	and	and	CCONJ
ap-652	98	8	g2	g2	PROPN
ap-652	98	9	are	be	AUX
ap-652	98	10	the	the	DET
ap-652	98	11	homogenized	homogenized	ADJ
ap-652	98	12	bulk	bulk	NOUN
ap-652	98	13	and	and	CCONJ
ap-652	98	14	two	two	NUM
ap-652	98	15	shear	shear	NOUN
ap-652	98	16	moduli	modulus	NOUN
ap-652	98	17	,	,	PUNCT
ap-652	98	18	respectively	respectively	ADV
ap-652	98	19	.	.	PUNCT
ap-652	99	1	their	their	PRON
ap-652	99	2	dimensionless	dimensionless	NOUN
ap-652	99	3	values	value	NOUN
ap-652	99	4	with	with	ADP
ap-652	99	5	respect	respect	NOUN
ap-652	99	6	to	to	ADP
ap-652	99	7	the	the	DET
ap-652	99	8	solid	solid	ADJ
ap-652	99	9	phase	phase	NOUN
ap-652	99	10	young	young	ADJ
ap-652	99	11	’s	’s	PART
ap-652	99	12	modulus	modulus	NOUN
ap-652	99	13	es	es	NOUN
ap-652	99	14	are	be	AUX
ap-652	99	15	identified	identify	VERB
ap-652	99	16	as	as	ADP
ap-652	99	17	:	:	PUNCT
ap-652	99	18	k	k	PROPN
ap-652	99	19	k	k	PROPN
ap-652	99	20	es	es	PROPN
ap-652	99	21	*	*	PUNCT
ap-652	99	22	�	�	PROPN
ap-652	99	23	,	,	PUNCT
ap-652	99	24	g	g	PROPN
ap-652	99	25	g	g	PROPN
ap-652	99	26	e1	e1	NOUN
ap-652	99	27	s1	s1	NOUN
ap-652	99	28	*	*	PUNCT
ap-652	99	29	�	�	PROPN
ap-652	99	30	and	and	CCONJ
ap-652	99	31	g	g	PROPN
ap-652	99	32	g	g	PROPN
ap-652	99	33	e2	e2	PROPN
ap-652	99	34	s2	s2	PROPN
ap-652	99	35	*	*	PUNCT
ap-652	99	36	�	�	PROPN
ap-652	99	37	.	.	PUNCT
ap-652	100	1	a	a	DET
ap-652	100	2	medium	medium	NOUN
ap-652	100	3	is	be	AUX
ap-652	100	4	effectively	effectively	ADV
ap-652	100	5	isotropic	isotropic	ADJ
ap-652	100	6	when	when	SCONJ
ap-652	100	7	g	g	PROPN
ap-652	100	8	g	g	PROPN
ap-652	100	9	g	g	PROPN
ap-652	100	10	*	*	PROPN
ap-652	100	11	1	1	NUM
ap-652	100	12	2	2	NUM
ap-652	100	13	*	*	PUNCT
ap-652	100	14	*	*	PUNCT
ap-652	100	15	�	�	PROPN
ap-652	100	16	�	�	PROPN
ap-652	100	17	.	.	PUNCT
ap-652	101	1	the	the	DET
ap-652	101	2	above	above	ADJ
ap-652	101	3	matrix	matrix	NOUN
ap-652	101	4	form	form	NOUN
ap-652	101	5	of	of	ADP
ap-652	101	6	the	the	DET
ap-652	101	7	fourth	fourth	ADJ
ap-652	101	8	order	order	NOUN
ap-652	101	9	tensor	tensor	NOUN
ap-652	101	10	of	of	ADP
ap-652	101	11	elastic	elastic	ADJ
ap-652	101	12	constants	constant	NOUN
ap-652	101	13	(	(	PUNCT
ap-652	101	14	lekhnitskii	lekhnitskii	PROPN
ap-652	101	15	(	(	PUNCT
ap-652	101	16	1981	1981	NUM
ap-652	101	17	)	)	PUNCT
ap-652	101	18	)	)	PUNCT
ap-652	101	19	in	in	ADP
ap-652	101	20	terms	term	NOUN
ap-652	101	21	of	of	ADP
ap-652	101	22	the	the	DET
ap-652	101	23	engineering	engineering	NOUN
ap-652	101	24	constants	constant	NOUN
ap-652	101	25	k	k	NOUN
ap-652	101	26	*	*	NOUN
ap-652	101	27	,	,	PUNCT
ap-652	101	28	g1	g1	PROPN
ap-652	101	29	*	*	PUNCT
ap-652	101	30	and	and	CCONJ
ap-652	101	31	g2	g2	PROPN
ap-652	101	32	*	*	PUNCT
ap-652	101	33	is	be	AUX
ap-652	101	34	presented	present	VERB
ap-652	101	35	in	in	ADP
ap-652	101	36	hashin	hashin	NOUN
ap-652	101	37	and	and	CCONJ
ap-652	101	38	shtrikman	shtrikman	NOUN
ap-652	101	39	(	(	PUNCT
ap-652	101	40	1962	1962	NUM
ap-652	101	41	)	)	PUNCT
ap-652	101	42	.	.	PUNCT
ap-652	102	1	at	at	ADP
ap-652	102	2	first	first	ADV
ap-652	102	3	,	,	PUNCT
ap-652	102	4	the	the	DET
ap-652	102	5	aim	aim	NOUN
ap-652	102	6	is	be	AUX
ap-652	102	7	to	to	PART
ap-652	102	8	determine	determine	VERB
ap-652	102	9	each	each	PRON
ap-652	102	10	of	of	ADP
ap-652	102	11	the	the	DET
ap-652	102	12	macroscopic	macroscopic	ADJ
ap-652	102	13	engineering	engineering	NOUN
ap-652	102	14	constants	constant	NOUN
ap-652	102	15	in	in	ADP
ap-652	102	16	terms	term	NOUN
ap-652	102	17	of	of	ADP
ap-652	102	18	the	the	DET
ap-652	102	19	generalized	generalized	ADJ
ap-652	102	20	internal	internal	ADJ
ap-652	102	21	forces	force	NOUN
ap-652	102	22	,	,	PUNCT
ap-652	102	23	which	which	PRON
ap-652	102	24	will	will	AUX
ap-652	102	25	form	form	VERB
ap-652	102	26	the	the	DET
ap-652	102	27	initial	initial	ADJ
ap-652	102	28	relation	relation	NOUN
ap-652	102	29	for	for	ADP
ap-652	102	30	the	the	DET
ap-652	102	31	bounding	bounding	NOUN
ap-652	102	32	procedure	procedure	NOUN
ap-652	102	33	.	.	PUNCT
ap-652	103	1	the	the	DET
ap-652	103	2	global	global	ADJ
ap-652	103	3	strain	strain	NOUN
ap-652	103	4	energy	energy	NOUN
ap-652	103	5	density	density	NOUN
ap-652	103	6	w	w	NOUN
ap-652	103	7	can	can	AUX
ap-652	103	8	be	be	AUX
ap-652	103	9	expressed	express	VERB
ap-652	103	10	for	for	ADP
ap-652	103	11	isotropic	isotropic	ADJ
ap-652	103	12	media	medium	NOUN
ap-652	103	13	as	as	ADP
ap-652	103	14	:	:	PUNCT
ap-652	103	15	w	w	PROPN
ap-652	103	16	e	e	X
ap-652	103	17	k	k	X
ap-652	103	18	gs	gs	INTJ
ap-652	103	19	m	m	ADJ
ap-652	103	20	d	d	X
ap-652	103	21	d	d	VERB
ap-652	103	22	�	�	PROPN
ap-652	103	23	�	�	PROPN
ap-652	103	24	�	�	PROPN
ap-652	103	25	�	�	PROPN
ap-652	103	26	�	�	PROPN
ap-652	103	27	�	�	PROPN
ap-652	103	28	�	�	PROPN
ap-652	103	29	1	1	NUM
ap-652	103	30	2	2	NUM
ap-652	103	31	2	2	NUM
ap-652	103	32	2	2	NUM
ap-652	103	33	�	�	NOUN
ap-652	103	34	*	*	PUNCT
ap-652	103	35	*	*	PUNCT
ap-652	103	36	:	:	PUNCT
ap-652	103	37	�	�	PROPN
ap-652	103	38	�	�	PROPN
ap-652	103	39	(	(	PUNCT
ap-652	103	40	2	2	NUM
ap-652	103	41	)	)	PUNCT
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ap-652	103	43	for	for	ADP
ap-652	103	44	media	medium	NOUN
ap-652	103	45	with	with	ADP
ap-652	103	46	effective	effective	ADJ
ap-652	103	47	cubic	cubic	ADJ
ap-652	103	48	symmetry	symmetry	NOUN
ap-652	103	49	as	as	ADP
ap-652	103	50	:	:	PUNCT
ap-652	103	51	w	w	PROPN
ap-652	103	52	e	e	X
ap-652	103	53	k	k	PROPN
ap-652	103	54	g	g	PROPN
ap-652	103	55	(	(	PUNCT
ap-652	103	56	s	s	PROPN
ap-652	103	57	m	m	VERB
ap-652	103	58	d,12	d,12	NOUN
ap-652	103	59	d,13	d,13	NOUN
ap-652	103	60	d,23	d,23	NOUN
ap-652	103	61	d,11	d,11	NOUN
ap-652	103	62	d	d	PROPN
ap-652	103	63	�	�	PROPN
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ap-652	103	66	1	1	NUM
ap-652	103	67	2	2	NUM
ap-652	103	68	2	2	NUM
ap-652	103	69	2	2	NUM
ap-652	103	70	2	2	NUM
ap-652	103	71	2	2	NUM
ap-652	103	72	2	2	NUM
ap-652	103	73	�	�	PROPN
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ap-652	104	1	*	*	PUNCT
ap-652	104	2	*	*	PUNCT
ap-652	104	3	,	,	PUNCT
ap-652	104	4	22	22	NUM
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ap-652	104	6	d,33	d,33	X
ap-652	104	7	d,22	d,22	X
ap-652	104	8	d,33	d,33	X
ap-652	104	9	(	(	PUNCT
ap-652	104	10	(	(	PUNCT
ap-652	104	11	6	6	NUM
ap-652	104	12	g	g	NOUN
ap-652	104	13	)	)	PUNCT
ap-652	104	14	)	)	PUNCT
ap-652	104	15	)	)	PUNCT
ap-652	104	16	,	,	PUNCT
ap-652	104	17	*	*	PUNCT
ap-652	104	18	2	2	NUM
ap-652	104	19	2	2	NUM
ap-652	104	20	2	2	NUM
ap-652	104	21	1	1	NUM
ap-652	104	22	�	�	PROPN
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ap-652	104	24	�	�	PROPN
ap-652	104	25	�	�	PROPN
ap-652	104	26	�	�	PROPN
ap-652	104	27	�	�	PROPN
ap-652	104	28	�	�	PROPN
ap-652	104	29	�	�	PROPN
ap-652	104	30	(	(	PUNCT
ap-652	104	31	3	3	NUM
ap-652	104	32	)	)	PUNCT
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ap-652	104	39	are	be	AUX
ap-652	104	40	the	the	DET
ap-652	104	41	volumetric	volumetric	NOUN
ap-652	104	42	and	and	CCONJ
ap-652	104	43	deviatoric	deviatoric	ADJ
ap-652	104	44	parts	part	NOUN
ap-652	104	45	of	of	ADP
ap-652	104	46	the	the	DET
ap-652	104	47	global	global	ADJ
ap-652	104	48	stress	stress	PROPN
ap-652	104	49	tensor	tensor	NOUN
ap-652	104	50	�	�	PROPN
ap-652	104	51	and	and	CCONJ
ap-652	104	52	�	�	PROPN
ap-652	104	53	�	�	PROPN
ap-652	104	54	d	d	PROPN
ap-652	104	55	d	d	PROPN
ap-652	105	1	d	d	PROPN
ap-652	105	2	,	,	PUNCT
ap-652	105	3	ij	ij	INTJ
ap-652	105	4	d	d	NOUN
ap-652	105	5	,	,	PUNCT
ap-652	105	6	ij	ij	ADP
ap-652	105	7	:	:	PUNCT
ap-652	105	8	�	�	PROPN
ap-652	105	9	�	�	PROPN
ap-652	105	10	�	�	PROPN
ap-652	105	11	(	(	PUNCT
ap-652	105	12	the	the	DET
ap-652	105	13	summation	summation	NOUN
ap-652	105	14	convention	convention	NOUN
ap-652	105	15	is	be	AUX
ap-652	105	16	adopted	adopt	VERB
ap-652	105	17	)	)	PUNCT
ap-652	105	18	.	.	PUNCT
ap-652	106	1	the	the	DET
ap-652	106	2	test	test	NOUN
ap-652	106	3	macroloads	macroload	NOUN
ap-652	106	4	to	to	PART
ap-652	106	5	be	be	AUX
ap-652	106	6	applied	apply	VERB
ap-652	106	7	on	on	ADP
ap-652	106	8	the	the	DET
ap-652	106	9	medium	medium	NOUN
ap-652	106	10	and	and	CCONJ
ap-652	106	11	consequently	consequently	ADV
ap-652	106	12	on	on	ADP
ap-652	106	13	the	the	DET
ap-652	106	14	basic	basic	ADJ
ap-652	106	15	cell	cell	NOUN
ap-652	106	16	can	can	AUX
ap-652	106	17	be	be	AUX
ap-652	106	18	chosen	choose	VERB
ap-652	106	19	so	so	SCONJ
ap-652	106	20	that	that	SCONJ
ap-652	106	21	only	only	ADV
ap-652	106	22	one	one	NUM
ap-652	106	23	effective	effective	ADJ
ap-652	106	24	engineering	engineering	NOUN
ap-652	106	25	constant	constant	ADJ
ap-652	106	26	will	will	AUX
ap-652	106	27	be	be	AUX
ap-652	106	28	left	leave	VERB
ap-652	106	29	in	in	ADP
ap-652	106	30	(	(	PUNCT
ap-652	106	31	2	2	NUM
ap-652	106	32	)	)	PUNCT
ap-652	106	33	or	or	CCONJ
ap-652	106	34	(	(	PUNCT
ap-652	106	35	3	3	NUM
ap-652	106	36	)	)	PUNCT
ap-652	106	37	,	,	PUNCT
ap-652	106	38	and	and	CCONJ
ap-652	106	39	can	can	AUX
ap-652	106	40	thus	thus	ADV
ap-652	106	41	be	be	AUX
ap-652	106	42	expressed	express	VERB
ap-652	106	43	independently	independently	ADV
ap-652	106	44	of	of	ADP
ap-652	106	45	the	the	DET
ap-652	106	46	others	other	NOUN
ap-652	106	47	and	and	CCONJ
ap-652	106	48	in	in	ADP
ap-652	106	49	terms	term	NOUN
ap-652	106	50	of	of	ADP
ap-652	106	51	�	�	PROPN
ap-652	106	52	components	component	NOUN
ap-652	106	53	and	and	CCONJ
ap-652	106	54	w.	w.	NOUN
ap-652	106	55	examples	example	NOUN
ap-652	106	56	of	of	ADP
ap-652	106	57	these	these	DET
ap-652	106	58	macroloads	macroload	NOUN
ap-652	106	59	are	be	AUX
ap-652	106	60	specified	specify	VERB
ap-652	106	61	in	in	ADP
ap-652	106	62	table	table	NOUN
ap-652	106	63	1	1	NUM
ap-652	106	64	.	.	PUNCT
ap-652	107	1	it	it	PRON
ap-652	107	2	is	be	AUX
ap-652	107	3	seen	see	VERB
ap-652	107	4	that	that	SCONJ
ap-652	107	5	the	the	DET
ap-652	107	6	corresponding	correspond	VERB
ap-652	107	7	macrostrain	macrostrain	NOUN
ap-652	107	8	e	e	NOUN
ap-652	107	9	must	must	AUX
ap-652	107	10	fulfill	fulfill	VERB
ap-652	107	11	similar	similar	ADJ
ap-652	107	12	conditions	condition	NOUN
ap-652	107	13	.	.	PUNCT
ap-652	108	1	macrostrain	macrostrain	NOUN
ap-652	108	2	e	e	PROPN
ap-652	108	3	is	be	AUX
ap-652	108	4	connected	connect	VERB
ap-652	108	5	to	to	PART
ap-652	108	6	macrostress	macrostress	VERB
ap-652	108	7	�	�	PROPN
ap-652	108	8	by	by	ADP
ap-652	108	9	�	�	PROPN
ap-652	108	10	�	�	PROPN
ap-652	108	11	�	�	PROPN
ap-652	108	12	esc	esc	NOUN
ap-652	108	13	e	e	PROPN
ap-652	108	14	*	*	PROPN
ap-652	108	15	,	,	PUNCT
ap-652	108	16	where	where	SCONJ
ap-652	108	17	�	�	PROPN
ap-652	108	18	�	�	PROPN
ap-652	108	19	�	�	PROPN
ap-652	108	20	�	�	PROPN
ap-652	108	21	�	�	PROPN
ap-652	108	22	�	�	PROPN
ap-652	108	23	�	�	PROPN
ap-652	108	24	�	�	PROPN
ap-652	108	25	�	�	PROPN
ap-652	108	26	�	�	PROPN
ap-652	108	27	11	11	NUM
ap-652	108	28	22	22	NUM
ap-652	108	29	33	33	NUM
ap-652	108	30	23	23	NUM
ap-652	108	31	31	31	NUM
ap-652	108	32	12	12	NUM
ap-652	108	33	,	,	PUNCT
ap-652	108	34	,	,	PUNCT
ap-652	108	35	,	,	PUNCT
ap-652	108	36	,	,	PUNCT
ap-652	108	37	,	,	PUNCT
ap-652	108	38	t	t	PROPN
ap-652	108	39	,	,	PUNCT
ap-652	108	40	�	�	PROPN
ap-652	108	41	�	�	PROPN
ap-652	108	42	e	e	NOUN
ap-652	108	43	�	�	PROPN
ap-652	108	44	e	e	X
ap-652	108	45	e	e	X
ap-652	108	46	e	e	X
ap-652	108	47	e	e	X
ap-652	108	48	e	e	X
ap-652	108	49	e11	e11	X
ap-652	108	50	2	2	NUM
ap-652	108	51	2	2	NUM
ap-652	108	52	2	2	NUM
ap-652	108	53	,	,	PUNCT
ap-652	108	54	,	,	PUNCT
ap-652	108	55	,	,	PUNCT
ap-652	108	56	,	,	PUNCT
ap-652	108	57	,	,	PUNCT
ap-652	108	58	22	22	NUM
ap-652	108	59	33	33	NUM
ap-652	108	60	23	23	NUM
ap-652	108	61	31	31	NUM
ap-652	108	62	12	12	NUM
ap-652	108	63	t	t	NOUN
ap-652	108	64	and	and	CCONJ
ap-652	108	65	“	"	PUNCT
ap-652	108	66	�	�	PROPN
ap-652	108	67	”	"	PUNCT
ap-652	108	68	stands	stand	VERB
ap-652	108	69	for	for	ADP
ap-652	108	70	matrix	matrix	NOUN
ap-652	108	71	multiplication	multiplication	NOUN
ap-652	108	72	.	.	PUNCT
ap-652	109	1	�	�	PROPN
ap-652	109	2	and	and	CCONJ
ap-652	109	3	w	w	PROPN
ap-652	109	4	can	can	AUX
ap-652	109	5	be	be	AUX
ap-652	109	6	expressed	express	VERB
ap-652	109	7	with	with	ADP
ap-652	109	8	the	the	DET
ap-652	109	9	help	help	NOUN
ap-652	109	10	of	of	ADP
ap-652	109	11	an	an	DET
ap-652	109	12	averaging	averaging	NOUN
ap-652	109	13	operator	operator	NOUN
ap-652	109	14	applied	apply	VERB
ap-652	109	15	on	on	ADP
ap-652	109	16	the	the	DET
ap-652	109	17	local	local	ADJ
ap-652	109	18	characteristics	characteristic	NOUN
ap-652	109	19	,	,	PUNCT
ap-652	109	20	�	�	PROPN
ap-652	109	21	and	and	CCONJ
ap-652	109	22	w	w	PROPN
ap-652	109	23	,	,	PUNCT
ap-652	109	24	(	(	PUNCT
ap-652	109	25	suquet	suquet	NOUN
ap-652	109	26	(	(	PUNCT
ap-652	109	27	1985	1985	NUM
ap-652	109	28	)	)	PUNCT
ap-652	109	29	):	):	PUNCT
ap-652	110	1	�	�	PROPN
ap-652	110	2	�	�	PROPN
ap-652	110	3	�	�	PROPN
ap-652	110	4	�	�	PROPN
ap-652	110	5	jk	jk	PROPN
ap-652	110	6	jk	jk	PROPN
ap-652	110	7	jk	jk	PROPN
ap-652	111	1	i	i	PRON
ap-652	112	1	jk	jk	VERB
ap-652	113	1	i	i	PRON
ap-652	113	2	i	i	PRON
ap-652	113	3	v	v	VERB
ap-652	113	4	d	d	X
ap-652	113	5	v	v	PROPN
ap-652	113	6	d	d	PROPN
ap-652	113	7	�	�	PROPN
ap-652	113	8	�	�	PROPN
ap-652	113	9	�	�	PROPN
ap-652	113	10	�	�	PROPN
ap-652	113	11	�	�	PROPN
ap-652	113	12	�	�	PROPN
ap-652	113	13	�	�	PROPN
ap-652	113	14	1	1	NUM
ap-652	113	15	1	1	NUM
ap-652	113	16	y	y	PROPN
ap-652	113	17	y	y	PROPN
ap-652	113	18	v	v	PROPN
ap-652	113	19	v	v	NUM
ap-652	113	20	ii	ii	NOUN
ap-652	113	21	#	#	NOUN
ap-652	113	22	#	#	NOUN
ap-652	113	23	,	,	PUNCT
ap-652	113	24	(	(	PUNCT
ap-652	113	25	4	4	NUM
ap-652	113	26	)	)	PUNCT
ap-652	113	27	w	w	NOUN
ap-652	113	28	v	v	NUM
ap-652	113	29	w	w	PROPN
ap-652	114	1	d	d	X
ap-652	114	2	v	v	PROPN
ap-652	114	3	w	w	PROPN
ap-652	114	4	d	d	X
ap-652	114	5	wi	wi	PROPN
ap-652	115	1	i	i	PRON
ap-652	115	2	i	i	PROPN
ap-652	115	3	�	�	PROPN
ap-652	115	4	�	�	PROPN
ap-652	115	5	�	�	PROPN
ap-652	115	6	�	�	PROPN
ap-652	115	7	�	�	PROPN
ap-652	115	8	�	�	PROPN
ap-652	115	9	�	�	PROPN
ap-652	115	10	1	1	NUM
ap-652	115	11	1	1	NUM
ap-652	115	12	y	y	PROPN
ap-652	115	13	y	y	PROPN
ap-652	115	14	v	v	PROPN
ap-652	115	15	v	v	NUM
ap-652	115	16	ii	ii	NOUN
ap-652	115	17	#	#	NOUN
ap-652	115	18	#	#	NOUN
ap-652	115	19	,	,	PUNCT
ap-652	115	20	(	(	PUNCT
ap-652	115	21	5	5	NUM
ap-652	115	22	)	)	PUNCT
ap-652	115	23	where	where	SCONJ
ap-652	115	24	�	�	PROPN
ap-652	115	25	i	i	PROPN
ap-652	115	26	and	and	CCONJ
ap-652	115	27	wi	wi	PROPN
ap-652	115	28	are	be	AUX
ap-652	115	29	the	the	DET
ap-652	115	30	local	local	ADJ
ap-652	115	31	stress	stress	NOUN
ap-652	115	32	and	and	CCONJ
ap-652	115	33	the	the	DET
ap-652	115	34	local	local	ADJ
ap-652	115	35	strain	strain	NOUN
ap-652	115	36	energy	energy	NOUN
ap-652	115	37	density	density	NOUN
ap-652	115	38	corresponding	correspond	VERB
ap-652	115	39	to	to	ADP
ap-652	115	40	the	the	DET
ap-652	115	41	ith	ith	PROPN
ap-652	115	42	beam	beam	NOUN
ap-652	115	43	(	(	PUNCT
ap-652	115	44	i	i	NOUN
ap-652	115	45	-	-	PUNCT
ap-652	115	46	beam	beam	NOUN
ap-652	115	47	)	)	PUNCT
ap-652	115	48	.	.	PUNCT
ap-652	116	1	the	the	DET
ap-652	116	2	volume	volume	NOUN
ap-652	116	3	of	of	ADP
ap-652	116	4	the	the	DET
ap-652	116	5	full	full	ADJ
ap-652	116	6	cell	cell	NOUN
ap-652	116	7	is	be	AUX
ap-652	116	8	v	v	NOUN
ap-652	116	9	while	while	SCONJ
ap-652	116	10	the	the	DET
ap-652	116	11	volume	volume	NOUN
ap-652	116	12	of	of	ADP
ap-652	116	13	the	the	DET
ap-652	116	14	i	i	NOUN
ap-652	116	15	-	-	PUNCT
ap-652	116	16	beam	beam	NOUN
ap-652	116	17	is	be	AUX
ap-652	116	18	vi	vi	NOUN
ap-652	116	19	#	#	NOUN
ap-652	116	20	.	.	PUNCT
ap-652	117	1	vi	vi	NOUN
ap-652	117	2	#	#	NOUN
ap-652	117	3	is	be	AUX
ap-652	117	4	composed	compose	VERB
ap-652	117	5	of	of	ADP
ap-652	117	6	the	the	DET
ap-652	117	7	volume	volume	NOUN
ap-652	117	8	corresponding	correspond	VERB
ap-652	117	9	to	to	ADP
ap-652	117	10	the	the	DET
ap-652	117	11	active	active	ADJ
ap-652	117	12	length	length	NOUN
ap-652	117	13	plus	plus	CCONJ
ap-652	117	14	the	the	DET
ap-652	117	15	corresponding	corresponding	ADJ
ap-652	117	16	volume	volume	NOUN
ap-652	117	17	in	in	ADP
ap-652	117	18	the	the	DET
ap-652	117	19	connected	connected	ADJ
ap-652	117	20	parts	part	NOUN
ap-652	117	21	within	within	ADP
ap-652	117	22	the	the	DET
ap-652	117	23	joints	joint	NOUN
ap-652	117	24	,	,	PUNCT
ap-652	117	25	so	so	SCONJ
ap-652	117	26	that	that	SCONJ
ap-652	117	27	v	v	ADP
ap-652	117	28	v	v	NOUN
ap-652	118	1	i	i	PRON
ap-652	118	2	ji	ji	PROPN
ap-652	118	3	#	#	NOUN
ap-652	118	4	j	j	PROPN
ap-652	118	5	#	#	SYM
ap-652	118	6	�	�	PROPN
ap-652	118	7	�	�	PROPN
ap-652	118	8	�	�	PROPN
ap-652	118	9	�	�	PROPN
ap-652	118	10	0	0	NUM
ap-652	118	11	and	and	CCONJ
ap-652	118	12	v	v	NOUN
ap-652	118	13	vi	vi	NOUN
ap-652	118	14	#	#	NOUN
ap-652	118	15	i	i	NOUN
ap-652	118	16	#	#	SYM
ap-652	118	17	�	�	PROPN
ap-652	118	18	�	�	PROPN
ap-652	118	19	.	.	PUNCT
ap-652	119	1	v	v	NOUN
ap-652	119	2	#	#	NOUN
ap-652	119	3	is	be	AUX
ap-652	119	4	the	the	DET
ap-652	119	5	volume	volume	NOUN
ap-652	119	6	of	of	ADP
ap-652	119	7	the	the	DET
ap-652	119	8	material	material	ADJ
ap-652	119	9	part	part	NOUN
ap-652	119	10	in	in	ADP
ap-652	119	11	the	the	DET
ap-652	119	12	cell	cell	NOUN
ap-652	119	13	.	.	PUNCT
ap-652	120	1	due	due	ADP
ap-652	120	2	to	to	ADP
ap-652	120	3	the	the	DET
ap-652	120	4	periodic	periodic	ADJ
ap-652	120	5	repetition	repetition	NOUN
ap-652	120	6	it	it	PRON
ap-652	120	7	is	be	AUX
ap-652	120	8	not	not	PART
ap-652	120	9	necessary	necessary	ADJ
ap-652	120	10	to	to	PART
ap-652	120	11	treat	treat	VERB
ap-652	120	12	separately	separately	ADV
ap-652	120	13	the	the	DET
ap-652	120	14	case	case	NOUN
ap-652	120	15	when	when	SCONJ
ap-652	120	16	the	the	DET
ap-652	120	17	i	i	NOUN
ap-652	120	18	-	-	PUNCT
ap-652	120	19	beam	beam	NOUN
ap-652	120	20	is	be	AUX
ap-652	120	21	cut	cut	VERB
ap-652	120	22	by	by	ADP
ap-652	120	23	the	the	DET
ap-652	120	24	boundary	boundary	NOUN
ap-652	120	25	of	of	ADP
ap-652	120	26	the	the	DET
ap-652	120	27	cell	cell	NOUN
ap-652	120	28	.	.	PUNCT
ap-652	121	1	next	next	ADV
ap-652	121	2	,	,	PUNCT
ap-652	121	3	it	it	PRON
ap-652	121	4	is	be	AUX
ap-652	121	5	necessary	necessary	ADJ
ap-652	121	6	to	to	PART
ap-652	121	7	express	express	VERB
ap-652	121	8	the	the	DET
ap-652	121	9	contributions	contribution	NOUN
ap-652	121	10	of	of	ADP
ap-652	121	11	each	each	DET
ap-652	121	12	i	i	NOUN
ap-652	121	13	-	-	PUNCT
ap-652	121	14	beam	beam	NOUN
ap-652	121	15	,	,	PUNCT
ap-652	121	16	�	�	PROPN
ap-652	121	17	i	i	PROPN
ap-652	121	18	and	and	CCONJ
ap-652	121	19	wi	wi	PROPN
ap-652	121	20	,	,	PUNCT
ap-652	121	21	in	in	ADP
ap-652	121	22	terms	term	NOUN
ap-652	121	23	of	of	ADP
ap-652	121	24	generalized	generalized	ADJ
ap-652	121	25	internal	internal	ADJ
ap-652	121	26	forces	force	NOUN
ap-652	121	27	.	.	PUNCT
ap-652	122	1	looking	look	VERB
ap-652	122	2	at	at	ADP
ap-652	122	3	�	�	PROPN
ap-652	122	4	i	i	PRON
ap-652	122	5	,	,	PUNCT
ap-652	122	6	the	the	DET
ap-652	122	7	formula	formula	NOUN
ap-652	122	8	from	from	ADP
ap-652	122	9	nemat	nemat	NOUN
ap-652	122	10	-	-	PUNCT
ap-652	122	11	nasser	nasser	PROPN
ap-652	122	12	and	and	CCONJ
ap-652	122	13	hori	hori	PROPN
ap-652	122	14	(	(	PUNCT
ap-652	122	15	1993	1993	NUM
ap-652	122	16	)	)	PUNCT
ap-652	122	17	�	�	PROPN
ap-652	122	18	�	�	PROPN
ap-652	122	19	mj	mj	NOUN
ap-652	123	1	i	i	PRON
ap-652	123	2	i	i	PRON
ap-652	123	3	#	#	NOUN
ap-652	123	4	jk	jk	NOUN
ap-652	124	1	i	i	PRON
ap-652	124	2	k	k	PROPN
ap-652	125	1	m	m	VERB
ap-652	125	2	v	v	INTJ
ap-652	126	1	i	i	PRON
ap-652	126	2	#	#	NOUN
ap-652	126	3	j	j	NOUN
ap-652	127	1	i	i	PRON
ap-652	127	2	m	m	VERB
ap-652	127	3	v	v	ADP
ap-652	127	4	v	v	ADP
ap-652	127	5	n	n	PROPN
ap-652	127	6	b	b	PROPN
ap-652	128	1	d	d	PROPN
ap-652	128	2	v	v	ADP
ap-652	128	3	t	t	PROPN
ap-652	128	4	b	b	PROPN
ap-652	129	1	d	d	NOUN
ap-652	130	1	i	i	PRON
ap-652	131	1	#	#	NOUN
ap-652	132	1	i	i	PRON
ap-652	132	2	#	#	PROPN
ap-652	132	3	�	�	PROPN
ap-652	132	4	�	�	PROPN
ap-652	132	5	�	�	PROPN
ap-652	132	6	�	�	PROPN
ap-652	132	7	1	1	NUM
ap-652	132	8	1	1	NUM
ap-652	132	9	s	s	NOUN
ap-652	132	10	s	s	NOUN
ap-652	132	11	�	�	PROPN
ap-652	132	12	�	�	PROPN
ap-652	132	13	(	(	PUNCT
ap-652	132	14	6	6	NUM
ap-652	132	15	)	)	PUNCT
ap-652	132	16	©	©	PROPN
ap-652	132	17	czech	czech	PROPN
ap-652	132	18	technical	technical	PROPN
ap-652	132	19	university	university	PROPN
ap-652	132	20	publishing	publishing	NOUN
ap-652	132	21	house	house	NOUN
ap-652	132	22	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	132	23	173	173	NUM
ap-652	132	24	acta	acta	PROPN
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ap-652	135	7	e	e	NOUN
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ap-652	135	10	e	e	PROPN
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ap-652	136	1	ij	ij	INTJ
ap-652	137	1	i	i	PROPN
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ap-652	137	7	e	e	NOUN
ap-652	137	8	e	e	X
ap-652	137	9	e	e	X
ap-652	137	10	e	e	X
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ap-652	137	46	22	22	NUM
ap-652	137	47	33	33	NUM
ap-652	137	48	0	0	NUM
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ap-652	137	50	�	�	PROPN
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ap-652	137	117	e	e	X
ap-652	137	118	e	e	X
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ap-652	137	130	e	e	NOUN
ap-652	138	1	i	i	PRON
ap-652	138	2	jij	jij	VERB
ap-652	138	3	ij	ij	INTJ
ap-652	138	4	s	s	VERB
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ap-652	138	6	*	*	ADJ
ap-652	138	7	(	(	PUNCT
ap-652	138	8	)	)	PUNCT
ap-652	138	9	,	,	PUNCT
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ap-652	138	13	(	(	PUNCT
ap-652	138	14	#	#	NOUN
ap-652	138	15	if	if	SCONJ
ap-652	138	16	the	the	DET
ap-652	138	17	macrostress	macrostress	NOUN
ap-652	138	18	component	component	NOUN
ap-652	138	19	is	be	AUX
ap-652	138	20	different	different	ADJ
ap-652	138	21	from	from	ADP
ap-652	138	22	zero	zero	NUM
ap-652	138	23	)	)	PUNCT
ap-652	138	24	table	table	NOUN
ap-652	138	25	1	1	NUM
ap-652	138	26	:	:	PUNCT
ap-652	138	27	test	test	NOUN
ap-652	138	28	macroloads	macroload	NOUN
ap-652	138	29	and	and	CCONJ
ap-652	138	30	the	the	DET
ap-652	138	31	corresponding	correspond	VERB
ap-652	138	32	specification	specification	NOUN
ap-652	138	33	of	of	ADP
ap-652	138	34	the	the	DET
ap-652	138	35	macrostress	macrostress	NOUN
ap-652	138	36	and	and	CCONJ
ap-652	138	37	the	the	DET
ap-652	138	38	macrostrain	macrostrain	NOUN
ap-652	138	39	can	can	AUX
ap-652	138	40	be	be	AUX
ap-652	138	41	exploited	exploit	VERB
ap-652	138	42	.	.	PUNCT
ap-652	139	1	in	in	ADP
ap-652	139	2	(	(	PUNCT
ap-652	139	3	6	6	NUM
ap-652	139	4	)	)	PUNCT
ap-652	139	5	,	,	PUNCT
ap-652	139	6	b	b	PROPN
ap-652	139	7	is	be	AUX
ap-652	139	8	the	the	DET
ap-652	139	9	position	position	NOUN
ap-652	139	10	vector	vector	NOUN
ap-652	139	11	of	of	ADP
ap-652	139	12	the	the	DET
ap-652	139	13	points	point	NOUN
ap-652	139	14	on	on	ADP
ap-652	139	15	�	�	NOUN
ap-652	139	16	vi	vi	NOUN
ap-652	139	17	#	#	NOUN
ap-652	139	18	and	and	CCONJ
ap-652	139	19	t	t	NOUN
ap-652	139	20	is	be	AUX
ap-652	139	21	the	the	DET
ap-652	139	22	boundary	boundary	ADJ
ap-652	139	23	traction	traction	NOUN
ap-652	139	24	.	.	PUNCT
ap-652	140	1	if	if	SCONJ
ap-652	140	2	t	t	PROPN
ap-652	140	3	is	be	AUX
ap-652	140	4	self	self	NOUN
ap-652	140	5	-	-	PUNCT
ap-652	140	6	equilibrated	equilibrate	VERB
ap-652	140	7	,	,	PUNCT
ap-652	140	8	then	then	ADV
ap-652	140	9	�	�	PROPN
ap-652	140	10	i	i	PRON
ap-652	140	11	is	be	AUX
ap-652	140	12	symmetric	symmetric	ADJ
ap-652	140	13	and	and	CCONJ
ap-652	140	14	the	the	DET
ap-652	140	15	integral	integral	ADJ
ap-652	140	16	in	in	ADP
ap-652	140	17	(	(	PUNCT
ap-652	140	18	6	6	NUM
ap-652	140	19	)	)	PUNCT
ap-652	140	20	does	do	AUX
ap-652	140	21	not	not	PART
ap-652	140	22	depend	depend	VERB
ap-652	140	23	on	on	ADP
ap-652	140	24	the	the	DET
ap-652	140	25	origin	origin	NOUN
ap-652	140	26	of	of	ADP
ap-652	140	27	the	the	DET
ap-652	140	28	coordinate	coordinate	NOUN
ap-652	140	29	system	system	NOUN
ap-652	140	30	for	for	ADP
ap-652	140	31	b.	b.	PROPN
ap-652	140	32	the	the	DET
ap-652	140	33	expression	expression	NOUN
ap-652	140	34	for	for	ADP
ap-652	140	35	wi	wi	PROPN
ap-652	140	36	can	can	AUX
ap-652	140	37	be	be	AUX
ap-652	140	38	,	,	PUNCT
ap-652	140	39	as	as	ADV
ap-652	140	40	usual	usual	ADJ
ap-652	140	41	,	,	PUNCT
ap-652	140	42	simplified	simplify	VERB
ap-652	140	43	by	by	ADP
ap-652	140	44	considering	consider	VERB
ap-652	140	45	that	that	SCONJ
ap-652	140	46	generalized	generalize	VERB
ap-652	140	47	internal	internal	ADJ
ap-652	140	48	forces	force	NOUN
ap-652	140	49	act	act	VERB
ap-652	140	50	over	over	ADP
ap-652	140	51	theoretical	theoretical	ADJ
ap-652	140	52	lengths	length	NOUN
ap-652	140	53	and	and	CCONJ
ap-652	140	54	that	that	SCONJ
ap-652	140	55	the	the	DET
ap-652	140	56	contribution	contribution	NOUN
ap-652	140	57	of	of	ADP
ap-652	140	58	the	the	DET
ap-652	140	59	joints	joint	NOUN
ap-652	140	60	is	be	AUX
ap-652	140	61	negligible	negligible	ADJ
ap-652	140	62	.	.	PUNCT
ap-652	141	1	2.2	2.2	NUM
ap-652	141	2	micro	micro	NOUN
ap-652	141	3	-	-	NOUN
ap-652	141	4	trusses	truss	NOUN
ap-652	141	5	with	with	ADP
ap-652	141	6	straight	straight	ADJ
ap-652	141	7	bars	bar	NOUN
ap-652	141	8	of	of	ADP
ap-652	141	9	constant	constant	ADJ
ap-652	141	10	cross	cross	PROPN
ap-652	141	11	sectional	sectional	ADJ
ap-652	141	12	area	area	NOUN
ap-652	141	13	versus	versus	ADP
ap-652	141	14	micro	micro	NOUN
ap-652	141	15	-	-	NOUN
ap-652	141	16	frames	frame	VERB
ap-652	141	17	optimal	optimal	ADJ
ap-652	141	18	low	low	ADJ
ap-652	141	19	-	-	PUNCT
ap-652	141	20	density	density	NOUN
ap-652	141	21	micro	micro	NOUN
ap-652	141	22	-	-	NOUN
ap-652	141	23	frame	frame	ADJ
ap-652	141	24	open	open	ADJ
ap-652	141	25	-	-	PUNCT
ap-652	141	26	cell	cell	NOUN
ap-652	141	27	foams	foam	NOUN
ap-652	141	28	will	will	AUX
ap-652	141	29	be	be	AUX
ap-652	141	30	defined	define	VERB
ap-652	141	31	as	as	ADP
ap-652	141	32	those	those	PRON
ap-652	141	33	for	for	ADP
ap-652	141	34	which	which	PRON
ap-652	141	35	the	the	DET
ap-652	141	36	related	relate	VERB
ap-652	141	37	micro	micro	NOUN
ap-652	141	38	-	-	ADJ
ap-652	141	39	truss	truss	ADJ
ap-652	141	40	is	be	AUX
ap-652	141	41	optimal	optimal	ADJ
ap-652	141	42	.	.	PUNCT
ap-652	142	1	justification	justification	NOUN
ap-652	142	2	of	of	ADP
ap-652	142	3	this	this	DET
ap-652	142	4	definition	definition	NOUN
ap-652	142	5	and	and	CCONJ
ap-652	142	6	more	more	ADJ
ap-652	142	7	details	detail	NOUN
ap-652	142	8	on	on	ADP
ap-652	142	9	optimal	optimal	ADJ
ap-652	142	10	micro	micro	NOUN
ap-652	142	11	-	-	NOUN
ap-652	142	12	trusses	truss	NOUN
ap-652	142	13	are	be	AUX
ap-652	142	14	presented	present	VERB
ap-652	142	15	in	in	ADP
ap-652	142	16	this	this	DET
ap-652	142	17	subsection	subsection	NOUN
ap-652	142	18	,	,	PUNCT
ap-652	142	19	namely	namely	ADV
ap-652	142	20	it	it	PRON
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ap-652	142	22	be	be	AUX
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ap-652	142	26	micro	micro	NOUN
ap-652	142	27	-	-	NOUN
ap-652	142	28	trusses	truss	NOUN
ap-652	142	29	can	can	AUX
ap-652	142	30	only	only	ADV
ap-652	142	31	be	be	AUX
ap-652	142	32	composed	compose	VERB
ap-652	142	33	of	of	ADP
ap-652	142	34	straight	straight	ADJ
ap-652	142	35	bars	bar	NOUN
ap-652	142	36	with	with	ADP
ap-652	142	37	a	a	DET
ap-652	142	38	constant	constant	ADJ
ap-652	142	39	cross	cross	NOUN
ap-652	142	40	section	section	NOUN
ap-652	142	41	.	.	PUNCT
ap-652	143	1	in	in	ADP
ap-652	143	2	order	order	NOUN
ap-652	143	3	to	to	PART
ap-652	143	4	justify	justify	VERB
ap-652	143	5	the	the	DET
ap-652	143	6	definition	definition	NOUN
ap-652	143	7	stated	state	VERB
ap-652	143	8	above	above	ADV
ap-652	143	9	,	,	PUNCT
ap-652	143	10	it	it	PRON
ap-652	143	11	is	be	AUX
ap-652	143	12	necessary	necessary	ADJ
ap-652	143	13	to	to	PART
ap-652	143	14	verify	verify	VERB
ap-652	143	15	that	that	SCONJ
ap-652	143	16	a	a	DET
ap-652	143	17	curved	curved	ADJ
ap-652	143	18	beam	beam	NOUN
ap-652	143	19	can	can	AUX
ap-652	143	20	not	not	PART
ap-652	143	21	from	from	ADP
ap-652	143	22	part	part	NOUN
ap-652	143	23	of	of	ADP
ap-652	143	24	the	the	DET
ap-652	143	25	optimal	optimal	ADJ
ap-652	143	26	low	low	ADJ
ap-652	143	27	-	-	PUNCT
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ap-652	143	29	media	medium	NOUN
ap-652	143	30	.	.	PUNCT
ap-652	144	1	let	let	VERB
ap-652	144	2	us	we	PRON
ap-652	144	3	suppose	suppose	VERB
ap-652	144	4	that	that	SCONJ
ap-652	144	5	the	the	DET
ap-652	144	6	i	i	NOUN
ap-652	144	7	-	-	PUNCT
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ap-652	144	9	of	of	ADP
ap-652	144	10	a	a	DET
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ap-652	144	12	-	-	NOUN
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ap-652	144	14	basic	basic	ADJ
ap-652	144	15	cell	cell	NOUN
ap-652	144	16	is	be	AUX
ap-652	144	17	curved	curve	VERB
ap-652	144	18	.	.	PUNCT
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ap-652	145	2	a	a	DET
ap-652	145	3	local	local	ADJ
ap-652	145	4	coordinate	coordinate	NOUN
ap-652	145	5	system	system	NOUN
ap-652	145	6	(	(	PUNCT
ap-652	145	7	z1	z1	NOUN
ap-652	145	8	,	,	PUNCT
ap-652	145	9	z2	z2	PROPN
ap-652	145	10	)	)	PUNCT
ap-652	145	11	can	can	AUX
ap-652	145	12	be	be	AUX
ap-652	145	13	introduced	introduce	VERB
ap-652	145	14	so	so	SCONJ
ap-652	145	15	that	that	SCONJ
ap-652	145	16	z1	z1	NOUN
ap-652	145	17	connects	connect	VERB
ap-652	145	18	the	the	DET
ap-652	145	19	centers	center	NOUN
ap-652	145	20	of	of	ADP
ap-652	145	21	the	the	DET
ap-652	145	22	joints	joint	NOUN
ap-652	145	23	(	(	PUNCT
ap-652	145	24	fig	fig	NOUN
ap-652	145	25	.	.	PUNCT
ap-652	146	1	2	2	NUM
ap-652	146	2	)	)	PUNCT
ap-652	146	3	.	.	PUNCT
ap-652	147	1	the	the	DET
ap-652	147	2	middle	middle	ADJ
ap-652	147	3	axis	axis	NOUN
ap-652	147	4	of	of	ADP
ap-652	147	5	the	the	DET
ap-652	147	6	beam	beam	NOUN
ap-652	147	7	is	be	AUX
ap-652	147	8	given	give	VERB
ap-652	147	9	by	by	ADP
ap-652	147	10	z2	z2	NOUN
ap-652	147	11	=	=	NOUN
ap-652	147	12	a(z1	a(z1	ADJ
ap-652	147	13	)	)	PUNCT
ap-652	147	14	and	and	CCONJ
ap-652	147	15	r	r	NOUN
ap-652	147	16	designates	designate	VERB
ap-652	147	17	the	the	DET
ap-652	147	18	curved	curved	ADJ
ap-652	147	19	coordinate	coordinate	NOUN
ap-652	147	20	.	.	PUNCT
ap-652	148	1	let	let	VERB
ap-652	148	2	us	we	PRON
ap-652	148	3	separate	separate	VERB
ap-652	148	4	the	the	DET
ap-652	148	5	beam	beam	NOUN
ap-652	148	6	of	of	ADP
ap-652	148	7	active	active	ADJ
ap-652	148	8	length	length	NOUN
ap-652	148	9	from	from	ADP
ap-652	148	10	the	the	DET
ap-652	148	11	joints	joint	NOUN
ap-652	148	12	by	by	ADP
ap-652	148	13	the	the	DET
ap-652	148	14	cuts	cut	NOUN
ap-652	148	15	shown	show	VERB
ap-652	148	16	in	in	ADP
ap-652	148	17	fig	fig	NOUN
ap-652	148	18	.	.	PUNCT
ap-652	149	1	2	2	X
ap-652	149	2	.	.	X
ap-652	149	3	it	it	PRON
ap-652	149	4	is	be	AUX
ap-652	149	5	assumed	assume	VERB
ap-652	149	6	that	that	SCONJ
ap-652	149	7	there	there	PRON
ap-652	149	8	exists	exist	VERB
ap-652	149	9	a	a	DET
ap-652	149	10	plane	plane	NOUN
ap-652	149	11	containing	contain	VERB
ap-652	149	12	the	the	DET
ap-652	149	13	i	i	PROPN
ap-652	149	14	-	-	PUNCT
ap-652	149	15	beam	beam	NOUN
ap-652	149	16	middle	middle	ADJ
ap-652	149	17	curve	curve	NOUN
ap-652	149	18	and	and	CCONJ
ap-652	149	19	that	that	SCONJ
ap-652	149	20	the	the	DET
ap-652	149	21	macroload	macroload	NOUN
ap-652	149	22	acts	act	VERB
ap-652	149	23	in	in	ADP
ap-652	149	24	such	such	DET
ap-652	149	25	a	a	DET
ap-652	149	26	way	way	NOUN
ap-652	149	27	that	that	PRON
ap-652	149	28	the	the	DET
ap-652	149	29	generalized	generalized	ADJ
ap-652	149	30	internal	internal	ADJ
ap-652	149	31	forces	force	NOUN
ap-652	149	32	in	in	ADP
ap-652	149	33	the	the	DET
ap-652	149	34	beam	beam	NOUN
ap-652	149	35	cuts	cut	NOUN
ap-652	149	36	are	be	AUX
ap-652	149	37	also	also	ADV
ap-652	149	38	contained	contain	VERB
ap-652	149	39	in	in	ADP
ap-652	149	40	this	this	DET
ap-652	149	41	plane	plane	NOUN
ap-652	149	42	.	.	PUNCT
ap-652	150	1	the	the	DET
ap-652	150	2	geometrical	geometrical	ADJ
ap-652	150	3	parameters	parameter	NOUN
ap-652	150	4	�	�	PROPN
ap-652	150	5	(	(	PUNCT
ap-652	150	6	r	r	NOUN
ap-652	150	7	)	)	PUNCT
ap-652	150	8	,	,	PUNCT
ap-652	150	9	�	�	NOUN
ap-652	150	10	0k	0k	NOUN
ap-652	150	11	,	,	PUNCT
ap-652	150	12	�	�	PROPN
ap-652	150	13	0	0	NUM
ap-652	150	14	m	m	PROPN
ap-652	150	15	,	,	PUNCT
ap-652	150	16	hk	hk	PROPN
ap-652	150	17	,	,	PUNCT
ap-652	150	18	hm	hm	INTJ
ap-652	150	19	,	,	PUNCT
ap-652	150	20	vk	vk	PROPN
ap-652	150	21	,	,	PUNCT
ap-652	150	22	vm	vm	NOUN
ap-652	150	23	,	,	PUNCT
ap-652	150	24	l	l	PROPN
ap-652	150	25	,	,	PUNCT
ap-652	150	26	p	p	X
ap-652	150	27	,	,	PUNCT
ap-652	150	28	the	the	DET
ap-652	150	29	generalized	generalize	VERB
ap-652	150	30	internal	internal	ADJ
ap-652	150	31	forces	force	NOUN
ap-652	150	32	in	in	ADP
ap-652	150	33	the	the	DET
ap-652	150	34	beam	beam	NOUN
ap-652	150	35	cuts	cut	NOUN
ap-652	150	36	f	f	PROPN
ap-652	150	37	,	,	PUNCT
ap-652	150	38	b	b	PROPN
ap-652	150	39	and	and	CCONJ
ap-652	150	40	d	d	PROPN
ap-652	150	41	and	and	CCONJ
ap-652	150	42	other	other	ADJ
ap-652	150	43	local	local	ADJ
ap-652	150	44	auxiliary	auxiliary	ADJ
ap-652	150	45	coordinate	coordinate	NOUN
ap-652	150	46	systems	system	NOUN
ap-652	150	47	(	(	PUNCT
ap-652	150	48	~	~	PUNCT
ap-652	150	49	,	,	PUNCT
ap-652	150	50	~z	~z	PUNCT
ap-652	150	51	z1	z1	NOUN
ap-652	150	52	2	2	NUM
ap-652	150	53	)	)	PUNCT
ap-652	150	54	and	and	CCONJ
ap-652	150	55	(	(	PUNCT
ap-652	150	56	�	�	PROPN
ap-652	150	57	,	,	PUNCT
ap-652	150	58	�	�	PROPN
ap-652	150	59	z	z	NOUN
ap-652	150	60	z1	z1	NOUN
ap-652	150	61	2	2	NUM
ap-652	150	62	)	)	PUNCT
ap-652	150	63	are	be	AUX
ap-652	150	64	specified	specify	VERB
ap-652	150	65	in	in	ADP
ap-652	150	66	fig	fig	NOUN
ap-652	150	67	.	.	PUNCT
ap-652	151	1	2	2	NUM
ap-652	151	2	.	.	X
ap-652	151	3	l	l	NOUN
ap-652	152	1	and	and	CCONJ
ap-652	152	2	p	p	NOUN
ap-652	152	3	are	be	AUX
ap-652	152	4	projections	projection	NOUN
ap-652	152	5	of	of	ADP
ap-652	152	6	the	the	DET
ap-652	152	7	theoretical	theoretical	ADJ
ap-652	152	8	and	and	CCONJ
ap-652	152	9	the	the	DET
ap-652	152	10	active	active	ADJ
ap-652	152	11	lengths	length	NOUN
ap-652	152	12	on	on	ADP
ap-652	152	13	z1	z1	NOUN
ap-652	152	14	and	and	CCONJ
ap-652	152	15	the	the	DET
ap-652	152	16	bending	bend	VERB
ap-652	152	17	moment	moment	NOUN
ap-652	152	18	along	along	ADP
ap-652	152	19	the	the	DET
ap-652	152	20	beam	beam	NOUN
ap-652	152	21	is	be	AUX
ap-652	152	22	separated	separate	VERB
ap-652	152	23	into	into	ADP
ap-652	152	24	its	its	PRON
ap-652	152	25	(	(	PUNCT
ap-652	152	26	average	average	ADJ
ap-652	152	27	)	)	PUNCT
ap-652	152	28	constant	constant	ADJ
ap-652	152	29	(	(	PUNCT
ap-652	152	30	d	d	NOUN
ap-652	152	31	)	)	PUNCT
ap-652	152	32	and	and	CCONJ
ap-652	152	33	“	"	PUNCT
ap-652	152	34	antisymmetric	antisymmetric	ADJ
ap-652	152	35	”	"	PUNCT
ap-652	152	36	parts	part	NOUN
ap-652	152	37	.	.	PUNCT
ap-652	153	1	for	for	ADP
ap-652	153	2	the	the	DET
ap-652	153	3	i	i	PROPN
ap-652	153	4	-	-	PUNCT
ap-652	153	5	beam	beam	NOUN
ap-652	153	6	let	let	VERB
ap-652	153	7	us	we	PRON
ap-652	153	8	express	express	VERB
ap-652	153	9	the	the	DET
ap-652	153	10	average	average	ADJ
ap-652	153	11	quantities	quantity	NOUN
ap-652	153	12	�	�	PROPN
ap-652	153	13	i	i	PROPN
ap-652	153	14	and	and	CCONJ
ap-652	153	15	wi	wi	PROPN
ap-652	153	16	in	in	ADP
ap-652	153	17	terms	term	NOUN
ap-652	153	18	of	of	ADP
ap-652	153	19	the	the	DET
ap-652	153	20	generalized	generalized	ADJ
ap-652	153	21	internal	internal	ADJ
ap-652	153	22	forces	force	NOUN
ap-652	153	23	and	and	CCONJ
ap-652	153	24	discuss	discuss	VERB
ap-652	153	25	the	the	DET
ap-652	153	26	possibility	possibility	NOUN
ap-652	153	27	of	of	ADP
ap-652	153	28	its	its	PRON
ap-652	153	29	position	position	NOUN
ap-652	153	30	in	in	ADP
ap-652	153	31	an	an	DET
ap-652	153	32	optimal	optimal	ADJ
ap-652	153	33	medium	medium	NOUN
ap-652	153	34	.	.	PUNCT
ap-652	154	1	superscript	superscript	PROPN
ap-652	154	2	“	"	PUNCT
ap-652	154	3	i	i	PROPN
ap-652	154	4	”	"	PUNCT
ap-652	154	5	will	will	AUX
ap-652	154	6	be	be	AUX
ap-652	154	7	omitted	omit	VERB
ap-652	154	8	for	for	ADP
ap-652	154	9	the	the	DET
ap-652	154	10	sake	sake	NOUN
ap-652	154	11	of	of	ADP
ap-652	154	12	simplicity	simplicity	NOUN
ap-652	154	13	,	,	PUNCT
ap-652	154	14	whenever	whenever	SCONJ
ap-652	154	15	no	no	DET
ap-652	154	16	confusion	confusion	NOUN
ap-652	154	17	is	be	AUX
ap-652	154	18	possible	possible	ADJ
ap-652	154	19	.	.	PUNCT
ap-652	155	1	it	it	PRON
ap-652	155	2	must	must	AUX
ap-652	155	3	be	be	AUX
ap-652	155	4	pointed	point	VERB
ap-652	155	5	out	out	ADP
ap-652	155	6	that	that	SCONJ
ap-652	155	7	local	local	ADJ
ap-652	155	8	stress	stress	NOUN
ap-652	155	9	averaging	averaging	NOUN
ap-652	155	10	can	can	AUX
ap-652	155	11	not	not	PART
ap-652	155	12	be	be	AUX
ap-652	155	13	performed	perform	VERB
ap-652	155	14	over	over	ADP
ap-652	155	15	the	the	DET
ap-652	155	16	theoretical	theoretical	ADJ
ap-652	155	17	length	length	NOUN
ap-652	155	18	,	,	PUNCT
ap-652	155	19	because	because	SCONJ
ap-652	155	20	this	this	PRON
ap-652	155	21	would	would	AUX
ap-652	155	22	cause	cause	VERB
ap-652	155	23	overlapping	overlapping	NOUN
ap-652	155	24	of	of	ADP
ap-652	155	25	the	the	DET
ap-652	155	26	joints	joint	NOUN
ap-652	155	27	.	.	PUNCT
ap-652	156	1	thus	thus	ADV
ap-652	156	2	the	the	DET
ap-652	156	3	i	i	NOUN
ap-652	156	4	-	-	PUNCT
ap-652	156	5	beam	beam	ADJ
ap-652	156	6	average	average	ADJ
ap-652	156	7	stress	stress	NOUN
ap-652	156	8	�	�	PROPN
ap-652	156	9	must	must	AUX
ap-652	156	10	be	be	AUX
ap-652	156	11	expressed	express	VERB
ap-652	156	12	as	as	SCONJ
ap-652	156	13	�	�	PROPN
ap-652	156	14	�	�	PROPN
ap-652	156	15	�	�	PROPN
ap-652	156	16	�	�	PROPN
ap-652	156	17	�	�	PROPN
ap-652	156	18	�	�	PROPN
ap-652	156	19	�	�	PROPN
ap-652	156	20	bm	bm	PROPN
ap-652	156	21	jk	jk	PROPN
ap-652	156	22	jm	jm	PROPN
ap-652	156	23	,	,	PUNCT
ap-652	156	24	where	where	SCONJ
ap-652	156	25	the	the	DET
ap-652	156	26	contribution	contribution	NOUN
ap-652	156	27	with	with	ADP
ap-652	156	28	subscript	subscript	NOUN
ap-652	156	29	“	"	PUNCT
ap-652	156	30	bm	bm	PROPN
ap-652	156	31	”	"	PUNCT
ap-652	156	32	relates	relate	VERB
ap-652	156	33	to	to	ADP
ap-652	156	34	the	the	DET
ap-652	156	35	beam	beam	NOUN
ap-652	156	36	with	with	ADP
ap-652	156	37	active	active	ADJ
ap-652	156	38	length	length	NOUN
ap-652	156	39	and	and	CCONJ
ap-652	156	40	thoses	those	NOUN
ap-652	156	41	with	with	ADP
ap-652	156	42	“	"	PUNCT
ap-652	156	43	jk	jk	PROPN
ap-652	156	44	”	"	PUNCT
ap-652	156	45	and	and	CCONJ
ap-652	156	46	“	"	PUNCT
ap-652	156	47	jm	jm	PROPN
ap-652	156	48	”	"	PUNCT
ap-652	156	49	subscripts	subscript	NOUN
ap-652	156	50	relate	relate	VERB
ap-652	156	51	to	to	ADP
ap-652	156	52	the	the	DET
ap-652	156	53	left	left	NOUN
ap-652	156	54	(	(	PUNCT
ap-652	156	55	k	k	NOUN
ap-652	156	56	)	)	PUNCT
ap-652	156	57	and	and	CCONJ
ap-652	156	58	right	right	ADJ
ap-652	156	59	(	(	PUNCT
ap-652	156	60	m	m	NOUN
ap-652	156	61	)	)	PUNCT
ap-652	156	62	adjacent	adjacent	ADJ
ap-652	156	63	joint	joint	ADJ
ap-652	156	64	parts	part	NOUN
ap-652	156	65	,	,	PUNCT
ap-652	156	66	respectively	respectively	ADV
ap-652	156	67	.	.	PUNCT
ap-652	157	1	strict	strict	ADJ
ap-652	157	2	application	application	NOUN
ap-652	157	3	of	of	ADP
ap-652	157	4	(	(	PUNCT
ap-652	157	5	6	6	NUM
ap-652	157	6	)	)	PUNCT
ap-652	157	7	,	,	PUNCT
ap-652	157	8	in	in	ADP
ap-652	157	9	the	the	DET
ap-652	157	10	previous	previous	ADJ
ap-652	157	11	expression	expression	NOUN
ap-652	157	12	,	,	PUNCT
ap-652	157	13	would	would	AUX
ap-652	157	14	imply	imply	VERB
ap-652	157	15	integration	integration	NOUN
ap-652	157	16	over	over	ADP
ap-652	157	17	the	the	DET
ap-652	157	18	internal	internal	ADJ
ap-652	157	19	faces	face	NOUN
ap-652	157	20	of	of	ADP
ap-652	157	21	the	the	DET
ap-652	157	22	joints	joint	NOUN
ap-652	157	23	,	,	PUNCT
ap-652	157	24	which	which	PRON
ap-652	157	25	is	be	AUX
ap-652	157	26	complicated	complicated	ADJ
ap-652	157	27	.	.	PUNCT
ap-652	158	1	to	to	PART
ap-652	158	2	overcome	overcome	VERB
ap-652	158	3	these	these	DET
ap-652	158	4	difficulties	difficulty	NOUN
ap-652	158	5	we	we	PRON
ap-652	158	6	can	can	AUX
ap-652	158	7	define	define	VERB
ap-652	158	8	~	~	PUNCT
ap-652	158	9	~	~	PUNCT
ap-652	158	10	~	~	PUNCT
ap-652	158	11	�	�	PROPN
ap-652	158	12	�	�	PROPN
ap-652	158	13	�	�	PROPN
ap-652	158	14	�	�	PROPN
ap-652	158	15	�	�	PROPN
ap-652	158	16	�	�	PROPN
ap-652	158	17	�	�	PROPN
ap-652	158	18	bm	bm	PROPN
ap-652	158	19	jk	jk	PROPN
ap-652	158	20	jm	jm	PROPN
ap-652	158	21	,	,	PUNCT
ap-652	158	22	where	where	SCONJ
ap-652	158	23	~	~	PUNCT
ap-652	158	24	�	�	PROPN
ap-652	158	25	jk	jk	PROPN
ap-652	158	26	and	and	CCONJ
ap-652	158	27	~	~	PROPN
ap-652	158	28	�	�	PROPN
ap-652	158	29	jm	jm	PROPN
ap-652	158	30	stand	stand	VERB
ap-652	158	31	only	only	ADV
ap-652	158	32	for	for	ADP
ap-652	158	33	the	the	DET
ap-652	158	34	contribution	contribution	NOUN
ap-652	158	35	of	of	ADP
ap-652	158	36	the	the	DET
ap-652	158	37	faces	face	NOUN
ap-652	158	38	where	where	SCONJ
ap-652	158	39	the	the	DET
ap-652	158	40	beam	beam	NOUN
ap-652	158	41	was	be	AUX
ap-652	158	42	cut	cut	VERB
ap-652	158	43	.	.	PUNCT
ap-652	159	1	then	then	ADV
ap-652	159	2	~	~	PUNCT
ap-652	159	3	�	�	PROPN
ap-652	159	4	jk	jk	PROPN
ap-652	159	5	and	and	CCONJ
ap-652	159	6	~	~	PROPN
ap-652	159	7	�	�	PROPN
ap-652	159	8	jm	jm	PROPN
ap-652	159	9	are	be	AUX
ap-652	159	10	coordinate	coordinate	ADJ
ap-652	159	11	system	system	NOUN
ap-652	159	12	dependent	dependent	ADJ
ap-652	159	13	and	and	CCONJ
ap-652	159	14	therefore	therefore	ADV
ap-652	159	15	their	their	PRON
ap-652	159	16	coordinate	coordinate	NOUN
ap-652	159	17	174	174	NUM
ap-652	159	18	©	©	PROPN
ap-652	159	19	czech	czech	PROPN
ap-652	159	20	technical	technical	PROPN
ap-652	159	21	university	university	PROPN
ap-652	159	22	publishing	publishing	NOUN
ap-652	159	23	house	house	NOUN
ap-652	159	24	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	159	25	acta	acta	PROPN
ap-652	159	26	polytechnica	polytechnica	PROPN
ap-652	159	27	vol	vol	NOUN
ap-652	159	28	.	.	PROPN
ap-652	160	1	44	44	NUM
ap-652	160	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	160	3	r	r	NOUN
ap-652	160	4	r	r	NOUN
ap-652	160	5	l	l	NOUN
ap-652	160	6	p	p	X
ap-652	160	7	kv	kv	PROPN
ap-652	160	8	mv	mv	PROPN
ap-652	160	9	1z	1z	PROPN
ap-652	160	10	2z	2z	NUM
ap-652	160	11	k0	k0	PROPN
ap-652	160	12	m0	m0	PROPN
ap-652	160	13	d	d	PROPN
ap-652	160	14	d	d	X
ap-652	160	15	dd	dd	ADJ
ap-652	160	16	2	2	NUM
ap-652	160	17	/	/	SYM
ap-652	160	18	bp	bp	PROPN
ap-652	160	19	2	2	NUM
ap-652	160	20	/	/	SYM
ap-652	160	21	bp	bp	PROPN
ap-652	160	22	2	2	NUM
ap-652	160	23	/	/	SYM
ap-652	160	24	bp	bp	PROPN
ap-652	160	25	2	2	NUM
ap-652	160	26	/	/	SYM
ap-652	160	27	bp	bp	PROPN
ap-652	161	1	kh	kh	PROPN
ap-652	162	1	mh	mh	PROPN
ap-652	163	1	f	f	PROPN
ap-652	164	1	f	f	PROPN
ap-652	165	1	f	f	PROPN
ap-652	165	2	f	f	PROPN
ap-652	165	3	b	b	PROPN
ap-652	165	4	b	b	PROPN
ap-652	165	5	b	b	PROPN
ap-652	165	6	b	b	PROPN
ap-652	165	7	1z~	1z~	NUM
ap-652	165	8	2z~	2z~	NOUN
ap-652	165	9	1z	1z	NOUN
ap-652	165	10	2z	2z	NUM
ap-652	165	11	12	12	NUM
ap-652	165	12	zaz	zaz	PROPN
ap-652	165	13	m	m	PROPN
ap-652	165	14	k	k	PROPN
ap-652	165	15	mv	mv	PROPN
ap-652	165	16	kv	kv	PROPN
ap-652	165	17	fig	fig	PROPN
ap-652	165	18	.	.	PUNCT
ap-652	166	1	2	2	NUM
ap-652	166	2	:	:	PUNCT
ap-652	166	3	specification	specification	NOUN
ap-652	166	4	of	of	ADP
ap-652	166	5	the	the	DET
ap-652	166	6	curved	curved	ADJ
ap-652	166	7	i	i	PROPN
ap-652	166	8	-	-	PUNCT
ap-652	166	9	beam	beam	ADJ
ap-652	166	10	origins	origin	NOUN
ap-652	166	11	of	of	ADP
ap-652	166	12	the	the	DET
ap-652	166	13	coordinate	coordinate	NOUN
ap-652	166	14	systems	system	NOUN
ap-652	166	15	(	(	PUNCT
ap-652	166	16	z1	z1	PROPN
ap-652	166	17	,	,	PUNCT
ap-652	166	18	z2	z2	PROPN
ap-652	166	19	)	)	PUNCT
ap-652	166	20	and	and	CCONJ
ap-652	166	21	(	(	PUNCT
ap-652	166	22	~	~	PUNCT
ap-652	166	23	,	,	PUNCT
ap-652	166	24	~z	~z	PUNCT
ap-652	166	25	z1	z1	NOUN
ap-652	166	26	2	2	NUM
ap-652	166	27	)	)	PUNCT
ap-652	166	28	are	be	AUX
ap-652	166	29	coincident	coincident	ADJ
ap-652	166	30	,	,	PUNCT
ap-652	166	31	therefore	therefore	ADV
ap-652	166	32	only	only	ADV
ap-652	166	33	the	the	DET
ap-652	166	34	face	face	NOUN
ap-652	166	35	of	of	ADP
ap-652	166	36	joint	joint	ADJ
ap-652	166	37	(	(	PUNCT
ap-652	166	38	m	m	NOUN
ap-652	166	39	)	)	PUNCT
ap-652	166	40	and	and	CCONJ
ap-652	166	41	the	the	DET
ap-652	166	42	corresponding	corresponding	ADJ
ap-652	166	43	face	face	NOUN
ap-652	166	44	of	of	ADP
ap-652	166	45	the	the	DET
ap-652	166	46	beam	beam	NOUN
ap-652	166	47	can	can	AUX
ap-652	166	48	be	be	AUX
ap-652	166	49	considered	consider	VERB
ap-652	166	50	to	to	PART
ap-652	166	51	obtain	obtain	VERB
ap-652	166	52	(	(	PUNCT
ap-652	166	53	10	10	NUM
ap-652	166	54	)	)	PUNCT
ap-652	166	55	.	.	PUNCT
ap-652	167	1	it	it	PRON
ap-652	167	2	is	be	AUX
ap-652	167	3	necessary	necessary	ADJ
ap-652	167	4	to	to	PART
ap-652	167	5	point	point	VERB
ap-652	167	6	out	out	ADP
ap-652	167	7	that	that	SCONJ
ap-652	167	8	the	the	DET
ap-652	167	9	reason	reason	NOUN
ap-652	167	10	for	for	ADP
ap-652	167	11	non	non	ADJ
ap-652	167	12	-	-	NOUN
ap-652	167	13	symmetry	symmetry	NOUN
ap-652	167	14	of	of	ADP
ap-652	167	15	~	~	PUNCT
ap-652	167	16	�	�	PROPN
ap-652	167	17	is	be	AUX
ap-652	167	18	the	the	DET
ap-652	167	19	omission	omission	NOUN
ap-652	167	20	of	of	ADP
ap-652	167	21	the	the	DET
ap-652	167	22	contributions	contribution	NOUN
ap-652	167	23	of	of	ADP
ap-652	167	24	the	the	DET
ap-652	167	25	internal	internal	ADJ
ap-652	167	26	faces	face	NOUN
ap-652	167	27	of	of	ADP
ap-652	167	28	the	the	DET
ap-652	167	29	joints	joint	NOUN
ap-652	167	30	in	in	ADP
ap-652	167	31	(	(	PUNCT
ap-652	167	32	8–9	8–9	NOUN
ap-652	167	33	)	)	PUNCT
ap-652	167	34	,	,	PUNCT
ap-652	167	35	as	as	SCONJ
ap-652	167	36	explained	explain	VERB
ap-652	167	37	above	above	ADV
ap-652	167	38	.	.	PUNCT
ap-652	168	1	this	this	PRON
ap-652	168	2	does	do	AUX
ap-652	168	3	not	not	PART
ap-652	168	4	mean	mean	VERB
ap-652	168	5	any	any	DET
ap-652	168	6	inaccuracy	inaccuracy	NOUN
ap-652	168	7	,	,	PUNCT
ap-652	168	8	because	because	SCONJ
ap-652	168	9	after	after	ADP
ap-652	168	10	rotation	rotation	NOUN
ap-652	168	11	of	of	ADP
ap-652	168	12	the	the	DET
ap-652	168	13	contributions	contribution	NOUN
ap-652	168	14	of	of	ADP
ap-652	168	15	all	all	DET
ap-652	168	16	beams	beam	NOUN
ap-652	168	17	to	to	ADP
ap-652	168	18	the	the	DET
ap-652	168	19	cell	cell	NOUN
ap-652	168	20	coordinate	coordinate	NOUN
ap-652	168	21	system	system	NOUN
ap-652	168	22	and	and	CCONJ
ap-652	168	23	after	after	ADP
ap-652	168	24	summation	summation	NOUN
ap-652	168	25	over	over	ADP
ap-652	168	26	all	all	DET
ap-652	168	27	the	the	DET
ap-652	168	28	beams	beam	NOUN
ap-652	168	29	,	,	PUNCT
ap-652	168	30	the	the	DET
ap-652	168	31	final	final	ADJ
ap-652	168	32	expression	expression	NOUN
ap-652	168	33	for	for	ADP
ap-652	168	34	�	�	PROPN
ap-652	168	35	will	will	AUX
ap-652	168	36	be	be	AUX
ap-652	168	37	complete	complete	ADJ
ap-652	168	38	and	and	CCONJ
ap-652	168	39	symmetric	symmetric	ADJ
ap-652	168	40	.	.	PUNCT
ap-652	169	1	when	when	SCONJ
ap-652	169	2	a	a	DET
ap-652	169	3	general	general	ADJ
ap-652	169	4	curved	curved	ADJ
ap-652	169	5	beam	beam	NOUN
ap-652	169	6	under	under	ADP
ap-652	169	7	a	a	DET
ap-652	169	8	general	general	ADJ
ap-652	169	9	macroload	macroload	NOUN
ap-652	169	10	is	be	AUX
ap-652	169	11	considered	consider	VERB
ap-652	169	12	,	,	PUNCT
ap-652	169	13	the	the	DET
ap-652	169	14	local	local	ADJ
ap-652	169	15	coordinate	coordinate	NOUN
ap-652	169	16	system	system	NOUN
ap-652	169	17	(	(	PUNCT
ap-652	169	18	z1	z1	NOUN
ap-652	169	19	,	,	PUNCT
ap-652	169	20	z2	z2	PROPN
ap-652	169	21	)	)	PUNCT
ap-652	169	22	connecting	connect	VERB
ap-652	169	23	the	the	DET
ap-652	169	24	centers	center	NOUN
ap-652	169	25	of	of	ADP
ap-652	169	26	the	the	DET
ap-652	169	27	jointscan	jointscan	PROPN
ap-652	169	28	also	also	ADV
ap-652	169	29	be	be	AUX
ap-652	169	30	introduced	introduce	VERB
ap-652	169	31	.	.	PUNCT
ap-652	170	1	then	then	ADV
ap-652	170	2	it	it	PRON
ap-652	170	3	is	be	AUX
ap-652	170	4	necessary	necessary	ADJ
ap-652	170	5	to	to	PART
ap-652	170	6	replace	replace	VERB
ap-652	170	7	internal	internal	ADJ
ap-652	170	8	force	force	NOUN
ap-652	170	9	b	b	PROPN
ap-652	170	10	by	by	ADP
ap-652	170	11	b1	b1	NOUN
ap-652	170	12	and	and	CCONJ
ap-652	170	13	b2	b2	NOUN
ap-652	170	14	,	,	PUNCT
ap-652	170	15	bending	bend	VERB
ap-652	170	16	moment	moment	NOUN
ap-652	170	17	d	d	NOUN
ap-652	170	18	by	by	ADP
ap-652	170	19	d1	d1	PROPN
ap-652	170	20	and	and	CCONJ
ap-652	170	21	d2	d2	PROPN
ap-652	170	22	,	,	PUNCT
ap-652	170	23	and	and	CCONJ
ap-652	170	24	to	to	PART
ap-652	170	25	introduce	introduce	VERB
ap-652	170	26	torsion	torsion	NOUN
ap-652	170	27	moment	moment	NOUN
ap-652	170	28	t.	t.	NOUN
ap-652	170	29	following	follow	VERB
ap-652	170	30	the	the	DET
ap-652	170	31	same	same	ADJ
ap-652	170	32	procedure	procedure	NOUN
ap-652	170	33	as	as	ADP
ap-652	170	34	above	above	ADV
ap-652	170	35	,	,	PUNCT
ap-652	170	36	we	we	PRON
ap-652	170	37	obtain	obtain	VERB
ap-652	170	38	:	:	PUNCT
ap-652	171	1	~	~	PUNCT
ap-652	171	2	�	�	PROPN
ap-652	171	3	�	�	PROPN
ap-652	171	4	�	�	PROPN
ap-652	171	5	�	�	PROPN
ap-652	171	6	�	�	PROPN
ap-652	171	7	�	�	PROPN
ap-652	171	8	�	�	PROPN
ap-652	171	9	�	�	PROPN
ap-652	171	10	�	�	PROPN
ap-652	171	11	�	�	PROPN
ap-652	171	12	�	�	PROPN
ap-652	171	13	�	�	PROPN
ap-652	171	14	l	l	PROPN
ap-652	171	15	v	v	PROPN
ap-652	171	16	f	f	PROPN
ap-652	171	17	b	b	PROPN
ap-652	171	18	b	b	PROPN
ap-652	171	19	0	0	NUM
ap-652	171	20	0	0	NUM
ap-652	171	21	0	0	NUM
ap-652	171	22	0	0	NUM
ap-652	171	23	0	0	NUM
ap-652	171	24	0	0	NUM
ap-652	171	25	1	1	NUM
ap-652	171	26	2	2	NUM
ap-652	171	27	.	.	PUNCT
ap-652	172	1	(	(	PUNCT
ap-652	172	2	11	11	NUM
ap-652	172	3	)	)	PUNCT
ap-652	172	4	it	it	PRON
ap-652	172	5	is	be	AUX
ap-652	172	6	important	important	ADJ
ap-652	172	7	to	to	PART
ap-652	172	8	realize	realize	VERB
ap-652	172	9	that	that	SCONJ
ap-652	172	10	(	(	PUNCT
ap-652	172	11	11	11	NUM
ap-652	172	12	)	)	PUNCT
ap-652	172	13	has	have	VERB
ap-652	172	14	the	the	DET
ap-652	172	15	same	same	ADJ
ap-652	172	16	form	form	NOUN
ap-652	172	17	as	as	SCONJ
ap-652	172	18	it	it	PRON
ap-652	172	19	would	would	AUX
ap-652	172	20	have	have	VERB
ap-652	172	21	for	for	ADP
ap-652	172	22	a	a	DET
ap-652	172	23	related	related	ADJ
ap-652	172	24	straight	straight	ADJ
ap-652	172	25	beam	beam	NOUN
ap-652	172	26	of	of	ADP
ap-652	172	27	theoretical	theoretical	ADJ
ap-652	172	28	length	length	NOUN
ap-652	172	29	l	l	NOUN
ap-652	172	30	,	,	PUNCT
ap-652	172	31	arbitrary	arbitrary	ADJ
ap-652	172	32	cross	cross	PROPN
ap-652	172	33	sectional	sectional	ADJ
ap-652	172	34	area	area	NOUN
ap-652	172	35	variation	variation	NOUN
ap-652	172	36	and	and	CCONJ
ap-652	172	37	with	with	ADP
ap-652	172	38	the	the	DET
ap-652	172	39	same	same	ADJ
ap-652	172	40	generalized	generalized	ADJ
ap-652	172	41	internal	internal	ADJ
ap-652	172	42	forces	force	NOUN
ap-652	172	43	in	in	ADP
ap-652	172	44	the	the	DET
ap-652	172	45	cuts	cut	NOUN
ap-652	172	46	.	.	PUNCT
ap-652	173	1	therefore	therefore	ADV
ap-652	173	2	there	there	PRON
ap-652	173	3	is	be	VERB
ap-652	173	4	no	no	DET
ap-652	173	5	distinction	distinction	NOUN
ap-652	173	6	between	between	ADP
ap-652	173	7	the	the	DET
ap-652	173	8	�	�	PROPN
ap-652	173	9	�	�	PROPN
ap-652	173	10	�	�	PROPN
ap-652	173	11	contribution	contribution	NOUN
ap-652	173	12	of	of	ADP
ap-652	173	13	a	a	DET
ap-652	173	14	straight	straight	NOUN
ap-652	173	15	or	or	CCONJ
ap-652	173	16	a	a	DET
ap-652	173	17	curved	curved	ADJ
ap-652	173	18	beam	beam	NOUN
ap-652	173	19	to	to	ADP
ap-652	173	20	�	�	PROPN
ap-652	173	21	.	.	PUNCT
ap-652	174	1	moreover	moreover	ADV
ap-652	174	2	,	,	PUNCT
ap-652	174	3	(	(	PUNCT
ap-652	174	4	11	11	NUM
ap-652	174	5	)	)	PUNCT
ap-652	174	6	includes	includes	AUX
ap-652	174	7	neither	neither	CCONJ
ap-652	174	8	include	include	VERB
ap-652	174	9	the	the	DET
ap-652	174	10	constant	constant	ADJ
ap-652	174	11	part	part	NOUN
ap-652	174	12	of	of	ADP
ap-652	174	13	bending	bend	VERB
ap-652	174	14	moments	moment	NOUN
ap-652	174	15	d1	d1	PROPN
ap-652	174	16	and	and	CCONJ
ap-652	174	17	d2	d2	PROPN
ap-652	174	18	nor	nor	CCONJ
ap-652	174	19	the	the	DET
ap-652	174	20	torsion	torsion	NOUN
ap-652	174	21	moment	moment	NOUN
ap-652	174	22	t.	t.	NOUN
ap-652	175	1	if	if	SCONJ
ap-652	175	2	the	the	DET
ap-652	175	3	i	i	PRON
ap-652	175	4	-	-	PUNCT
ap-652	175	5	were	be	AUX
ap-652	175	6	to	to	PART
ap-652	175	7	have	have	VERB
ap-652	175	8	pin	pin	PROPN
ap-652	175	9	joints	joint	NOUN
ap-652	175	10	,	,	PUNCT
ap-652	175	11	then	then	ADV
ap-652	175	12	from	from	ADP
ap-652	175	13	equilibrium	equilibrium	NOUN
ap-652	175	14	b1	b1	PROPN
ap-652	175	15	�	�	PROPN
ap-652	175	16	b2	b2	PROPN
ap-652	175	17	�	�	PROPN
ap-652	175	18	0	0	NUM
ap-652	175	19	.	.	PUNCT
ap-652	176	1	we	we	PRON
ap-652	176	2	point	point	VERB
ap-652	176	3	outd	outd	NOUN
ap-652	176	4	that	that	SCONJ
ap-652	176	5	in	in	ADP
ap-652	176	6	order	order	NOUN
ap-652	176	7	to	to	PART
ap-652	176	8	express	express	VERB
ap-652	176	9	�	�	PROPN
ap-652	176	10	,	,	PUNCT
ap-652	176	11	(	(	PUNCT
ap-652	176	12	11	11	NUM
ap-652	176	13	)	)	PUNCT
ap-652	176	14	should	should	AUX
ap-652	176	15	be	be	AUX
ap-652	176	16	rotated	rotate	VERB
ap-652	176	17	to	to	ADP
ap-652	176	18	the	the	DET
ap-652	176	19	basic	basic	ADJ
ap-652	176	20	cell	cell	NOUN
ap-652	176	21	coordinates	coordinate	NOUN
ap-652	176	22	and	and	CCONJ
ap-652	176	23	summed	sum	VERB
ap-652	176	24	over	over	ADP
ap-652	176	25	all	all	DET
ap-652	176	26	the	the	DET
ap-652	176	27	beams	beam	NOUN
ap-652	176	28	.	.	PUNCT
ap-652	177	1	now	now	ADV
ap-652	177	2	the	the	DET
ap-652	177	3	average	average	ADJ
ap-652	177	4	�	�	PROPN
ap-652	177	5	w	w	PROPN
ap-652	177	6	�	�	PROPN
ap-652	177	7	will	will	AUX
ap-652	177	8	be	be	AUX
ap-652	177	9	determined	determine	VERB
ap-652	177	10	.	.	PUNCT
ap-652	178	1	for	for	ADP
ap-652	178	2	the	the	DET
ap-652	178	3	sake	sake	NOUN
ap-652	178	4	of	of	ADP
ap-652	178	5	simplicity	simplicity	NOUN
ap-652	178	6	it	it	PRON
ap-652	178	7	is	be	AUX
ap-652	178	8	again	again	ADV
ap-652	178	9	firstly	firstly	ADV
ap-652	178	10	assumed	assume	VERB
ap-652	178	11	that	that	SCONJ
ap-652	178	12	a	a	DET
ap-652	178	13	curved	curved	ADJ
ap-652	178	14	beam	beam	NOUN
ap-652	178	15	and	and	CCONJ
ap-652	178	16	the	the	DET
ap-652	178	17	generalized	generalized	ADJ
ap-652	178	18	forces	force	NOUN
ap-652	178	19	are	be	AUX
ap-652	178	20	contained	contain	VERB
ap-652	178	21	in	in	ADP
ap-652	178	22	a	a	DET
ap-652	178	23	plane	plane	NOUN
ap-652	178	24	.	.	PUNCT
ap-652	179	1	as	as	ADP
ap-652	179	2	usual	usual	ADJ
ap-652	179	3	,	,	PUNCT
ap-652	179	4	the	the	DET
ap-652	179	5	strain	strain	ADJ
ap-652	179	6	energy	energy	NOUN
ap-652	179	7	density	density	NOUN
ap-652	179	8	corresponding	correspond	VERB
ap-652	179	9	to	to	ADP
ap-652	179	10	the	the	DET
ap-652	179	11	shear	shear	NOUN
ap-652	179	12	forces	force	NOUN
ap-652	179	13	can	can	AUX
ap-652	179	14	be	be	AUX
ap-652	179	15	omitted	omit	VERB
ap-652	179	16	.	.	PUNCT
ap-652	180	1	then	then	ADV
ap-652	180	2	we	we	PRON
ap-652	180	3	can	can	AUX
ap-652	180	4	write	write	VERB
ap-652	180	5	:	:	PUNCT
ap-652	180	6	w	w	NOUN
ap-652	180	7	v	v	X
ap-652	180	8	e	e	NOUN
ap-652	180	9	n	n	ADP
ap-652	180	10	r	r	NOUN
ap-652	180	11	a	a	DET
ap-652	180	12	r	r	NOUN
ap-652	180	13	dr	dr	PROPN
ap-652	181	1	+	+	NOUN
ap-652	181	2	m	m	VERB
ap-652	181	3	r	r	NOUN
ap-652	182	1	i	i	NOUN
ap-652	182	2	r	r	NOUN
ap-652	182	3	dr	dr	PROPN
ap-652	182	4	s	s	PROPN
ap-652	182	5	2	2	NUM
ap-652	182	6	2	2	NUM
ap-652	182	7	aa	aa	PROPN
ap-652	182	8	�	�	PROPN
ap-652	182	9	�	�	PROPN
ap-652	182	10	�	�	PROPN
ap-652	182	11	�	�	PROPN
ap-652	182	12	�	�	PROPN
ap-652	182	13	�	�	PROPN
ap-652	182	14	�	�	PROPN
ap-652	182	15	�	�	PROPN
ap-652	182	16	�	�	PROPN
ap-652	182	17	�	�	PROPN
ap-652	182	18	1	1	NUM
ap-652	182	19	2	2	NUM
ap-652	182	20	(	(	PUNCT
ap-652	182	21	)	)	PUNCT
ap-652	182	22	(	(	PUNCT
ap-652	182	23	)	)	PUNCT
ap-652	182	24	(	(	PUNCT
ap-652	182	25	)	)	PUNCT
ap-652	182	26	(	(	PUNCT
ap-652	182	27	)	)	PUNCT
ap-652	182	28	(	(	PUNCT
ap-652	182	29	)	)	PUNCT
ap-652	182	30	(	(	PUNCT
ap-652	182	31	)	)	PUNCT
ap-652	182	32	,	,	PUNCT
ap-652	182	33	(	(	PUNCT
ap-652	182	34	12	12	NUM
ap-652	182	35	)	)	PUNCT
ap-652	182	36	©	©	PROPN
ap-652	182	37	czech	czech	PROPN
ap-652	182	38	technical	technical	PROPN
ap-652	182	39	university	university	PROPN
ap-652	182	40	publishing	publishing	NOUN
ap-652	182	41	house	house	NOUN
ap-652	182	42	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	182	43	175	175	NUM
ap-652	182	44	acta	acta	PROPN
ap-652	182	45	polytechnica	polytechnica	PROPN
ap-652	182	46	vol	vol	NOUN
ap-652	182	47	.	.	PROPN
ap-652	183	1	44	44	NUM
ap-652	183	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	183	3	systems	system	NOUN
ap-652	183	4	must	must	AUX
ap-652	183	5	be	be	AUX
ap-652	183	6	uniquely	uniquely	ADV
ap-652	183	7	defined	define	VERB
ap-652	183	8	in	in	ADP
ap-652	183	9	a	a	DET
ap-652	183	10	way	way	NOUN
ap-652	183	11	applicable	applicable	ADJ
ap-652	183	12	to	to	ADP
ap-652	183	13	any	any	DET
ap-652	183	14	beam	beam	NOUN
ap-652	183	15	from	from	ADP
ap-652	183	16	the	the	DET
ap-652	183	17	basic	basic	ADJ
ap-652	183	18	cell	cell	NOUN
ap-652	183	19	.	.	PUNCT
ap-652	184	1	coordinate	coordinate	NOUN
ap-652	184	2	systems	system	NOUN
ap-652	184	3	(	(	PUNCT
ap-652	184	4	~	~	PUNCT
ap-652	184	5	,	,	PUNCT
ap-652	184	6	~z	~z	PUNCT
ap-652	184	7	z1	z1	ADJ
ap-652	184	8	2	2	NUM
ap-652	184	9	)	)	PUNCT
ap-652	184	10	and(z	and(z	NOUN
ap-652	184	11	z1	z1	NOUN
ap-652	184	12	2	2	NUM
ap-652	184	13	�	�	PROPN
ap-652	184	14	,	,	PUNCT
ap-652	184	15	�	�	PROPN
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ap-652	184	22	fig	fig	NOUN
ap-652	184	23	.	.	PUNCT
ap-652	185	1	2	2	X
ap-652	185	2	.	.	X
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ap-652	185	4	respect	respect	NOUN
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ap-652	185	6	(	(	PUNCT
ap-652	185	7	z1	z1	PROPN
ap-652	185	8	,	,	PUNCT
ap-652	185	9	z2	z2	PROPN
ap-652	185	10	)	)	PUNCT
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ap-652	185	12	yields	yield	NOUN
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ap-652	185	14	(	(	PUNCT
ap-652	185	15	6	6	NUM
ap-652	185	16	):	):	PUNCT
ap-652	185	17	v	v	NOUN
ap-652	185	18	fp	fp	NUM
ap-652	185	19	1	1	NUM
ap-652	185	20	2	2	NUM
ap-652	185	21	bp	bp	NOUN
ap-652	186	1	d	d	NOUN
ap-652	186	2	k	k	PROPN
ap-652	186	3	k	k	PROPN
ap-652	186	4	m	m	VERB
ap-652	186	5	m	m	VERB
ap-652	186	6	k	k	PROPN
ap-652	186	7	�	�	PROPN
ap-652	186	8	bm	bm	PROPN
ap-652	186	9	�	�	PROPN
ap-652	186	10	(	(	PUNCT
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ap-652	186	12	cos	cos	PROPN
ap-652	186	13	sin	sin	PROPN
ap-652	186	14	cos	cos	PROPN
ap-652	186	15	)	)	PUNCT
ap-652	186	16	(	(	PUNCT
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ap-652	186	18	co	co	ADJ
ap-652	186	19	�	�	PROPN
ap-652	186	20	�	�	PROPN
ap-652	186	21	�	�	PROPN
ap-652	186	22	�	�	PROPN
ap-652	186	23	�	�	PROPN
ap-652	186	24	0	0	NUM
ap-652	186	25	0	0	NUM
ap-652	186	26	0	0	NUM
ap-652	186	27	0	0	NUM
ap-652	186	28	0	0	NUM
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ap-652	186	30	sin	sin	NOUN
ap-652	186	31	cos	cos	PROPN
ap-652	186	32	)	)	PUNCT
ap-652	186	33	)	)	PUNCT
ap-652	186	34	�	�	PROPN
ap-652	186	35	�	�	PROPN
ap-652	186	36	�	�	PROPN
ap-652	186	37	�	�	PROPN
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ap-652	186	39	�	�	PROPN
ap-652	186	40	0	0	NUM
ap-652	186	41	0	0	NUM
ap-652	186	42	0	0	NUM
ap-652	186	43	0	0	NUM
ap-652	186	44	0	0	NUM
ap-652	186	45	0	0	NUM
ap-652	187	1	k	k	NOUN
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ap-652	187	4	2	2	NUM
ap-652	187	5	k	k	SYM
ap-652	187	6	2	2	NUM
ap-652	187	7	m	m	NOUN
ap-652	187	8	2	2	NUM
ap-652	187	9	k	k	PROPN
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ap-652	187	11	cos	cos	PROPN
ap-652	187	12	d(cos	d(cos	PROPN
ap-652	187	13	�	�	PROPN
ap-652	187	14	cos	cos	PROPN
ap-652	187	15	f(v	f(v	PROPN
ap-652	187	16	v	v	ADP
ap-652	187	17	bp(cos	bp(cos	PROPN
ap-652	187	18	cos	cos	ADP
ap-652	187	19	d(cos	d(cos	PROPN
ap-652	187	20	2	2	NUM
ap-652	187	21	m	m	NOUN
ap-652	187	22	k	k	NOUN
ap-652	187	23	m	m	VERB
ap-652	187	24	2	2	NUM
ap-652	187	25	k	k	SYM
ap-652	187	26	2	2	NUM
ap-652	187	27	m	m	NOUN
ap-652	187	28	2	2	NUM
ap-652	187	29	k	k	PROPN
ap-652	187	30	�	�	PROPN
ap-652	187	31	�	�	PROPN
ap-652	187	32	�	�	PROPN
ap-652	187	33	�	�	PROPN
ap-652	187	34	0	0	NUM
ap-652	187	35	0	0	NUM
ap-652	187	36	0	0	NUM
ap-652	187	37	0	0	NUM
ap-652	187	38	)	)	PUNCT
ap-652	187	39	)	)	PUNCT
ap-652	187	40	)	)	PUNCT
ap-652	188	1	�	�	PROPN
ap-652	188	2	�	�	PROPN
ap-652	188	3	cos	cos	PROPN
ap-652	188	4	1	1	NUM
ap-652	188	5	2	2	NUM
ap-652	188	6	bp	bp	PROPN
ap-652	188	7	b(v	b(v	PROPN
ap-652	188	8	v	v	ADP
ap-652	188	9	d2	d2	PROPN
ap-652	188	10	m	m	PROPN
ap-652	188	11	k	k	PROPN
ap-652	188	12	k	k	PROPN
ap-652	188	13	m	m	VERB
ap-652	188	14	m	m	VERB
ap-652	188	15	k	k	PROPN
ap-652	188	16	m	m	VERB
ap-652	188	17	�	�	PROPN
ap-652	188	18	�	�	PROPN
ap-652	188	19	�	�	PROPN
ap-652	188	20	�	�	PROPN
ap-652	188	21	�	�	PROPN
ap-652	188	22	0	0	NUM
ap-652	188	23	0	0	NUM
ap-652	188	24	0	0	NUM
ap-652	188	25	0	0	NUM
ap-652	188	26	0	0	NUM
ap-652	188	27	)	)	PUNCT
ap-652	188	28	(	(	PUNCT
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ap-652	188	30	cos	cos	PROPN
ap-652	188	31	sin	sin	PROPN
ap-652	188	32	cos	cos	PROPN
ap-652	188	33	)	)	PUNCT
ap-652	188	34	)	)	PUNCT
ap-652	188	35	(	(	PUNCT
ap-652	188	36	sin	sin	NOUN
ap-652	188	37	cos	cos	PROPN
ap-652	188	38	sin	sin	PROPN
ap-652	188	39	cos	cos	PROPN
ap-652	188	40	)	)	PUNCT
ap-652	188	41	�	�	PROPN
ap-652	188	42	�	�	PROPN
ap-652	188	43	�	�	PROPN
ap-652	188	44	�	�	PROPN
ap-652	188	45	0	0	NUM
ap-652	188	46	0	0	NUM
ap-652	188	47	0	0	NUM
ap-652	188	48	0k	0k	NOUN
ap-652	188	49	k	k	PROPN
ap-652	188	50	m	m	VERB
ap-652	188	51	m	m	VERB
ap-652	188	52	�	�	PROPN
ap-652	188	53	�	�	PROPN
ap-652	188	54	�	�	PROPN
ap-652	188	55	�	�	PROPN
ap-652	188	56	�	�	PROPN
ap-652	188	57	�	�	PROPN
ap-652	188	58	�	�	PROPN
ap-652	188	59	�	�	PROPN
ap-652	188	60	�	�	PROPN
ap-652	188	61	�	�	PROPN
ap-652	188	62	�	�	PROPN
ap-652	188	63	�	�	PROPN
ap-652	188	64	�	�	PROPN
ap-652	188	65	�	�	PROPN
ap-652	188	66	�	�	PROPN
ap-652	188	67	�	�	PROPN
ap-652	188	68	�	�	PROPN
ap-652	188	69	�	�	PROPN
ap-652	188	70	�	�	PROPN
ap-652	188	71	�	�	PROPN
ap-652	188	72	�	�	PROPN
ap-652	188	73	�	�	PROPN
ap-652	188	74	�	�	PROPN
ap-652	188	75	�	�	PROPN
ap-652	188	76	�	�	PROPN
ap-652	188	77	�	�	PROPN
ap-652	188	78	�	�	PROPN
ap-652	188	79	�	�	PROPN
ap-652	188	80	.	.	PUNCT
ap-652	189	1	(	(	PUNCT
ap-652	189	2	7	7	X
ap-652	189	3	)	)	PUNCT
ap-652	189	4	with	with	ADP
ap-652	189	5	respect	respect	NOUN
ap-652	189	6	to	to	ADP
ap-652	189	7	(	(	PUNCT
ap-652	189	8	~	~	PUNCT
ap-652	189	9	,	,	PUNCT
ap-652	189	10	~z	~z	PUNCT
ap-652	189	11	z1	z1	NOUN
ap-652	189	12	2	2	NUM
ap-652	189	13	)	)	PUNCT
ap-652	189	14	and	and	CCONJ
ap-652	189	15	(	(	PUNCT
ap-652	189	16	�	�	PROPN
ap-652	189	17	,	,	PUNCT
ap-652	189	18	�	�	PROPN
ap-652	189	19	z	z	NOUN
ap-652	189	20	z1	z1	NOUN
ap-652	189	21	2	2	NUM
ap-652	189	22	)	)	PUNCT
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ap-652	189	24	can	can	AUX
ap-652	189	25	obtain	obtain	VERB
ap-652	189	26	:	:	PUNCT
ap-652	189	27	v	v	NUM
ap-652	189	28	�	�	PROPN
ap-652	189	29	�	�	PROPN
ap-652	189	30	�	�	PROPN
ap-652	189	31	�	�	PROPN
ap-652	189	32	�	�	PROPN
ap-652	189	33	�	�	PROPN
ap-652	189	34	�	�	PROPN
ap-652	189	35	�	�	PROPN
ap-652	189	36	~	~	PUNCT
ap-652	189	37	�	�	PROPN
ap-652	189	38	jk	jk	PROPN
ap-652	189	39	k	k	PROPN
ap-652	189	40	k	k	PROPN
ap-652	189	41	k	k	PROPN
ap-652	189	42	kfh	kfh	PROPN
ap-652	189	43	bv	bv	PROPN
ap-652	189	44	fv	fv	PROPN
ap-652	189	45	bh	bh	PROPN
ap-652	189	46	bp	bp	PROPN
ap-652	189	47	2	2	NUM
ap-652	189	48	d	d	NOUN
ap-652	189	49	0	0	NUM
ap-652	189	50	and	and	CCONJ
ap-652	189	51	v	v	ADP
ap-652	189	52	�	�	PROPN
ap-652	189	53	�	�	PROPN
ap-652	189	54	�	�	PROPN
ap-652	189	55	�	�	PROPN
ap-652	189	56	�	�	PROPN
ap-652	189	57	�	�	PROPN
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ap-652	189	59	�	�	PROPN
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ap-652	189	61	�	�	PROPN
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ap-652	189	63	m	m	PROPN
ap-652	189	64	m	m	VERB
ap-652	189	65	m	m	PROPN
ap-652	189	66	mfh	mfh	PROPN
ap-652	189	67	bv	bv	PROPN
ap-652	189	68	fv	fv	PROPN
ap-652	189	69	bh	bh	PROPN
ap-652	189	70	bp	bp	PROPN
ap-652	189	71	2	2	PROPN
ap-652	189	72	d	d	PROPN
ap-652	189	73	0	0	NUM
ap-652	189	74	,	,	PUNCT
ap-652	189	75	(	(	PUNCT
ap-652	189	76	8)	8)	NUM
ap-652	189	77	which	which	PRON
ap-652	189	78	after	after	ADP
ap-652	189	79	rotation	rotation	NOUN
ap-652	189	80	to	to	ADP
ap-652	189	81	(	(	PUNCT
ap-652	189	82	z1	z1	PROPN
ap-652	189	83	,	,	PUNCT
ap-652	189	84	z2	z2	NUM
ap-652	189	85	)	)	PUNCT
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ap-652	189	87	:	:	PUNCT
ap-652	189	88	v	v	ADP
ap-652	189	89	k	k	PROPN
ap-652	189	90	k	k	PROPN
ap-652	189	91	k	k	PROPN
ap-652	189	92	k	k	PROPN
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ap-652	189	94	�	�	PROPN
ap-652	189	95	~	~	PUNCT
ap-652	189	96	cos	cos	ADP
ap-652	189	97	sin	sin	PROPN
ap-652	189	98	cos	cos	PROPN
ap-652	189	99	sin	sin	PROPN
ap-652	189	100	s	s	PROPN
ap-652	189	101	�	�	PROPN
ap-652	189	102	jk	jk	PROPN
ap-652	189	103	k	k	PROPN
ap-652	189	104	kfh	kfh	PROPN
ap-652	189	105	bp	bp	PROPN
ap-652	189	106	d	d	X
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ap-652	189	108	bp1	bp1	PROPN
ap-652	189	109	2	2	NUM
ap-652	189	110	1	1	NUM
ap-652	189	111	20	20	NUM
ap-652	189	112	0	0	NUM
ap-652	189	113	0	0	NUM
ap-652	189	114	0	0	NUM
ap-652	189	115	�	�	PROPN
ap-652	189	116	�	�	PROPN
ap-652	189	117	�	�	PROPN
ap-652	189	118	�	�	PROPN
ap-652	189	119	in	in	ADP
ap-652	189	120	sin	sin	PROPN
ap-652	189	121	cos	cos	PROPN
ap-652	189	122	cos	cos	PROPN
ap-652	189	123	cos	cos	PROPN
ap-652	189	124	2	2	NUM
ap-652	189	125	0	0	NUM
ap-652	189	126	2	2	NUM
ap-652	189	127	0	0	NUM
ap-652	189	128	2	2	NUM
ap-652	189	129	0	0	NUM
ap-652	189	130	2	2	NUM
ap-652	189	131	0	0	NUM
ap-652	189	132	1	1	NUM
ap-652	189	133	2	2	NUM
ap-652	189	134	1	1	NUM
ap-652	189	135	2	2	NUM
ap-652	189	136	�	�	PROPN
ap-652	189	137	�	�	PROPN
ap-652	189	138	�	�	PROPN
ap-652	189	139	�	�	PROPN
ap-652	190	1	k	k	PROPN
ap-652	190	2	k	k	PROPN
ap-652	191	1	k	k	PROPN
ap-652	191	2	k	k	PROPN
ap-652	192	1	d	d	X
ap-652	192	2	fv	fv	PROPN
ap-652	192	3	bp	bp	PROPN
ap-652	192	4	d	d	PROPN
ap-652	192	5	bv	bv	PROPN
ap-652	192	6	bpk	bpk	PROPN
ap-652	192	7	k	k	PROPN
ap-652	192	8	�	�	PROPN
ap-652	192	9	�	�	PROPN
ap-652	192	10	�	�	PROPN
ap-652	192	11	�	�	PROPN
ap-652	192	12	0	0	NUM
ap-652	192	13	0	0	NUM
ap-652	192	14	0	0	NUM
ap-652	192	15	0	0	NUM
ap-652	193	1	k	k	NOUN
ap-652	193	2	k	k	PROPN
ap-652	193	3	k	k	PROPN
ap-652	193	4	k	k	PROPN
ap-652	193	5	sin	sin	PROPN
ap-652	193	6	cos	cos	ADP
ap-652	193	7	sin	sin	PROPN
ap-652	193	8	�	�	PROPN
ap-652	193	9	�	�	PROPN
ap-652	193	10	�	�	PROPN
ap-652	193	11	�	�	PROPN
ap-652	193	12	�	�	PROPN
ap-652	193	13	�	�	PROPN
ap-652	193	14	�	�	PROPN
ap-652	193	15	�	�	PROPN
ap-652	193	16	�	�	PROPN
ap-652	193	17	�	�	PROPN
ap-652	193	18	�	�	PROPN
ap-652	193	19	�	�	PROPN
ap-652	193	20	�	�	PROPN
ap-652	193	21	�	�	PROPN
ap-652	193	22	�	�	PROPN
ap-652	193	23	�	�	PROPN
ap-652	193	24	�	�	PROPN
ap-652	193	25	�	�	PROPN
ap-652	193	26	d	d	PROPN
ap-652	193	27	and	and	CCONJ
ap-652	193	28	(	(	PUNCT
ap-652	193	29	9a	9a	NOUN
ap-652	193	30	)	)	PUNCT
ap-652	193	31	v	v	PROPN
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ap-652	193	34	~	~	PUNCT
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ap-652	193	38	sin	sin	PROPN
ap-652	193	39	s	s	PROPN
ap-652	193	40	�	�	PROPN
ap-652	193	41	jm	jm	PROPN
ap-652	193	42	m	m	PROPN
ap-652	193	43	m	m	VERB
ap-652	193	44	m	m	VERB
ap-652	193	45	m	m	VERB
ap-652	193	46	m	m	PROPN
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ap-652	193	48	bp	bp	PROPN
ap-652	193	49	d	d	PROPN
ap-652	193	50	bh	bh	PROPN
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ap-652	193	52	2	2	NUM
ap-652	193	53	1	1	NUM
ap-652	193	54	20	20	NUM
ap-652	193	55	0	0	NUM
ap-652	193	56	0	0	NUM
ap-652	193	57	0	0	NUM
ap-652	193	58	�	�	PROPN
ap-652	193	59	�	�	PROPN
ap-652	193	60	�	�	PROPN
ap-652	193	61	�	�	PROPN
ap-652	193	62	in	in	ADP
ap-652	193	63	sin	sin	PROPN
ap-652	193	64	cos	cos	PROPN
ap-652	193	65	cos	cos	PROPN
ap-652	193	66	c	c	PROPN
ap-652	193	67	2	2	NUM
ap-652	193	68	0	0	NUM
ap-652	193	69	2	2	NUM
ap-652	193	70	0	0	NUM
ap-652	193	71	2	2	NUM
ap-652	193	72	0	0	NUM
ap-652	193	73	2	2	NUM
ap-652	193	74	0	0	NUM
ap-652	193	75	1	1	NUM
ap-652	193	76	2	2	NUM
ap-652	193	77	1	1	NUM
ap-652	193	78	2	2	NUM
ap-652	193	79	�	�	PROPN
ap-652	193	80	�	�	PROPN
ap-652	193	81	�	�	PROPN
ap-652	193	82	�	�	PROPN
ap-652	193	83	m	m	VERB
ap-652	193	84	m	m	VERB
ap-652	193	85	m	m	VERB
ap-652	193	86	m	m	VERB
ap-652	193	87	m	m	VERB
ap-652	193	88	m	m	VERB
ap-652	193	89	d	d	NOUN
ap-652	193	90	fv	fv	PROPN
ap-652	193	91	bp	bp	PROPN
ap-652	194	1	+	+	PROPN
ap-652	194	2	d	d	PROPN
ap-652	194	3	bv	bv	PROPN
ap-652	194	4	bp	bp	PROPN
ap-652	194	5	os	os	PROPN
ap-652	194	6	sin	sin	PROPN
ap-652	194	7	cos	cos	ADP
ap-652	194	8	sin	sin	PROPN
ap-652	194	9	�	�	PROPN
ap-652	194	10	�	�	PROPN
ap-652	194	11	�	�	PROPN
ap-652	194	12	�	�	PROPN
ap-652	194	13	0	0	NUM
ap-652	194	14	0	0	NUM
ap-652	194	15	0	0	NUM
ap-652	194	16	0	0	NUM
ap-652	194	17	m	m	VERB
ap-652	194	18	m	m	VERB
ap-652	194	19	m	m	VERB
ap-652	194	20	md	md	PROPN
ap-652	194	21	�	�	PROPN
ap-652	194	22	�	�	PROPN
ap-652	194	23	�	�	PROPN
ap-652	194	24	�	�	PROPN
ap-652	194	25	�	�	PROPN
ap-652	194	26	�	�	PROPN
ap-652	194	27	�	�	PROPN
ap-652	194	28	�	�	PROPN
ap-652	194	29	�	�	PROPN
ap-652	194	30	�	�	PROPN
ap-652	194	31	�	�	PROPN
ap-652	194	32	�	�	PROPN
ap-652	194	33	�	�	PROPN
ap-652	194	34	�	�	PROPN
ap-652	194	35	�	�	PROPN
ap-652	194	36	�	�	PROPN
ap-652	194	37	�	�	PROPN
ap-652	194	38	�	�	PROPN
ap-652	194	39	,	,	PUNCT
ap-652	194	40	(	(	PUNCT
ap-652	194	41	9b	9b	NOUN
ap-652	194	42	)	)	PUNCT
ap-652	194	43	which	which	PRON
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ap-652	194	46	~	~	PUNCT
ap-652	194	47	�	�	PROPN
ap-652	194	48	�	�	PROPN
ap-652	194	49	�	�	PROPN
ap-652	194	50	�	�	PROPN
ap-652	194	51	�	�	PROPN
ap-652	194	52	�	�	PROPN
ap-652	194	53	�	�	PROPN
ap-652	194	54	�	�	PROPN
ap-652	194	55	l	l	PROPN
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ap-652	194	57	f	f	PROPN
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ap-652	194	60	0	0	NUM
ap-652	194	61	.	.	PUNCT
ap-652	195	1	(	(	PUNCT
ap-652	195	2	10	10	NUM
ap-652	195	3	)	)	PUNCT
ap-652	195	4	where	where	SCONJ
ap-652	195	5	a(r	a(r	NOUN
ap-652	195	6	)	)	PUNCT
ap-652	195	7	and	and	CCONJ
ap-652	195	8	i(r	i(r	PROPN
ap-652	195	9	)	)	PUNCT
ap-652	195	10	stand	stand	VERB
ap-652	195	11	for	for	ADP
ap-652	195	12	cross	cross	PROPN
ap-652	195	13	sectional	sectional	ADJ
ap-652	195	14	area	area	NOUN
ap-652	195	15	and	and	CCONJ
ap-652	195	16	moment	moment	NOUN
ap-652	195	17	of	of	ADP
ap-652	195	18	inertia	inertia	NOUN
ap-652	195	19	,	,	PUNCT
ap-652	195	20	respectively	respectively	ADV
ap-652	195	21	,	,	PUNCT
ap-652	195	22	n(r	n(r	NUM
ap-652	195	23	)	)	PUNCT
ap-652	195	24	and	and	CCONJ
ap-652	195	25	m(r	m(r	PROPN
ap-652	195	26	)	)	PUNCT
ap-652	195	27	are	be	AUX
ap-652	195	28	normal	normal	ADJ
ap-652	195	29	forces	force	NOUN
ap-652	195	30	and	and	CCONJ
ap-652	195	31	bending	bend	VERB
ap-652	195	32	moments	moment	NOUN
ap-652	195	33	and	and	CCONJ
ap-652	195	34	(	(	PUNCT
ap-652	195	35	a	a	X
ap-652	195	36	)	)	PUNCT
ap-652	195	37	stands	stand	VERB
ap-652	195	38	for	for	ADP
ap-652	195	39	the	the	DET
ap-652	195	40	integration	integration	NOUN
ap-652	195	41	along	along	ADP
ap-652	195	42	the	the	DET
ap-652	195	43	curved	curved	ADJ
ap-652	195	44	theoretical	theoretical	ADJ
ap-652	195	45	length	length	NOUN
ap-652	195	46	of	of	ADP
ap-652	195	47	the	the	DET
ap-652	195	48	beam	beam	NOUN
ap-652	195	49	.	.	PUNCT
ap-652	196	1	it	it	PRON
ap-652	196	2	may	may	AUX
ap-652	196	3	be	be	AUX
ap-652	196	4	pointed	point	VERB
ap-652	196	5	out	out	ADP
ap-652	196	6	that	that	SCONJ
ap-652	196	7	using	use	VERB
ap-652	196	8	theoretical	theoretical	ADJ
ap-652	196	9	lengths	length	NOUN
ap-652	196	10	and	and	CCONJ
ap-652	196	11	overlapping	overlap	VERB
ap-652	196	12	in	in	ADP
ap-652	196	13	joints	joint	NOUN
ap-652	196	14	is	be	AUX
ap-652	196	15	an	an	DET
ap-652	196	16	allowable	allowable	ADJ
ap-652	196	17	and	and	CCONJ
ap-652	196	18	common	common	ADJ
ap-652	196	19	simplification	simplification	NOUN
ap-652	196	20	in	in	ADP
ap-652	196	21	strain	strain	ADJ
ap-652	196	22	energy	energy	NOUN
ap-652	196	23	.	.	PUNCT
ap-652	197	1	in	in	ADP
ap-652	197	2	accordance	accordance	NOUN
ap-652	197	3	with	with	ADP
ap-652	197	4	this	this	DET
ap-652	197	5	approximation	approximation	NOUN
ap-652	197	6	,	,	PUNCT
ap-652	197	7	the	the	DET
ap-652	197	8	originally	originally	ADV
ap-652	197	9	introduced	introduce	VERB
ap-652	197	10	generalized	generalized	ADJ
ap-652	197	11	forces	force	NOUN
ap-652	197	12	f	f	PROPN
ap-652	197	13	,	,	PUNCT
ap-652	197	14	b	b	PROPN
ap-652	197	15	and	and	CCONJ
ap-652	197	16	d	d	PROPN
ap-652	197	17	in	in	ADP
ap-652	197	18	the	the	DET
ap-652	197	19	beam	beam	NOUN
ap-652	197	20	cuts	cut	NOUN
ap-652	197	21	do	do	AUX
ap-652	197	22	not	not	PART
ap-652	197	23	have	have	VERB
ap-652	197	24	to	to	PART
ap-652	197	25	change	change	VERB
ap-652	197	26	.	.	PUNCT
ap-652	198	1	a	a	DET
ap-652	198	2	cross	cross	ADJ
ap-652	198	3	sectional	sectional	ADJ
ap-652	198	4	area	area	NOUN
ap-652	198	5	a0	a0	PROPN
ap-652	198	6	of	of	ADP
ap-652	198	7	a	a	DET
ap-652	198	8	related	related	ADJ
ap-652	198	9	straight	straight	ADJ
ap-652	198	10	beam	beam	NOUN
ap-652	198	11	with	with	ADP
ap-652	198	12	constant	constant	ADJ
ap-652	198	13	cross	cross	NOUN
ap-652	198	14	section	section	NOUN
ap-652	198	15	and	and	CCONJ
ap-652	198	16	the	the	DET
ap-652	198	17	same	same	ADJ
ap-652	198	18	volume	volume	NOUN
ap-652	198	19	as	as	ADP
ap-652	198	20	the	the	DET
ap-652	198	21	original	original	ADJ
ap-652	198	22	curved	curved	ADJ
ap-652	198	23	beam	beam	NOUN
ap-652	198	24	,	,	PUNCT
ap-652	198	25	can	can	AUX
ap-652	198	26	be	be	AUX
ap-652	198	27	introduced	introduce	VERB
ap-652	198	28	by	by	ADP
ap-652	198	29	(	(	PUNCT
ap-652	198	30	overlapping	overlap	VERB
ap-652	198	31	in	in	ADP
ap-652	198	32	the	the	DET
ap-652	198	33	junctions	junction	NOUN
ap-652	198	34	can	can	AUX
ap-652	198	35	also	also	ADV
ap-652	198	36	be	be	AUX
ap-652	198	37	neglected	neglect	VERB
ap-652	198	38	here	here	ADV
ap-652	198	39	):	):	PUNCT
ap-652	198	40	a	a	DET
ap-652	198	41	a	a	DET
ap-652	198	42	z	z	NOUN
ap-652	198	43	a	a	DET
ap-652	198	44	z	z	NOUN
ap-652	198	45	d0	d0	NOUN
ap-652	198	46	1	1	NUM
ap-652	198	47	1	1	NUM
ap-652	198	48	2	2	NUM
ap-652	198	49	1	1	NUM
ap-652	198	50	0	0	NUM
ap-652	198	51	1l	1l	NUM
ap-652	198	52	z	z	SYM
ap-652	198	53	l	l	X
ap-652	198	54	�	�	PROPN
ap-652	198	55	�	�	PROPN
ap-652	198	56	�	�	PROPN
ap-652	198	57	(	(	PUNCT
ap-652	198	58	)	)	PUNCT
ap-652	198	59	(	(	PUNCT
ap-652	198	60	(	(	PUNCT
ap-652	198	61	)	)	PUNCT
ap-652	198	62	)	)	PUNCT
ap-652	198	63	,	,	PUNCT
ap-652	198	64	(	(	PUNCT
ap-652	198	65	13	13	NUM
ap-652	198	66	)	)	PUNCT
ap-652	198	67	where	where	SCONJ
ap-652	198	68	�	�	PROPN
ap-652	198	69	�	�	PROPN
ap-652	198	70	a	a	DET
ap-652	198	71	z	z	NOUN
ap-652	198	72	da	da	PROPN
ap-652	198	73	z	z	PROPN
ap-652	198	74	dz	dz	NOUN
ap-652	198	75	(	(	PUNCT
ap-652	198	76	)	)	PUNCT
ap-652	198	77	(	(	PUNCT
ap-652	198	78	)	)	PUNCT
ap-652	198	79	1	1	NUM
ap-652	198	80	1	1	NUM
ap-652	198	81	1	1	NUM
ap-652	198	82	.	.	PUNCT
ap-652	199	1	because	because	SCONJ
ap-652	199	2	there	there	PRON
ap-652	199	3	is	be	VERB
ap-652	199	4	no	no	DET
ap-652	199	5	distinction	distinction	NOUN
ap-652	199	6	between	between	ADP
ap-652	199	7	the	the	DET
ap-652	199	8	�	�	PROPN
ap-652	199	9	contribution	contribution	NOUN
ap-652	199	10	of	of	ADP
ap-652	199	11	a	a	DET
ap-652	199	12	straight	straight	NOUN
ap-652	199	13	or	or	CCONJ
ap-652	199	14	a	a	DET
ap-652	199	15	curved	curved	ADJ
ap-652	199	16	beam	beam	NOUN
ap-652	199	17	to	to	ADP
ap-652	199	18	�	�	PROPN
ap-652	199	19	,	,	PUNCT
ap-652	199	20	let	let	VERB
ap-652	199	21	us	we	PRON
ap-652	199	22	minimize	minimize	VERB
ap-652	199	23	w	w	ADP
ap-652	199	24	in	in	ADP
ap-652	199	25	order	order	NOUN
ap-652	199	26	to	to	PART
ap-652	199	27	discuss	discuss	VERB
ap-652	199	28	the	the	DET
ap-652	199	29	position	position	NOUN
ap-652	199	30	of	of	ADP
ap-652	199	31	the	the	DET
ap-652	199	32	i	i	NOUN
ap-652	199	33	-	-	NOUN
ap-652	199	34	beam	beam	NOUN
ap-652	199	35	in	in	ADP
ap-652	199	36	an	an	DET
ap-652	199	37	optimal	optimal	ADJ
ap-652	199	38	medium	medium	NOUN
ap-652	199	39	.	.	PUNCT
ap-652	200	1	this	this	DET
ap-652	200	2	minimization	minimization	NOUN
ap-652	200	3	must	must	AUX
ap-652	200	4	be	be	AUX
ap-652	200	5	performed	perform	VERB
ap-652	200	6	over	over	ADP
ap-652	200	7	all	all	DET
ap-652	200	8	possible	possible	ADJ
ap-652	200	9	shapes	shape	NOUN
ap-652	200	10	a(z1	a(z1	ADJ
ap-652	200	11	)	)	PUNCT
ap-652	200	12	and	and	CCONJ
ap-652	200	13	volume	volume	NOUN
ap-652	200	14	distributions	distribution	NOUN
ap-652	200	15	along	along	ADP
ap-652	200	16	the	the	DET
ap-652	200	17	middle	middle	ADJ
ap-652	200	18	curve	curve	NOUN
ap-652	200	19	:	:	PUNCT
ap-652	200	20	2e	2e	NUM
ap-652	200	21	v	v	PROPN
ap-652	200	22	w	w	PROPN
ap-652	200	23	n	n	ADP
ap-652	200	24	r	r	NOUN
ap-652	201	1	a	a	DET
ap-652	201	2	s	s	NOUN
ap-652	201	3	a(z	a(z	PROPN
ap-652	201	4	)	)	PUNCT
ap-652	201	5	;a(r);i(r	;a(r);i(r	PROPN
ap-652	201	6	)	)	PUNCT
ap-652	202	1	a(z	a(z	PROPN
ap-652	202	2	)	)	PUNCT
ap-652	202	3	;a(r);i(r	;a(r);i(r	PROPN
ap-652	202	4	)	)	PUNCT
ap-652	202	5	2	2	NUM
ap-652	202	6	1	1	NUM
ap-652	202	7	1	1	NUM
ap-652	202	8	�	�	PROPN
ap-652	202	9	�	�	PROPN
ap-652	202	10	�	�	PROPN
ap-652	202	11	min	min	PROPN
ap-652	202	12	min	min	PROPN
ap-652	202	13	(	(	PUNCT
ap-652	202	14	)	)	PUNCT
ap-652	202	15	(	(	PUNCT
ap-652	202	16	)	)	PUNCT
ap-652	202	17	(	(	PUNCT
ap-652	202	18	)	)	PUNCT
ap-652	202	19	(	(	PUNCT
ap-652	202	20	)	)	PUNCT
ap-652	202	21	min	min	NOUN
ap-652	202	22	(	(	PUNCT
ap-652	202	23	)	)	PUNCT
ap-652	202	24	(	(	PUNCT
ap-652	202	25	)	)	PUNCT
ap-652	202	26	r	r	NOUN
ap-652	202	27	dr	dr	PROPN
ap-652	203	1	+	+	NOUN
ap-652	203	2	m	m	VERB
ap-652	203	3	r	r	NOUN
ap-652	204	1	i	i	NOUN
ap-652	204	2	r	r	NOUN
ap-652	204	3	dr	dr	PROPN
ap-652	204	4	2	2	NUM
ap-652	204	5	aa	aa	NOUN
ap-652	204	6	a(z	a(z	PROPN
ap-652	204	7	)	)	PUNCT
ap-652	204	8	;a(r)1	;a(r)1	PROPN
ap-652	204	9	�	�	PROPN
ap-652	204	10	�	�	PROPN
ap-652	204	11	�	�	PROPN
ap-652	204	12	�	�	PROPN
ap-652	204	13	�	�	PROPN
ap-652	204	14	�	�	PROPN
ap-652	204	15	�	�	PROPN
ap-652	204	16	�	�	PROPN
ap-652	204	17	�	�	PROPN
ap-652	204	18	�	�	PROPN
ap-652	204	19	�	�	PROPN
ap-652	204	20	n	n	CCONJ
ap-652	204	21	r	r	NOUN
ap-652	204	22	a	a	DET
ap-652	204	23	r	r	NOUN
ap-652	204	24	dr	dr	PROPN
ap-652	205	1	+	+	NOUN
ap-652	205	2	m	m	VERB
ap-652	205	3	r	r	NOUN
ap-652	206	1	i	i	NOUN
ap-652	206	2	r	r	NOUN
ap-652	206	3	dr	dr	PROPN
ap-652	206	4	2	2	NUM
ap-652	206	5	a(z	a(z	PROPN
ap-652	206	6	)	)	PUNCT
ap-652	206	7	;i(r	;i(r	PROPN
ap-652	206	8	)	)	PUNCT
ap-652	206	9	2	2	NUM
ap-652	206	10	aa	aa	NOUN
ap-652	206	11	1	1	NUM
ap-652	206	12	(	(	PUNCT
ap-652	206	13	)	)	PUNCT
ap-652	206	14	(	(	PUNCT
ap-652	206	15	)	)	PUNCT
ap-652	206	16	min	min	NOUN
ap-652	206	17	(	(	PUNCT
ap-652	206	18	)	)	PUNCT
ap-652	206	19	(	(	PUNCT
ap-652	206	20	)	)	PUNCT
ap-652	206	21	.	.	PUNCT
ap-652	207	1	(	(	PUNCT
ap-652	207	2	)	)	PUNCT
ap-652	207	3	(	(	PUNCT
ap-652	207	4	)	)	PUNCT
ap-652	207	5	�	�	PROPN
ap-652	207	6	�	�	PROPN
ap-652	207	7	(	(	PUNCT
ap-652	207	8	14	14	NUM
ap-652	207	9	)	)	PUNCT
ap-652	207	10	equality	equality	NOUN
ap-652	207	11	in	in	ADP
ap-652	207	12	(	(	PUNCT
ap-652	207	13	14	14	NUM
ap-652	207	14	)	)	PUNCT
ap-652	207	15	can	can	AUX
ap-652	207	16	be	be	AUX
ap-652	207	17	achieved	achieve	VERB
ap-652	207	18	,	,	PUNCT
ap-652	207	19	if	if	SCONJ
ap-652	207	20	the	the	DET
ap-652	207	21	minimizing	minimizing	NOUN
ap-652	207	22	shape	shape	NOUN
ap-652	207	23	and	and	CCONJ
ap-652	207	24	volume	volume	NOUN
ap-652	207	25	distribution	distribution	NOUN
ap-652	207	26	are	be	AUX
ap-652	207	27	the	the	DET
ap-652	207	28	same	same	ADJ
ap-652	207	29	for	for	ADP
ap-652	207	30	both	both	DET
ap-652	207	31	terms	term	NOUN
ap-652	207	32	in	in	ADP
ap-652	207	33	the	the	DET
ap-652	207	34	last	last	ADJ
ap-652	207	35	part	part	NOUN
ap-652	207	36	of	of	ADP
ap-652	207	37	(	(	PUNCT
ap-652	207	38	14	14	NUM
ap-652	207	39	)	)	PUNCT
ap-652	207	40	.	.	PUNCT
ap-652	208	1	the	the	DET
ap-652	208	2	distribution	distribution	NOUN
ap-652	208	3	of	of	ADP
ap-652	208	4	the	the	DET
ap-652	208	5	normal	normal	ADJ
ap-652	208	6	forces	force	NOUN
ap-652	208	7	can	can	AUX
ap-652	208	8	be	be	AUX
ap-652	208	9	written	write	VERB
ap-652	208	10	as	as	ADP
ap-652	208	11	:	:	PUNCT
ap-652	208	12	n	n	PROPN
ap-652	208	13	r	r	NOUN
ap-652	208	14	f	f	NOUN
ap-652	208	15	r	r	NOUN
ap-652	208	16	b	b	X
ap-652	208	17	r	r	NOUN
ap-652	208	18	(	(	PUNCT
ap-652	208	19	)	)	PUNCT
ap-652	208	20	cos	cos	PROPN
ap-652	208	21	(	(	PUNCT
ap-652	208	22	)	)	PUNCT
ap-652	208	23	sin	sin	NOUN
ap-652	208	24	(	(	PUNCT
ap-652	208	25	)	)	PUNCT
ap-652	208	26	�	�	PROPN
ap-652	208	27	�	�	PROPN
ap-652	208	28	�	�	PROPN
ap-652	208	29	.	.	PUNCT
ap-652	209	1	(	(	PUNCT
ap-652	209	2	15	15	NUM
ap-652	209	3	)	)	PUNCT
ap-652	209	4	therefore	therefore	ADV
ap-652	209	5	:	:	PUNCT
ap-652	209	6	n	n	CCONJ
ap-652	209	7	r	r	NOUN
ap-652	209	8	a	a	DET
ap-652	209	9	r	r	NOUN
ap-652	209	10	dr	dr	NOUN
ap-652	209	11	=	=	PUNCT
ap-652	209	12	(	(	PUNCT
ap-652	209	13	f+ba	f+ba	VERB
ap-652	209	14	(	(	PUNCT
ap-652	209	15	z	z	X
ap-652	209	16	a(z	a(z	NOUN
ap-652	209	17	a	a	PRON
ap-652	209	18	(	(	PUNCT
ap-652	209	19	z	z	NOUN
ap-652	209	20	dz	dz	NOUN
ap-652	209	21	2	2	NUM
ap-652	209	22	1	1	NUM
ap-652	209	23	1	1	NUM
ap-652	209	24	1	1	NUM
ap-652	209	25	1	1	NUM
ap-652	209	26	0a	0a	PROPN
ap-652	209	27	(	(	PUNCT
ap-652	209	28	)	)	PUNCT
ap-652	209	29	(	(	PUNCT
ap-652	209	30	)	)	PUNCT
ap-652	209	31	)	)	PUNCT
ap-652	209	32	)	)	PUNCT
ap-652	209	33	)	)	PUNCT
ap-652	209	34	(	(	PUNCT
ap-652	209	35	)	)	PUNCT
ap-652	209	36	)	)	PUNCT
ap-652	209	37	(	(	PUNCT
ap-652	209	38	)	)	PUNCT
ap-652	209	39	�	�	PROPN
ap-652	209	40	�	�	PROPN
ap-652	209	41	�	�	PROPN
ap-652	209	42	�	�	PROPN
ap-652	209	43	2	2	NUM
ap-652	209	44	21	21	NUM
ap-652	209	45	l	l	NOUN
ap-652	209	46	.	.	PUNCT
ap-652	210	1	(	(	PUNCT
ap-652	210	2	16	16	NUM
ap-652	210	3	)	)	PUNCT
ap-652	210	4	using	use	VERB
ap-652	210	5	the	the	DET
ap-652	210	6	schwarz	schwarz	PROPN
ap-652	210	7	inequality	inequality	NOUN
ap-652	210	8	in	in	ADP
ap-652	210	9	the	the	DET
ap-652	210	10	form	form	NOUN
ap-652	210	11	of	of	ADP
ap-652	210	12	:	:	PUNCT
ap-652	210	13	f	f	PROPN
ap-652	210	14	(	(	PUNCT
ap-652	210	15	f+ba	f+ba	VERB
ap-652	210	16	(	(	PUNCT
ap-652	210	17	z	z	NOUN
ap-652	210	18	dz	dz	ADJ
ap-652	210	19	f+ba	f+ba	NOUN
ap-652	210	20	(	(	PUNCT
ap-652	210	21	z	z	NOUN
ap-652	210	22	a(z	a(z	NOUN
ap-652	210	23	1	1	NUM
ap-652	210	24	1	1	NUM
ap-652	210	25	1	1	NUM
ap-652	210	26	1	1	NUM
ap-652	210	27	2	2	NUM
ap-652	210	28	2	2	NUM
ap-652	210	29	0	0	NUM
ap-652	210	30	2	2	NUM
ap-652	210	31	1	1	NUM
ap-652	210	32	l	l	NOUN
ap-652	210	33	l	l	X
ap-652	210	34	�	�	PROPN
ap-652	210	35	�	�	PROPN
ap-652	210	36	�	�	PROPN
ap-652	210	37	�	�	PROPN
ap-652	210	38	�	�	PROPN
ap-652	210	39	�	�	PROPN
ap-652	210	40	�	�	PROPN
ap-652	210	41	�	�	PROPN
ap-652	210	42	�	�	PROPN
ap-652	210	43	�	�	PROPN
ap-652	210	44	�	�	PROPN
ap-652	210	45	�	�	PROPN
ap-652	210	46	�	�	PROPN
ap-652	210	47	)	)	PUNCT
ap-652	210	48	)	)	PUNCT
ap-652	210	49	)	)	PUNCT
ap-652	210	50	)	)	PUNCT
ap-652	210	51	�	�	PROPN
ap-652	210	52	�	�	PROPN
ap-652	210	53	�	�	PROPN
ap-652	210	54	�	�	PROPN
ap-652	210	55	�	�	PROPN
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ap-652	210	66	(	(	PUNCT
ap-652	210	67	)	)	PUNCT
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ap-652	211	1	(	(	PUNCT
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ap-652	211	4	a	a	PRON
ap-652	211	5	(	(	PUNCT
ap-652	211	6	z	z	X
ap-652	211	7	a(z	a(z	NOUN
ap-652	211	8	a	a	PRON
ap-652	211	9	(	(	PUNCT
ap-652	211	10	z	z	NOUN
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ap-652	211	12	1	1	NUM
ap-652	211	13	1	1	NUM
ap-652	211	14	1	1	NUM
ap-652	211	15	1	1	NUM
ap-652	211	16	0	0	NUM
ap-652	211	17	24	24	NUM
ap-652	211	18	241	241	NUM
ap-652	211	19	l	l	PROPN
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ap-652	211	21	�	�	PROPN
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ap-652	211	25	�	�	PROPN
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ap-652	211	34	2	2	NUM
ap-652	211	35	2	2	NUM
ap-652	211	36	21	21	NUM
ap-652	211	37	(	(	PUNCT
ap-652	211	38	f+ba	f+ba	VERB
ap-652	211	39	(	(	PUNCT
ap-652	211	40	z	z	X
ap-652	211	41	a(z	a(z	NOUN
ap-652	211	42	a	a	PRON
ap-652	211	43	(	(	PUNCT
ap-652	211	44	z	z	NOUN
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ap-652	211	46	a1	a1	NOUN
ap-652	211	47	1	1	NUM
ap-652	211	48	1	1	NUM
ap-652	211	49	1	1	NUM
ap-652	211	50	0	0	NUM
ap-652	211	51	)	)	PUNCT
ap-652	211	52	)	)	PUNCT
ap-652	211	53	)	)	PUNCT
ap-652	211	54	(	(	PUNCT
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ap-652	211	56	)	)	PUNCT
ap-652	212	1	l	l	NOUN
ap-652	212	2	(	(	PUNCT
ap-652	212	3	z	z	NOUN
ap-652	212	4	a	a	PRON
ap-652	212	5	(	(	PUNCT
ap-652	212	6	z	z	NOUN
ap-652	212	7	dz	dz	PROPN
ap-652	212	8	a	a	PRON
ap-652	212	9	(	(	PUNCT
ap-652	212	10	f+ba	f+ba	NOUN
ap-652	212	11	(	(	PUNCT
ap-652	212	12	z	z	NOUN
ap-652	212	13	a	a	X
ap-652	212	14	(	(	PUNCT
ap-652	212	15	1	1	NUM
ap-652	212	16	1	1	NUM
ap-652	212	17	1	1	NUM
ap-652	212	18	0	0	NUM
ap-652	212	19	0	0	NUM
ap-652	212	20	1	1	NUM
ap-652	212	21	)	)	PUNCT
ap-652	212	22	(	(	PUNCT
ap-652	212	23	)	)	PUNCT
ap-652	212	24	)	)	PUNCT
ap-652	212	25	)	)	PUNCT
ap-652	212	26	)	)	PUNCT
ap-652	213	1	1	1	NUM
ap-652	213	2	2	2	NUM
ap-652	213	3	2	2	NUM
ap-652	213	4	�	�	PROPN
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ap-652	213	7	�	�	PROPN
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ap-652	213	10	�	�	PROPN
ap-652	213	11	�	�	PROPN
ap-652	213	12	�	�	PROPN
ap-652	213	13	�	�	PROPN
ap-652	213	14	�	�	PROPN
ap-652	213	15	�	�	PROPN
ap-652	213	16	l	l	PROPN
ap-652	213	17	l	l	NOUN
ap-652	213	18	z	z	X
ap-652	214	1	a	a	PRON
ap-652	214	2	(	(	PUNCT
ap-652	214	3	z	z	NOUN
ap-652	214	4	dz	dz	NOUN
ap-652	214	5	1	1	NUM
ap-652	214	6	1	1	NUM
ap-652	214	7	1	1	NUM
ap-652	214	8	0	0	NUM
ap-652	214	9	)	)	PUNCT
ap-652	214	10	(	(	PUNCT
ap-652	214	11	)	)	PUNCT
ap-652	214	12	)	)	PUNCT
ap-652	214	13	1	1	NUM
ap-652	214	14	2	2	NUM
ap-652	214	15	�	�	PROPN
ap-652	214	16	�	�	PROPN
ap-652	214	17	l	l	NOUN
ap-652	214	18	(	(	PUNCT
ap-652	214	19	17	17	NUM
ap-652	214	20	)	)	PUNCT
ap-652	214	21	gives	give	VERB
ap-652	214	22	the	the	DET
ap-652	214	23	following	follow	VERB
ap-652	214	24	inequality	inequality	NOUN
ap-652	214	25	:	:	PUNCT
ap-652	214	26	(	(	PUNCT
ap-652	214	27	f+ba	f+ba	VERB
ap-652	214	28	(	(	PUNCT
ap-652	214	29	z	z	X
ap-652	214	30	a(z	a(z	NOUN
ap-652	214	31	a	a	PRON
ap-652	214	32	(	(	PUNCT
ap-652	214	33	z	z	NOUN
ap-652	214	34	dz	dz	PROPN
ap-652	214	35	f	f	PROPN
ap-652	214	36	a	a	DET
ap-652	214	37	1	1	NUM
ap-652	214	38	1	1	NUM
ap-652	214	39	1	1	NUM
ap-652	214	40	1	1	NUM
ap-652	214	41	0	0	NUM
ap-652	214	42	0	0	NUM
ap-652	214	43	�	�	PROPN
ap-652	214	44	�	�	PROPN
ap-652	214	45	�	�	PROPN
ap-652	214	46	�	�	PROPN
ap-652	214	47	)	)	PUNCT
ap-652	214	48	)	)	PUNCT
ap-652	214	49	)	)	PUNCT
ap-652	215	1	(	(	PUNCT
ap-652	215	2	)	)	PUNCT
ap-652	215	3	)	)	PUNCT
ap-652	215	4	2	2	NUM
ap-652	215	5	2	2	NUM
ap-652	215	6	2	2	NUM
ap-652	215	7	1	1	NUM
ap-652	215	8	l	l	NOUN
ap-652	215	9	l	l	NOUN
ap-652	215	10	.	.	PUNCT
ap-652	216	1	(	(	PUNCT
ap-652	216	2	18	18	NUM
ap-652	216	3	)	)	PUNCT
ap-652	216	4	equality	equality	NOUN
ap-652	216	5	in	in	ADP
ap-652	216	6	(	(	PUNCT
ap-652	216	7	18	18	NUM
ap-652	216	8	or	or	CCONJ
ap-652	216	9	17	17	NUM
ap-652	216	10	)	)	PUNCT
ap-652	216	11	can	can	AUX
ap-652	216	12	only	only	ADV
ap-652	216	13	be	be	AUX
ap-652	216	14	achieved	achieve	VERB
ap-652	216	15	if	if	SCONJ
ap-652	216	16	f+ba	f+ba	ADJ
ap-652	216	17	(	(	PUNCT
ap-652	216	18	z	z	X
ap-652	216	19	a(z	a(z	NOUN
ap-652	216	20	a	a	DET
ap-652	216	21	(	(	PUNCT
ap-652	216	22	z	z	NOUN
ap-652	216	23	1	1	NUM
ap-652	216	24	1	1	NUM
ap-652	216	25	1	1	NUM
ap-652	216	26	�	�	PROPN
ap-652	216	27	�	�	PROPN
ap-652	216	28	)	)	PUNCT
ap-652	216	29	)	)	PUNCT
ap-652	217	1	(	(	PUNCT
ap-652	217	2	)	)	PUNCT
ap-652	217	3	)	)	PUNCT
ap-652	217	4	1	1	NUM
ap-652	217	5	2	2	NUM
ap-652	217	6	is	be	AUX
ap-652	217	7	constant	constant	ADJ
ap-652	217	8	with	with	ADP
ap-652	217	9	respect	respect	NOUN
ap-652	217	10	to	to	ADP
ap-652	217	11	z1	z1	PROPN
ap-652	217	12	,	,	PUNCT
ap-652	217	13	which	which	PRON
ap-652	217	14	implies	imply	VERB
ap-652	217	15	that	that	SCONJ
ap-652	217	16	the	the	DET
ap-652	217	17	beam	beam	NOUN
ap-652	217	18	must	must	AUX
ap-652	217	19	be	be	AUX
ap-652	217	20	straight	straight	ADJ
ap-652	217	21	and	and	CCONJ
ap-652	217	22	with	with	ADP
ap-652	217	23	a	a	DET
ap-652	217	24	constant	constant	ADJ
ap-652	217	25	cross	cross	NOUN
ap-652	217	26	sectional	sectional	ADJ
ap-652	217	27	area	area	NOUN
ap-652	217	28	.	.	PUNCT
ap-652	218	1	then	then	ADV
ap-652	218	2	contribution	contribution	NOUN
ap-652	218	3	of	of	ADP
ap-652	218	4	the	the	DET
ap-652	218	5	normal	normal	ADJ
ap-652	218	6	forces	force	NOUN
ap-652	218	7	to	to	PART
ap-652	218	8	w	w	PROPN
ap-652	218	9	does	do	AUX
ap-652	218	10	not	not	PART
ap-652	218	11	include	include	VERB
ap-652	218	12	b.	b.	NOUN
ap-652	218	13	the	the	DET
ap-652	218	14	distribution	distribution	NOUN
ap-652	218	15	of	of	ADP
ap-652	218	16	the	the	DET
ap-652	218	17	bending	bend	VERB
ap-652	218	18	moments	moment	NOUN
ap-652	218	19	can	can	AUX
ap-652	218	20	be	be	AUX
ap-652	218	21	expressed	express	VERB
ap-652	218	22	as	as	ADP
ap-652	218	23	:	:	PUNCT
ap-652	218	24	m	m	PROPN
ap-652	218	25	z	z	NOUN
ap-652	218	26	d	d	X
ap-652	218	27	fa	fa	PROPN
ap-652	218	28	z	z	PROPN
ap-652	218	29	z	z	PROPN
ap-652	218	30	(	(	PUNCT
ap-652	218	31	)	)	PUNCT
ap-652	218	32	(	(	PUNCT
ap-652	218	33	)	)	SYM
ap-652	218	34	1	1	NUM
ap-652	218	35	1	1	NUM
ap-652	218	36	12	12	NUM
ap-652	218	37	�	�	PROPN
ap-652	218	38	�	�	PROPN
ap-652	218	39	�	�	PROPN
ap-652	218	40	�	�	PROPN
ap-652	218	41	�	�	PROPN
ap-652	218	42	�	�	PROPN
ap-652	218	43	b	b	PROPN
ap-652	218	44	l	l	NOUN
ap-652	218	45	.	.	PUNCT
ap-652	219	1	(	(	PUNCT
ap-652	219	2	19	19	NUM
ap-652	219	3	)	)	PUNCT
ap-652	219	4	when	when	SCONJ
ap-652	219	5	minimizing	minimize	VERB
ap-652	219	6	conditions	condition	NOUN
ap-652	219	7	for	for	ADP
ap-652	219	8	normal	normal	ADJ
ap-652	219	9	forces	force	NOUN
ap-652	219	10	contribution	contribution	NOUN
ap-652	219	11	to	to	ADP
ap-652	219	12	w	w	PROPN
ap-652	219	13	are	be	AUX
ap-652	219	14	used	use	VERB
ap-652	219	15	,	,	PUNCT
ap-652	219	16	it	it	PRON
ap-652	219	17	is	be	AUX
ap-652	219	18	sufficient	sufficient	ADJ
ap-652	219	19	to	to	PART
ap-652	219	20	look	look	VERB
ap-652	219	21	at	at	ADP
ap-652	219	22	d	d	PROPN
ap-652	219	23	b	b	PROPN
ap-652	219	24	z	z	NOUN
ap-652	219	25	dz	dz	PROPN
ap-652	219	26	d	d	PROPN
ap-652	219	27	+	+	PROPN
ap-652	219	28	b1	b1	PROPN
ap-652	219	29	�	�	PROPN
ap-652	219	30	�	�	PROPN
ap-652	219	31	�	�	PROPN
ap-652	219	32	�	�	PROPN
ap-652	219	33	�	�	PROPN
ap-652	219	34	�	�	PROPN
ap-652	219	35	�	�	PROPN
ap-652	219	36	�	�	PROPN
ap-652	219	37	�	�	PROPN
ap-652	219	38	�	�	PROPN
ap-652	219	39	�	�	PROPN
ap-652	219	40	�	�	PROPN
ap-652	219	41	l	l	NOUN
ap-652	219	42	l	l	NOUN
ap-652	219	43	l	l	NOUN
ap-652	219	44	l	l	NOUN
ap-652	219	45	2	2	NUM
ap-652	219	46	121	121	NUM
ap-652	219	47	2	2	NUM
ap-652	219	48	0	0	NUM
ap-652	219	49	2	2	NUM
ap-652	219	50	2	2	NUM
ap-652	219	51	3	3	NUM
ap-652	219	52	.	.	PUNCT
ap-652	220	1	the	the	DET
ap-652	220	2	optimal	optimal	ADJ
ap-652	220	3	media	medium	NOUN
ap-652	220	4	require	require	VERB
ap-652	220	5	d	d	X
ap-652	220	6	�	�	PROPN
ap-652	220	7	0	0	NUM
ap-652	220	8	,	,	PUNCT
ap-652	220	9	because	because	SCONJ
ap-652	220	10	d	d	PROPN
ap-652	220	11	does	do	AUX
ap-652	220	12	not	not	PART
ap-652	220	13	appear	appear	VERB
ap-652	220	14	in	in	ADP
ap-652	220	15	(	(	PUNCT
ap-652	220	16	10	10	NUM
ap-652	220	17	)	)	PUNCT
ap-652	220	18	.	.	PUNCT
ap-652	221	1	if	if	SCONJ
ap-652	221	2	moreover	moreover	ADV
ap-652	221	3	b	b	PROPN
ap-652	221	4	�	�	PROPN
ap-652	221	5	0	0	NUM
ap-652	221	6	,	,	PUNCT
ap-652	221	7	as	as	ADP
ap-652	221	8	a	a	DET
ap-652	221	9	consequence	consequence	NOUN
ap-652	221	10	of	of	ADP
ap-652	221	11	constant	constant	ADJ
ap-652	221	12	cross	cross	PROPN
ap-652	221	13	sectional	sectional	ADJ
ap-652	221	14	area	area	NOUN
ap-652	221	15	and	and	CCONJ
ap-652	221	16	the	the	DET
ap-652	221	17	material	material	NOUN
ap-652	221	18	volume	volume	NOUN
ap-652	221	19	fraction	fraction	NOUN
ap-652	221	20	going	go	VERB
ap-652	221	21	to	to	ADP
ap-652	221	22	zero	zero	NUM
ap-652	221	23	,	,	PUNCT
ap-652	221	24	then	then	ADV
ap-652	221	25	the	the	DET
ap-652	221	26	contribution	contribution	NOUN
ap-652	221	27	of	of	ADP
ap-652	221	28	the	the	DET
ap-652	221	29	bending	bend	VERB
ap-652	221	30	moments	moment	NOUN
ap-652	221	31	is	be	AUX
ap-652	221	32	zero	zero	NUM
ap-652	221	33	and	and	CCONJ
ap-652	221	34	the	the	DET
ap-652	221	35	last	last	ADJ
ap-652	221	36	term	term	NOUN
ap-652	221	37	in	in	ADP
ap-652	221	38	(	(	PUNCT
ap-652	221	39	14	14	NUM
ap-652	221	40	)	)	PUNCT
ap-652	221	41	reaches	reach	VERB
ap-652	221	42	its	its	PRON
ap-652	221	43	trivial	trivial	ADJ
ap-652	221	44	minimum	minimum	NOUN
ap-652	221	45	.	.	PUNCT
ap-652	222	1	extension	extension	NOUN
ap-652	222	2	of	of	ADP
ap-652	222	3	this	this	DET
ap-652	222	4	statement	statement	NOUN
ap-652	222	5	to	to	ADP
ap-652	222	6	a	a	DET
ap-652	222	7	general	general	ADJ
ap-652	222	8	curved	curved	ADJ
ap-652	222	9	beam	beam	NOUN
ap-652	222	10	under	under	ADP
ap-652	222	11	a	a	DET
ap-652	222	12	general	general	ADJ
ap-652	222	13	macroload	macroload	NOUN
ap-652	222	14	is	be	AUX
ap-652	222	15	clear	clear	ADJ
ap-652	222	16	,	,	PUNCT
ap-652	222	17	there	there	PRON
ap-652	222	18	would	would	AUX
ap-652	222	19	only	only	ADV
ap-652	222	20	be	be	AUX
ap-652	222	21	one	one	NUM
ap-652	222	22	more	more	ADV
ap-652	222	23	integral	integral	ADJ
ap-652	222	24	in	in	ADP
ap-652	222	25	the	the	DET
ap-652	222	26	form	form	NOUN
ap-652	222	27	of	of	ADP
ap-652	222	28	(	(	PUNCT
ap-652	222	29	19	19	NUM
ap-652	222	30	)	)	PUNCT
ap-652	222	31	and	and	CCONJ
ap-652	222	32	a	a	DET
ap-652	222	33	separate	separate	ADJ
ap-652	222	34	t	t	NOUN
ap-652	222	35	contribution	contribution	NOUN
ap-652	222	36	,	,	PUNCT
ap-652	222	37	which	which	PRON
ap-652	222	38	can	can	AUX
ap-652	222	39	be	be	AUX
ap-652	222	40	required	require	VERB
ap-652	222	41	to	to	PART
ap-652	222	42	be	be	AUX
ap-652	222	43	zero	zero	NUM
ap-652	222	44	,	,	PUNCT
ap-652	222	45	because	because	SCONJ
ap-652	222	46	t	t	PROPN
ap-652	222	47	does	do	AUX
ap-652	222	48	not	not	PART
ap-652	222	49	appear	appear	VERB
ap-652	222	50	in	in	ADP
ap-652	222	51	(	(	PUNCT
ap-652	222	52	11	11	NUM
ap-652	222	53	)	)	PUNCT
ap-652	222	54	.	.	PUNCT
ap-652	223	1	this	this	PRON
ap-652	223	2	justifies	justify	VERB
ap-652	223	3	the	the	DET
ap-652	223	4	definition	definition	NOUN
ap-652	223	5	of	of	ADP
ap-652	223	6	optimal	optimal	ADJ
ap-652	223	7	media	medium	NOUN
ap-652	223	8	stated	state	VERB
ap-652	223	9	at	at	ADP
ap-652	223	10	the	the	DET
ap-652	223	11	beginning	beginning	NOUN
ap-652	223	12	of	of	ADP
ap-652	223	13	this	this	DET
ap-652	223	14	subsection	subsection	NOUN
ap-652	223	15	,	,	PUNCT
ap-652	223	16	and	and	CCONJ
ap-652	223	17	proves	prove	VERB
ap-652	223	18	that	that	SCONJ
ap-652	223	19	optimal	optimal	ADJ
ap-652	223	20	micro	micro	NOUN
ap-652	223	21	-	-	NOUN
ap-652	223	22	trusses	truss	NOUN
ap-652	223	23	must	must	AUX
ap-652	223	24	be	be	AUX
ap-652	223	25	composed	compose	VERB
ap-652	223	26	of	of	ADP
ap-652	223	27	straight	straight	ADJ
ap-652	223	28	bars	bar	NOUN
ap-652	223	29	with	with	ADP
ap-652	223	30	constant	constant	PROPN
ap-652	223	31	cross	cross	NOUN
ap-652	223	32	sectional	sectional	ADJ
ap-652	223	33	areas	area	NOUN
ap-652	223	34	.	.	PUNCT
ap-652	224	1	nevertheless	nevertheless	ADV
ap-652	224	2	the	the	DET
ap-652	224	3	contribution	contribution	NOUN
ap-652	224	4	of	of	ADP
ap-652	224	5	bending	bending	NOUN
ap-652	224	6	is	be	AUX
ap-652	224	7	not	not	PART
ap-652	224	8	excluded	exclude	VERB
ap-652	224	9	from	from	ADP
ap-652	224	10	the	the	DET
ap-652	224	11	optimal	optimal	ADJ
ap-652	224	12	media	medium	NOUN
ap-652	224	13	,	,	PUNCT
ap-652	224	14	when	when	SCONJ
ap-652	224	15	behaving	behave	VERB
ap-652	224	16	as	as	ADP
ap-652	224	17	micro	micro	NOUN
ap-652	224	18	-	-	NOUN
ap-652	224	19	frames	frame	NOUN
ap-652	224	20	.	.	PUNCT
ap-652	225	1	in	in	ADP
ap-652	225	2	summary	summary	NOUN
ap-652	225	3	,	,	PUNCT
ap-652	225	4	optimal	optimal	ADJ
ap-652	225	5	open	open	ADJ
ap-652	225	6	-	-	PUNCT
ap-652	225	7	cell	cell	NOUN
ap-652	225	8	foams	foam	NOUN
ap-652	225	9	can	can	AUX
ap-652	225	10	be	be	AUX
ap-652	225	11	searched	search	VERB
ap-652	225	12	within	within	ADP
ap-652	225	13	the	the	DET
ap-652	225	14	class	class	NOUN
ap-652	225	15	of	of	ADP
ap-652	225	16	micro	micro	NOUN
ap-652	225	17	-	-	NOUN
ap-652	225	18	trusses	truss	NOUN
ap-652	225	19	with	with	ADP
ap-652	225	20	straight	straight	ADJ
ap-652	225	21	bars	bar	NOUN
ap-652	225	22	of	of	ADP
ap-652	225	23	constant	constant	ADJ
ap-652	225	24	cross	cross	NOUN
ap-652	225	25	section	section	NOUN
ap-652	225	26	.	.	PUNCT
ap-652	226	1	in	in	ADP
ap-652	226	2	this	this	DET
ap-652	226	3	class	class	NOUN
ap-652	226	4	the	the	DET
ap-652	226	5	bound	bound	ADJ
ap-652	226	6	can	can	AUX
ap-652	226	7	be	be	AUX
ap-652	226	8	expressed	express	VERB
ap-652	226	9	as	as	ADP
ap-652	226	10	a	a	DET
ap-652	226	11	linear	linear	ADJ
ap-652	226	12	function	function	NOUN
ap-652	226	13	of	of	ADP
ap-652	226	14	the	the	DET
ap-652	226	15	material	material	NOUN
ap-652	226	16	volume	volume	NOUN
ap-652	226	17	fraction	fraction	NOUN
ap-652	226	18	,	,	PUNCT
ap-652	226	19	s	s	AUX
ap-652	226	20	,	,	PUNCT
ap-652	226	21	as	as	SCONJ
ap-652	226	22	shown	show	VERB
ap-652	226	23	in	in	ADP
ap-652	226	24	dimitrovová	dimitrovová	NOUN
ap-652	226	25	and	and	CCONJ
ap-652	226	26	faria	faria	PROPN
ap-652	226	27	(	(	PUNCT
ap-652	226	28	1999	1999	NUM
ap-652	226	29	)	)	PUNCT
ap-652	226	30	and	and	CCONJ
ap-652	226	31	as	as	SCONJ
ap-652	226	32	clarified	clarify	VERB
ap-652	226	33	in	in	ADP
ap-652	226	34	section	section	NOUN
ap-652	226	35	3	3	NUM
ap-652	226	36	.	.	PUNCT
ap-652	226	37	related	relate	VERB
ap-652	226	38	optimal	optimal	ADJ
ap-652	226	39	micro	micro	NOUN
ap-652	226	40	-	-	NOUN
ap-652	226	41	frames	frame	NOUN
ap-652	226	42	can	can	AUX
ap-652	226	43	develop	develop	VERB
ap-652	226	44	non	non	ADJ
ap-652	226	45	-	-	ADJ
ap-652	226	46	zero	zero	ADJ
ap-652	226	47	bending	bend	VERB
ap-652	226	48	moments	moment	NOUN
ap-652	226	49	,	,	PUNCT
ap-652	226	50	but	but	CCONJ
ap-652	226	51	only	only	ADV
ap-652	226	52	in	in	ADP
ap-652	226	53	their	their	PRON
ap-652	226	54	antisymmetric	antisymmetric	ADJ
ap-652	226	55	form	form	NOUN
ap-652	226	56	(	(	PUNCT
ap-652	226	57	in	in	ADP
ap-652	226	58	terms	term	NOUN
ap-652	226	59	of	of	ADP
ap-652	226	60	b1	b1	NOUN
ap-652	226	61	and/or	and/or	CCONJ
ap-652	226	62	b2	b2	NOUN
ap-652	226	63	)	)	PUNCT
ap-652	226	64	.	.	PUNCT
ap-652	227	1	if	if	SCONJ
ap-652	227	2	bending	bend	VERB
ap-652	227	3	moments	moment	NOUN
ap-652	227	4	are	be	AUX
ap-652	227	5	presented	present	VERB
ap-652	227	6	,	,	PUNCT
ap-652	227	7	the	the	DET
ap-652	227	8	corresponding	corresponding	ADJ
ap-652	227	9	effective	effective	ADJ
ap-652	227	10	engineering	engineering	NOUN
ap-652	227	11	constant	constant	ADJ
ap-652	227	12	,	,	PUNCT
ap-652	227	13	written	write	VERB
ap-652	227	14	as	as	ADP
ap-652	227	15	a	a	DET
ap-652	227	16	taylor	taylor	PROPN
ap-652	227	17	’s	’s	PART
ap-652	227	18	expansion	expansion	NOUN
ap-652	227	19	in	in	ADP
ap-652	227	20	s	s	PROPN
ap-652	227	21	,	,	PUNCT
ap-652	227	22	contains	contain	VERB
ap-652	227	23	a	a	DET
ap-652	227	24	quadratic	quadratic	ADJ
ap-652	227	25	term	term	NOUN
ap-652	227	26	(	(	PUNCT
ap-652	227	27	a	a	DET
ap-652	227	28	detailed	detailed	ADJ
ap-652	227	29	discussion	discussion	NOUN
ap-652	227	30	is	be	AUX
ap-652	227	31	provided	provide	VERB
ap-652	227	32	in	in	ADP
ap-652	227	33	dimitrovová	dimitrovová	NOUN
ap-652	227	34	and	and	CCONJ
ap-652	227	35	faria	faria	PROPN
ap-652	227	36	(	(	PUNCT
ap-652	227	37	1999	1999	NUM
ap-652	227	38	)	)	PUNCT
ap-652	227	39	)	)	PUNCT
ap-652	227	40	.	.	PUNCT
ap-652	228	1	the	the	DET
ap-652	228	2	tangent	tangent	NOUN
ap-652	228	3	at	at	ADP
ap-652	228	4	s	s	PROPN
ap-652	228	5	�	�	PROPN
ap-652	228	6	0	0	NUM
ap-652	228	7	,	,	PUNCT
ap-652	228	8	i.e.	i.e.	X
ap-652	228	9	the	the	DET
ap-652	228	10	linearized	linearize	VERB
ap-652	228	11	bound	bind	VERB
ap-652	228	12	,	,	PUNCT
ap-652	228	13	relates	relate	VERB
ap-652	228	14	to	to	ADP
ap-652	228	15	the	the	DET
ap-652	228	16	same	same	ADJ
ap-652	228	17	property	property	NOUN
ap-652	228	18	of	of	ADP
ap-652	228	19	the	the	DET
ap-652	228	20	corresponding	corresponding	PROPN
ap-652	228	21	micro	micro	NOUN
ap-652	228	22	-	-	NOUN
ap-652	228	23	truss	truss	ADJ
ap-652	228	24	.	.	PUNCT
ap-652	229	1	please	please	INTJ
ap-652	229	2	note	note	VERB
ap-652	229	3	,	,	PUNCT
ap-652	229	4	however	however	ADV
ap-652	229	5	,	,	PUNCT
ap-652	229	6	(	(	PUNCT
ap-652	229	7	see	see	VERB
ap-652	229	8	fig	fig	NOUN
ap-652	229	9	.	.	PUNCT
ap-652	230	1	3	3	X
ap-652	230	2	)	)	PUNCT
ap-652	230	3	that	that	SCONJ
ap-652	230	4	for	for	ADP
ap-652	230	5	a	a	DET
ap-652	230	6	particularly	particularly	ADV
ap-652	230	7	high	high	ADJ
ap-652	230	8	material	material	NOUN
ap-652	230	9	volume	volume	NOUN
ap-652	230	10	fraction	fraction	NOUN
ap-652	230	11	,	,	PUNCT
ap-652	230	12	s0	s0	PROPN
ap-652	230	13	,	,	PUNCT
ap-652	230	14	there	there	PRON
ap-652	230	15	can	can	AUX
ap-652	230	16	exist	exist	VERB
ap-652	230	17	a	a	DET
ap-652	230	18	micro	micro	NOUN
ap-652	230	19	-	-	NOUN
ap-652	230	20	frame	frame	NOUN
ap-652	230	21	with	with	ADP
ap-652	230	22	a	a	DET
ap-652	230	23	higher	high	ADJ
ap-652	230	24	elastic	elastic	ADJ
ap-652	230	25	property	property	NOUN
ap-652	230	26	than	than	ADP
ap-652	230	27	that	that	PRON
ap-652	230	28	which	which	PRON
ap-652	230	29	is	be	AUX
ap-652	230	30	obtained	obtain	VERB
ap-652	230	31	from	from	ADP
ap-652	230	32	the	the	DET
ap-652	230	33	optimal	optimal	ADJ
ap-652	230	34	micro	micro	NOUN
ap-652	230	35	-	-	NOUN
ap-652	230	36	truss	truss	ADJ
ap-652	230	37	.	.	PUNCT
ap-652	231	1	these	these	DET
ap-652	231	2	cases	case	NOUN
ap-652	231	3	are	be	AUX
ap-652	231	4	of	of	ADP
ap-652	231	5	no	no	DET
ap-652	231	6	interest	interest	NOUN
ap-652	231	7	here	here	ADV
ap-652	231	8	since	since	SCONJ
ap-652	231	9	for	for	ADP
ap-652	231	10	low	low	ADJ
ap-652	231	11	-	-	PUNCT
ap-652	231	12	density	density	NOUN
ap-652	231	13	media	medium	NOUN
ap-652	231	14	only	only	ADV
ap-652	231	15	the	the	DET
ap-652	231	16	initial	initial	ADJ
ap-652	231	17	slope	slope	NOUN
ap-652	231	18	(	(	PUNCT
ap-652	231	19	linearized	linearize	VERB
ap-652	231	20	property	property	NOUN
ap-652	231	21	)	)	PUNCT
ap-652	231	22	matters	matter	NOUN
ap-652	231	23	.	.	PUNCT
ap-652	232	1	for	for	ADP
ap-652	232	2	the	the	DET
ap-652	232	3	same	same	ADJ
ap-652	232	4	reasons	reason	NOUN
ap-652	232	5	media	medium	NOUN
ap-652	232	6	with	with	ADP
ap-652	232	7	only	only	ADV
ap-652	232	8	a	a	DET
ap-652	232	9	bending	bend	VERB
ap-652	232	10	response	response	NOUN
ap-652	232	11	are	be	AUX
ap-652	232	12	strictly	strictly	ADV
ap-652	232	13	excluded	exclude	VERB
ap-652	232	14	from	from	ADP
ap-652	232	15	the	the	DET
ap-652	232	16	class	class	NOUN
ap-652	232	17	of	of	ADP
ap-652	232	18	optimal	optimal	ADJ
ap-652	232	19	micro	micro	NOUN
ap-652	232	20	-	-	NOUN
ap-652	232	21	frames	frame	NOUN
ap-652	232	22	,	,	PUNCT
ap-652	232	23	because	because	SCONJ
ap-652	232	24	the	the	DET
ap-652	232	25	corresponding	corresponding	PROPN
ap-652	232	26	micro	micro	NOUN
ap-652	232	27	-	-	NOUN
ap-652	232	28	truss	truss	NOUN
ap-652	232	29	is	be	AUX
ap-652	232	30	a	a	DET
ap-652	232	31	kinematic	kinematic	ADJ
ap-652	232	32	mechanism	mechanism	NOUN
ap-652	232	33	and	and	CCONJ
ap-652	232	34	the	the	DET
ap-652	232	35	linearized	linearize	VERB
ap-652	232	36	bound	bind	VERB
ap-652	232	37	is	be	AUX
ap-652	232	38	zero	zero	NUM
ap-652	232	39	.	.	PUNCT
ap-652	233	1	176	176	NUM
ap-652	233	2	©	©	PROPN
ap-652	233	3	czech	czech	PROPN
ap-652	233	4	technical	technical	PROPN
ap-652	233	5	university	university	PROPN
ap-652	233	6	publishing	publishing	NOUN
ap-652	233	7	house	house	NOUN
ap-652	233	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	233	9	acta	acta	PROPN
ap-652	233	10	polytechnica	polytechnica	PROPN
ap-652	233	11	vol	vol	NOUN
ap-652	233	12	.	.	PUNCT
ap-652	234	1	44	44	NUM
ap-652	234	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	234	3	it	it	PRON
ap-652	234	4	was	be	AUX
ap-652	234	5	shown	show	VERB
ap-652	234	6	in	in	ADP
ap-652	234	7	dimitrovová	dimitrovová	PROPN
ap-652	234	8	and	and	CCONJ
ap-652	234	9	faria	faria	PROPN
ap-652	234	10	(	(	PUNCT
ap-652	234	11	1999	1999	NUM
ap-652	234	12	)	)	PUNCT
ap-652	234	13	that	that	SCONJ
ap-652	234	14	if	if	SCONJ
ap-652	234	15	the	the	DET
ap-652	234	16	bulk	bulk	ADJ
ap-652	234	17	modulus	modulus	NOUN
ap-652	234	18	is	be	AUX
ap-652	234	19	under	under	ADP
ap-652	234	20	consideration	consideration	NOUN
ap-652	234	21	,	,	PUNCT
ap-652	234	22	then	then	ADV
ap-652	234	23	the	the	DET
ap-652	234	24	macrostress	macrostress	NOUN
ap-652	234	25	components	component	NOUN
ap-652	234	26	that	that	PRON
ap-652	234	27	are	be	AUX
ap-652	234	28	necessary	necessary	ADJ
ap-652	234	29	to	to	PART
ap-652	234	30	express	express	VERB
ap-652	234	31	this	this	DET
ap-652	234	32	property	property	NOUN
ap-652	234	33	do	do	AUX
ap-652	234	34	not	not	PART
ap-652	234	35	contain	contain	VERB
ap-652	234	36	a	a	DET
ap-652	234	37	contribution	contribution	NOUN
ap-652	234	38	of	of	ADP
ap-652	234	39	b.	b.	PROPN
ap-652	234	40	then	then	ADV
ap-652	234	41	bending	bend	VERB
ap-652	234	42	moments	moment	NOUN
ap-652	234	43	are	be	AUX
ap-652	234	44	excluded	exclude	VERB
ap-652	234	45	from	from	ADP
ap-652	234	46	optimal	optimal	ADJ
ap-652	234	47	media	medium	NOUN
ap-652	234	48	,	,	PUNCT
ap-652	234	49	not	not	PART
ap-652	234	50	only	only	ADV
ap-652	234	51	in	in	ADP
ap-652	234	52	the	the	DET
ap-652	234	53	limit	limit	NOUN
ap-652	234	54	at	at	ADP
ap-652	234	55	s	s	PROPN
ap-652	234	56	�	�	PROPN
ap-652	234	57	0	0	NUM
ap-652	234	58	,	,	PUNCT
ap-652	234	59	but	but	CCONJ
ap-652	234	60	in	in	ADP
ap-652	234	61	the	the	DET
ap-652	234	62	full	full	ADJ
ap-652	234	63	range	range	NOUN
ap-652	234	64	of	of	ADP
ap-652	234	65	low	low	ADJ
ap-652	234	66	-	-	PUNCT
ap-652	234	67	density	density	NOUN
ap-652	234	68	s	s	PART
ap-652	234	69	values	value	NOUN
ap-652	234	70	.	.	PUNCT
ap-652	235	1	this	this	DET
ap-652	235	2	result	result	NOUN
ap-652	235	3	is	be	AUX
ap-652	235	4	readily	readily	ADV
ap-652	235	5	extendable	extendable	ADJ
ap-652	235	6	to	to	ADP
ap-652	235	7	3d	3d	NUM
ap-652	235	8	.	.	PUNCT
ap-652	236	1	in	in	ADP
ap-652	236	2	section	section	NOUN
ap-652	236	3	3.2	3.2	NUM
ap-652	236	4	,	,	PUNCT
ap-652	236	5	optimal	optimal	ADJ
ap-652	236	6	micro	micro	NOUN
ap-652	236	7	-	-	NOUN
ap-652	236	8	trusses	truss	NOUN
ap-652	236	9	for	for	ADP
ap-652	236	10	shear	shear	NOUN
ap-652	236	11	modulus	modulus	NOUN
ap-652	236	12	g1	g1	NOUN
ap-652	236	13	*	*	PUNCT
ap-652	236	14	of	of	ADP
ap-652	236	15	media	medium	NOUN
ap-652	236	16	with	with	ADP
ap-652	236	17	effective	effective	ADJ
ap-652	236	18	cubic	cubic	ADJ
ap-652	236	19	symmetry	symmetry	NOUN
ap-652	236	20	will	will	AUX
ap-652	236	21	be	be	AUX
ap-652	236	22	fully	fully	ADV
ap-652	236	23	geometrically	geometrically	ADV
ap-652	236	24	specified	specify	VERB
ap-652	236	25	.	.	PUNCT
ap-652	237	1	in	in	ADP
ap-652	237	2	this	this	DET
ap-652	237	3	case	case	NOUN
ap-652	237	4	it	it	PRON
ap-652	237	5	will	will	AUX
ap-652	237	6	be	be	AUX
ap-652	237	7	seen	see	VERB
ap-652	237	8	that	that	SCONJ
ap-652	237	9	switching	switch	VERB
ap-652	237	10	to	to	ADP
ap-652	237	11	micro	micro	NOUN
ap-652	237	12	-	-	NOUN
ap-652	237	13	frames	frame	NOUN
ap-652	237	14	will	will	AUX
ap-652	237	15	not	not	PART
ap-652	237	16	develop	develop	VERB
ap-652	237	17	bending	bend	VERB
ap-652	237	18	moments	moment	NOUN
ap-652	237	19	.	.	PUNCT
ap-652	238	1	so	so	ADV
ap-652	238	2	also	also	ADV
ap-652	238	3	here	here	ADV
ap-652	238	4	the	the	DET
ap-652	238	5	upper	upper	ADJ
ap-652	238	6	bound	bind	VERB
ap-652	238	7	is	be	AUX
ap-652	238	8	linear	linear	ADJ
ap-652	238	9	within	within	ADP
ap-652	238	10	the	the	DET
ap-652	238	11	validity	validity	NOUN
ap-652	238	12	of	of	ADP
ap-652	238	13	structural	structural	ADJ
ap-652	238	14	theories	theory	NOUN
ap-652	238	15	.	.	PUNCT
ap-652	239	1	the	the	DET
ap-652	239	2	bending	bend	VERB
ap-652	239	3	contribution	contribution	NOUN
ap-652	239	4	is	be	AUX
ap-652	239	5	present	present	ADJ
ap-652	239	6	only	only	ADV
ap-652	239	7	in	in	ADP
ap-652	239	8	isotropic	isotropic	ADJ
ap-652	239	9	shear	shear	NOUN
ap-652	239	10	g	g	PROPN
ap-652	239	11	*	*	PROPN
ap-652	239	12	and	and	CCONJ
ap-652	239	13	in	in	ADP
ap-652	239	14	g2	g2	PROPN
ap-652	239	15	*	*	PUNCT
ap-652	239	16	.	.	PUNCT
ap-652	240	1	2.3	2.3	NUM
ap-652	240	2	review	review	NOUN
ap-652	240	3	of	of	ADP
ap-652	240	4	the	the	DET
ap-652	240	5	methodology	methodology	NOUN
ap-652	240	6	in	in	ADP
ap-652	240	7	the	the	DET
ap-652	240	8	class	class	NOUN
ap-652	240	9	of	of	ADP
ap-652	240	10	micro	micro	ADJ
ap-652	240	11	-	-	ADJ
ap-652	240	12	truss	truss	ADJ
ap-652	240	13	media	medium	NOUN
ap-652	240	14	with	with	ADP
ap-652	240	15	straight	straight	ADJ
ap-652	240	16	bars	bar	NOUN
ap-652	240	17	of	of	ADP
ap-652	240	18	constant	constant	ADJ
ap-652	240	19	cross	cross	NOUN
ap-652	240	20	section	section	NOUN
ap-652	240	21	in	in	ADP
ap-652	240	22	the	the	DET
ap-652	240	23	class	class	NOUN
ap-652	240	24	of	of	ADP
ap-652	240	25	micro	micro	NOUN
ap-652	240	26	-	-	NOUN
ap-652	240	27	trusses	truss	NOUN
ap-652	240	28	,	,	PUNCT
ap-652	240	29	the	the	DET
ap-652	240	30	normal	normal	ADJ
ap-652	240	31	force	force	NOUN
ap-652	240	32	is	be	AUX
ap-652	240	33	the	the	DET
ap-652	240	34	only	only	ADJ
ap-652	240	35	generalized	generalized	ADJ
ap-652	240	36	internal	internal	ADJ
ap-652	240	37	force	force	NOUN
ap-652	240	38	in	in	ADP
ap-652	240	39	the	the	DET
ap-652	240	40	medium	medium	NOUN
ap-652	240	41	.	.	PUNCT
ap-652	241	1	let	let	VERB
ap-652	241	2	an	an	DET
ap-652	241	3	arbitrary	arbitrary	ADJ
ap-652	241	4	basic	basic	ADJ
ap-652	241	5	cell	cell	NOUN
ap-652	241	6	consisting	consist	VERB
ap-652	241	7	of	of	ADP
ap-652	241	8	n	n	PRON
ap-652	241	9	bars	bar	NOUN
ap-652	241	10	be	be	AUX
ap-652	241	11	assumed	assume	VERB
ap-652	241	12	.	.	PUNCT
ap-652	242	1	the	the	DET
ap-652	242	2	contributions	contribution	NOUN
ap-652	242	3	�	�	PROPN
ap-652	242	4	i	i	PROPN
ap-652	242	5	and	and	CCONJ
ap-652	242	6	wi	wi	PROPN
ap-652	242	7	of	of	ADP
ap-652	242	8	each	each	DET
ap-652	242	9	i	i	PROPN
ap-652	242	10	-	-	PUNCT
ap-652	242	11	bar	bar	NOUN
ap-652	242	12	of	of	ADP
ap-652	242	13	theoretical	theoretical	ADJ
ap-652	242	14	length	length	NOUN
ap-652	242	15	li	li	PROPN
ap-652	242	16	,	,	PUNCT
ap-652	242	17	cross	cross	VERB
ap-652	242	18	sectional	sectional	ADJ
ap-652	242	19	area	area	NOUN
ap-652	242	20	ai	ai	VERB
ap-652	242	21	and	and	CCONJ
ap-652	242	22	normal	normal	ADJ
ap-652	242	23	force	force	NOUN
ap-652	242	24	ni	ni	PROPN
ap-652	242	25	can	can	AUX
ap-652	242	26	be	be	AUX
ap-652	242	27	specified	specify	VERB
ap-652	242	28	in	in	ADP
ap-652	242	29	the	the	DET
ap-652	242	30	following	follow	VERB
ap-652	242	31	way	way	NOUN
ap-652	242	32	(	(	PUNCT
ap-652	242	33	compare	compare	VERB
ap-652	242	34	with	with	ADP
ap-652	242	35	(	(	PUNCT
ap-652	242	36	11	11	NUM
ap-652	242	37	)	)	PUNCT
ap-652	242	38	):	):	PUNCT
ap-652	243	1	�	�	PROPN
ap-652	244	1	i	i	PRON
ap-652	245	1	i	i	PRON
ap-652	246	1	i	i	PRON
ap-652	247	1	i	i	PRON
ap-652	248	1	i	i	PRON
ap-652	249	1	i	i	PRON
ap-652	250	1	i	i	PRON
ap-652	251	1	i	i	PRON
ap-652	252	1	i	i	VERB
ap-652	253	1	i	i	PRON
ap-652	253	2	n	n	VERB
ap-652	253	3	v	v	ADP
ap-652	253	4	�	�	PROPN
ap-652	253	5	�	�	PROPN
ap-652	253	6	�	�	PROPN
ap-652	253	7	l	l	PROPN
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ap-652	253	10	;	;	VERB
ap-652	253	11	sin	sin	PROPN
ap-652	253	12	cos	cos	PROPN
ap-652	253	13	sin	sin	PROPN
ap-652	253	14	;	;	PROPN
ap-652	253	15	cos	cos	PROPN
ap-652	253	16	sin2	sin2	PROPN
ap-652	253	17	2	2	NUM
ap-652	253	18	2	2	NUM
ap-652	253	19	�	�	PROPN
ap-652	253	20	�	�	PROPN
ap-652	253	21	�	�	PROPN
ap-652	253	22	cos	cos	PROPN
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ap-652	253	25	;	;	X
ap-652	253	26	sin	sin	PROPN
ap-652	253	27	sin	sin	PROPN
ap-652	253	28	cos	cos	PROPN
ap-652	253	29	cos	cos	PROPN
ap-652	253	30	�	�	PROPN
ap-652	253	31	�	�	PROPN
ap-652	253	32	�	�	PROPN
ap-652	253	33	�	�	PROPN
ap-652	253	34	�	�	PROPN
ap-652	253	35	�	�	PROPN
ap-652	254	1	i	i	PRON
ap-652	254	2	i	i	PRON
ap-652	255	1	i	i	PRON
ap-652	255	2	i	i	PRON
ap-652	256	1	i	i	PRON
ap-652	256	2	i	i	PRON
ap-652	256	3	isymm	isymm	VERB
ap-652	256	4	2	2	NUM
ap-652	256	5	2	2	NUM
ap-652	256	6	2	2	NUM
ap-652	256	7	�	�	PROPN
ap-652	256	8	�	�	PROPN
ap-652	256	9	�	�	PROPN
ap-652	256	10	�	�	PROPN
ap-652	256	11	�	�	PROPN
ap-652	256	12	�	�	PROPN
ap-652	256	13	�	�	PROPN
ap-652	256	14	�	�	PROPN
ap-652	256	15	�	�	PROPN
ap-652	256	16	�	�	PROPN
ap-652	256	17	,	,	PUNCT
ap-652	256	18	(	(	PUNCT
ap-652	256	19	2	2	NUM
ap-652	256	20	0	0	NUM
ap-652	256	21	)	)	PUNCT
ap-652	256	22	where	where	SCONJ
ap-652	256	23	the	the	DET
ap-652	256	24	two	two	NUM
ap-652	256	25	spherical	spherical	ADJ
ap-652	256	26	angles	angle	NOUN
ap-652	256	27	�	�	PROPN
ap-652	256	28	�	�	PROPN
ap-652	256	29	�	�	PROPN
ap-652	256	30	i	i	PRON
ap-652	256	31	�	�	PROPN
ap-652	256	32	0	0	NUM
ap-652	256	33	,	,	PUNCT
ap-652	256	34	and	and	CCONJ
ap-652	256	35	�	�	PROPN
ap-652	256	36	�	�	PROPN
ap-652	256	37	i	i	PRON
ap-652	256	38	�	�	PROPN
ap-652	256	39	0	0	NUM
ap-652	256	40	2	2	NUM
ap-652	256	41	,	,	PUNCT
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ap-652	256	43	the	the	DET
ap-652	256	44	i	i	NOUN
ap-652	256	45	-	-	PUNCT
ap-652	256	46	bar	bar	NOUN
ap-652	256	47	position	position	NOUN
ap-652	256	48	with	with	ADP
ap-652	256	49	respect	respect	NOUN
ap-652	256	50	to	to	ADP
ap-652	256	51	the	the	DET
ap-652	256	52	cell	cell	NOUN
ap-652	256	53	coordinates	coordinate	NOUN
ap-652	256	54	yj	yj	PROPN
ap-652	256	55	,	,	PUNCT
ap-652	256	56	j	j	PROPN
ap-652	256	57	�	�	PROPN
ap-652	256	58	1	1	NUM
ap-652	256	59	,	,	PUNCT
ap-652	256	60	2	2	NUM
ap-652	256	61	,	,	PUNCT
ap-652	256	62	3	3	NUM
ap-652	256	63	,	,	PUNCT
ap-652	256	64	(	(	PUNCT
ap-652	256	65	fig	fig	NOUN
ap-652	256	66	.	.	PUNCT
ap-652	257	1	4);	4);	NUM
ap-652	258	1	and	and	CCONJ
ap-652	258	2	(	(	PUNCT
ap-652	258	3	see	see	VERB
ap-652	258	4	(	(	PUNCT
ap-652	258	5	14	14	NUM
ap-652	258	6	)	)	PUNCT
ap-652	258	7	and	and	CCONJ
ap-652	258	8	(	(	PUNCT
ap-652	258	9	18	18	NUM
ap-652	258	10	)	)	PUNCT
ap-652	258	11	)	)	PUNCT
ap-652	259	1	w	w	NOUN
ap-652	259	2	v	v	NUM
ap-652	259	3	e	e	PROPN
ap-652	259	4	n	n	CCONJ
ap-652	259	5	a	a	PRON
ap-652	260	1	i	i	PRON
ap-652	260	2	s	s	VERB
ap-652	260	3	i	i	PRON
ap-652	260	4	2	2	NUM
ap-652	261	1	i	i	PRON
ap-652	261	2	i	i	PRON
ap-652	261	3	�	�	PROPN
ap-652	261	4	�	�	PROPN
ap-652	261	5	�	�	PROPN
ap-652	261	6	�	�	PROPN
ap-652	261	7	�	�	PROPN
ap-652	261	8	�	�	PROPN
ap-652	261	9	�	�	PROPN
ap-652	261	10	1	1	NUM
ap-652	261	11	2	2	NUM
ap-652	261	12	l	l	NOUN
ap-652	261	13	.	.	PUNCT
ap-652	262	1	(	(	PUNCT
ap-652	262	2	21	21	NUM
ap-652	262	3	)	)	PUNCT
ap-652	262	4	let	let	VERB
ap-652	262	5	the	the	DET
ap-652	262	6	following	follow	VERB
ap-652	262	7	designation	designation	NOUN
ap-652	262	8	be	be	AUX
ap-652	262	9	introduced	introduce	VERB
ap-652	262	10	:	:	PUNCT
ap-652	262	11	�	�	PROPN
ap-652	262	12	�	�	PROPN
ap-652	262	13	�	�	PROPN
ap-652	262	14	�	�	PROPN
ap-652	262	15	1	1	NUM
ap-652	262	16	2	2	NUM
ap-652	262	17	2	2	NUM
ap-652	262	18	2	2	NUM
ap-652	262	19	2	2	NUM
ap-652	262	20	2	2	NUM
ap-652	262	21	3	3	NUM
ap-652	262	22	2	2	NUM
ap-652	262	23	1	1	NUM
ap-652	262	24	,	,	PUNCT
ap-652	262	25	,	,	PUNCT
ap-652	262	26	,	,	PUNCT
ap-652	263	1	cos	cos	ADP
ap-652	263	2	sin	sin	NOUN
ap-652	263	3	,	,	PUNCT
ap-652	263	4	sin	sin	NOUN
ap-652	263	5	sin	sin	NOUN
ap-652	263	6	,	,	PUNCT
ap-652	263	7	cos	cos	PROPN
ap-652	263	8	;	;	VERB
ap-652	263	9	i	i	PRON
ap-652	264	1	i	i	PRON
ap-652	264	2	i	i	PRON
ap-652	265	1	i	i	PRON
ap-652	265	2	i	i	PRON
ap-652	266	1	i	i	PRON
ap-652	267	1	i	i	PRON
ap-652	267	2	i	i	PRON
ap-652	267	3	�	�	PROPN
ap-652	267	4	�	�	PROPN
ap-652	267	5	�	�	PROPN
ap-652	267	6	�	�	PROPN
ap-652	267	7	�	�	PROPN
ap-652	267	8	�	�	PROPN
ap-652	267	9	,	,	PUNCT
ap-652	267	10	,	,	PUNCT
ap-652	267	11	,	,	PUNCT
ap-652	267	12	sin	sin	VERB
ap-652	267	13	sin	sin	PROPN
ap-652	267	14	cos	cos	PROPN
ap-652	267	15	,	,	PUNCT
ap-652	267	16	cos	cos	PROPN
ap-652	267	17	sin	sin	PROPN
ap-652	267	18	cos	cos	PROPN
ap-652	267	19	,	,	PUNCT
ap-652	267	20	sin	sin	VERB
ap-652	268	1	i	i	PRON
ap-652	268	2	i	i	PRON
ap-652	269	1	i	i	PRON
ap-652	269	2	i	i	PRON
ap-652	270	1	i	i	PRON
ap-652	270	2	i	i	PRON
ap-652	271	1	i	i	PRON
ap-652	271	2	i	i	PRON
ap-652	272	1	i	i	PRON
ap-652	272	2	i	i	PRON
ap-652	272	3	�	�	PROPN
ap-652	272	4	�	�	PROPN
ap-652	272	5	�	�	PROPN
ap-652	272	6	�	�	PROPN
ap-652	272	7	�	�	PROPN
ap-652	272	8	�	�	PROPN
ap-652	272	9	�	�	PROPN
ap-652	272	10	�	�	PROPN
ap-652	272	11	�	�	PROPN
ap-652	272	12	2	2	NUM
ap-652	272	13	3	3	NUM
ap-652	272	14	cos	cos	PROPN
ap-652	272	15	sin	sin	NOUN
ap-652	272	16	;	;	VERB
ap-652	272	17	sin	sin	PROPN
ap-652	272	18	sin	sin	PROPN
ap-652	272	19	cos	cos	PROPN
ap-652	272	20	,	,	PUNCT
ap-652	272	21	cos	cos	PROPN
ap-652	272	22	c	c	PROPN
ap-652	272	23	,	,	PUNCT
ap-652	272	24	,	,	PUNCT
ap-652	272	25	�	�	PROPN
ap-652	272	26	�	�	PROPN
ap-652	272	27	�	�	PROPN
ap-652	272	28	�	�	PROPN
ap-652	273	1	i	i	PRON
ap-652	273	2	i	i	PRON
ap-652	274	1	i	i	PRON
ap-652	274	2	i	i	PRON
ap-652	275	1	i	i	PRON
ap-652	275	2	i	i	PRON
ap-652	276	1	i	i	PRON
ap-652	276	2	i	i	VERB
ap-652	276	3	2	2	NUM
ap-652	276	4	1	1	NUM
ap-652	276	5	2	2	NUM
ap-652	276	6	2	2	NUM
ap-652	276	7	2	2	NUM
ap-652	276	8	2	2	NUM
ap-652	276	9	2	2	NUM
ap-652	276	10	�	�	PROPN
ap-652	276	11	�	�	PROPN
ap-652	276	12	�	�	PROPN
ap-652	276	13	�	�	PROPN
ap-652	276	14	os	os	PROPN
ap-652	276	15	sin	sin	PROPN
ap-652	276	16	;	;	PROPN
ap-652	276	17	cos	cos	PROPN
ap-652	276	18	(	(	PUNCT
ap-652	276	19	)	)	PUNCT
ap-652	276	20	sin	sin	NOUN
ap-652	276	21	;	;	VERB
ap-652	276	22	,	,	PUNCT
ap-652	276	23	2	2	NUM
ap-652	276	24	2	2	NUM
ap-652	276	25	3	3	NUM
ap-652	276	26	22	22	NUM
ap-652	276	27	�	�	PROPN
ap-652	276	28	�	�	PROPN
ap-652	277	1	i	i	PRON
ap-652	277	2	i	i	PRON
ap-652	278	1	i	i	PRON
ap-652	278	2	i	i	PRON
ap-652	279	1	i	i	PROPN
ap-652	279	2	�	�	PROPN
ap-652	279	3	�	�	PROPN
ap-652	279	4	(	(	PUNCT
ap-652	279	5	22	22	NUM
ap-652	279	6	)	)	PUNCT
ap-652	279	7	then	then	ADV
ap-652	279	8	the	the	DET
ap-652	279	9	vectors	vector	NOUN
ap-652	279	10	n	n	CCONJ
ap-652	279	11	,	,	PUNCT
ap-652	279	12	r	r	NOUN
ap-652	279	13	,	,	PUNCT
ap-652	279	14	q	q	NOUN
ap-652	279	15	and	and	CCONJ
ap-652	279	16	l	l	NOUN
ap-652	279	17	(	(	PUNCT
ap-652	279	18	compare	compare	VERB
ap-652	279	19	with	with	ADP
ap-652	279	20	dimitrovová	dimitrovová	NOUN
ap-652	279	21	and	and	CCONJ
ap-652	279	22	faria	faria	PROPN
ap-652	279	23	(	(	PUNCT
ap-652	279	24	1999	1999	NUM
ap-652	279	25	)	)	PUNCT
ap-652	279	26	)	)	PUNCT
ap-652	279	27	can	can	AUX
ap-652	279	28	be	be	AUX
ap-652	279	29	defined	define	VERB
ap-652	279	30	as	as	ADP
ap-652	279	31	:	:	PUNCT
ap-652	279	32	n	n	CCONJ
ap-652	279	33	r	r	NOUN
ap-652	279	34	�	�	PROPN
ap-652	279	35	�	�	PROPN
ap-652	279	36	!	!	PUNCT
ap-652	279	37	"	"	PUNCT
ap-652	280	1	#	#	NOUN
ap-652	280	2	$	$	SYM
ap-652	280	3	�	�	PROPN
ap-652	280	4	n	n	CCONJ
ap-652	280	5	a	a	PRON
ap-652	280	6	n	n	NOUN
ap-652	280	7	a	a	DET
ap-652	280	8	n	n	NOUN
ap-652	280	9	a	a	DET
ap-652	280	10	l	l	NOUN
ap-652	280	11	a	a	DET
ap-652	280	12	l	l	NOUN
ap-652	280	13	a	a	DET
ap-652	280	14	1	1	NUM
ap-652	280	15	1	1	NUM
ap-652	280	16	1	1	NUM
ap-652	280	17	2	2	NUM
ap-652	280	18	2	2	NUM
ap-652	280	19	2	2	NUM
ap-652	280	20	n	n	ADP
ap-652	280	21	n	n	CCONJ
ap-652	280	22	n	n	ADV
ap-652	280	23	j	j	PROPN
ap-652	280	24	j	j	NOUN
ap-652	280	25	1	1	NUM
ap-652	280	26	1	1	NUM
ap-652	280	27	j	j	NOUN
ap-652	280	28	2	2	NUM
ap-652	280	29	l	l	NOUN
ap-652	280	30	l	l	NOUN
ap-652	280	31	l	l	NOUN
ap-652	280	32	,	,	PUNCT
ap-652	280	33	,	,	PUNCT
ap-652	280	34	,	,	PUNCT
ap-652	280	35	,	,	PUNCT
ap-652	280	36	,	,	PUNCT
ap-652	280	37	,	,	PUNCT
ap-652	280	38	,	,	PUNCT
ap-652	280	39	�	�	PROPN
ap-652	280	40	�	�	PROPN
ap-652	280	41	�	�	PROPN
ap-652	280	42	1	1	NUM
ap-652	280	43	2	2	NUM
ap-652	280	44	�	�	PROPN
ap-652	280	45	�	�	PROPN
ap-652	280	46	2	2	NUM
ap-652	280	47	j	j	PROPN
ap-652	280	48	n	n	CCONJ
ap-652	280	49	n	n	CCONJ
ap-652	280	50	n	n	ADV
ap-652	280	51	j	j	PROPN
ap-652	280	52	j	j	NOUN
ap-652	280	53	1	1	NUM
ap-652	280	54	1	1	NUM
ap-652	280	55	j	j	NOUN
ap-652	280	56	2	2	NUM
ap-652	280	57	2	2	NUM
ap-652	280	58	j	j	PROPN
ap-652	280	59	n	n	CCONJ
ap-652	280	60	n	n	PROPN
ap-652	280	61	l	l	NOUN
ap-652	280	62	a	a	DET
ap-652	280	63	j	j	PROPN
ap-652	280	64	l	l	NOUN
ap-652	280	65	a	a	PROPN
ap-652	280	66	l	l	NOUN
ap-652	280	67	a	a	X
ap-652	280	68	l	l	NOUN
ap-652	280	69	,	,	PUNCT
ap-652	280	70	,	,	PUNCT
ap-652	280	71	,	,	PUNCT
ap-652	280	72	,	,	PUNCT
ap-652	280	73	,	,	PUNCT
ap-652	280	74	,	,	PUNCT
ap-652	280	75	,	,	PUNCT
ap-652	280	76	,	,	PUNCT
ap-652	280	77	,	,	PUNCT
ap-652	280	78	,	,	PUNCT
ap-652	280	79	,	,	PUNCT
ap-652	280	80	,	,	PUNCT
ap-652	280	81	,	,	PUNCT
ap-652	280	82	�	�	PROPN
ap-652	280	83	�	�	PROPN
ap-652	280	84	�	�	PROPN
ap-652	280	85	�	�	PROPN
ap-652	280	86	�	�	PROPN
ap-652	280	87	�	�	PROPN
ap-652	280	88	�	�	PROPN
ap-652	280	89	�	�	PROPN
ap-652	280	90	1	1	NUM
ap-652	280	91	2	2	NUM
ap-652	280	92	3	3	NUM
ap-652	280	93	1	1	NUM
ap-652	280	94	2q	2q	NUM
ap-652	280	95	�	�	PROPN
ap-652	280	96	�	�	PROPN
ap-652	280	97	�	�	PROPN
ap-652	280	98	�	�	PROPN
ap-652	280	99	a	a	DET
ap-652	280	100	j	j	PROPN
ap-652	280	101	a	a	DET
ap-652	280	102	a	a	DET
ap-652	280	103	a	a	DET
ap-652	280	104	n	n	NUM
ap-652	280	105	1	1	NUM
ap-652	280	106	1	1	NUM
ap-652	280	107	2	2	NUM
ap-652	280	108	2	2	NUM
ap-652	280	109	n	n	NUM
ap-652	280	110	n	n	NOUN
ap-652	280	111	,	,	PUNCT
ap-652	280	112	,	,	PUNCT
ap-652	280	113	,	,	PUNCT
ap-652	280	114	,	,	PUNCT
ap-652	280	115	,	,	PUNCT
ap-652	280	116	,	,	PUNCT
ap-652	280	117	,	,	PUNCT
ap-652	280	118	�	�	PROPN
ap-652	280	119	�	�	PROPN
ap-652	280	120	1	1	NUM
ap-652	280	121	2	2	NUM
ap-652	280	122	3	3	NUM
ap-652	280	123	l	l	NOUN
ap-652	280	124	l	l	NOUN
ap-652	280	125	l	l	X
ap-652	280	126	l	l	X
ap-652	280	127	�	�	PROPN
ap-652	280	128	(	(	PUNCT
ap-652	280	129	23	23	NUM
ap-652	280	130	)	)	PUNCT
ap-652	280	131	in	in	ADP
ap-652	280	132	addition	addition	NOUN
ap-652	280	133	,	,	PUNCT
ap-652	280	134	let	let	VERB
ap-652	280	135	us	we	PRON
ap-652	280	136	denote	denote	VERB
ap-652	280	137	:	:	PUNCT
ap-652	280	138	p	p	NOUN
ap-652	280	139	r	r	NOUN
ap-652	280	140	r1	r1	NOUN
ap-652	280	141	2	2	NUM
ap-652	280	142	3	3	NUM
ap-652	280	143	�	�	PROPN
ap-652	280	144	,	,	PUNCT
ap-652	280	145	p	p	NOUN
ap-652	280	146	r	r	NOUN
ap-652	280	147	r2	r2	NOUN
ap-652	280	148	3	3	NUM
ap-652	280	149	1	1	NUM
ap-652	280	150	�	�	PROPN
ap-652	280	151	,	,	PUNCT
ap-652	280	152	p	p	NOUN
ap-652	280	153	r	r	NOUN
ap-652	280	154	r3	r3	PROPN
ap-652	280	155	1	1	NUM
ap-652	280	156	2	2	NUM
ap-652	280	157	�	�	PROPN
ap-652	280	158	.	.	PUNCT
ap-652	281	1	(	(	PUNCT
ap-652	281	2	24	24	NUM
ap-652	281	3	)	)	PUNCT
ap-652	281	4	thus	thus	ADV
ap-652	281	5	:	:	PUNCT
ap-652	281	6	�	�	PROPN
ap-652	281	7	�	�	PROPN
ap-652	281	8	p	p	PROPN
ap-652	281	9	j	j	PROPN
ap-652	281	10	j,1	j,1	PROPN
ap-652	281	11	1	1	NUM
ap-652	281	12	1	1	NUM
ap-652	281	13	j,2	j,2	NOUN
ap-652	281	14	2	2	NUM
ap-652	281	15	2	2	NUM
ap-652	281	16	j	j	PROPN
ap-652	281	17	,	,	PUNCT
ap-652	281	18	n	n	PROPN
ap-652	281	19	n	n	NOUN
ap-652	281	20	nl	nl	NOUN
ap-652	281	21	a	a	DET
ap-652	281	22	l	l	NOUN
ap-652	281	23	a	a	DET
ap-652	281	24	l	l	NOUN
ap-652	281	25	a	a	DET
ap-652	281	26	j	j	PROPN
ap-652	281	27	�	�	PROPN
ap-652	281	28	�	�	PROPN
ap-652	281	29	�	�	PROPN
ap-652	281	30	�	�	PROPN
ap-652	281	31	�	�	PROPN
ap-652	281	32	,	,	PUNCT
ap-652	281	33	,	,	PUNCT
ap-652	281	34	,	,	PUNCT
ap-652	281	35	,	,	PUNCT
ap-652	281	36	,	,	PUNCT
ap-652	281	37	,	,	PUNCT
ap-652	281	38	�	�	PROPN
ap-652	281	39	1	1	NUM
ap-652	281	40	2	2	NUM
ap-652	281	41	3	3	NUM
ap-652	281	42	,	,	PUNCT
ap-652	281	43	(	(	PUNCT
ap-652	281	44	25	25	NUM
ap-652	281	45	)	)	PUNCT
ap-652	281	46	and	and	CCONJ
ap-652	281	47	it	it	PRON
ap-652	281	48	holds	hold	VERB
ap-652	281	49	:	:	PUNCT
ap-652	282	1	p	p	X
ap-652	282	2	p	p	X
ap-652	282	3	p	p	NOUN
ap-652	282	4	0	0	NUM
ap-652	282	5	r	r	NOUN
ap-652	282	6	r	r	NOUN
ap-652	282	7	r	r	NOUN
ap-652	282	8	l	l	NOUN
ap-652	283	1	p	p	NOUN
ap-652	283	2	p	p	X
ap-652	283	3	p	p	X
ap-652	283	4	q	q	X
ap-652	283	5	q	q	X
ap-652	283	6	q	q	NOUN
ap-652	283	7	l	l	NOUN
ap-652	283	8	1	1	NUM
ap-652	283	9	2	2	NUM
ap-652	283	10	3	3	NUM
ap-652	283	11	1	1	NUM
ap-652	283	12	2	2	NUM
ap-652	283	13	3	3	NUM
ap-652	283	14	1	1	NUM
ap-652	283	15	2	2	NUM
ap-652	283	16	2	2	NUM
ap-652	283	17	2	2	NUM
ap-652	283	18	3	3	NUM
ap-652	283	19	2	2	NUM
ap-652	283	20	1	1	NUM
ap-652	283	21	2	2	NUM
ap-652	283	22	2	2	NUM
ap-652	283	23	2	2	NUM
ap-652	283	24	3	3	NUM
ap-652	283	25	2	2	NUM
ap-652	283	26	22	22	NUM
ap-652	283	27	�	�	PROPN
ap-652	283	28	�	�	PROPN
ap-652	283	29	�	�	PROPN
ap-652	283	30	,	,	PUNCT
ap-652	283	31	,	,	PUNCT
ap-652	283	32	,	,	PUNCT
ap-652	283	33	(	(	PUNCT
ap-652	283	34	26	26	NUM
ap-652	283	35	)	)	PUNCT
ap-652	283	36	where	where	SCONJ
ap-652	283	37	is	be	AUX
ap-652	283	38	the	the	DET
ap-652	283	39	euclidean	euclidean	ADJ
ap-652	283	40	norm	norm	NOUN
ap-652	283	41	.	.	PUNCT
ap-652	284	1	the	the	DET
ap-652	284	2	material	material	NOUN
ap-652	284	3	volume	volume	NOUN
ap-652	284	4	fraction	fraction	NOUN
ap-652	284	5	,	,	PUNCT
ap-652	284	6	s	s	AUX
ap-652	284	7	,	,	PUNCT
ap-652	284	8	can	can	AUX
ap-652	284	9	be	be	AUX
ap-652	284	10	approximated	approximate	VERB
ap-652	284	11	neglecting	neglect	VERB
ap-652	284	12	the	the	DET
ap-652	284	13	higher	high	ADJ
ap-652	284	14	order	order	NOUN
ap-652	284	15	terms	term	NOUN
ap-652	284	16	as	as	ADP
ap-652	284	17	:	:	PUNCT
ap-652	284	18	s	s	PROPN
ap-652	284	19	v	v	ADP
ap-652	284	20	�	�	PROPN
ap-652	284	21	l	l	NOUN
ap-652	284	22	2	2	NUM
ap-652	284	23	.	.	PUNCT
ap-652	285	1	(	(	PUNCT
ap-652	285	2	27	27	NUM
ap-652	285	3	)	)	PUNCT
ap-652	285	4	©	©	PROPN
ap-652	285	5	czech	czech	PROPN
ap-652	285	6	technical	technical	PROPN
ap-652	285	7	university	university	PROPN
ap-652	285	8	publishing	publishing	NOUN
ap-652	285	9	house	house	NOUN
ap-652	285	10	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	285	11	177	177	NUM
ap-652	285	12	acta	acta	PROPN
ap-652	285	13	polytechnica	polytechnica	PROPN
ap-652	285	14	vol	vol	NOUN
ap-652	285	15	.	.	PROPN
ap-652	286	1	44	44	NUM
ap-652	286	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	286	3	s0	s0	NOUN
ap-652	286	4	s	s	PART
ap-652	286	5	elastic	elastic	ADJ
ap-652	286	6	property	property	NOUN
ap-652	286	7	under	under	ADP
ap-652	286	8	consideration	consideration	NOUN
ap-652	286	9	optimal	optimal	ADJ
ap-652	286	10	micro	micro	ADJ
ap-652	286	11	-	-	ADJ
ap-652	286	12	truss	truss	ADJ
ap-652	286	13	micro	micro	NOUN
ap-652	286	14	-	-	NOUN
ap-652	286	15	frame	frame	NOUN
ap-652	286	16	corresponding	corresponding	NOUN
ap-652	286	17	to	to	ADP
ap-652	286	18	optimal	optimal	ADJ
ap-652	286	19	micro	micro	ADJ
ap-652	286	20	-	-	ADJ
ap-652	286	21	truss	truss	ADJ
ap-652	286	22	micro	micro	NOUN
ap-652	286	23	-	-	NOUN
ap-652	286	24	frame	frame	NOUN
ap-652	286	25	corresponding	corresponding	NOUN
ap-652	286	26	to	to	ADP
ap-652	286	27	non	non	ADJ
ap-652	286	28	-	-	ADJ
ap-652	286	29	optimal	optimal	ADJ
ap-652	286	30	micro	micro	ADJ
ap-652	286	31	-	-	ADJ
ap-652	286	32	truss	truss	ADJ
ap-652	286	33	non	non	ADJ
ap-652	286	34	-	-	ADJ
ap-652	286	35	optimal	optimal	ADJ
ap-652	286	36	micro	micro	ADJ
ap-652	286	37	-	-	ADJ
ap-652	286	38	truss	truss	ADJ
ap-652	286	39	fig	fig	NOUN
ap-652	286	40	.	.	PUNCT
ap-652	287	1	3	3	NUM
ap-652	287	2	:	:	PUNCT
ap-652	287	3	specification	specification	NOUN
ap-652	287	4	of	of	ADP
ap-652	287	5	optimal	optimal	ADJ
ap-652	287	6	media	medium	NOUN
ap-652	287	7	response	response	NOUN
ap-652	288	1	i	i	PRON
ap-652	288	2	1y	1y	VERB
ap-652	288	3	2y	2y	VERB
ap-652	288	4	3y	3y	NOUN
ap-652	288	5	in	in	ADP
ap-652	288	6	in	in	ADP
ap-652	288	7	i	i	PROPN
ap-652	288	8	�	�	PROPN
ap-652	288	9	il	il	PROPN
ap-652	288	10	ia	ia	PROPN
ap-652	288	11	bari	bari	PROPN
ap-652	288	12	fig	fig	NOUN
ap-652	288	13	.	.	PUNCT
ap-652	289	1	4	4	NUM
ap-652	289	2	:	:	PUNCT
ap-652	289	3	specification	specification	NOUN
ap-652	289	4	of	of	ADP
ap-652	289	5	the	the	DET
ap-652	289	6	i	i	PROPN
ap-652	289	7	-	-	NOUN
ap-652	289	8	bar	bar	NOUN
ap-652	289	9	within	within	ADP
ap-652	289	10	the	the	DET
ap-652	289	11	basic	basic	ADJ
ap-652	289	12	cell	cell	NOUN
ap-652	289	13	taking	take	VERB
ap-652	289	14	into	into	ADP
ap-652	289	15	account	account	NOUN
ap-652	289	16	(	(	PUNCT
ap-652	289	17	22–23	22–23	PROPN
ap-652	289	18	)	)	PUNCT
ap-652	289	19	,	,	PUNCT
ap-652	289	20	(	(	PUNCT
ap-652	289	21	20	20	NUM
ap-652	289	22	)	)	PUNCT
ap-652	289	23	can	can	AUX
ap-652	289	24	be	be	AUX
ap-652	289	25	substituted	substitute	VERB
ap-652	289	26	into	into	ADP
ap-652	289	27	(	(	PUNCT
ap-652	289	28	4	4	X
ap-652	289	29	)	)	PUNCT
ap-652	289	30	giving	giving	NOUN
ap-652	289	31	:	:	PUNCT
ap-652	289	32	�	�	PROPN
ap-652	289	33	�	�	PROPN
ap-652	289	34	�	�	PROPN
ap-652	289	35	�	�	PROPN
ap-652	289	36	�	�	PROPN
ap-652	289	37	�	�	PROPN
ap-652	289	38	�	�	PROPN
ap-652	289	39	1	1	NUM
ap-652	289	40	1	1	NUM
ap-652	289	41	1	1	NUM
ap-652	289	42	2	2	NUM
ap-652	289	43	3	3	NUM
ap-652	289	44	1	1	NUM
ap-652	289	45	2	2	NUM
ap-652	289	46	3v	3v	NUM
ap-652	289	47	v	v	ADP
ap-652	289	48	t	t	PROPN
ap-652	289	49	t	t	NOUN
ap-652	289	50	ts	ts	ADP
ap-652	289	51	n	n	CCONJ
ap-652	289	52	r	r	NOUN
ap-652	289	53	r	r	NOUN
ap-652	289	54	r	r	NOUN
ap-652	289	55	q	q	NOUN
ap-652	289	56	q	q	NOUN
ap-652	289	57	q	q	NOUN
ap-652	289	58	n	n	CCONJ
ap-652	289	59	,	,	PUNCT
ap-652	289	60	,	,	PUNCT
ap-652	289	61	,	,	PUNCT
ap-652	289	62	,	,	PUNCT
ap-652	289	63	,	,	PUNCT
ap-652	289	64	,	,	PUNCT
ap-652	289	65	(	(	PUNCT
ap-652	289	66	28	28	NUM
ap-652	289	67	)	)	PUNCT
ap-652	289	68	and	and	CCONJ
ap-652	289	69	(	(	PUNCT
ap-652	289	70	21	21	NUM
ap-652	289	71	)	)	PUNCT
ap-652	289	72	into	into	ADP
ap-652	289	73	(	(	PUNCT
ap-652	289	74	5	5	NUM
ap-652	289	75	)	)	PUNCT
ap-652	289	76	as	as	ADP
ap-652	289	77	:	:	PUNCT
ap-652	289	78	w	w	NOUN
ap-652	289	79	v	v	X
ap-652	289	80	es	es	X
ap-652	289	81	�	�	PROPN
ap-652	289	82	n	n	CCONJ
ap-652	289	83	2	2	NUM
ap-652	289	84	2	2	NUM
ap-652	289	85	,	,	PUNCT
ap-652	289	86	(	(	PUNCT
ap-652	289	87	29	29	NUM
ap-652	289	88	)	)	PUNCT
ap-652	289	89	where	where	SCONJ
ap-652	289	90	s	s	NOUN
ap-652	289	91	will	will	AUX
ap-652	289	92	be	be	AUX
ap-652	289	93	named	name	VERB
ap-652	289	94	as	as	ADP
ap-652	289	95	the	the	DET
ap-652	289	96	modified	modified	ADJ
ap-652	289	97	static	static	ADJ
ap-652	289	98	matrix	matrix	NOUN
ap-652	289	99	.	.	PUNCT
ap-652	290	1	as	as	SCONJ
ap-652	290	2	written	write	VERB
ap-652	290	3	in	in	ADP
ap-652	290	4	section	section	NOUN
ap-652	290	5	2.1	2.1	NUM
ap-652	290	6	,	,	PUNCT
ap-652	290	7	a	a	DET
ap-652	290	8	particular	particular	ADJ
ap-652	290	9	engineering	engineering	NOUN
ap-652	290	10	constant	constant	ADJ
ap-652	290	11	can	can	AUX
ap-652	290	12	be	be	AUX
ap-652	290	13	expressed	express	VERB
ap-652	290	14	,	,	PUNCT
ap-652	290	15	from	from	ADP
ap-652	290	16	(	(	PUNCT
ap-652	290	17	2	2	NUM
ap-652	290	18	)	)	PUNCT
ap-652	290	19	or	or	CCONJ
ap-652	290	20	(	(	PUNCT
ap-652	290	21	3	3	NUM
ap-652	290	22	)	)	PUNCT
ap-652	290	23	,	,	PUNCT
ap-652	290	24	independently	independently	ADV
ap-652	290	25	of	of	ADP
ap-652	290	26	the	the	DET
ap-652	290	27	others	other	NOUN
ap-652	290	28	,	,	PUNCT
ap-652	290	29	if	if	SCONJ
ap-652	290	30	the	the	DET
ap-652	290	31	corresponding	correspond	VERB
ap-652	290	32	macroload	macroload	NOUN
ap-652	290	33	from	from	ADP
ap-652	290	34	table	table	NOUN
ap-652	290	35	1	1	NUM
ap-652	290	36	is	be	AUX
ap-652	290	37	applied	apply	VERB
ap-652	290	38	.	.	PUNCT
ap-652	291	1	then	then	ADV
ap-652	291	2	expressions	expression	NOUN
ap-652	291	3	(	(	PUNCT
ap-652	291	4	28–29	28–29	NUM
ap-652	291	5	)	)	PUNCT
ap-652	291	6	can	can	AUX
ap-652	291	7	be	be	AUX
ap-652	291	8	introduced	introduce	VERB
ap-652	291	9	and	and	CCONJ
ap-652	291	10	the	the	DET
ap-652	291	11	initial	initial	ADJ
ap-652	291	12	expression	expression	NOUN
ap-652	291	13	for	for	ADP
ap-652	291	14	the	the	DET
ap-652	291	15	bounding	bounding	NOUN
ap-652	291	16	procedure	procedure	NOUN
ap-652	291	17	,	,	PUNCT
ap-652	291	18	in	in	ADP
ap-652	291	19	terms	term	NOUN
ap-652	291	20	of	of	ADP
ap-652	291	21	normal	normal	ADJ
ap-652	291	22	forces	force	NOUN
ap-652	291	23	and	and	CCONJ
ap-652	291	24	geometrical	geometrical	ADJ
ap-652	291	25	parameters	parameter	NOUN
ap-652	291	26	,	,	PUNCT
ap-652	291	27	is	be	AUX
ap-652	291	28	obtained	obtain	VERB
ap-652	291	29	.	.	PUNCT
ap-652	292	1	the	the	DET
ap-652	292	2	bounding	bounding	NOUN
ap-652	292	3	procedure	procedure	NOUN
ap-652	292	4	is	be	AUX
ap-652	292	5	performed	perform	VERB
ap-652	292	6	using	use	VERB
ap-652	292	7	basic	basic	ADJ
ap-652	292	8	knowledge	knowledge	NOUN
ap-652	292	9	from	from	ADP
ap-652	292	10	linear	linear	ADJ
ap-652	292	11	algebra	algebra	PROPN
ap-652	292	12	and	and	CCONJ
ap-652	292	13	the	the	DET
ap-652	292	14	voigt	voigt	PROPN
ap-652	292	15	assumption	assumption	NOUN
ap-652	292	16	for	for	ADP
ap-652	292	17	the	the	DET
ap-652	292	18	upper	upper	ADJ
ap-652	292	19	bound	bind	VERB
ap-652	292	20	derivation	derivation	NOUN
ap-652	292	21	(	(	PUNCT
ap-652	292	22	uniform	uniform	ADJ
ap-652	292	23	local	local	ADJ
ap-652	292	24	strain	strain	NOUN
ap-652	292	25	)	)	PUNCT
ap-652	292	26	,	,	PUNCT
ap-652	292	27	and	and	CCONJ
ap-652	292	28	the	the	DET
ap-652	292	29	bound	bind	VERB
ap-652	292	30	is	be	AUX
ap-652	292	31	finally	finally	ADV
ap-652	292	32	expressed	express	VERB
ap-652	292	33	as	as	ADP
ap-652	292	34	a	a	DET
ap-652	292	35	linear	linear	ADJ
ap-652	292	36	function	function	NOUN
ap-652	292	37	of	of	ADP
ap-652	292	38	the	the	DET
ap-652	292	39	material	material	NOUN
ap-652	292	40	volume	volume	NOUN
ap-652	292	41	fraction	fraction	NOUN
ap-652	292	42	.	.	PUNCT
ap-652	293	1	the	the	DET
ap-652	293	2	maximality	maximality	NOUN
ap-652	293	3	conditions	condition	NOUN
ap-652	293	4	on	on	ADP
ap-652	293	5	possible	possible	ADJ
ap-652	293	6	normal	normal	ADJ
ap-652	293	7	forces	force	NOUN
ap-652	293	8	are	be	AUX
ap-652	293	9	then	then	ADV
ap-652	293	10	obtained	obtain	VERB
ap-652	293	11	as	as	ADP
ap-652	293	12	conditions	condition	NOUN
ap-652	293	13	that	that	PRON
ap-652	293	14	ensure	ensure	VERB
ap-652	293	15	equality	equality	NOUN
ap-652	293	16	with	with	ADP
ap-652	293	17	the	the	DET
ap-652	293	18	bound	bind	VERB
ap-652	293	19	.	.	PUNCT
ap-652	294	1	the	the	DET
ap-652	294	2	specifications	specification	NOUN
ap-652	294	3	in	in	ADP
ap-652	294	4	tab	tab	NOUN
ap-652	294	5	.	.	PUNCT
ap-652	294	6	1	1	NUM
ap-652	294	7	provide	provide	VERB
ap-652	294	8	the	the	DET
ap-652	294	9	additional	additional	ADJ
ap-652	294	10	constraints	constraint	NOUN
ap-652	294	11	on	on	ADP
ap-652	294	12	the	the	DET
ap-652	294	13	possible	possible	ADJ
ap-652	294	14	normal	normal	ADJ
ap-652	294	15	forces	force	NOUN
ap-652	294	16	that	that	PRON
ap-652	294	17	can	can	AUX
ap-652	294	18	be	be	AUX
ap-652	294	19	developed	develop	VERB
ap-652	294	20	in	in	ADP
ap-652	294	21	an	an	DET
ap-652	294	22	optimal	optimal	ADJ
ap-652	294	23	medium	medium	NOUN
ap-652	294	24	.	.	PUNCT
ap-652	295	1	using	use	VERB
ap-652	295	2	the	the	DET
ap-652	295	3	maximality	maximality	NOUN
ap-652	295	4	conditions	condition	NOUN
ap-652	295	5	,	,	PUNCT
ap-652	295	6	these	these	DET
ap-652	295	7	additional	additional	ADJ
ap-652	295	8	constraints	constraint	NOUN
ap-652	295	9	can	can	AUX
ap-652	295	10	be	be	AUX
ap-652	295	11	written	write	VERB
ap-652	295	12	in	in	ADP
ap-652	295	13	terms	term	NOUN
ap-652	295	14	of	of	ADP
ap-652	295	15	microstructure	microstructure	ADJ
ap-652	295	16	geometrical	geometrical	ADJ
ap-652	295	17	parameters	parameter	NOUN
ap-652	295	18	,	,	PUNCT
ap-652	295	19	as	as	SCONJ
ap-652	295	20	will	will	AUX
ap-652	295	21	be	be	AUX
ap-652	295	22	seen	see	VERB
ap-652	295	23	in	in	ADP
ap-652	295	24	section	section	NOUN
ap-652	295	25	3	3	NUM
ap-652	295	26	.	.	PUNCT
ap-652	296	1	for	for	ADP
ap-652	296	2	more	more	ADJ
ap-652	296	3	details	detail	NOUN
ap-652	296	4	on	on	ADP
ap-652	296	5	the	the	DET
ap-652	296	6	voigt	voigt	PROPN
ap-652	296	7	assumption	assumption	NOUN
ap-652	296	8	and	and	CCONJ
ap-652	296	9	bound	bind	VERB
ap-652	296	10	see	see	VERB
ap-652	296	11	e.g.	e.g.	ADV
ap-652	296	12	hill	hill	NOUN
ap-652	296	13	(	(	PUNCT
ap-652	296	14	1963	1963	NUM
ap-652	296	15	)	)	PUNCT
ap-652	296	16	.	.	PUNCT
ap-652	297	1	we	we	PRON
ap-652	297	2	only	only	ADV
ap-652	297	3	remark	remark	VERB
ap-652	297	4	that	that	SCONJ
ap-652	297	5	,	,	PUNCT
ap-652	297	6	when	when	SCONJ
ap-652	297	7	the	the	DET
ap-652	297	8	local	local	ADJ
ap-652	297	9	strains	strain	NOUN
ap-652	297	10	are	be	AUX
ap-652	297	11	uniform	uniform	ADJ
ap-652	297	12	throughout	throughout	ADP
ap-652	297	13	the	the	DET
ap-652	297	14	medium	medium	NOUN
ap-652	297	15	,	,	PUNCT
ap-652	297	16	then	then	ADV
ap-652	297	17	they	they	PRON
ap-652	297	18	are	be	AUX
ap-652	297	19	equal	equal	ADJ
ap-652	297	20	to	to	ADP
ap-652	297	21	the	the	DET
ap-652	297	22	macroscopic	macroscopic	ADJ
ap-652	297	23	strain	strain	NOUN
ap-652	297	24	and	and	CCONJ
ap-652	297	25	the	the	DET
ap-652	297	26	global	global	ADJ
ap-652	297	27	engineering	engineering	NOUN
ap-652	297	28	constant	constant	ADJ
ap-652	297	29	corresponding	correspond	VERB
ap-652	297	30	to	to	ADP
ap-652	297	31	such	such	DET
ap-652	297	32	a	a	DET
ap-652	297	33	macroload	macroload	NOUN
ap-652	297	34	reaches	reach	VERB
ap-652	297	35	its	its	PRON
ap-652	297	36	maximum	maximum	NOUN
ap-652	297	37	.	.	PUNCT
ap-652	298	1	since	since	SCONJ
ap-652	298	2	micro	micro	ADJ
ap-652	298	3	-	-	ADJ
ap-652	298	4	truss	truss	ADJ
ap-652	298	5	media	medium	NOUN
ap-652	298	6	are	be	AUX
ap-652	298	7	characterized	characterize	VERB
ap-652	298	8	by	by	ADP
ap-652	298	9	the	the	DET
ap-652	298	10	middle	middle	ADJ
ap-652	298	11	axes	axis	NOUN
ap-652	298	12	of	of	ADP
ap-652	298	13	the	the	DET
ap-652	298	14	bars	bar	NOUN
ap-652	298	15	,	,	PUNCT
ap-652	298	16	which	which	PRON
ap-652	298	17	(	(	PUNCT
ap-652	298	18	except	except	SCONJ
ap-652	298	19	for	for	ADP
ap-652	298	20	the	the	DET
ap-652	298	21	joints	joint	NOUN
ap-652	298	22	)	)	PUNCT
ap-652	298	23	correspond	correspond	VERB
ap-652	298	24	to	to	ADP
ap-652	298	25	the	the	DET
ap-652	298	26	”	"	PUNCT
ap-652	298	27	direction	direction	NOUN
ap-652	298	28	”	"	PUNCT
ap-652	298	29	of	of	ADP
ap-652	298	30	the	the	DET
ap-652	298	31	local	local	ADJ
ap-652	298	32	strain	strain	NOUN
ap-652	298	33	,	,	PUNCT
ap-652	298	34	voigt	voigt	PROPN
ap-652	298	35	assumption	assumption	NOUN
ap-652	298	36	implies	imply	VERB
ap-652	298	37	that	that	SCONJ
ap-652	298	38	the	the	DET
ap-652	298	39	local	local	ADJ
ap-652	298	40	displacements	displacement	NOUN
ap-652	298	41	of	of	ADP
ap-652	298	42	middle	middle	ADJ
ap-652	298	43	axes	axis	NOUN
ap-652	298	44	of	of	ADP
ap-652	298	45	the	the	DET
ap-652	298	46	bars	bar	NOUN
ap-652	298	47	,	,	PUNCT
ap-652	298	48	u	u	NOUN
ap-652	298	49	,	,	PUNCT
ap-652	298	50	coincide	coincide	VERB
ap-652	298	51	with	with	ADP
ap-652	298	52	the	the	DET
ap-652	298	53	linear	linear	ADJ
ap-652	298	54	part	part	NOUN
ap-652	298	55	of	of	ADP
ap-652	298	56	the	the	DET
ap-652	298	57	displacements	displacement	NOUN
ap-652	298	58	,	,	PUNCT
ap-652	298	59	i.e.	i.e.	X
ap-652	298	60	u	u	X
ap-652	298	61	e	e	X
ap-652	298	62	yi	yi	PROPN
ap-652	298	63	ij	ij	INTJ
ap-652	298	64	j	j	PROPN
ap-652	298	65	�	�	PROPN
ap-652	298	66	(	(	PUNCT
ap-652	298	67	the	the	DET
ap-652	298	68	summation	summation	NOUN
ap-652	298	69	convention	convention	NOUN
ap-652	298	70	is	be	AUX
ap-652	298	71	adopted	adopt	VERB
ap-652	298	72	)	)	PUNCT
ap-652	298	73	.	.	PUNCT
ap-652	299	1	this	this	DET
ap-652	299	2	requirement	requirement	NOUN
ap-652	299	3	states	state	VERB
ap-652	299	4	the	the	DET
ap-652	299	5	necessary	necessary	ADJ
ap-652	299	6	maximality	maximality	NOUN
ap-652	299	7	conditions	condition	NOUN
ap-652	299	8	on	on	ADP
ap-652	299	9	possible	possible	ADJ
ap-652	299	10	normal	normal	ADJ
ap-652	299	11	forces	force	NOUN
ap-652	299	12	,	,	PUNCT
ap-652	299	13	which	which	PRON
ap-652	299	14	can	can	AUX
ap-652	299	15	be	be	AUX
ap-652	299	16	written	write	VERB
ap-652	299	17	as	as	ADP
ap-652	299	18	:	:	PUNCT
ap-652	299	19	s	s	X
ap-652	299	20	e	e	NOUN
ap-652	299	21	nt	not	PART
ap-652	299	22	t	t	PROPN
ap-652	299	23	se	se	PROPN
ap-652	299	24	�	�	PROPN
ap-652	299	25	�	�	PROPN
ap-652	299	26	.	.	PUNCT
ap-652	300	1	(	(	PUNCT
ap-652	300	2	30	30	X
ap-652	300	3	)	)	PUNCT
ap-652	300	4	maximality	maximality	NOUN
ap-652	300	5	conditions	condition	NOUN
ap-652	300	6	(	(	PUNCT
ap-652	300	7	30	30	NUM
ap-652	300	8	)	)	PUNCT
ap-652	300	9	are	be	AUX
ap-652	300	10	not	not	PART
ap-652	300	11	sufficient	sufficient	ADJ
ap-652	300	12	,	,	PUNCT
ap-652	300	13	because	because	SCONJ
ap-652	300	14	the	the	DET
ap-652	300	15	requirement	requirement	NOUN
ap-652	300	16	of	of	ADP
ap-652	300	17	uniform	uniform	ADJ
ap-652	300	18	strain	strain	NOUN
ap-652	300	19	does	do	AUX
ap-652	300	20	not	not	PART
ap-652	300	21	exclude	exclude	VERB
ap-652	300	22	bars	bar	NOUN
ap-652	300	23	with	with	ADP
ap-652	300	24	zero	zero	NUM
ap-652	300	25	normal	normal	ADJ
ap-652	300	26	force	force	NOUN
ap-652	300	27	(	(	PUNCT
ap-652	300	28	zero	zero	NUM
ap-652	300	29	bars	bar	NOUN
ap-652	300	30	)	)	PUNCT
ap-652	300	31	.	.	PUNCT
ap-652	301	1	more	more	ADJ
ap-652	301	2	facts	fact	NOUN
ap-652	301	3	about	about	ADP
ap-652	301	4	the	the	DET
ap-652	301	5	relation	relation	NOUN
ap-652	301	6	between	between	ADP
ap-652	301	7	optimal	optimal	ADJ
ap-652	301	8	micro	micro	NOUN
ap-652	301	9	-	-	NOUN
ap-652	301	10	frames	frame	NOUN
ap-652	301	11	and	and	CCONJ
ap-652	301	12	the	the	DET
ap-652	301	13	voigt	voigt	PROPN
ap-652	301	14	bound	bind	VERB
ap-652	301	15	are	be	AUX
ap-652	301	16	given	give	VERB
ap-652	301	17	in	in	ADP
ap-652	301	18	the	the	DET
ap-652	301	19	appendix	appendix	NOUN
ap-652	301	20	.	.	PUNCT
ap-652	302	1	obviously	obviously	ADV
ap-652	302	2	,	,	PUNCT
ap-652	302	3	upper	upper	ADJ
ap-652	302	4	bounds	bound	NOUN
ap-652	302	5	determined	determine	VERB
ap-652	302	6	in	in	ADP
ap-652	302	7	the	the	DET
ap-652	302	8	way	way	NOUN
ap-652	302	9	described	describe	VERB
ap-652	302	10	in	in	ADP
ap-652	302	11	this	this	DET
ap-652	302	12	subsection	subsection	NOUN
ap-652	302	13	can	can	AUX
ap-652	302	14	be	be	AUX
ap-652	302	15	extremely	extremely	ADV
ap-652	302	16	large	large	ADJ
ap-652	302	17	and	and	CCONJ
ap-652	302	18	unrealistic	unrealistic	ADJ
ap-652	302	19	,	,	PUNCT
ap-652	302	20	because	because	SCONJ
ap-652	302	21	none	none	NOUN
ap-652	302	22	of	of	ADP
ap-652	302	23	the	the	DET
ap-652	302	24	restrictions	restriction	NOUN
ap-652	302	25	,	,	PUNCT
ap-652	302	26	e.g.	e.g.	ADV
ap-652	302	27	,	,	PUNCT
ap-652	302	28	topological	topological	ADJ
ap-652	302	29	connectivity	connectivity	NOUN
ap-652	302	30	or	or	CCONJ
ap-652	302	31	equilibrium	equilibrium	NOUN
ap-652	302	32	of	of	ADP
ap-652	302	33	the	the	DET
ap-652	302	34	joints	joint	NOUN
ap-652	302	35	,	,	PUNCT
ap-652	302	36	were	be	AUX
ap-652	302	37	considered	consider	VERB
ap-652	302	38	.	.	PUNCT
ap-652	303	1	however	however	ADV
ap-652	303	2	,	,	PUNCT
ap-652	303	3	if	if	SCONJ
ap-652	303	4	a	a	DET
ap-652	303	5	physical	physical	ADJ
ap-652	303	6	medium	medium	NOUN
ap-652	303	7	saturating	saturate	VERB
ap-652	303	8	the	the	DET
ap-652	303	9	bound	bind	VERB
ap-652	303	10	can	can	AUX
ap-652	303	11	be	be	AUX
ap-652	303	12	found	find	VERB
ap-652	303	13	,	,	PUNCT
ap-652	303	14	the	the	DET
ap-652	303	15	bound	bind	VERB
ap-652	303	16	would	would	AUX
ap-652	303	17	be	be	AUX
ap-652	303	18	proven	prove	VERB
ap-652	303	19	as	as	ADV
ap-652	303	20	optimal	optimal	ADJ
ap-652	303	21	.	.	PUNCT
ap-652	304	1	this	this	PRON
ap-652	304	2	is	be	AUX
ap-652	304	3	actually	actually	ADV
ap-652	304	4	achieved	achieve	VERB
ap-652	304	5	in	in	ADP
ap-652	304	6	all	all	DET
ap-652	304	7	the	the	DET
ap-652	304	8	cases	case	NOUN
ap-652	304	9	considered	consider	VERB
ap-652	304	10	in	in	ADP
ap-652	304	11	this	this	DET
ap-652	304	12	paper	paper	NOUN
ap-652	304	13	.	.	PUNCT
ap-652	305	1	3	3	NUM
ap-652	305	2	linearized	linearize	VERB
ap-652	305	3	bounds	bound	NOUN
ap-652	305	4	on	on	ADP
ap-652	305	5	effective	effective	ADJ
ap-652	305	6	properties	property	NOUN
ap-652	305	7	3.1	3.1	NUM
ap-652	305	8	bulk	bulk	ADJ
ap-652	305	9	modulus	modulus	NOUN
ap-652	305	10	k	k	X
ap-652	305	11	*	*	PUNCT
ap-652	305	12	(	(	PUNCT
ap-652	305	13	for	for	ADP
ap-652	305	14	effective	effective	ADJ
ap-652	305	15	isotropy	isotropy	NOUN
ap-652	305	16	or	or	CCONJ
ap-652	305	17	cubic	cubic	ADJ
ap-652	305	18	symmetry	symmetry	NOUN
ap-652	305	19	)	)	PUNCT
ap-652	305	20	if	if	SCONJ
ap-652	305	21	the	the	DET
ap-652	305	22	macroload	macroload	NOUN
ap-652	305	23	�	�	PROPN
ap-652	305	24	k	k	PROPN
ap-652	305	25	(	(	PUNCT
ap-652	305	26	table	table	NOUN
ap-652	305	27	1	1	NUM
ap-652	305	28	)	)	PUNCT
ap-652	305	29	is	be	AUX
ap-652	305	30	imposed	impose	VERB
ap-652	305	31	,	,	PUNCT
ap-652	305	32	then	then	ADV
ap-652	305	33	starting	start	VERB
ap-652	305	34	with	with	ADP
ap-652	305	35	(	(	PUNCT
ap-652	305	36	2	2	NUM
ap-652	305	37	)	)	PUNCT
ap-652	305	38	and	and	CCONJ
ap-652	305	39	introducing	introduce	VERB
ap-652	305	40	(	(	PUNCT
ap-652	305	41	28–29	28–29	NUM
ap-652	305	42	)	)	PUNCT
ap-652	305	43	,	,	PUNCT
ap-652	305	44	(	(	PUNCT
ap-652	305	45	26	26	NUM
ap-652	305	46	)	)	PUNCT
ap-652	305	47	and	and	CCONJ
ap-652	305	48	(	(	PUNCT
ap-652	305	49	27	27	NUM
ap-652	305	50	)	)	PUNCT
ap-652	305	51	,	,	PUNCT
ap-652	305	52	the	the	DET
ap-652	305	53	bulk	bulk	ADJ
ap-652	305	54	modulus	modulus	NOUN
ap-652	305	55	k	k	NOUN
ap-652	305	56	*	*	VERB
ap-652	305	57	can	can	AUX
ap-652	305	58	be	be	AUX
ap-652	305	59	expressed	express	VERB
ap-652	305	60	as	as	ADP
ap-652	305	61	:	:	PUNCT
ap-652	305	62	k	k	PROPN
ap-652	305	63	e	e	PROPN
ap-652	305	64	w	w	PROPN
ap-652	305	65	v	v	PROPN
ap-652	305	66	(	(	PUNCT
ap-652	305	67	v	v	PROPN
ap-652	305	68	v	v	NOUN
ap-652	305	69	m	m	NOUN
ap-652	305	70	2	2	NUM
ap-652	305	71	s	s	NOUN
ap-652	305	72	t	t	NOUN
ap-652	305	73	t	t	NOUN
ap-652	305	74	*	*	PUNCT
ap-652	305	75	)	)	PUNCT
ap-652	305	76	(	(	PUNCT
ap-652	305	77	)	)	PUNCT
ap-652	305	78	�	�	PROPN
ap-652	305	79	�	�	PROPN
ap-652	305	80	�	�	PROPN
ap-652	305	81	�	�	PROPN
ap-652	305	82	�	�	PROPN
ap-652	305	83	�	�	PROPN
ap-652	305	84	�	�	PROPN
ap-652	305	85	�	�	PROPN
ap-652	305	86	�	�	PROPN
ap-652	305	87	�	�	PROPN
ap-652	305	88	�	�	PROPN
ap-652	305	89	�	�	PROPN
ap-652	305	90	�	�	PROPN
ap-652	305	91	�	�	PROPN
ap-652	305	92	2	2	NUM
ap-652	305	93	3	3	NUM
ap-652	305	94	1	1	NUM
ap-652	305	95	9	9	NUM
ap-652	305	96	2	2	NUM
ap-652	305	97	1	1	NUM
ap-652	305	98	2	2	NUM
ap-652	305	99	3	3	NUM
ap-652	305	100	2	2	NUM
ap-652	305	101	n	n	NOUN
ap-652	305	102	r	r	NOUN
ap-652	305	103	r	r	NOUN
ap-652	305	104	r	r	NOUN
ap-652	305	105	n	n	NOUN
ap-652	305	106	l	l	NOUN
ap-652	305	107	n	n	NUM
ap-652	305	108	2	2	NUM
ap-652	305	109	2	2	NUM
ap-652	305	110	9n	9n	NUM
ap-652	305	111	�	�	PROPN
ap-652	305	112	s	s	PART
ap-652	305	113	,	,	PUNCT
ap-652	305	114	,	,	PUNCT
ap-652	305	115	(	(	PUNCT
ap-652	305	116	31	31	NUM
ap-652	305	117	)	)	PUNCT
ap-652	305	118	providing	provide	VERB
ap-652	305	119	the	the	DET
ap-652	305	120	maximality	maximality	NOUN
ap-652	305	121	condition	condition	NOUN
ap-652	305	122	n	n	PROPN
ap-652	305	123	//	//	NUM
ap-652	305	124	l	l	NOUN
ap-652	305	125	,	,	PUNCT
ap-652	305	126	(	(	PUNCT
ap-652	305	127	32	32	NUM
ap-652	305	128	)	)	PUNCT
ap-652	305	129	(	(	PUNCT
ap-652	305	130	i.e.	i.e.	X
ap-652	305	131	the	the	DET
ap-652	305	132	local	local	ADJ
ap-652	305	133	stresses	stress	NOUN
ap-652	305	134	are	be	AUX
ap-652	305	135	required	require	VERB
ap-652	305	136	to	to	PART
ap-652	305	137	be	be	AUX
ap-652	305	138	constant	constant	ADJ
ap-652	305	139	all	all	PRON
ap-652	305	140	ever	ever	ADV
ap-652	305	141	the	the	DET
ap-652	305	142	bars	bar	NOUN
ap-652	305	143	)	)	PUNCT
ap-652	305	144	and	and	CCONJ
ap-652	305	145	the	the	DET
ap-652	305	146	bound	bound	ADJ
ap-652	305	147	k	k	PROPN
ap-652	305	148	s	s	PROPN
ap-652	305	149	�	�	PROPN
ap-652	305	150	*	*	PROPN
ap-652	305	151	9	9	NUM
ap-652	305	152	.	.	X
ap-652	306	1	using	use	VERB
ap-652	306	2	(	(	PUNCT
ap-652	306	3	32	32	NUM
ap-652	306	4	)	)	PUNCT
ap-652	306	5	,	,	PUNCT
ap-652	306	6	additional	additional	ADJ
ap-652	306	7	constraints	constraint	NOUN
ap-652	306	8	from	from	ADP
ap-652	306	9	table	table	NOUN
ap-652	306	10	1	1	NUM
ap-652	306	11	can	can	AUX
ap-652	306	12	be	be	AUX
ap-652	306	13	written	write	VERB
ap-652	306	14	in	in	ADP
ap-652	306	15	terms	term	NOUN
ap-652	306	16	of	of	ADP
ap-652	306	17	geometrical	geometrical	ADJ
ap-652	306	18	parameters	parameter	NOUN
ap-652	306	19	as	as	ADP
ap-652	306	20	:	:	PUNCT
ap-652	306	21	r	r	NOUN
ap-652	306	22	l	l	NOUN
ap-652	306	23	r	r	NOUN
ap-652	306	24	l	l	NOUN
ap-652	306	25	r	r	NOUN
ap-652	306	26	l	l	NOUN
ap-652	306	27	q	q	X
ap-652	306	28	l1	l1	PROPN
ap-652	306	29	2	2	NUM
ap-652	306	30	3	3	NUM
ap-652	306	31	1	1	NUM
ap-652	306	32	2	2	NUM
ap-652	306	33	3	3	NUM
ap-652	306	34	�	�	PROPN
ap-652	306	35	�	�	PROPN
ap-652	306	36	�	�	PROPN
ap-652	306	37	�	�	PROPN
ap-652	306	38	�	�	PROPN
ap-652	306	39	%	%	PROPN
ap-652	306	40	�	�	PROPN
ap-652	306	41	�	�	PROPN
ap-652	306	42	t	t	PROPN
ap-652	306	43	t	t	PROPN
ap-652	306	44	t	t	PROPN
ap-652	306	45	j	j	PROPN
ap-652	306	46	j	j	PROPN
ap-652	306	47	,	,	PUNCT
ap-652	306	48	,	,	PUNCT
ap-652	306	49	&	&	CCONJ
ap-652	306	50	.	.	PUNCT
ap-652	307	1	(	(	PUNCT
ap-652	307	2	33	33	NUM
ap-652	307	3	)	)	PUNCT
ap-652	307	4	equation	equation	NOUN
ap-652	307	5	(	(	PUNCT
ap-652	307	6	30	30	NUM
ap-652	307	7	)	)	PUNCT
ap-652	307	8	,	,	PUNCT
ap-652	307	9	which	which	PRON
ap-652	307	10	should	should	AUX
ap-652	307	11	also	also	ADV
ap-652	307	12	be	be	AUX
ap-652	307	13	implemented	implement	VERB
ap-652	307	14	,	,	PUNCT
ap-652	307	15	does	do	AUX
ap-652	307	16	not	not	PART
ap-652	307	17	in	in	ADP
ap-652	307	18	this	this	DET
ap-652	307	19	case	case	NOUN
ap-652	307	20	bring	bring	VERB
ap-652	307	21	anything	anything	PRON
ap-652	307	22	new	new	ADJ
ap-652	307	23	.	.	PUNCT
ap-652	308	1	it	it	PRON
ap-652	308	2	is	be	AUX
ap-652	308	3	seen	see	VERB
ap-652	308	4	that	that	SCONJ
ap-652	308	5	it	it	PRON
ap-652	308	6	corresponds	correspond	VERB
ap-652	308	7	directly	directly	ADV
ap-652	308	8	to	to	ADP
ap-652	308	9	(	(	PUNCT
ap-652	308	10	32	32	NUM
ap-652	308	11	)	)	PUNCT
ap-652	308	12	,	,	PUNCT
ap-652	308	13	after	after	SCONJ
ap-652	308	14	conditions	condition	NOUN
ap-652	308	15	from	from	ADP
ap-652	308	16	table	table	NOUN
ap-652	308	17	1	1	NUM
ap-652	308	18	have	have	AUX
ap-652	308	19	been	be	AUX
ap-652	308	20	implemented	implement	VERB
ap-652	308	21	,	,	PUNCT
ap-652	308	22	n	n	CCONJ
ap-652	308	23	l	l	PROPN
ap-652	308	24	�	�	PROPN
ap-652	308	25	�	�	PROPN
ap-652	308	26	3k	3k	X
ap-652	308	27	*	*	PUNCT
ap-652	308	28	.	.	PUNCT
ap-652	309	1	we	we	PRON
ap-652	309	2	can	can	AUX
ap-652	309	3	check	check	VERB
ap-652	309	4	that	that	PRON
ap-652	309	5	in	in	ADP
ap-652	309	6	this	this	DET
ap-652	309	7	case	case	NOUN
ap-652	309	8	(	(	PUNCT
ap-652	309	9	30	30	NUM
ap-652	309	10	)	)	PUNCT
ap-652	309	11	ensures	ensure	VERB
ap-652	309	12	not	not	PART
ap-652	309	13	only	only	ADV
ap-652	309	14	a	a	DET
ap-652	309	15	necessary	necessary	ADJ
ap-652	309	16	but	but	CCONJ
ap-652	309	17	also	also	ADV
ap-652	309	18	a	a	DET
ap-652	309	19	sufficient	sufficient	ADJ
ap-652	309	20	maximality	maximality	NOUN
ap-652	309	21	condition	condition	NOUN
ap-652	309	22	,	,	PUNCT
ap-652	309	23	because	because	SCONJ
ap-652	309	24	zero	zero	NUM
ap-652	309	25	bars	bar	NOUN
ap-652	309	26	are	be	AUX
ap-652	309	27	excluded	exclude	VERB
ap-652	309	28	as	as	ADP
ap-652	309	29	n	n	PROPN
ap-652	309	30	a	a	DET
ap-652	309	31	ii	ii	PROPN
ap-652	309	32	i~	i~	PROPN
ap-652	309	33	�	�	PROPN
ap-652	309	34	�	�	PROPN
ap-652	309	35	0	0	NUM
ap-652	309	36	,	,	PUNCT
ap-652	309	37	where	where	SCONJ
ap-652	309	38	“	"	PUNCT
ap-652	309	39	~	~	NOUN
ap-652	309	40	”	"	PUNCT
ap-652	309	41	means	mean	VERB
ap-652	309	42	proportionality	proportionality	NOUN
ap-652	309	43	.	.	PUNCT
ap-652	310	1	the	the	DET
ap-652	310	2	conditions	condition	NOUN
ap-652	310	3	stated	state	VERB
ap-652	310	4	in	in	ADP
ap-652	310	5	(	(	PUNCT
ap-652	310	6	32–33	32–33	NUM
ap-652	310	7	)	)	PUNCT
ap-652	310	8	are	be	AUX
ap-652	310	9	the	the	DET
ap-652	310	10	necessary	necessary	ADJ
ap-652	310	11	and	and	CCONJ
ap-652	310	12	sufficient	sufficient	ADJ
ap-652	310	13	conditions	condition	NOUN
ap-652	310	14	on	on	ADP
ap-652	310	15	k*-optimal	k*-optimal	ADJ
ap-652	310	16	media	medium	NOUN
ap-652	310	17	.	.	PUNCT
ap-652	311	1	(	(	PUNCT
ap-652	311	2	32	32	NUM
ap-652	311	3	)	)	PUNCT
ap-652	311	4	can	can	AUX
ap-652	311	5	not	not	PART
ap-652	311	6	be	be	AUX
ap-652	311	7	expressed	express	VERB
ap-652	311	8	only	only	ADV
ap-652	311	9	in	in	ADP
ap-652	311	10	terms	term	NOUN
ap-652	311	11	of	of	ADP
ap-652	311	12	geometrical	geometrical	ADJ
ap-652	311	13	parameters	parameter	NOUN
ap-652	311	14	,	,	PUNCT
ap-652	311	15	and	and	CCONJ
ap-652	311	16	therefore	therefore	ADV
ap-652	311	17	verification	verification	NOUN
ap-652	311	18	of	of	ADP
ap-652	311	19	the	the	DET
ap-652	311	20	k*-optimality	k*-optimality	NOUN
ap-652	311	21	of	of	ADP
ap-652	311	22	some	some	DET
ap-652	311	23	medium	medium	NOUN
ap-652	311	24	requires	require	VERB
ap-652	311	25	the	the	DET
ap-652	311	26	determination	determination	NOUN
ap-652	311	27	of	of	ADP
ap-652	311	28	the	the	DET
ap-652	311	29	normal	normal	ADJ
ap-652	311	30	forces	force	NOUN
ap-652	311	31	in	in	ADP
ap-652	311	32	n.	n.	NOUN
ap-652	311	33	the	the	DET
ap-652	311	34	bound	bind	VERB
ap-652	311	35	is	be	AUX
ap-652	311	36	optimal	optimal	ADJ
ap-652	311	37	,	,	PUNCT
ap-652	311	38	because	because	SCONJ
ap-652	311	39	several	several	ADJ
ap-652	311	40	known	know	VERB
ap-652	311	41	media	medium	NOUN
ap-652	311	42	saturate	saturate	VERB
ap-652	311	43	it	it	PRON
ap-652	311	44	.	.	PUNCT
ap-652	312	1	the	the	DET
ap-652	312	2	simplest	simple	ADJ
ap-652	312	3	k*-optimal	k*-optimal	ADJ
ap-652	312	4	medium	medium	NOUN
ap-652	312	5	is	be	AUX
ap-652	312	6	a	a	DET
ap-652	312	7	regular	regular	ADJ
ap-652	312	8	cubic	cubic	ADJ
ap-652	312	9	lattice	lattice	NOUN
ap-652	312	10	(	(	PUNCT
ap-652	312	11	fig	fig	NOUN
ap-652	312	12	.	.	PUNCT
ap-652	312	13	5	5	NUM
ap-652	312	14	)	)	PUNCT
ap-652	312	15	(	(	PUNCT
ap-652	312	16	see	see	VERB
ap-652	312	17	warren	warren	PROPN
ap-652	312	18	and	and	CCONJ
ap-652	312	19	kraynik	kraynik	X
ap-652	312	20	(	(	PUNCT
ap-652	312	21	1988	1988	NUM
ap-652	312	22	)	)	PUNCT
ap-652	312	23	,	,	PUNCT
ap-652	312	24	dimitrovová	dimitrovová	NOUN
ap-652	312	25	(	(	PUNCT
ap-652	312	26	1999));	1999));	NUM
ap-652	312	27	where	where	SCONJ
ap-652	312	28	it	it	PRON
ap-652	312	29	is	be	AUX
ap-652	312	30	easy	easy	ADJ
ap-652	312	31	to	to	PART
ap-652	312	32	verify	verify	VERB
ap-652	312	33	conditions	condition	NOUN
ap-652	312	34	(	(	PUNCT
ap-652	312	35	32–33	32–33	NUM
ap-652	312	36	)	)	PUNCT
ap-652	312	37	.	.	PUNCT
ap-652	313	1	the	the	DET
ap-652	313	2	class	class	NOUN
ap-652	313	3	of	of	ADP
ap-652	313	4	periodic	periodic	ADJ
ap-652	313	5	k*-optimal	k*-optimal	ADJ
ap-652	313	6	media	medium	NOUN
ap-652	313	7	can	can	AUX
ap-652	313	8	be	be	AUX
ap-652	313	9	extended	extend	VERB
ap-652	313	10	by	by	ADP
ap-652	313	11	the	the	DET
ap-652	313	12	class	class	NOUN
ap-652	313	13	of	of	ADP
ap-652	313	14	media	medium	NOUN
ap-652	313	15	with	with	ADP
ap-652	313	16	a	a	DET
ap-652	313	17	random	random	ADJ
ap-652	313	18	microstructure	microstructure	NOUN
ap-652	313	19	,	,	PUNCT
ap-652	313	20	where	where	SCONJ
ap-652	313	21	a	a	DET
ap-652	313	22	basic	basic	ADJ
ap-652	313	23	cell	cell	NOUN
ap-652	313	24	of	of	ADP
ap-652	313	25	some	some	DET
ap-652	313	26	k*-optimal	k*-optimal	ADJ
ap-652	313	27	medium	medium	NOUN
ap-652	313	28	appears	appear	VERB
ap-652	313	29	in	in	ADP
ap-652	313	30	the	the	DET
ap-652	313	31	representative	representative	ADJ
ap-652	313	32	volume	volume	NOUN
ap-652	313	33	178	178	NUM
ap-652	313	34	©	©	PROPN
ap-652	313	35	czech	czech	PROPN
ap-652	313	36	technical	technical	PROPN
ap-652	313	37	university	university	PROPN
ap-652	313	38	publishing	publishing	NOUN
ap-652	313	39	house	house	NOUN
ap-652	313	40	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	313	41	acta	acta	PROPN
ap-652	313	42	polytechnica	polytechnica	PROPN
ap-652	313	43	vol	vol	NOUN
ap-652	313	44	.	.	PROPN
ap-652	314	1	44	44	NUM
ap-652	314	2	no.5–6/2004	no.5–6/2004	PROPN
ap-652	314	3	1y	1y	NUM
ap-652	314	4	2y	2y	ADJ
ap-652	314	5	3y	3y	ADJ
ap-652	314	6	g1a	g1a	VERB
ap-652	314	7	fig	fig	NOUN
ap-652	314	8	.	.	PUNCT
ap-652	315	1	5	5	NUM
ap-652	315	2	:	:	PUNCT
ap-652	315	3	the	the	DET
ap-652	315	4	regular	regular	ADJ
ap-652	315	5	cubic	cubic	ADJ
ap-652	315	6	lattice	lattice	NOUN
ap-652	315	7	element	element	NOUN
ap-652	315	8	with	with	ADP
ap-652	315	9	all	all	DET
ap-652	315	10	possible	possible	ADJ
ap-652	315	11	rotations	rotation	NOUN
ap-652	315	12	with	with	ADP
ap-652	315	13	the	the	DET
ap-652	315	14	same	same	ADJ
ap-652	315	15	probability	probability	NOUN
ap-652	315	16	.	.	PUNCT
ap-652	316	1	because	because	SCONJ
ap-652	316	2	the	the	DET
ap-652	316	3	bulk	bulk	ADJ
ap-652	316	4	modulus	modulus	NOUN
ap-652	316	5	is	be	AUX
ap-652	316	6	invariant	invariant	ADJ
ap-652	316	7	under	under	ADP
ap-652	316	8	orientational	orientational	ADJ
ap-652	316	9	averaging	averaging	NOUN
ap-652	316	10	,	,	PUNCT
ap-652	316	11	the	the	DET
ap-652	316	12	bulk	bulk	ADJ
ap-652	316	13	modulus	modulus	NOUN
ap-652	316	14	of	of	ADP
ap-652	316	15	the	the	DET
ap-652	316	16	new	new	ADJ
ap-652	316	17	random	random	ADJ
ap-652	316	18	medium	medium	NOUN
ap-652	316	19	will	will	AUX
ap-652	316	20	be	be	AUX
ap-652	316	21	the	the	DET
ap-652	316	22	same	same	ADJ
ap-652	316	23	as	as	ADP
ap-652	316	24	for	for	ADP
ap-652	316	25	the	the	DET
ap-652	316	26	corresponding	corresponding	ADJ
ap-652	316	27	periodic	periodic	ADJ
ap-652	316	28	medium	medium	NOUN
ap-652	316	29	,	,	PUNCT
ap-652	316	30	dimitrovová	dimitrovová	NOUN
ap-652	316	31	(	(	PUNCT
ap-652	316	32	1999	1999	NUM
ap-652	316	33	)	)	PUNCT
ap-652	316	34	.	.	PUNCT
ap-652	317	1	3.2	3.2	NUM
ap-652	317	2	shear	shear	NOUN
ap-652	317	3	modulus	modulus	NOUN
ap-652	317	4	g1	g1	PROPN
ap-652	317	5	*	*	PUNCT
ap-652	317	6	(	(	PUNCT
ap-652	317	7	for	for	ADP
ap-652	317	8	effective	effective	ADJ
ap-652	317	9	cubic	cubic	ADJ
ap-652	317	10	symmetry	symmetry	NOUN
ap-652	317	11	)	)	PUNCT
ap-652	317	12	if	if	SCONJ
ap-652	317	13	macroload	macroload	VERB
ap-652	317	14	�	�	PROPN
ap-652	317	15	1	1	NUM
ap-652	317	16	g	g	NOUN
ap-652	317	17	(	(	PUNCT
ap-652	317	18	see	see	VERB
ap-652	317	19	table	table	NOUN
ap-652	317	20	1	1	NUM
ap-652	317	21	)	)	PUNCT
ap-652	317	22	is	be	AUX
ap-652	317	23	imposed	impose	VERB
ap-652	317	24	,	,	PUNCT
ap-652	317	25	then	then	ADV
ap-652	317	26	one	one	PRON
ap-652	317	27	has	have	VERB
ap-652	317	28	:	:	PUNCT
ap-652	317	29	g	g	PROPN
ap-652	317	30	v	v	PROPN
ap-652	317	31	s	s	ADP
ap-652	317	32	t	t	NOUN
ap-652	317	33	t	t	PROPN
ap-652	317	34	t	t	PROPN
ap-652	317	35	1	1	NUM
ap-652	317	36	3	3	NUM
ap-652	317	37	2	2	NUM
ap-652	317	38	2	2	NUM
ap-652	317	39	2	2	NUM
ap-652	317	40	1	1	NUM
ap-652	317	41	2	2	NUM
ap-652	317	42	2	2	NUM
ap-652	317	43	1	1	NUM
ap-652	317	44	2	2	NUM
ap-652	317	45	2	2	NUM
ap-652	317	46	1	1	NUM
ap-652	317	47	6	6	NUM
ap-652	317	48	6	6	NUM
ap-652	317	49	*	*	PUNCT
ap-652	317	50	(	(	PUNCT
ap-652	317	51	)	)	PUNCT
ap-652	317	52	(	(	PUNCT
ap-652	317	53	)	)	PUNCT
ap-652	317	54	(	(	PUNCT
ap-652	317	55	)	)	PUNCT
ap-652	317	56	cos	cos	PROPN
ap-652	317	57	(	(	PUNCT
ap-652	317	58	�	�	PROPN
ap-652	317	59	�	�	PROPN
ap-652	317	60	�	�	PROPN
ap-652	317	61	�	�	PROPN
ap-652	317	62	�	�	PROPN
ap-652	317	63	�	�	PROPN
ap-652	317	64	�	�	PROPN
ap-652	317	65	�	�	PROPN
ap-652	317	66	p	p	PROPN
ap-652	318	1	n	n	PROPN
ap-652	318	2	p	p	NOUN
ap-652	318	3	n	n	CCONJ
ap-652	318	4	p	p	NOUN
ap-652	318	5	n	n	CCONJ
ap-652	318	6	n	n	NOUN
ap-652	318	7	p	p	NOUN
ap-652	318	8	n	n	NOUN
ap-652	318	9	,	,	PUNCT
ap-652	319	1	)	)	PUNCT
ap-652	319	2	cos	cos	PROPN
ap-652	319	3	(	(	PUNCT
ap-652	319	4	,	,	PUNCT
ap-652	319	5	)	)	PUNCT
ap-652	319	6	cos	cos	PROPN
ap-652	319	7	(	(	PUNCT
ap-652	319	8	,	,	PUNCT
ap-652	319	9	)	)	PUNCT
ap-652	320	1	p	p	X
ap-652	320	2	p	p	X
ap-652	320	3	n	n	PROPN
ap-652	320	4	p	p	NOUN
ap-652	320	5	l	l	NOUN
ap-652	320	6	p	p	NOUN
ap-652	320	7	n	n	CCONJ
ap-652	320	8	p	p	NOUN
ap-652	320	9	l	l	NOUN
ap-652	320	10	1	1	NUM
ap-652	320	11	2	2	NUM
ap-652	320	12	2	2	NUM
ap-652	320	13	2	2	NUM
ap-652	320	14	2	2	NUM
ap-652	320	15	2	2	NUM
ap-652	320	16	3	3	NUM
ap-652	320	17	2	2	NUM
ap-652	320	18	2	2	NUM
ap-652	320	19	3	3	NUM
ap-652	320	20	2	2	NUM
ap-652	320	21	3	3	NUM
ap-652	320	22	�	�	PROPN
ap-652	320	23	�	�	PROPN
ap-652	320	24	�	�	PROPN
ap-652	320	25	�	�	PROPN
ap-652	320	26	�	�	PROPN
ap-652	320	27	�	�	PROPN
ap-652	320	28	�	�	PROPN
ap-652	320	29	�	�	PROPN
ap-652	320	30	�	�	PROPN
ap-652	320	31	s	s	PART
ap-652	320	32	p	p	NOUN
ap-652	320	33	n	n	PRON
ap-652	320	34	p	p	NOUN
ap-652	320	35	p	p	PROPN
ap-652	320	36	n	n	PROPN
ap-652	320	37	p	p	NOUN
ap-652	320	38	p	p	PROPN
ap-652	320	39	p	p	X
ap-652	320	40	p	p	X
ap-652	320	41	q	q	X
ap-652	320	42	q	q	X
ap-652	320	43	q	q	NOUN
ap-652	320	44	1	1	NUM
ap-652	320	45	2	2	NUM
ap-652	320	46	2	2	NUM
ap-652	320	47	1	1	NUM
ap-652	320	48	2	2	NUM
ap-652	320	49	2	2	NUM
ap-652	320	50	2	2	NUM
ap-652	320	51	2	2	NUM
ap-652	320	52	1	1	NUM
ap-652	320	53	2	2	NUM
ap-652	320	54	2	2	NUM
ap-652	320	55	2	2	NUM
ap-652	320	56	3	3	NUM
ap-652	320	57	2	2	NUM
ap-652	320	58	1	1	NUM
ap-652	320	59	2	2	NUM
ap-652	320	60	2	2	NUM
ap-652	320	61	2	2	NUM
ap-652	320	62	3	3	NUM
ap-652	320	63	2	2	NUM
ap-652	320	64	cos	cos	X
ap-652	320	65	(	(	PUNCT
ap-652	320	66	,	,	PUNCT
ap-652	320	67	)	)	PUNCT
ap-652	320	68	cos	cos	PROPN
ap-652	320	69	(	(	PUNCT
ap-652	320	70	,	,	PUNCT
ap-652	320	71	)	)	PUNCT
ap-652	320	72	�	�	PROPN
ap-652	320	73	�	�	PROPN
ap-652	320	74	�	�	PROPN
ap-652	320	75	�	�	PROPN
ap-652	320	76	�	�	PROPN
ap-652	320	77	�	�	PROPN
ap-652	320	78	p	p	PROPN
ap-652	320	79	n	n	PROPN
ap-652	320	80	p	p	NOUN
ap-652	320	81	p	p	PROPN
ap-652	320	82	p	p	X
ap-652	320	83	p	p	X
ap-652	320	84	q	q	X
ap-652	320	85	q	q	X
ap-652	320	86	q	q	NOUN
ap-652	320	87	3	3	NUM
ap-652	320	88	2	2	NUM
ap-652	320	89	2	2	NUM
ap-652	320	90	3	3	NUM
ap-652	320	91	1	1	NUM
ap-652	320	92	2	2	NUM
ap-652	320	93	2	2	NUM
ap-652	320	94	2	2	NUM
ap-652	320	95	3	3	NUM
ap-652	320	96	2	2	NUM
ap-652	320	97	1	1	NUM
ap-652	320	98	2	2	NUM
ap-652	320	99	2	2	NUM
ap-652	320	100	2	2	NUM
ap-652	320	101	3	3	NUM
ap-652	320	102	2	2	NUM
ap-652	320	103	cos	cos	X
ap-652	320	104	(	(	PUNCT
ap-652	320	105	,	,	PUNCT
ap-652	320	106	)	)	PUNCT
ap-652	320	107	.	.	PUNCT
ap-652	321	1	(	(	PUNCT
ap-652	321	2	34	34	NUM
ap-652	321	3	)	)	PUNCT
ap-652	321	4	according	accord	VERB
ap-652	321	5	to	to	ADP
ap-652	321	6	table	table	NOUN
ap-652	321	7	1	1	NUM
ap-652	321	8	,	,	PUNCT
ap-652	321	9	additional	additional	ADJ
ap-652	321	10	constraints	constraint	NOUN
ap-652	321	11	on	on	ADP
ap-652	321	12	possible	possible	ADJ
ap-652	321	13	n	n	NUM
ap-652	321	14	are	be	AUX
ap-652	321	15	:	:	PUNCT
ap-652	321	16	n	n	PRON
ap-652	321	17	l	l	NOUN
ap-652	321	18	n	n	NUM
ap-652	321	19	q%	q%	NOUN
ap-652	321	20	%	%	INTJ
ap-652	321	21	�	�	PROPN
ap-652	321	22	�	�	PROPN
ap-652	321	23	&	&	CCONJ
ap-652	321	24	jj	jj	PROPN
ap-652	321	25	1	1	NUM
ap-652	321	26	2	2	NUM
ap-652	321	27	3	3	NUM
ap-652	321	28	,	,	PUNCT
ap-652	321	29	,	,	PUNCT
ap-652	321	30	.	.	PUNCT
ap-652	322	1	(	(	PUNCT
ap-652	322	2	35	35	NUM
ap-652	322	3	)	)	PUNCT
ap-652	322	4	if	if	SCONJ
ap-652	322	5	q	q	PROPN
ap-652	322	6	0j	0j	NUM
ap-652	322	7	j	j	PROPN
ap-652	322	8	�	�	PROPN
ap-652	322	9	�	�	PROPN
ap-652	322	10	�	�	PROPN
ap-652	322	11	1	1	NUM
ap-652	322	12	2	2	NUM
ap-652	322	13	3	3	NUM
ap-652	322	14	,	,	PUNCT
ap-652	322	15	,	,	PUNCT
ap-652	322	16	and	and	CCONJ
ap-652	322	17	n	n	PRON
ap-652	322	18	p/	p/	NOUN
ap-652	322	19	/	/	PUNCT
ap-652	322	20	,	,	PUNCT
ap-652	322	21	,	,	PUNCT
ap-652	322	22	j	j	PROPN
ap-652	322	23	j	j	PROPN
ap-652	322	24	�	�	PROPN
ap-652	322	25	�	�	PROPN
ap-652	322	26	1	1	NUM
ap-652	322	27	2	2	NUM
ap-652	322	28	3	3	NUM
ap-652	322	29	,	,	PUNCT
ap-652	322	30	then	then	ADV
ap-652	322	31	the	the	DET
ap-652	322	32	maximum	maximum	NOUN
ap-652	322	33	in	in	ADP
ap-652	322	34	(	(	PUNCT
ap-652	322	35	34	34	NUM
ap-652	322	36	)	)	PUNCT
ap-652	322	37	would	would	AUX
ap-652	322	38	be	be	AUX
ap-652	322	39	s/3	s/3	NOUN
ap-652	322	40	.	.	PUNCT
ap-652	323	1	however	however	ADV
ap-652	323	2	none	none	NOUN
ap-652	323	3	physical	physical	ADJ
ap-652	323	4	medium	medium	NOUN
ap-652	323	5	could	could	AUX
ap-652	323	6	fulfill	fulfill	VERB
ap-652	323	7	all	all	DET
ap-652	323	8	these	these	DET
ap-652	323	9	conditions	condition	NOUN
ap-652	323	10	,	,	PUNCT
ap-652	323	11	as	as	SCONJ
ap-652	323	12	will	will	AUX
ap-652	323	13	be	be	AUX
ap-652	323	14	shown	show	VERB
ap-652	323	15	in	in	ADP
ap-652	323	16	the	the	DET
ap-652	323	17	following	following	NOUN
ap-652	323	18	.	.	PUNCT
ap-652	324	1	in	in	ADP
ap-652	324	2	order	order	NOUN
ap-652	324	3	to	to	PART
ap-652	324	4	determine	determine	VERB
ap-652	324	5	the	the	DET
ap-652	324	6	real	real	ADJ
ap-652	324	7	maximum	maximum	NOUN
ap-652	324	8	,	,	PUNCT
ap-652	324	9	it	it	PRON
ap-652	324	10	is	be	AUX
ap-652	324	11	necessary	necessary	ADJ
ap-652	324	12	to	to	PART
ap-652	324	13	realize	realize	VERB
ap-652	324	14	that	that	SCONJ
ap-652	324	15	any	any	DET
ap-652	324	16	�	�	NOUN
ap-652	324	17	1	1	NUM
ap-652	324	18	g	g	NOUN
ap-652	324	19	can	can	AUX
ap-652	324	20	be	be	AUX
ap-652	324	21	written	write	VERB
ap-652	324	22	as	as	ADP
ap-652	324	23	a	a	DET
ap-652	324	24	linear	linear	ADJ
ap-652	324	25	combination	combination	NOUN
ap-652	324	26	of	of	ADP
ap-652	324	27	three	three	NUM
ap-652	324	28	basic	basic	ADJ
ap-652	324	29	cases	case	NOUN
ap-652	324	30	�	�	PROPN
ap-652	324	31	�	�	PROPN
ap-652	324	32	22	22	NUM
ap-652	324	33	33	33	NUM
ap-652	324	34	1	1	NUM
ap-652	324	35	�	�	PROPN
ap-652	324	36	�	�	PROPN
ap-652	324	37	,	,	PUNCT
ap-652	324	38	�	�	PROPN
ap-652	324	39	�	�	PROPN
ap-652	324	40	33	33	NUM
ap-652	324	41	11	11	NUM
ap-652	324	42	1	1	NUM
ap-652	324	43	�	�	PROPN
ap-652	324	44	�	�	PROPN
ap-652	324	45	and	and	CCONJ
ap-652	324	46	�	�	PROPN
ap-652	324	47	�	�	PROPN
ap-652	324	48	11	11	NUM
ap-652	324	49	22	22	NUM
ap-652	324	50	1	1	NUM
ap-652	324	51	�	�	PROPN
ap-652	324	52	�	�	PROPN
ap-652	324	53	.	.	PUNCT
ap-652	325	1	in	in	ADP
ap-652	325	2	each	each	DET
ap-652	325	3	of	of	ADP
ap-652	325	4	them	they	PRON
ap-652	325	5	local	local	ADJ
ap-652	325	6	strains	strain	NOUN
ap-652	325	7	must	must	AUX
ap-652	325	8	be	be	AUX
ap-652	325	9	uniform	uniform	ADJ
ap-652	325	10	according	accord	VERB
ap-652	325	11	to	to	ADP
ap-652	325	12	(	(	PUNCT
ap-652	325	13	30	30	NUM
ap-652	325	14	)	)	PUNCT
ap-652	325	15	and	and	CCONJ
ap-652	325	16	the	the	DET
ap-652	325	17	value	value	NOUN
ap-652	325	18	of	of	ADP
ap-652	325	19	the	the	DET
ap-652	325	20	correspondingg1	correspondingg1	NOUN
ap-652	325	21	*	*	PUNCT
ap-652	325	22	must	must	AUX
ap-652	325	23	be	be	AUX
ap-652	325	24	the	the	DET
ap-652	325	25	same	same	ADJ
ap-652	325	26	,	,	PUNCT
ap-652	325	27	as	as	SCONJ
ap-652	325	28	specified	specify	VERB
ap-652	325	29	in	in	ADP
ap-652	325	30	table	table	NOUN
ap-652	325	31	2	2	NUM
ap-652	325	32	.	.	PUNCT
ap-652	325	33	using	use	VERB
ap-652	325	34	superposition	superposition	NOUN
ap-652	325	35	,	,	PUNCT
ap-652	325	36	the	the	DET
ap-652	325	37	necessary	necessary	ADJ
ap-652	325	38	maximality	maximality	NOUN
ap-652	325	39	condition	condition	NOUN
ap-652	325	40	from	from	ADP
ap-652	325	41	table	table	NOUN
ap-652	325	42	2	2	NUM
ap-652	325	43	reads	read	NOUN
ap-652	325	44	as	as	ADP
ap-652	325	45	:	:	PUNCT
ap-652	325	46	n	n	CCONJ
ap-652	325	47	(	(	PUNCT
ap-652	325	48	p	p	X
ap-652	325	49	p	p	X
ap-652	325	50	p	p	X
ap-652	325	51	p	p	PROPN
ap-652	325	52	p	p	X
ap-652	325	53	p	p	X
ap-652	325	54	�	�	X
ap-652	325	55	�	�	PROPN
ap-652	326	1	1	1	NUM
ap-652	326	2	2	2	NUM
ap-652	326	3	1	1	NUM
ap-652	326	4	1	1	NUM
ap-652	326	5	1	1	NUM
ap-652	326	6	2	2	NUM
ap-652	326	7	2	2	NUM
ap-652	326	8	3	3	NUM
ap-652	326	9	3	3	NUM
ap-652	326	10	1	1	NUM
ap-652	326	11	1	1	NUM
ap-652	326	12	2	2	NUM
ap-652	326	13	2	2	NUM
ap-652	326	14	3	3	NUM
ap-652	326	15	3	3	NUM
ap-652	326	16	g	g	NOUN
ap-652	326	17	*	*	PROPN
ap-652	326	18	)	)	PUNCT
ap-652	326	19	,	,	PUNCT
ap-652	326	20	�	�	PROPN
ap-652	326	21	�	�	PROPN
ap-652	326	22	�	�	PROPN
ap-652	326	23	�	�	PROPN
ap-652	326	24	�	�	PROPN
ap-652	326	25	�	�	PROPN
ap-652	326	26	(	(	PUNCT
ap-652	326	27	36	36	NUM
ap-652	326	28	)	)	PUNCT
ap-652	326	29	where	where	SCONJ
ap-652	326	30	the	the	DET
ap-652	326	31	coefficients	coefficient	NOUN
ap-652	326	32	�	�	VERB
ap-652	326	33	i	i	PRON
ap-652	326	34	are	be	AUX
ap-652	326	35	expressing	express	VERB
ap-652	326	36	the	the	DET
ap-652	326	37	particular	particular	ADJ
ap-652	326	38	basic	basic	ADJ
ap-652	326	39	cases	case	NOUN
ap-652	326	40	combination	combination	NOUN
ap-652	326	41	,	,	PUNCT
ap-652	326	42	corresponding	correspond	VERB
ap-652	326	43	to	to	ADP
ap-652	326	44	the	the	DET
ap-652	326	45	imposed	impose	VERB
ap-652	326	46	macroload	macroload	NOUN
ap-652	326	47	.	.	PUNCT
ap-652	327	1	additional	additional	ADJ
ap-652	327	2	constraints	constraint	NOUN
ap-652	327	3	from	from	ADP
ap-652	327	4	table	table	NOUN
ap-652	327	5	2	2	NUM
ap-652	327	6	must	must	AUX
ap-652	327	7	be	be	AUX
ap-652	327	8	satisfied	satisfied	ADJ
ap-652	327	9	simultaneously	simultaneously	ADV
ap-652	327	10	,	,	PUNCT
ap-652	327	11	giving	give	VERB
ap-652	327	12	:	:	PUNCT
ap-652	327	13	q	q	NOUN
ap-652	328	1	p	p	NOUN
ap-652	328	2	r	r	NOUN
ap-652	328	3	r	r	NOUN
ap-652	328	4	r	r	NOUN
ap-652	328	5	r	r	NOUN
ap-652	328	6	r	r	NOUN
ap-652	328	7	r	r	NOUN
ap-652	328	8	r	r	NOUN
ap-652	328	9	j	j	PROPN
ap-652	328	10	k	k	PROPN
ap-652	328	11	j	j	PROPN
ap-652	328	12	,	,	PUNCT
ap-652	328	13	k%	k%	VERB
ap-652	328	14	�	�	PROPN
ap-652	328	15	�	�	PROPN
ap-652	328	16	�	�	PROPN
ap-652	328	17	�	�	PROPN
ap-652	328	18	�	�	PROPN
ap-652	328	19	�	�	PROPN
ap-652	328	20	1	1	NUM
ap-652	328	21	2	2	NUM
ap-652	328	22	3	3	NUM
ap-652	328	23	1	1	NUM
ap-652	328	24	2	2	NUM
ap-652	328	25	3	3	NUM
ap-652	328	26	1	1	NUM
ap-652	328	27	2	2	NUM
ap-652	328	28	2	2	NUM
ap-652	328	29	3	3	NUM
ap-652	328	30	,	,	PUNCT
ap-652	328	31	,	,	PUNCT
ap-652	328	32	,	,	PUNCT
ap-652	328	33	,	,	PUNCT
ap-652	328	34	cos	cos	PROPN
ap-652	328	35	(	(	PUNCT
ap-652	328	36	,	,	PUNCT
ap-652	328	37	)	)	PUNCT
ap-652	328	38	cos	cos	PROPN
ap-652	328	39	(	(	PUNCT
ap-652	328	40	,	,	PUNCT
ap-652	328	41	)	)	PUNCT
ap-652	328	42	cos	cos	PROPN
ap-652	328	43	(	(	PUNCT
ap-652	328	44	,	,	PUNCT
ap-652	328	45	)	)	PUNCT
ap-652	328	46	r	r	NOUN
ap-652	328	47	r3	r3	PROPN
ap-652	328	48	1	1	NUM
ap-652	328	49	(	(	PUNCT
ap-652	328	50	37	37	NUM
ap-652	328	51	)	)	PUNCT
ap-652	328	52	and	and	CCONJ
ap-652	328	53	p	p	X
ap-652	328	54	p	p	PROPN
ap-652	328	55	p1	p1	NOUN
ap-652	328	56	2	2	NUM
ap-652	328	57	3	3	NUM
ap-652	328	58	12	12	NUM
ap-652	328	59	�	�	PROPN
ap-652	328	60	�	�	PROPN
ap-652	328	61	�	�	PROPN
ap-652	328	62	g	g	PROPN
ap-652	328	63	v	v	PROPN
ap-652	328	64	*	*	PROPN
ap-652	328	65	.	.	PUNCT
ap-652	329	1	(	(	PUNCT
ap-652	329	2	38	38	NUM
ap-652	329	3	)	)	PUNCT
ap-652	329	4	(	(	PUNCT
ap-652	329	5	38	38	NUM
ap-652	329	6	)	)	PUNCT
ap-652	329	7	could	could	AUX
ap-652	329	8	be	be	AUX
ap-652	329	9	obtained	obtain	VERB
ap-652	329	10	directly	directly	ADV
ap-652	329	11	as	as	SCONJ
ap-652	329	12	the	the	DET
ap-652	329	13	condition	condition	NOUN
ap-652	329	14	ensuring	ensure	VERB
ap-652	329	15	the	the	DET
ap-652	329	16	same	same	ADJ
ap-652	329	17	g1	g1	NOUN
ap-652	329	18	*	*	PUNCT
ap-652	329	19	in	in	ADP
ap-652	329	20	all	all	DET
ap-652	329	21	basic	basic	ADJ
ap-652	329	22	cases	case	NOUN
ap-652	329	23	.	.	PUNCT
ap-652	330	1	if	if	SCONJ
ap-652	330	2	(	(	PUNCT
ap-652	330	3	38	38	NUM
ap-652	330	4	)	)	PUNCT
ap-652	330	5	were	be	AUX
ap-652	330	6	to	to	PART
ap-652	330	7	be	be	AUX
ap-652	330	8	derived	derive	VERB
ap-652	330	9	first	first	ADV
ap-652	330	10	,	,	PUNCT
ap-652	330	11	then	then	ADV
ap-652	330	12	using	use	VERB
ap-652	330	13	some	some	DET
ap-652	330	14	statements	statement	NOUN
ap-652	330	15	about	about	ADP
ap-652	330	16	finite	finite	ADJ
ap-652	330	17	dimensional	dimensional	ADJ
ap-652	330	18	spaces	space	NOUN
ap-652	330	19	,	,	PUNCT
ap-652	330	20	condition	condition	NOUN
ap-652	330	21	(	(	PUNCT
ap-652	330	22	36	36	NUM
ap-652	330	23	)	)	PUNCT
ap-652	330	24	is	be	AUX
ap-652	330	25	the	the	DET
ap-652	330	26	maximality	maximality	NOUN
ap-652	330	27	condition	condition	NOUN
ap-652	330	28	for	for	ADP
ap-652	330	29	the	the	DET
ap-652	330	30	sum	sum	NOUN
ap-652	330	31	:	:	PUNCT
ap-652	330	32	cos	cos	PROPN
ap-652	330	33	(	(	PUNCT
ap-652	330	34	,	,	PUNCT
ap-652	330	35	)	)	PUNCT
ap-652	330	36	cos	cos	PROPN
ap-652	330	37	(	(	PUNCT
ap-652	330	38	,	,	PUNCT
ap-652	330	39	)	)	PUNCT
ap-652	330	40	cos	cos	PROPN
ap-652	330	41	(	(	PUNCT
ap-652	330	42	,	,	PUNCT
ap-652	330	43	)	)	PUNCT
ap-652	330	44	2	2	NUM
ap-652	330	45	1	1	NUM
ap-652	330	46	2	2	NUM
ap-652	330	47	2	2	NUM
ap-652	330	48	2	2	NUM
ap-652	330	49	3n	3n	NUM
ap-652	330	50	p	p	NOUN
ap-652	330	51	n	n	PROPN
ap-652	330	52	p	p	NOUN
ap-652	330	53	n	n	PRON
ap-652	330	54	p	p	NOUN
ap-652	330	55	.	.	PUNCT
ap-652	331	1	here	here	ADV
ap-652	331	2	it	it	PRON
ap-652	331	3	holds	hold	VERB
ap-652	331	4	:	:	PUNCT
ap-652	332	1	cos	cos	PROPN
ap-652	332	2	(	(	PUNCT
ap-652	332	3	,	,	PUNCT
ap-652	332	4	)	)	PUNCT
ap-652	332	5	cos	cos	PROPN
ap-652	332	6	(	(	PUNCT
ap-652	332	7	,	,	PUNCT
ap-652	332	8	)	)	PUNCT
ap-652	332	9	cos	cos	PROPN
ap-652	332	10	(	(	PUNCT
ap-652	332	11	,	,	PUNCT
ap-652	332	12	)	)	PUNCT
ap-652	332	13	2	2	NUM
ap-652	332	14	1	1	NUM
ap-652	332	15	2	2	NUM
ap-652	332	16	2	2	NUM
ap-652	332	17	2	2	NUM
ap-652	332	18	3	3	NUM
ap-652	332	19	3	3	NUM
ap-652	332	20	2	2	NUM
ap-652	332	21	n	n	NOUN
ap-652	332	22	p	p	NOUN
ap-652	332	23	n	n	CCONJ
ap-652	332	24	p	p	NOUN
ap-652	332	25	n	n	CCONJ
ap-652	332	26	p	p	PROPN
ap-652	332	27	�	�	PROPN
ap-652	332	28	.	.	PUNCT
ap-652	333	1	(	(	PUNCT
ap-652	333	2	39	39	NUM
ap-652	333	3	)	)	PUNCT
ap-652	333	4	then	then	ADV
ap-652	333	5	the	the	DET
ap-652	333	6	bound	bound	ADJ
ap-652	333	7	g	g	PROPN
ap-652	333	8	s1	s1	PROPN
ap-652	333	9	6	6	NUM
ap-652	333	10	,	,	PUNCT
ap-652	333	11	*	*	PUNCT
ap-652	333	12	�	�	PROPN
ap-652	333	13	can	can	AUX
ap-652	333	14	be	be	AUX
ap-652	333	15	obtained	obtain	VERB
ap-652	333	16	from	from	ADP
ap-652	333	17	(	(	PUNCT
ap-652	333	18	34	34	NUM
ap-652	333	19	)	)	PUNCT
ap-652	333	20	if	if	SCONJ
ap-652	333	21	q	q	PROPN
ap-652	333	22	0j	0j	NUM
ap-652	333	23	j	j	PROPN
ap-652	333	24	�	�	PROPN
ap-652	333	25	�	�	PROPN
ap-652	333	26	�	�	PROPN
ap-652	333	27	1	1	NUM
ap-652	333	28	2	2	NUM
ap-652	333	29	3	3	NUM
ap-652	333	30	,	,	PUNCT
ap-652	333	31	,	,	PUNCT
ap-652	333	32	.	.	PUNCT
ap-652	334	1	thus	thus	ADV
ap-652	334	2	the	the	DET
ap-652	334	3	proof	proof	NOUN
ap-652	334	4	of	of	ADP
ap-652	334	5	g	g	PROPN
ap-652	334	6	s1	s1	PROPN
ap-652	334	7	6	6	NUM
ap-652	334	8	,	,	PUNCT
ap-652	334	9	*	*	PUNCT
ap-652	334	10	�	�	PROPN
ap-652	334	11	would	would	AUX
ap-652	334	12	be	be	AUX
ap-652	334	13	completed	complete	VERB
ap-652	334	14	if	if	SCONJ
ap-652	334	15	at	at	ADV
ap-652	334	16	least	least	ADJ
ap-652	334	17	one	one	NUM
ap-652	334	18	optimal	optimal	ADJ
ap-652	334	19	medium	medium	NOUN
ap-652	334	20	can	can	AUX
ap-652	334	21	be	be	AUX
ap-652	334	22	found	find	VERB
ap-652	334	23	,	,	PUNCT
ap-652	334	24	i.e.	i.e.	X
ap-652	334	25	if	if	SCONJ
ap-652	334	26	there	there	PRON
ap-652	334	27	exists	exist	VERB
ap-652	334	28	a	a	DET
ap-652	334	29	medium	medium	NOUN
ap-652	334	30	in	in	ADP
ap-652	334	31	whichq	whichq	PROPN
ap-652	334	32	0j	0j	NOUN
ap-652	334	33	j	j	PROPN
ap-652	334	34	�	�	PROPN
ap-652	334	35	�	�	PROPN
ap-652	334	36	�	�	PROPN
ap-652	334	37	1	1	NUM
ap-652	334	38	2	2	NUM
ap-652	334	39	3	3	NUM
ap-652	334	40	,	,	PUNCT
ap-652	334	41	,	,	PUNCT
ap-652	334	42	,	,	PUNCT
ap-652	334	43	expressions	expression	NOUN
ap-652	334	44	(	(	PUNCT
ap-652	334	45	36–38	36–38	NUM
ap-652	334	46	)	)	PUNCT
ap-652	334	47	hold	hold	VERB
ap-652	334	48	and	and	CCONJ
ap-652	334	49	no	no	DET
ap-652	334	50	zero	zero	NUM
ap-652	334	51	bars	bar	NOUN
ap-652	334	52	are	be	AUX
ap-652	334	53	contained	contain	VERB
ap-652	334	54	in	in	ADP
ap-652	334	55	it	it	PRON
ap-652	334	56	.	.	PUNCT
ap-652	335	1	in	in	ADP
ap-652	335	2	order	order	NOUN
ap-652	335	3	to	to	PART
ap-652	335	4	justify	justify	VERB
ap-652	335	5	the	the	DET
ap-652	335	6	existence	existence	NOUN
ap-652	335	7	of	of	ADP
ap-652	335	8	such	such	DET
ap-652	335	9	a	a	DET
ap-652	335	10	medium	medium	NOUN
ap-652	335	11	,	,	PUNCT
ap-652	335	12	first	first	ADV
ap-652	335	13	of	of	ADP
ap-652	335	14	all	all	PRON
ap-652	335	15	,	,	PUNCT
ap-652	335	16	the	the	DET
ap-652	335	17	spherical	spherical	ADJ
ap-652	335	18	angles	angle	NOUN
ap-652	335	19	that	that	PRON
ap-652	335	20	will	will	AUX
ap-652	335	21	ensure	ensure	VERB
ap-652	335	22	q	q	PROPN
ap-652	335	23	0j	0j	NOUN
ap-652	335	24	j	j	PROPN
ap-652	335	25	�	�	PROPN
ap-652	335	26	�	�	PROPN
ap-652	335	27	�	�	PROPN
ap-652	335	28	1	1	NUM
ap-652	335	29	2	2	NUM
ap-652	335	30	3	3	NUM
ap-652	335	31	,	,	PUNCT
ap-652	335	32	,	,	PUNCT
ap-652	335	33	must	must	AUX
ap-652	335	34	be	be	AUX
ap-652	335	35	found	find	VERB
ap-652	335	36	.	.	PUNCT
ap-652	336	1	this	this	DET
ap-652	336	2	requirement	requirement	NOUN
ap-652	336	3	is	be	AUX
ap-652	336	4	equivalent	equivalent	ADJ
ap-652	336	5	to	to	ADP
ap-652	336	6	the	the	DET
ap-652	336	7	condition	condition	NOUN
ap-652	336	8	under	under	ADP
ap-652	336	9	which	which	PRON
ap-652	336	10	&	&	CCONJ
ap-652	336	11	�	�	PROPN
ap-652	336	12	max	max	PROPN
ap-652	336	13	,	,	PUNCT
ap-652	336	14	,	,	PUNCT
ap-652	336	15	,	,	PUNCT
ap-652	336	16	�	�	PROPN
ap-652	336	17	�	�	PROPN
ap-652	336	18	�	�	PROPN
ap-652	336	19	1	1	NUM
ap-652	336	20	2	2	NUM
ap-652	336	21	3i	3i	NUM
ap-652	336	22	i	i	PRON
ap-652	336	23	i	i	PRON
ap-652	336	24	(	(	PUNCT
ap-652	336	25	40	40	NUM
ap-652	336	26	)	)	PUNCT
ap-652	336	27	is	be	AUX
ap-652	336	28	obtained	obtain	VERB
ap-652	336	29	for	for	ADP
ap-652	336	30	each	each	DET
ap-652	336	31	i.	i.	NOUN
ap-652	336	32	solution	solution	NOUN
ap-652	336	33	of	of	ADP
ap-652	336	34	problem	problem	NOUN
ap-652	336	35	(	(	PUNCT
ap-652	336	36	40	40	NUM
ap-652	336	37	)	)	PUNCT
ap-652	336	38	results	result	NOUN
ap-652	336	39	in	in	ADP
ap-652	336	40	three	three	NUM
ap-652	336	41	groups	group	NOUN
ap-652	336	42	of	of	ADP
ap-652	336	43	angles	angle	NOUN
ap-652	336	44	,	,	PUNCT
ap-652	336	45	which	which	PRON
ap-652	336	46	predict	predict	VERB
ap-652	336	47	the	the	DET
ap-652	336	48	bars	bar	NOUN
ap-652	336	49	directions	direction	NOUN
ap-652	336	50	of	of	ADP
ap-652	336	51	the	the	DET
ap-652	336	52	bars	bar	NOUN
ap-652	336	53	in	in	ADP
ap-652	336	54	an	an	DET
ap-652	336	55	optimal	optimal	ADJ
ap-652	336	56	medium	medium	NOUN
ap-652	336	57	,	,	PUNCT
ap-652	336	58	as	as	SCONJ
ap-652	336	59	stated	state	VERB
ap-652	336	60	in	in	ADP
ap-652	336	61	table	table	NOUN
ap-652	336	62	3	3	NUM
ap-652	336	63	.	.	PUNCT
ap-652	337	1	it	it	PRON
ap-652	337	2	is	be	AUX
ap-652	337	3	therefore	therefore	ADV
ap-652	337	4	convenient	convenient	ADJ
ap-652	337	5	to	to	PART
ap-652	337	6	choose	choose	VERB
ap-652	337	7	a	a	DET
ap-652	337	8	rectangular	rectangular	ADJ
ap-652	337	9	basic	basic	ADJ
ap-652	337	10	cell	cell	NOUN
ap-652	337	11	with	with	ADP
ap-652	337	12	faces	face	NOUN
ap-652	337	13	perpendicular	perpendicular	NOUN
ap-652	337	14	to	to	ADP
ap-652	337	15	the	the	DET
ap-652	337	16	directions	direction	NOUN
ap-652	337	17	of	of	ADP
ap-652	337	18	the	the	DET
ap-652	337	19	bars	bar	NOUN
ap-652	337	20	.	.	PUNCT
ap-652	338	1	due	due	ADP
ap-652	338	2	to	to	ADP
ap-652	338	3	the	the	DET
ap-652	338	4	equilibrium	equilibrium	NOUN
ap-652	338	5	in	in	ADP
ap-652	338	6	the	the	DET
ap-652	338	7	joints	joint	NOUN
ap-652	338	8	,	,	PUNCT
ap-652	338	9	only	only	ADV
ap-652	338	10	continuous	continuous	ADJ
ap-652	338	11	bars	bar	NOUN
ap-652	338	12	passing	pass	VERB
ap-652	338	13	through	through	ADP
ap-652	338	14	the	the	DET
ap-652	338	15	cell	cell	NOUN
ap-652	338	16	can	can	AUX
ap-652	338	17	be	be	AUX
ap-652	338	18	present	present	ADJ
ap-652	338	19	.	.	PUNCT
ap-652	339	1	from	from	ADP
ap-652	339	2	table	table	NOUN
ap-652	339	3	3	3	NUM
ap-652	339	4	it	it	PRON
ap-652	339	5	follows	follow	VERB
ap-652	339	6	immediately	immediately	ADV
ap-652	339	7	that	that	SCONJ
ap-652	339	8	r	r	NOUN
ap-652	339	9	r	r	NOUN
ap-652	339	10	r1	r1	NOUN
ap-652	339	11	2	2	NUM
ap-652	339	12	3	3	NUM
ap-652	339	13	%	%	NOUN
ap-652	339	14	%	%	NOUN
ap-652	339	15	,	,	PUNCT
ap-652	339	16	but	but	CCONJ
ap-652	339	17	in	in	ADP
ap-652	339	18	order	order	NOUN
ap-652	339	19	to	to	PART
ap-652	339	20	ensure	ensure	VERB
ap-652	339	21	r	r	NOUN
ap-652	339	22	r	r	NOUN
ap-652	339	23	r1	r1	NOUN
ap-652	339	24	2	2	NUM
ap-652	339	25	3	3	NUM
ap-652	339	26	�	�	PROPN
ap-652	339	27	�	�	PROPN
ap-652	339	28	,	,	PUNCT
ap-652	339	29	the	the	DET
ap-652	339	30	following	follow	VERB
ap-652	339	31	condition	condition	NOUN
ap-652	339	32	must	must	AUX
ap-652	339	33	be	be	AUX
ap-652	339	34	satisfied	satisfied	ADJ
ap-652	339	35	:	:	PUNCT
ap-652	339	36	l	l	X
ap-652	339	37	l	l	NOUN
ap-652	339	38	li	li	PROPN
ap-652	340	1	i	i	PRON
ap-652	340	2	group	group	PROPN
ap-652	340	3	j	j	PROPN
ap-652	340	4	j	j	PROPN
ap-652	340	5	group	group	PROPN
ap-652	340	6	k	k	PROPN
ap-652	340	7	k	k	PROPN
ap-652	340	8	group	group	PROPN
ap-652	340	9	a	a	DET
ap-652	340	10	a	a	DET
ap-652	340	11	a	a	DET
ap-652	340	12	1	1	NUM
ap-652	340	13	2	2	NUM
ap-652	340	14	3	3	NUM
ap-652	340	15	.	.	PUNCT
ap-652	340	16	.	.	PUNCT
ap-652	340	17	.	.	PUNCT
ap-652	341	1	�	�	PROPN
ap-652	341	2	�	�	PROPN
ap-652	341	3	�	�	PROPN
ap-652	341	4	�	�	PROPN
ap-652	341	5	�	�	PROPN
ap-652	341	6	,	,	PUNCT
ap-652	341	7	(	(	PUNCT
ap-652	341	8	41	41	NUM
ap-652	341	9	)	)	PUNCT
ap-652	341	10	i.e.	i.e.	X
ap-652	341	11	in	in	ADP
ap-652	341	12	each	each	PRON
ap-652	341	13	of	of	ADP
ap-652	341	14	the	the	DET
ap-652	341	15	three	three	NUM
ap-652	341	16	perpendicular	perpendicular	ADJ
ap-652	341	17	directions	direction	NOUN
ap-652	341	18	in	in	ADP
ap-652	341	19	the	the	DET
ap-652	341	20	cell	cell	NOUN
ap-652	341	21	,	,	PUNCT
ap-652	341	22	the	the	DET
ap-652	341	23	volume	volume	NOUN
ap-652	341	24	of	of	ADP
ap-652	341	25	the	the	DET
ap-652	341	26	bars	bar	NOUN
ap-652	341	27	must	must	AUX
ap-652	341	28	be	be	AUX
ap-652	341	29	the	the	DET
ap-652	341	30	same	same	ADJ
ap-652	341	31	.	.	PUNCT
ap-652	342	1	it	it	PRON
ap-652	342	2	remains	remain	VERB
ap-652	342	3	to	to	PART
ap-652	342	4	ensure	ensure	VERB
ap-652	342	5	(	(	PUNCT
ap-652	342	6	36	36	NUM
ap-652	342	7	)	)	PUNCT
ap-652	342	8	and	and	CCONJ
ap-652	342	9	impose	impose	VERB
ap-652	342	10	conditions	condition	NOUN
ap-652	342	11	to	to	PART
ap-652	342	12	eliminate	eliminate	VERB
ap-652	342	13	zero	zero	NUM
ap-652	342	14	bars	bar	NOUN
ap-652	342	15	.	.	PUNCT
ap-652	343	1	let	let	VERB
ap-652	343	2	us	we	PRON
ap-652	343	3	take	take	VERB
ap-652	343	4	for	for	ADP
ap-652	343	5	example	example	NOUN
ap-652	343	6	one	one	NUM
ap-652	343	7	continuous	continuous	ADJ
ap-652	343	8	bar	bar	NOUN
ap-652	343	9	from	from	ADP
ap-652	343	10	the	the	DET
ap-652	343	11	first	first	ADJ
ap-652	343	12	group	group	NOUN
ap-652	343	13	.	.	PUNCT
ap-652	344	1	from	from	ADP
ap-652	344	2	(	(	PUNCT
ap-652	344	3	36	36	NUM
ap-652	344	4	)	)	PUNCT
ap-652	344	5	it	it	PRON
ap-652	344	6	follows	follow	VERB
ap-652	344	7	that	that	SCONJ
ap-652	344	8	all	all	ADV
ap-652	344	9	over	over	ADP
ap-652	344	10	the	the	DET
ap-652	344	11	bar	bar	NOUN
ap-652	344	12	n	n	CCONJ
ap-652	344	13	ai	ai	VERB
ap-652	344	14	i	i	PRON
ap-652	344	15	�	�	PROPN
ap-652	344	16	�	�	PROPN
ap-652	344	17	�	�	PROPN
ap-652	344	18	3	3	NUM
ap-652	344	19	2	2	NUM
ap-652	344	20	holds	hold	NOUN
ap-652	344	21	.	.	PUNCT
ap-652	345	1	therefore	therefore	ADV
ap-652	345	2	the	the	DET
ap-652	345	3	normal	normal	ADJ
ap-652	345	4	forces	force	NOUN
ap-652	345	5	between	between	ADP
ap-652	345	6	the	the	DET
ap-652	345	7	respective	respective	ADJ
ap-652	345	8	joints	joint	NOUN
ap-652	345	9	must	must	AUX
ap-652	345	10	be	be	AUX
ap-652	345	11	proportional	proportional	ADJ
ap-652	345	12	to	to	ADP
ap-652	345	13	the	the	DET
ap-652	345	14	cross	cross	NOUN
ap-652	345	15	sectional	sectional	ADJ
ap-652	345	16	areas	area	NOUN
ap-652	345	17	with	with	ADP
ap-652	345	18	the	the	DET
ap-652	345	19	©	©	PROPN
ap-652	345	20	czech	czech	PROPN
ap-652	345	21	technical	technical	PROPN
ap-652	345	22	university	university	PROPN
ap-652	345	23	publishing	publishing	NOUN
ap-652	345	24	house	house	NOUN
ap-652	345	25	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	345	26	179	179	NUM
ap-652	345	27	acta	acta	PROPN
ap-652	345	28	polytechnica	polytechnica	PROPN
ap-652	345	29	vol	vol	NOUN
ap-652	345	30	.	.	PROPN
ap-652	346	1	44	44	NUM
ap-652	346	2	no.5–6/2004	no.5–6/2004	PROPN
ap-652	346	3	basic	basic	ADJ
ap-652	346	4	case	case	NOUN
ap-652	346	5	1	1	NUM
ap-652	346	6	.	.	NOUN
ap-652	346	7	2	2	NUM
ap-652	346	8	.	.	NOUN
ap-652	346	9	3	3	X
ap-652	346	10	.	.	X
ap-652	346	11	macrostress	macrostress	PROPN
ap-652	346	12	�	�	PROPN
ap-652	346	13	�	�	PROPN
ap-652	346	14	22	22	NUM
ap-652	346	15	33	33	NUM
ap-652	346	16	1	1	NUM
ap-652	346	17	�	�	PROPN
ap-652	346	18	�	�	PROPN
ap-652	346	19	�	�	PROPN
ap-652	346	20	�	�	PROPN
ap-652	346	21	33	33	NUM
ap-652	346	22	11	11	NUM
ap-652	346	23	1	1	NUM
ap-652	346	24	�	�	PROPN
ap-652	346	25	�	�	PROPN
ap-652	346	26	�	�	PROPN
ap-652	346	27	�	�	PROPN
ap-652	346	28	11	11	NUM
ap-652	346	29	22	22	NUM
ap-652	346	30	1	1	NUM
ap-652	346	31	�	�	PROPN
ap-652	346	32	�	�	PROPN
ap-652	346	33	macrostrain	macrostrain	NOUN
ap-652	346	34	e	e	PROPN
ap-652	346	35	e	e	ADP
ap-652	346	36	g	g	PROPN
ap-652	346	37	es	es	ADP
ap-652	346	38	22	22	NUM
ap-652	346	39	33	33	NUM
ap-652	346	40	11	11	NUM
ap-652	346	41	2	2	NUM
ap-652	346	42	�	�	PROPN
ap-652	346	43	�	�	PROPN
ap-652	346	44	�	�	PROPN
ap-652	346	45	(	(	PUNCT
ap-652	346	46	)	)	PUNCT
ap-652	346	47	*	*	PUNCT
ap-652	346	48	e	e	X
ap-652	346	49	e	e	X
ap-652	346	50	g	g	NOUN
ap-652	346	51	es	es	ADP
ap-652	346	52	33	33	NUM
ap-652	346	53	11	11	NUM
ap-652	346	54	11	11	NUM
ap-652	346	55	2	2	NUM
ap-652	346	56	�	�	PROPN
ap-652	346	57	�	�	PROPN
ap-652	346	58	�	�	PROPN
ap-652	346	59	(	(	PUNCT
ap-652	346	60	)	)	PUNCT
ap-652	346	61	*	*	PUNCT
ap-652	346	62	e	e	X
ap-652	346	63	e	e	X
ap-652	346	64	g	g	NOUN
ap-652	346	65	es	es	ADP
ap-652	346	66	11	11	NUM
ap-652	346	67	22	22	NUM
ap-652	346	68	11	11	NUM
ap-652	346	69	2	2	NUM
ap-652	346	70	�	�	PROPN
ap-652	346	71	�	�	PROPN
ap-652	346	72	�	�	PROPN
ap-652	346	73	(	(	PUNCT
ap-652	346	74	)	)	PUNCT
ap-652	346	75	*	*	PUNCT
ap-652	346	76	maximality	maximality	NOUN
ap-652	346	77	condition	condition	NOUN
ap-652	346	78	from	from	ADP
ap-652	346	79	eq	eq	PROPN
ap-652	346	80	.	.	PUNCT
ap-652	346	81	(	(	PUNCT
ap-652	346	82	30	30	NUM
ap-652	346	83	)	)	PUNCT
ap-652	346	84	n	n	CCONJ
ap-652	347	1	p	p	X
ap-652	347	2	�	�	PROPN
ap-652	347	3	1	1	NUM
ap-652	347	4	2	2	NUM
ap-652	347	5	1	1	NUM
ap-652	347	6	1	1	NUM
ap-652	347	7	g	g	NOUN
ap-652	347	8	*	*	PROPN
ap-652	347	9	n	n	ADP
ap-652	347	10	p	p	X
ap-652	347	11	�	�	PROPN
ap-652	347	12	1	1	NUM
ap-652	347	13	2	2	NUM
ap-652	347	14	1	1	NUM
ap-652	347	15	2	2	NUM
ap-652	347	16	g	g	NOUN
ap-652	347	17	*	*	PROPN
ap-652	347	18	n	n	ADP
ap-652	347	19	p	p	X
ap-652	347	20	�	�	PROPN
ap-652	347	21	1	1	NUM
ap-652	347	22	2	2	NUM
ap-652	347	23	1	1	NUM
ap-652	347	24	3	3	NUM
ap-652	347	25	g	g	NOUN
ap-652	347	26	*	*	PUNCT
ap-652	347	27	additional	additional	ADJ
ap-652	347	28	constraints	constraint	NOUN
ap-652	347	29	r	r	NOUN
ap-652	347	30	r	r	NOUN
ap-652	347	31	r	r	NOUN
ap-652	347	32	p2	p2	NOUN
ap-652	347	33	3	3	NUM
ap-652	347	34	1	1	NUM
ap-652	347	35	1	1	NUM
ap-652	347	36	�	�	NUM
ap-652	347	37	%	%	NOUN
ap-652	347	38	,	,	PUNCT
ap-652	347	39	,	,	PUNCT
ap-652	347	40	q	q	PROPN
ap-652	347	41	pj	pj	PROPN
ap-652	347	42	1	1	NUM
ap-652	347	43	j%	j%	PROPN
ap-652	347	44	�	�	PROPN
ap-652	347	45	�	�	PROPN
ap-652	347	46	1	1	NUM
ap-652	347	47	2	2	NUM
ap-652	347	48	3	3	NUM
ap-652	347	49	,	,	PUNCT
ap-652	347	50	,	,	PUNCT
ap-652	347	51	r	r	NOUN
ap-652	347	52	r	r	NOUN
ap-652	347	53	r	r	NOUN
ap-652	347	54	p3	p3	NOUN
ap-652	347	55	1	1	NUM
ap-652	347	56	2	2	NUM
ap-652	347	57	2	2	NUM
ap-652	347	58	�	�	NUM
ap-652	347	59	%	%	NOUN
ap-652	347	60	,	,	PUNCT
ap-652	347	61	,	,	PUNCT
ap-652	347	62	q	q	PROPN
ap-652	347	63	pj	pj	PROPN
ap-652	347	64	2	2	NUM
ap-652	347	65	j%	j%	PROPN
ap-652	347	66	�	�	PROPN
ap-652	347	67	�	�	PROPN
ap-652	347	68	1	1	NUM
ap-652	347	69	2	2	NUM
ap-652	347	70	3	3	NUM
ap-652	347	71	,	,	PUNCT
ap-652	347	72	,	,	PUNCT
ap-652	347	73	r	r	NOUN
ap-652	347	74	r	r	NOUN
ap-652	347	75	r	r	NOUN
ap-652	347	76	p1	p1	NOUN
ap-652	347	77	2	2	NUM
ap-652	347	78	3	3	NUM
ap-652	347	79	3	3	NUM
ap-652	347	80	�	�	NUM
ap-652	347	81	%	%	NOUN
ap-652	347	82	,	,	PUNCT
ap-652	347	83	,	,	PUNCT
ap-652	347	84	q	q	PROPN
ap-652	347	85	pj	pj	PROPN
ap-652	347	86	3	3	NUM
ap-652	347	87	j%	j%	PROPN
ap-652	347	88	�	�	PROPN
ap-652	347	89	�	�	PROPN
ap-652	347	90	1	1	NUM
ap-652	347	91	2	2	NUM
ap-652	347	92	3	3	NUM
ap-652	347	93	,	,	PUNCT
ap-652	347	94	,	,	PUNCT
ap-652	347	95	table	table	NOUN
ap-652	347	96	2	2	NUM
ap-652	347	97	:	:	PUNCT
ap-652	347	98	basic	basic	ADJ
ap-652	347	99	load	load	NOUN
ap-652	347	100	cases	case	NOUN
ap-652	347	101	in	in	ADP
ap-652	347	102	�	�	PROPN
ap-652	347	103	1	1	NUM
ap-652	347	104	g	g	NOUN
ap-652	347	105	same	same	ADJ
ap-652	347	106	coefficient	coefficient	NOUN
ap-652	347	107	of	of	ADP
ap-652	347	108	proportionality	proportionality	NOUN
ap-652	347	109	in	in	ADP
ap-652	347	110	each	each	DET
ap-652	347	111	group	group	NOUN
ap-652	347	112	.	.	PUNCT
ap-652	348	1	due	due	ADP
ap-652	348	2	to	to	ADP
ap-652	348	3	the	the	DET
ap-652	348	4	equilibrium	equilibrium	NOUN
ap-652	348	5	in	in	ADP
ap-652	348	6	the	the	DET
ap-652	348	7	joints	joint	NOUN
ap-652	348	8	,	,	PUNCT
ap-652	348	9	the	the	DET
ap-652	348	10	normal	normal	ADJ
ap-652	348	11	forces	force	NOUN
ap-652	348	12	must	must	AUX
ap-652	348	13	be	be	AUX
ap-652	348	14	the	the	DET
ap-652	348	15	same	same	ADJ
ap-652	348	16	within	within	ADP
ap-652	348	17	each	each	DET
ap-652	348	18	continuous	continuous	ADJ
ap-652	348	19	bar	bar	NOUN
ap-652	348	20	,	,	PUNCT
ap-652	348	21	which	which	PRON
ap-652	348	22	implies	imply	VERB
ap-652	348	23	that	that	SCONJ
ap-652	348	24	the	the	DET
ap-652	348	25	cross	cross	NOUN
ap-652	348	26	sectional	sectional	ADJ
ap-652	348	27	areas	area	NOUN
ap-652	348	28	are	be	AUX
ap-652	348	29	also	also	ADV
ap-652	348	30	constant	constant	ADJ
ap-652	348	31	within	within	ADP
ap-652	348	32	the	the	DET
ap-652	348	33	continuous	continuous	ADJ
ap-652	348	34	bar	bar	NOUN
ap-652	348	35	,	,	PUNCT
ap-652	348	36	as	as	ADV
ap-652	348	37	well	well	ADV
ap-652	348	38	.	.	PUNCT
ap-652	349	1	let	let	VERB
ap-652	349	2	us	we	PRON
ap-652	349	3	now	now	ADV
ap-652	349	4	summarize	summarize	VERB
ap-652	349	5	the	the	DET
ap-652	349	6	results	result	NOUN
ap-652	349	7	.	.	PUNCT
ap-652	350	1	g	g	ADP
ap-652	350	2	s1	s1	PROPN
ap-652	350	3	6	6	NUM
ap-652	350	4	,	,	PUNCT
ap-652	350	5	*	*	PUNCT
ap-652	350	6	�	�	PROPN
ap-652	350	7	and	and	CCONJ
ap-652	350	8	all	all	DET
ap-652	350	9	g1	g1	NOUN
ap-652	350	10	*	*	PUNCT
ap-652	350	11	-optimal	-optimal	ADJ
ap-652	350	12	media	medium	NOUN
ap-652	350	13	can	can	AUX
ap-652	350	14	be	be	AUX
ap-652	350	15	fully	fully	ADV
ap-652	350	16	geometrically	geometrically	ADV
ap-652	350	17	specified	specify	VERB
ap-652	350	18	in	in	ADP
ap-652	350	19	the	the	DET
ap-652	350	20	following	following	ADJ
ap-652	350	21	way	way	NOUN
ap-652	350	22	:	:	PUNCT
ap-652	350	23	g1	g1	NOUN
ap-652	350	24	*	*	PUNCT
ap-652	350	25	-optimal	-optimal	ADJ
ap-652	350	26	media	medium	NOUN
ap-652	350	27	are	be	AUX
ap-652	350	28	continuous	continuous	ADJ
ap-652	350	29	lattices	lattice	NOUN
ap-652	350	30	for	for	ADP
ap-652	350	31	which	which	PRON
ap-652	350	32	:	:	PUNCT
ap-652	350	33	�	�	PROPN
ap-652	350	34	a	a	DET
ap-652	350	35	rectangular	rectangular	ADJ
ap-652	350	36	basic	basic	ADJ
ap-652	350	37	cell	cell	NOUN
ap-652	350	38	(	(	PUNCT
ap-652	350	39	with	with	ADP
ap-652	350	40	dimensions	dimension	NOUN
ap-652	350	41	li	li	PROPN
ap-652	350	42	in	in	ADP
ap-652	350	43	yi	yi	NOUN
ap-652	350	44	-	-	PUNCT
ap-652	350	45	directions	direction	NOUN
ap-652	350	46	,	,	PUNCT
ap-652	350	47	i	i	PRON
ap-652	350	48	�	�	PROPN
ap-652	350	49	1	1	NUM
ap-652	350	50	,	,	PUNCT
ap-652	350	51	2	2	NUM
ap-652	350	52	,	,	PUNCT
ap-652	350	53	3	3	NUM
ap-652	350	54	)	)	PUNCT
ap-652	350	55	can	can	AUX
ap-652	350	56	be	be	AUX
ap-652	350	57	found	find	VERB
ap-652	350	58	,	,	PUNCT
ap-652	350	59	consisting	consist	VERB
ap-652	350	60	only	only	ADV
ap-652	350	61	of	of	ADP
ap-652	350	62	continuous	continuous	ADJ
ap-652	350	63	orthogonal	orthogonal	ADJ
ap-652	350	64	bars	bar	NOUN
ap-652	350	65	in	in	ADP
ap-652	350	66	yi	yi	NOUN
ap-652	350	67	-	-	PUNCT
ap-652	350	68	directions	direction	NOUN
ap-652	350	69	,	,	PUNCT
ap-652	350	70	�	�	PROPN
ap-652	350	71	each	each	DET
ap-652	350	72	bar	bar	NOUN
ap-652	350	73	has	have	VERB
ap-652	350	74	a	a	DET
ap-652	350	75	constant	constant	ADJ
ap-652	350	76	cross	cross	NOUN
ap-652	350	77	sectional	sectional	ADJ
ap-652	350	78	area	area	NOUN
ap-652	350	79	within	within	ADP
ap-652	350	80	the	the	DET
ap-652	350	81	basic	basic	ADJ
ap-652	350	82	cell	cell	NOUN
ap-652	350	83	and	and	CCONJ
ap-652	350	84	the	the	DET
ap-652	350	85	condition	condition	NOUN
ap-652	350	86	l	l	NOUN
ap-652	350	87	a	a	PROPN
ap-652	350	88	l	l	NOUN
ap-652	350	89	a	a	DET
ap-652	350	90	l	l	NOUN
ap-652	350	91	ai	ai	VERB
ap-652	350	92	i	i	PRON
ap-652	350	93	n	n	PROPN
ap-652	351	1	j	j	PROPN
ap-652	351	2	j	j	PROPN
ap-652	351	3	n	n	CCONJ
ap-652	351	4	k	k	PROPN
ap-652	351	5	k	k	PROPN
ap-652	351	6	n	n	PROPN
ap-652	351	7	1	1	NUM
ap-652	351	8	1	1	NUM
ap-652	351	9	2	2	NUM
ap-652	351	10	1	1	NUM
ap-652	351	11	3	3	NUM
ap-652	351	12	1	1	NUM
ap-652	351	13	1	1	NUM
ap-652	351	14	2	2	NUM
ap-652	351	15	3	3	NUM
ap-652	351	16	�	�	PROPN
ap-652	351	17	�	�	PROPN
ap-652	351	18	�	�	PROPN
ap-652	351	19	�	�	PROPN
ap-652	351	20	�	�	PROPN
ap-652	351	21	�	�	PROPN
ap-652	351	22	�	�	PROPN
ap-652	351	23	�	�	PROPN
ap-652	351	24	is	be	AUX
ap-652	351	25	satisfied	satisfied	ADJ
ap-652	351	26	(	(	PUNCT
ap-652	351	27	ni	ni	PROPN
ap-652	351	28	is	be	AUX
ap-652	351	29	the	the	DET
ap-652	351	30	number	number	NOUN
ap-652	351	31	of	of	ADP
ap-652	351	32	bars	bar	NOUN
ap-652	351	33	in	in	ADP
ap-652	351	34	the	the	DET
ap-652	351	35	yi	yi	NOUN
ap-652	351	36	-	-	PUNCT
ap-652	351	37	direction	direction	NOUN
ap-652	351	38	,	,	PUNCT
ap-652	351	39	i	i	PRON
ap-652	351	40	�	�	PROPN
ap-652	351	41	1	1	NUM
ap-652	351	42	,	,	PUNCT
ap-652	351	43	2	2	NUM
ap-652	351	44	,	,	PUNCT
ap-652	351	45	3	3	NUM
ap-652	351	46	)	)	PUNCT
ap-652	351	47	.	.	PUNCT
ap-652	352	1	the	the	DET
ap-652	352	2	group	group	NOUN
ap-652	352	3	of	of	ADP
ap-652	352	4	media	medium	NOUN
ap-652	352	5	specified	specify	VERB
ap-652	352	6	above	above	ADV
ap-652	352	7	is	be	AUX
ap-652	352	8	the	the	DET
ap-652	352	9	only	only	ADJ
ap-652	352	10	group	group	NOUN
ap-652	352	11	of	of	ADP
ap-652	352	12	g1	g1	NOUN
ap-652	352	13	*	*	PUNCT
ap-652	352	14	-optimal	-optimal	ADJ
ap-652	352	15	media	medium	NOUN
ap-652	352	16	.	.	PUNCT
ap-652	353	1	they	they	PRON
ap-652	353	2	are	be	AUX
ap-652	353	3	in	in	ADP
ap-652	353	4	fact	fact	NOUN
ap-652	353	5	a	a	DET
ap-652	353	6	3d	3d	NUM
ap-652	353	7	extension	extension	NOUN
ap-652	353	8	of	of	ADP
ap-652	353	9	upl	upl	PROPN
ap-652	353	10	(	(	PUNCT
ap-652	353	11	the	the	DET
ap-652	353	12	uniform	uniform	ADJ
ap-652	353	13	perpendicular	perpendicular	ADJ
ap-652	353	14	lattices	lattice	NOUN
ap-652	353	15	)	)	PUNCT
ap-652	353	16	introduced	introduce	VERB
ap-652	353	17	in	in	ADP
ap-652	353	18	dimitrovová	dimitrovová	PROPN
ap-652	353	19	and	and	CCONJ
ap-652	353	20	faria	faria	PROPN
ap-652	353	21	(	(	PUNCT
ap-652	353	22	1999	1999	NUM
ap-652	353	23	)	)	PUNCT
ap-652	353	24	.	.	PUNCT
ap-652	354	1	the	the	DET
ap-652	354	2	simplest	simple	ADJ
ap-652	354	3	example	example	NOUN
ap-652	354	4	from	from	ADP
ap-652	354	5	this	this	DET
ap-652	354	6	group	group	NOUN
ap-652	354	7	is	be	AUX
ap-652	354	8	the	the	DET
ap-652	354	9	regular	regular	ADJ
ap-652	354	10	cubic	cubic	ADJ
ap-652	354	11	lattice	lattice	NOUN
ap-652	354	12	(	(	PUNCT
ap-652	354	13	fig	fig	NOUN
ap-652	354	14	.	.	PUNCT
ap-652	354	15	5	5	NUM
ap-652	354	16	)	)	PUNCT
ap-652	354	17	.	.	PUNCT
ap-652	355	1	the	the	DET
ap-652	355	2	value	value	NOUN
ap-652	355	3	of	of	ADP
ap-652	355	4	its	its	PRON
ap-652	355	5	g1	g1	NOUN
ap-652	355	6	*	*	PUNCT
ap-652	355	7	(	(	PUNCT
ap-652	355	8	not	not	PART
ap-652	355	9	the	the	DET
ap-652	355	10	proof	proof	NOUN
ap-652	355	11	of	of	ADP
ap-652	355	12	maximality	maximality	NOUN
ap-652	355	13	)	)	PUNCT
ap-652	355	14	can	can	AUX
ap-652	355	15	be	be	AUX
ap-652	355	16	obtained	obtain	VERB
ap-652	355	17	directly	directly	ADV
ap-652	355	18	from	from	ADP
ap-652	355	19	g1	g1	PROPN
ap-652	355	20	*	*	PUNCT
ap-652	355	21	of	of	ADP
ap-652	355	22	its	its	PRON
ap-652	355	23	2d	2d	NUM
ap-652	355	24	analog	analog	NOUN
ap-652	355	25	:	:	PUNCT
ap-652	355	26	the	the	DET
ap-652	355	27	regular	regular	ADJ
ap-652	355	28	square	square	ADJ
ap-652	355	29	lattice	lattice	NOUN
ap-652	355	30	.	.	PUNCT
ap-652	356	1	if	if	SCONJ
ap-652	356	2	we	we	PRON
ap-652	356	3	denote	denote	VERB
ap-652	356	4	by	by	ADP
ap-652	356	5	s2d	s2d	PROPN
ap-652	356	6	and	and	CCONJ
ap-652	356	7	s3d	s3d	PRON
ap-652	356	8	the	the	DET
ap-652	356	9	material	material	NOUN
ap-652	356	10	volume	volume	NOUN
ap-652	356	11	fractions	fraction	NOUN
ap-652	356	12	of	of	ADP
ap-652	356	13	2d	2d	NUM
ap-652	356	14	and	and	CCONJ
ap-652	356	15	3d	3d	NUM
ap-652	356	16	regular	regular	ADJ
ap-652	356	17	lattices	lattice	NOUN
ap-652	356	18	,	,	PUNCT
ap-652	356	19	respectively	respectively	ADV
ap-652	356	20	,	,	PUNCT
ap-652	356	21	it	it	PRON
ap-652	356	22	holds	hold	VERB
ap-652	356	23	s	s	PRON
ap-652	356	24	sd	sd	ADP
ap-652	356	25	d2	d2	PROPN
ap-652	356	26	32	32	NUM
ap-652	356	27	3	3	NUM
ap-652	356	28	�	�	PROPN
ap-652	356	29	,	,	PUNCT
ap-652	356	30	and	and	CCONJ
ap-652	356	31	consequently	consequently	ADV
ap-652	356	32	g	g	PROPN
ap-652	356	33	s	s	PART
ap-652	356	34	sd	sd	ADP
ap-652	356	35	d1	d1	PROPN
ap-652	356	36	2	2	NUM
ap-652	356	37	3	3	NUM
ap-652	356	38	1	1	NUM
ap-652	356	39	4	4	NUM
ap-652	356	40	1	1	NUM
ap-652	356	41	6	6	NUM
ap-652	356	42	*	*	PUNCT
ap-652	356	43	�	�	PROPN
ap-652	356	44	�	�	PROPN
ap-652	356	45	.	.	PUNCT
ap-652	357	1	(	(	PUNCT
ap-652	357	2	42	42	NUM
ap-652	357	3	)	)	SYM
ap-652	357	4	3.3	3.3	NUM
ap-652	357	5	shear	shear	NOUN
ap-652	357	6	modulus	modulus	NOUN
ap-652	357	7	g2	g2	PROPN
ap-652	357	8	*	*	PUNCT
ap-652	358	1	(	(	PUNCT
ap-652	358	2	for	for	ADP
ap-652	358	3	effective	effective	ADJ
ap-652	358	4	cubic	cubic	ADJ
ap-652	358	5	symmetry	symmetry	NOUN
ap-652	358	6	)	)	PUNCT
ap-652	358	7	first	first	ADV
ap-652	358	8	of	of	ADP
ap-652	358	9	all	all	PRON
ap-652	358	10	,	,	PUNCT
ap-652	358	11	we	we	PRON
ap-652	358	12	point	point	VERB
ap-652	358	13	out	out	ADP
ap-652	358	14	that	that	SCONJ
ap-652	358	15	in	in	ADP
ap-652	358	16	3d	3d	NOUN
ap-652	358	17	there	there	PRON
ap-652	358	18	exists	exist	VERB
ap-652	358	19	no	no	DET
ap-652	358	20	such	such	ADJ
ap-652	358	21	rotation	rotation	NOUN
ap-652	358	22	of	of	ADP
ap-652	358	23	the	the	DET
ap-652	358	24	global	global	ADJ
ap-652	358	25	coordinates	coordinate	NOUN
ap-652	358	26	that	that	PRON
ap-652	358	27	would	would	AUX
ap-652	358	28	interchange	interchange	VERB
ap-652	358	29	the	the	DET
ap-652	358	30	positions	position	NOUN
ap-652	358	31	ofg1	ofg1	NOUN
ap-652	358	32	*	*	PUNCT
ap-652	358	33	andg2	andg2	NOUN
ap-652	359	1	*	*	PUNCT
ap-652	359	2	in	in	ADP
ap-652	359	3	c	c	PROPN
ap-652	359	4	*	*	NOUN
ap-652	359	5	,	,	PUNCT
ap-652	359	6	as	as	SCONJ
ap-652	359	7	it	it	PRON
ap-652	359	8	does	do	AUX
ap-652	359	9	in	in	ADP
ap-652	359	10	2d	2d	PROPN
ap-652	359	11	(	(	PUNCT
ap-652	359	12	see	see	VERB
ap-652	359	13	dimitrovová	dimitrovová	NOUN
ap-652	359	14	and	and	CCONJ
ap-652	359	15	faria	faria	PROPN
ap-652	359	16	(	(	PUNCT
ap-652	359	17	1999	1999	NUM
ap-652	359	18	)	)	PUNCT
ap-652	359	19	)	)	PUNCT
ap-652	359	20	.	.	PUNCT
ap-652	360	1	thus	thus	ADV
ap-652	360	2	g2	g2	PROPN
ap-652	360	3	*	*	PUNCT
ap-652	360	4	-optimal	-optimal	ADJ
ap-652	360	5	media	medium	NOUN
ap-652	360	6	can	can	AUX
ap-652	360	7	not	not	PART
ap-652	360	8	be	be	AUX
ap-652	360	9	derived	derive	VERB
ap-652	360	10	from	from	ADP
ap-652	360	11	g1	g1	NOUN
ap-652	360	12	*	*	PUNCT
ap-652	360	13	-optimal	-optimal	ADJ
ap-652	360	14	media	medium	NOUN
ap-652	360	15	.	.	PUNCT
ap-652	361	1	for	for	ADP
ap-652	361	2	macroload	macroload	NOUN
ap-652	361	3	�	�	NOUN
ap-652	361	4	2	2	NUM
ap-652	361	5	g	g	NOUN
ap-652	361	6	we	we	PRON
ap-652	361	7	can	can	AUX
ap-652	361	8	obtain	obtain	VERB
ap-652	361	9	:	:	PUNCT
ap-652	361	10	g	g	PROPN
ap-652	361	11	v	v	PROPN
ap-652	361	12	s	s	ADP
ap-652	361	13	t	t	NOUN
ap-652	361	14	t	t	NOUN
ap-652	361	15	t	t	PROPN
ap-652	361	16	2	2	NUM
ap-652	361	17	1	1	NUM
ap-652	361	18	2	2	NUM
ap-652	361	19	2	2	NUM
ap-652	361	20	2	2	NUM
ap-652	361	21	3	3	NUM
ap-652	361	22	2	2	NUM
ap-652	361	23	2	2	NUM
ap-652	361	24	1	1	NUM
ap-652	361	25	2	2	NUM
ap-652	361	26	2	2	NUM
ap-652	361	27	1	1	NUM
ap-652	361	28	6	6	NUM
ap-652	361	29	3	3	NUM
ap-652	361	30	*	*	PUNCT
ap-652	361	31	(	(	PUNCT
ap-652	361	32	)	)	PUNCT
ap-652	361	33	(	(	PUNCT
ap-652	361	34	)	)	PUNCT
ap-652	361	35	(	(	PUNCT
ap-652	361	36	)	)	PUNCT
ap-652	361	37	cos	cos	PROPN
ap-652	361	38	(	(	PUNCT
ap-652	361	39	�	�	PROPN
ap-652	361	40	�	�	PROPN
ap-652	361	41	�	�	PROPN
ap-652	361	42	�	�	PROPN
ap-652	361	43	�	�	PROPN
ap-652	361	44	�	�	PROPN
ap-652	361	45	�	�	PROPN
ap-652	361	46	�	�	PROPN
ap-652	361	47	q	q	PROPN
ap-652	361	48	n	n	PROPN
ap-652	361	49	q	q	NOUN
ap-652	361	50	n	n	CCONJ
ap-652	361	51	q	q	NOUN
ap-652	361	52	n	n	CCONJ
ap-652	361	53	n	n	CCONJ
ap-652	361	54	q	q	NOUN
ap-652	361	55	n	n	CCONJ
ap-652	361	56	,	,	PUNCT
ap-652	361	57	)	)	PUNCT
ap-652	361	58	cos	cos	PROPN
ap-652	361	59	(	(	PUNCT
ap-652	361	60	,	,	PUNCT
ap-652	361	61	)	)	PUNCT
ap-652	361	62	q	q	NOUN
ap-652	361	63	q	q	PROPN
ap-652	362	1	n	n	PROPN
ap-652	362	2	q	q	NOUN
ap-652	363	1	p	p	X
ap-652	363	2	p	p	X
ap-652	363	3	p	p	X
ap-652	363	4	q	q	X
ap-652	363	5	q	q	X
ap-652	363	6	q	q	X
ap-652	363	7	q	q	NOUN
ap-652	363	8	1	1	NUM
ap-652	363	9	2	2	NUM
ap-652	363	10	2	2	NUM
ap-652	363	11	2	2	NUM
ap-652	363	12	2	2	NUM
ap-652	363	13	1	1	NUM
ap-652	363	14	2	2	NUM
ap-652	363	15	2	2	NUM
ap-652	363	16	2	2	NUM
ap-652	363	17	3	3	NUM
ap-652	363	18	2	2	NUM
ap-652	363	19	1	1	NUM
ap-652	363	20	2	2	NUM
ap-652	363	21	2	2	NUM
ap-652	363	22	2	2	NUM
ap-652	363	23	3	3	NUM
ap-652	363	24	2	2	NUM
ap-652	363	25	3	3	NUM
ap-652	363	26	2	2	NUM
ap-652	363	27	�	�	PROPN
ap-652	363	28	�	�	PROPN
ap-652	363	29	cos	cos	PROPN
ap-652	363	30	(	(	PUNCT
ap-652	363	31	,	,	PUNCT
ap-652	363	32	)	)	PUNCT
ap-652	363	33	.	.	PUNCT
ap-652	364	1	2	2	NUM
ap-652	364	2	3	3	NUM
ap-652	364	3	1	1	NUM
ap-652	364	4	2	2	NUM
ap-652	364	5	2	2	NUM
ap-652	364	6	2	2	NUM
ap-652	364	7	3	3	NUM
ap-652	364	8	2	2	NUM
ap-652	364	9	1	1	NUM
ap-652	364	10	2	2	NUM
ap-652	364	11	2	2	NUM
ap-652	364	12	2	2	NUM
ap-652	364	13	3	3	NUM
ap-652	364	14	2	2	NUM
ap-652	364	15	n	n	NOUN
ap-652	364	16	q	q	NOUN
ap-652	364	17	p	p	X
ap-652	364	18	p	p	X
ap-652	364	19	p	p	X
ap-652	364	20	q	q	X
ap-652	364	21	q	q	X
ap-652	364	22	q	q	ADJ
ap-652	364	23	�	�	PROPN
ap-652	364	24	�	�	PROPN
ap-652	364	25	�	�	PROPN
ap-652	364	26	�	�	PROPN
ap-652	364	27	(	(	PUNCT
ap-652	364	28	43	43	NUM
ap-652	364	29	)	)	PUNCT
ap-652	364	30	additional	additional	ADJ
ap-652	364	31	constraints	constraint	NOUN
ap-652	364	32	on	on	ADP
ap-652	364	33	possible	possible	ADJ
ap-652	364	34	n	n	NUM
ap-652	364	35	are	be	AUX
ap-652	364	36	:	:	PUNCT
ap-652	364	37	n	n	PRON
ap-652	364	38	r%	r%	VERB
ap-652	364	39	�	�	PROPN
ap-652	364	40	�	�	PROPN
ap-652	364	41	j	j	PROPN
ap-652	364	42	j	j	PROPN
ap-652	364	43	1	1	NUM
ap-652	364	44	2	2	NUM
ap-652	364	45	3	3	NUM
ap-652	364	46	,	,	PUNCT
ap-652	364	47	,	,	PUNCT
ap-652	364	48	.	.	PUNCT
ap-652	365	1	(	(	PUNCT
ap-652	365	2	44	44	NUM
ap-652	365	3	)	)	PUNCT
ap-652	365	4	the	the	DET
ap-652	365	5	obvious	obvious	ADJ
ap-652	365	6	maximum	maximum	ADJ
ap-652	365	7	s/3	s/3	NOUN
ap-652	365	8	can	can	AUX
ap-652	365	9	not	not	PART
ap-652	365	10	be	be	AUX
ap-652	365	11	achieved	achieve	VERB
ap-652	365	12	by	by	ADP
ap-652	365	13	any	any	DET
ap-652	365	14	medium	medium	NOUN
ap-652	365	15	,	,	PUNCT
ap-652	365	16	similarly	similarly	ADV
ap-652	365	17	as	as	ADP
ap-652	365	18	in	in	ADP
ap-652	365	19	section	section	NOUN
ap-652	365	20	3.2	3.2	NUM
ap-652	365	21	.	.	PUNCT
ap-652	366	1	also	also	ADV
ap-652	366	2	,	,	PUNCT
ap-652	366	3	combining	combine	VERB
ap-652	366	4	the	the	DET
ap-652	366	5	2d	2d	NUM
ap-652	366	6	results	result	NOUN
ap-652	366	7	(	(	PUNCT
ap-652	366	8	unlike	unlike	ADP
ap-652	366	9	to	to	ADP
ap-652	366	10	(	(	PUNCT
ap-652	366	11	42	42	NUM
ap-652	366	12	)	)	PUNCT
ap-652	366	13	)	)	PUNCT
ap-652	366	14	would	would	AUX
ap-652	366	15	lead	lead	VERB
ap-652	366	16	to	to	ADP
ap-652	366	17	a	a	DET
ap-652	366	18	wrong	wrong	ADJ
ap-652	366	19	conclusion	conclusion	NOUN
ap-652	366	20	,	,	PUNCT
ap-652	366	21	as	as	SCONJ
ap-652	366	22	can	can	AUX
ap-652	366	23	be	be	AUX
ap-652	366	24	demonstrated	demonstrate	VERB
ap-652	366	25	:	:	PUNCT
ap-652	366	26	let	let	VERB
ap-652	366	27	only	only	ADV
ap-652	366	28	�	�	PROPN
ap-652	366	29	23	23	NUM
ap-652	366	30	0	0	NUM
ap-652	366	31	�	�	PROPN
ap-652	366	32	in	in	ADP
ap-652	366	33	�	�	PROPN
ap-652	366	34	2	2	NUM
ap-652	366	35	g	g	NOUN
ap-652	366	36	,	,	PUNCT
ap-652	366	37	then	then	ADV
ap-652	366	38	an	an	DET
ap-652	366	39	optimal	optimal	ADJ
ap-652	366	40	medium	medium	NOUN
ap-652	366	41	should	should	AUX
ap-652	366	42	have	have	VERB
ap-652	366	43	bars	bar	NOUN
ap-652	366	44	in	in	ADP
ap-652	366	45	the	the	DET
ap-652	366	46	directions	direction	NOUN
ap-652	366	47	of	of	ADP
ap-652	366	48	the	the	DET
ap-652	366	49	unit	unit	NOUN
ap-652	366	50	square	square	ADJ
ap-652	366	51	diagonals	diagonal	NOUN
ap-652	366	52	in	in	ADP
ap-652	366	53	(	(	PUNCT
ap-652	366	54	2	2	NUM
ap-652	366	55	,	,	PUNCT
ap-652	366	56	3)-planes	3)-planes	NUM
ap-652	366	57	,	,	PUNCT
ap-652	366	58	according	accord	VERB
ap-652	366	59	to	to	ADP
ap-652	366	60	dimitrovová	dimitrovová	PROPN
ap-652	366	61	and	and	CCONJ
ap-652	366	62	faria	faria	PROPN
ap-652	366	63	(	(	PUNCT
ap-652	366	64	1999	1999	NUM
ap-652	366	65	)	)	PUNCT
ap-652	366	66	.	.	PUNCT
ap-652	367	1	by	by	ADP
ap-652	367	2	analogy	analogy	NOUN
ap-652	367	3	,	,	PUNCT
ap-652	367	4	the	the	DET
ap-652	367	5	other	other	ADJ
ap-652	367	6	load	load	NOUN
ap-652	367	7	cases	case	NOUN
ap-652	367	8	�	�	PROPN
ap-652	367	9	12	12	NUM
ap-652	367	10	0	0	NUM
ap-652	367	11	�	�	PROPN
ap-652	367	12	and	and	CCONJ
ap-652	367	13	�	�	PROPN
ap-652	367	14	13	13	NUM
ap-652	367	15	0	0	NUM
ap-652	367	16	�	�	PROPN
ap-652	367	17	imply	imply	VERB
ap-652	367	18	directions	direction	NOUN
ap-652	367	19	of	of	ADP
ap-652	367	20	the	the	DET
ap-652	367	21	bars	bar	NOUN
ap-652	367	22	in	in	ADP
ap-652	367	23	(	(	PUNCT
ap-652	367	24	1	1	NUM
ap-652	367	25	,	,	PUNCT
ap-652	367	26	2	2	NUM
ap-652	367	27	)	)	PUNCT
ap-652	367	28	and	and	CCONJ
ap-652	367	29	(	(	PUNCT
ap-652	367	30	1	1	NUM
ap-652	367	31	,	,	PUNCT
ap-652	367	32	3)-planes	3)-planes	NUM
ap-652	367	33	,	,	PUNCT
ap-652	367	34	respectively	respectively	ADV
ap-652	367	35	.	.	PUNCT
ap-652	368	1	the	the	DET
ap-652	368	2	2d	2d	PROPN
ap-652	368	3	result	result	VERB
ap-652	368	4	g	g	PROPN
ap-652	368	5	s	s	PROPN
ap-652	368	6	d2	d2	PROPN
ap-652	368	7	2	2	NUM
ap-652	368	8	4	4	NUM
ap-652	368	9	,	,	PUNCT
ap-652	368	10	*	*	PUNCT
ap-652	368	11	�	�	PROPN
ap-652	368	12	and	and	CCONJ
ap-652	368	13	the	the	DET
ap-652	368	14	fact	fact	NOUN
ap-652	368	15	that	that	SCONJ
ap-652	368	16	s	s	AUX
ap-652	368	17	sd	sd	ADP
ap-652	368	18	d2	d2	PROPN
ap-652	368	19	3	3	NUM
ap-652	368	20	3	3	NUM
ap-652	368	21	�	�	PROPN
ap-652	368	22	thus	thus	ADV
ap-652	368	23	yield	yield	VERB
ap-652	368	24	g	g	PROPN
ap-652	368	25	s3d2	s3d2	ADP
ap-652	368	26	12	12	NUM
ap-652	368	27	*	*	PUNCT
ap-652	368	28	�	�	PROPN
ap-652	368	29	,	,	PUNCT
ap-652	368	30	because	because	SCONJ
ap-652	368	31	the	the	DET
ap-652	368	32	directions	direction	NOUN
ap-652	368	33	of	of	ADP
ap-652	368	34	180	180	NUM
ap-652	368	35	©	©	PROPN
ap-652	368	36	czech	czech	PROPN
ap-652	368	37	technical	technical	PROPN
ap-652	368	38	university	university	PROPN
ap-652	368	39	publishing	publishing	NOUN
ap-652	368	40	house	house	NOUN
ap-652	368	41	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	368	42	acta	acta	PROPN
ap-652	368	43	polytechnica	polytechnica	PROPN
ap-652	368	44	vol	vol	NOUN
ap-652	368	45	.	.	PROPN
ap-652	368	46	44	44	NUM
ap-652	368	47	no.5–6/2004	no.5–6/2004	NOUN
ap-652	368	48	group	group	NOUN
ap-652	368	49	1	1	NUM
ap-652	368	50	.	.	NOUN
ap-652	368	51	2	2	NUM
ap-652	368	52	.	.	NOUN
ap-652	368	53	3	3	X
ap-652	368	54	.	.	X
ap-652	368	55	spherical	spherical	ADJ
ap-652	368	56	angles	angle	NOUN
ap-652	368	57	�	�	PROPN
ap-652	368	58	�	�	PROPN
ap-652	368	59	1	1	NUM
ap-652	368	60	12	12	NUM
ap-652	368	61	0	0	NUM
ap-652	368	62	�	�	PROPN
ap-652	368	63	�	�	PROPN
ap-652	368	64	,	,	PUNCT
ap-652	368	65	�	�	PROPN
ap-652	368	66	�	�	PROPN
ap-652	368	67	�	�	PROPN
ap-652	368	68	2	2	NUM
ap-652	368	69	22	22	NUM
ap-652	368	70	2	2	NUM
ap-652	368	71	�	�	PROPN
ap-652	368	72	�	�	PROPN
ap-652	368	73	,	,	PUNCT
ap-652	368	74	�	�	PROPN
ap-652	368	75	3	3	NUM
ap-652	368	76	0	0	NUM
ap-652	368	77	�	�	PROPN
ap-652	368	78	values	value	NOUN
ap-652	368	79	of	of	ADP
ap-652	368	80	�	�	PROPN
ap-652	368	81	1	1	NUM
ap-652	368	82	,	,	PUNCT
ap-652	368	83	�	�	PROPN
ap-652	368	84	2	2	NUM
ap-652	368	85	,	,	PUNCT
ap-652	368	86	�	�	PROPN
ap-652	368	87	3	3	NUM
ap-652	368	88	0	0	NUM
ap-652	368	89	,	,	PUNCT
ap-652	368	90	1	1	NUM
ap-652	368	91	,	,	PUNCT
ap-652	368	92	1	1	NUM
ap-652	368	93	1	1	NUM
ap-652	368	94	,	,	PUNCT
ap-652	368	95	0	0	NUM
ap-652	368	96	,	,	PUNCT
ap-652	368	97	1	1	NUM
ap-652	368	98	1	1	NUM
ap-652	368	99	,	,	PUNCT
ap-652	368	100	1	1	NUM
ap-652	368	101	,	,	PUNCT
ap-652	368	102	0	0	NUM
ap-652	368	103	values	value	NOUN
ap-652	368	104	of	of	ADP
ap-652	368	105	�	�	NOUN
ap-652	368	106	1	1	NUM
ap-652	368	107	,	,	PUNCT
ap-652	368	108	�	�	PROPN
ap-652	368	109	2	2	NUM
ap-652	368	110	,	,	PUNCT
ap-652	368	111	�	�	PROPN
ap-652	368	112	3	3	NUM
ap-652	368	113	1	1	NUM
ap-652	368	114	,	,	PUNCT
ap-652	368	115	0	0	NUM
ap-652	368	116	,	,	PUNCT
ap-652	368	117	0	0	NUM
ap-652	368	118	0	0	NUM
ap-652	368	119	,	,	PUNCT
ap-652	368	120	1	1	NUM
ap-652	368	121	,	,	PUNCT
ap-652	368	122	0	0	NUM
ap-652	368	123	0	0	NUM
ap-652	368	124	,	,	PUNCT
ap-652	368	125	0	0	NUM
ap-652	368	126	,	,	PUNCT
ap-652	368	127	1	1	NUM
ap-652	368	128	table	table	NOUN
ap-652	368	129	3	3	NUM
ap-652	368	130	:	:	PUNCT
ap-652	368	131	characterization	characterization	NOUN
ap-652	368	132	of	of	ADP
ap-652	368	133	g1	g1	NOUN
ap-652	368	134	*	*	PUNCT
ap-652	368	135	-optimal	-optimal	ADJ
ap-652	368	136	media	medium	NOUN
ap-652	368	137	basic	basic	ADJ
ap-652	368	138	case	case	NOUN
ap-652	368	139	1	1	NUM
ap-652	368	140	.	.	NOUN
ap-652	368	141	2	2	NUM
ap-652	368	142	.	.	NOUN
ap-652	368	143	3	3	X
ap-652	368	144	.	.	X
ap-652	368	145	macrostress	macrostress	NOUN
ap-652	368	146	�	�	PROPN
ap-652	368	147	23	23	NUM
ap-652	368	148	1	1	NUM
ap-652	368	149	�	�	PROPN
ap-652	368	150	�	�	PROPN
ap-652	368	151	13	13	NUM
ap-652	368	152	1	1	NUM
ap-652	368	153	�	�	PROPN
ap-652	368	154	�	�	PROPN
ap-652	368	155	12	12	NUM
ap-652	368	156	1	1	NUM
ap-652	368	157	�	�	PROPN
ap-652	368	158	macrostrain	macrostrain	NOUN
ap-652	368	159	�	�	PROPN
ap-652	368	160	23	23	NUM
ap-652	368	161	21	21	NUM
ap-652	368	162	2	2	NUM
ap-652	368	163	�	�	PROPN
ap-652	368	164	(	(	PUNCT
ap-652	368	165	)	)	PUNCT
ap-652	368	166	*	*	PUNCT
ap-652	368	167	g	g	ADP
ap-652	368	168	es	es	PRON
ap-652	368	169	�	�	PROPN
ap-652	368	170	13	13	NUM
ap-652	368	171	21	21	NUM
ap-652	368	172	2	2	NUM
ap-652	368	173	�	�	PROPN
ap-652	368	174	(	(	PUNCT
ap-652	368	175	)	)	PUNCT
ap-652	368	176	*	*	PUNCT
ap-652	368	177	g	g	ADP
ap-652	368	178	es	es	PRON
ap-652	368	179	�	�	PROPN
ap-652	368	180	12	12	NUM
ap-652	368	181	21	21	NUM
ap-652	368	182	2	2	NUM
ap-652	368	183	�	�	PROPN
ap-652	368	184	(	(	PUNCT
ap-652	368	185	)	)	PUNCT
ap-652	368	186	*	*	PUNCT
ap-652	368	187	g	g	NOUN
ap-652	368	188	es	es	X
ap-652	368	189	maximality	maximality	NOUN
ap-652	368	190	condition	condition	NOUN
ap-652	368	191	from	from	ADP
ap-652	368	192	eq	eq	PROPN
ap-652	368	193	.	.	PUNCT
ap-652	369	1	(	(	PUNCT
ap-652	369	2	30	30	NUM
ap-652	369	3	)	)	PUNCT
ap-652	369	4	n	n	PRON
ap-652	369	5	q	q	PROPN
ap-652	369	6	�	�	PROPN
ap-652	369	7	1	1	NUM
ap-652	369	8	2	2	NUM
ap-652	369	9	1	1	NUM
ap-652	369	10	g	g	NOUN
ap-652	369	11	*	*	PROPN
ap-652	369	12	n	n	PRON
ap-652	369	13	q	q	PROPN
ap-652	369	14	�	�	PROPN
ap-652	369	15	1	1	NUM
ap-652	369	16	2	2	NUM
ap-652	369	17	2	2	NUM
ap-652	369	18	g	g	NOUN
ap-652	369	19	*	*	PROPN
ap-652	369	20	n	n	PRON
ap-652	369	21	q	q	PROPN
ap-652	369	22	�	�	PROPN
ap-652	369	23	1	1	NUM
ap-652	369	24	2	2	NUM
ap-652	369	25	3	3	NUM
ap-652	369	26	g	g	NOUN
ap-652	369	27	*	*	PUNCT
ap-652	369	28	additional	additional	ADJ
ap-652	369	29	constraints	constraint	NOUN
ap-652	369	30	1	1	NUM
ap-652	369	31	2	2	NUM
ap-652	369	32	1	1	NUM
ap-652	369	33	3	3	NUM
ap-652	369	34	1	1	NUM
ap-652	369	35	1	1	NUM
ap-652	369	36	2	2	NUM
ap-652	369	37	2	2	NUM
ap-652	369	38	q	q	NOUN
ap-652	369	39	q	q	NOUN
ap-652	369	40	q	q	X
ap-652	369	41	q	q	X
ap-652	369	42	q	q	NOUN
ap-652	369	43	r	r	NOUN
ap-652	369	44	q	q	NOUN
ap-652	370	1	%	%	NOUN
ap-652	370	2	%	%	INTJ
ap-652	370	3	%	%	INTJ
ap-652	370	4	�	�	PROPN
ap-652	370	5	�	�	PROPN
ap-652	370	6	&	&	CCONJ
ap-652	370	7	*	*	PUNCT
ap-652	371	1	i	i	PRON
ap-652	371	2	i	i	PRON
ap-652	372	1	g	g	VERB
ap-652	372	2	v	v	NUM
ap-652	372	3	2	2	NUM
ap-652	372	4	1	1	NUM
ap-652	372	5	2	2	NUM
ap-652	372	6	3	3	NUM
ap-652	372	7	2	2	NUM
ap-652	372	8	2	2	NUM
ap-652	372	9	2	2	NUM
ap-652	372	10	2	2	NUM
ap-652	372	11	q	q	NOUN
ap-652	372	12	q	q	NOUN
ap-652	372	13	q	q	X
ap-652	372	14	q	q	X
ap-652	372	15	q	q	NOUN
ap-652	372	16	r	r	NOUN
ap-652	372	17	q	q	NOUN
ap-652	373	1	%	%	NOUN
ap-652	373	2	%	%	INTJ
ap-652	373	3	%	%	INTJ
ap-652	373	4	�	�	PROPN
ap-652	373	5	�	�	PROPN
ap-652	373	6	&	&	CCONJ
ap-652	373	7	*	*	PUNCT
ap-652	374	1	i	i	PRON
ap-652	374	2	i	i	PRON
ap-652	375	1	g	g	VERB
ap-652	375	2	v	v	NUM
ap-652	375	3	3	3	NUM
ap-652	375	4	1	1	NUM
ap-652	375	5	3	3	NUM
ap-652	375	6	2	2	NUM
ap-652	375	7	3	3	NUM
ap-652	375	8	3	3	NUM
ap-652	375	9	2	2	NUM
ap-652	375	10	2	2	NUM
ap-652	375	11	q	q	NOUN
ap-652	375	12	q	q	NOUN
ap-652	375	13	q	q	X
ap-652	375	14	q	q	X
ap-652	375	15	q	q	NOUN
ap-652	375	16	r	r	NOUN
ap-652	375	17	q	q	NOUN
ap-652	376	1	%	%	NOUN
ap-652	376	2	%	%	INTJ
ap-652	376	3	%	%	INTJ
ap-652	376	4	�	�	PROPN
ap-652	376	5	�	�	PROPN
ap-652	376	6	&	&	CCONJ
ap-652	376	7	*	*	PUNCT
ap-652	377	1	i	i	PRON
ap-652	377	2	i	i	PRON
ap-652	377	3	g	g	VERB
ap-652	377	4	v	v	NUM
ap-652	377	5	table	table	NOUN
ap-652	377	6	4	4	NUM
ap-652	377	7	:	:	PUNCT
ap-652	377	8	basic	basic	ADJ
ap-652	377	9	load	load	NOUN
ap-652	377	10	cases	case	NOUN
ap-652	377	11	in	in	ADP
ap-652	377	12	�	�	PROPN
ap-652	377	13	2	2	NUM
ap-652	377	14	g	g	NOUN
ap-652	377	15	the	the	DET
ap-652	377	16	bars	bar	NOUN
ap-652	377	17	stated	state	VERB
ap-652	377	18	previously	previously	ADV
ap-652	377	19	do	do	AUX
ap-652	377	20	not	not	PART
ap-652	377	21	coincide	coincide	VERB
ap-652	377	22	.	.	PUNCT
ap-652	378	1	however	however	ADV
ap-652	378	2	,	,	PUNCT
ap-652	378	3	it	it	PRON
ap-652	378	4	will	will	AUX
ap-652	378	5	be	be	AUX
ap-652	378	6	proven	prove	VERB
ap-652	378	7	that	that	SCONJ
ap-652	378	8	g	g	PROPN
ap-652	378	9	s2	s2	PROPN
ap-652	378	10	9	9	NUM
ap-652	378	11	,	,	PUNCT
ap-652	378	12	*	*	PUNCT
ap-652	378	13	�	�	PROPN
ap-652	378	14	.	.	PUNCT
ap-652	379	1	an	an	DET
ap-652	379	2	arbitrary	arbitrary	ADJ
ap-652	379	3	�	�	NOUN
ap-652	379	4	2	2	NUM
ap-652	379	5	g	g	NOUN
ap-652	379	6	can	can	AUX
ap-652	379	7	be	be	AUX
ap-652	379	8	expressed	express	VERB
ap-652	379	9	as	as	ADP
ap-652	379	10	a	a	DET
ap-652	379	11	linear	linear	ADJ
ap-652	379	12	combination	combination	NOUN
ap-652	379	13	of	of	ADP
ap-652	379	14	three	three	NUM
ap-652	379	15	basic	basic	ADJ
ap-652	379	16	cases	case	NOUN
ap-652	379	17	(	(	PUNCT
ap-652	379	18	table	table	NOUN
ap-652	379	19	4	4	NUM
ap-652	379	20	)	)	PUNCT
ap-652	379	21	.	.	PUNCT
ap-652	380	1	using	use	VERB
ap-652	380	2	superposition	superposition	NOUN
ap-652	380	3	,	,	PUNCT
ap-652	380	4	the	the	DET
ap-652	380	5	necessary	necessary	ADJ
ap-652	380	6	maximality	maximality	NOUN
ap-652	380	7	condition	condition	NOUN
ap-652	380	8	reads	read	VERB
ap-652	380	9	as	as	ADP
ap-652	380	10	:	:	PUNCT
ap-652	380	11	n	n	CCONJ
ap-652	380	12	�	�	PROPN
ap-652	380	13	�	�	PROPN
ap-652	380	14	1	1	NUM
ap-652	380	15	2	2	NUM
ap-652	380	16	1	1	NUM
ap-652	380	17	1	1	NUM
ap-652	380	18	2	2	NUM
ap-652	380	19	2	2	NUM
ap-652	380	20	3	3	NUM
ap-652	380	21	3	3	NUM
ap-652	380	22	1	1	NUM
ap-652	380	23	1	1	NUM
ap-652	380	24	2	2	NUM
ap-652	380	25	2	2	NUM
ap-652	380	26	3	3	NUM
ap-652	380	27	3	3	NUM
ap-652	380	28	g	g	NOUN
ap-652	380	29	*	*	PROPN
ap-652	380	30	)	)	PUNCT
ap-652	380	31	(	(	PUNCT
ap-652	380	32	q	q	NOUN
ap-652	380	33	q	q	X
ap-652	380	34	q	q	X
ap-652	380	35	q	q	X
ap-652	380	36	q	q	X
ap-652	380	37	q	q	PROPN
ap-652	380	38	�	�	PROPN
ap-652	380	39	�	�	PROPN
ap-652	380	40	�	�	PROPN
ap-652	380	41	�	�	PROPN
ap-652	380	42	�	�	PROPN
ap-652	380	43	�	�	PROPN
ap-652	380	44	,	,	PUNCT
ap-652	380	45	(	(	PUNCT
ap-652	380	46	45	45	NUM
ap-652	380	47	)	)	PUNCT
ap-652	380	48	where	where	SCONJ
ap-652	380	49	the	the	DET
ap-652	380	50	coefficients	coefficient	NOUN
ap-652	380	51	�	�	VERB
ap-652	380	52	i	i	PRON
ap-652	380	53	express	express	VERB
ap-652	380	54	a	a	DET
ap-652	380	55	combination	combination	NOUN
ap-652	380	56	of	of	ADP
ap-652	380	57	the	the	DET
ap-652	380	58	specific	specific	ADJ
ap-652	380	59	basic	basic	ADJ
ap-652	380	60	cases	case	NOUN
ap-652	380	61	,	,	PUNCT
ap-652	380	62	corresponding	correspond	VERB
ap-652	380	63	to	to	ADP
ap-652	380	64	the	the	DET
ap-652	380	65	imposed	impose	VERB
ap-652	380	66	macroload	macroload	NOUN
ap-652	380	67	.	.	PUNCT
ap-652	381	1	additional	additional	ADJ
ap-652	381	2	constraints	constraint	NOUN
ap-652	381	3	are	be	AUX
ap-652	381	4	:	:	PUNCT
ap-652	381	5	q	q	PUNCT
ap-652	381	6	r	r	NOUN
ap-652	381	7	q	q	X
ap-652	381	8	q	q	X
ap-652	381	9	qj	qj	PROPN
ap-652	381	10	k	k	PROPN
ap-652	381	11	1	1	NUM
ap-652	381	12	3j	3j	NUM
ap-652	381	13	,	,	PUNCT
ap-652	381	14	k	k	PROPN
ap-652	381	15	&	&	CCONJ
ap-652	381	16	%	%	PROPN
ap-652	381	17	�	�	PROPN
ap-652	381	18	�	�	PROPN
ap-652	382	1	%	%	NOUN
ap-652	382	2	%	%	NOUN
ap-652	382	3	1	1	NUM
ap-652	382	4	2	2	NUM
ap-652	382	5	3	3	NUM
ap-652	382	6	2	2	NUM
ap-652	382	7	,	,	PUNCT
ap-652	382	8	,	,	PUNCT
ap-652	382	9	(	(	PUNCT
ap-652	382	10	46	46	NUM
ap-652	382	11	)	)	PUNCT
ap-652	382	12	and	and	CCONJ
ap-652	382	13	q	q	DET
ap-652	382	14	q	q	PROPN
ap-652	382	15	q1	q1	PROPN
ap-652	382	16	2	2	NUM
ap-652	382	17	3	3	NUM
ap-652	382	18	2	2	NUM
ap-652	382	19	�	�	PROPN
ap-652	382	20	�	�	PROPN
ap-652	382	21	�	�	PROPN
ap-652	382	22	g	g	ADP
ap-652	382	23	v	v	PROPN
ap-652	382	24	*	*	PUNCT
ap-652	382	25	(	(	PUNCT
ap-652	382	26	47	47	NUM
ap-652	382	27	)	)	PUNCT
ap-652	382	28	if	if	SCONJ
ap-652	382	29	(	(	PUNCT
ap-652	382	30	47	47	NUM
ap-652	382	31	)	)	PUNCT
ap-652	382	32	were	be	AUX
ap-652	382	33	to	to	PART
ap-652	382	34	be	be	AUX
ap-652	382	35	derived	derive	VERB
ap-652	382	36	first	first	ADV
ap-652	382	37	,	,	PUNCT
ap-652	382	38	then	then	ADV
ap-652	382	39	using	use	VERB
ap-652	382	40	some	some	DET
ap-652	382	41	statements	statement	NOUN
ap-652	382	42	about	about	ADP
ap-652	382	43	finite	finite	ADJ
ap-652	382	44	dimensional	dimensional	ADJ
ap-652	382	45	spaces	space	NOUN
ap-652	382	46	,	,	PUNCT
ap-652	382	47	(	(	PUNCT
ap-652	382	48	45	45	NUM
ap-652	382	49	)	)	PUNCT
ap-652	382	50	is	be	AUX
ap-652	382	51	the	the	DET
ap-652	382	52	maximality	maximality	NOUN
ap-652	382	53	condition	condition	NOUN
ap-652	382	54	for	for	ADP
ap-652	382	55	the	the	DET
ap-652	382	56	sum	sum	NOUN
ap-652	382	57	of	of	ADP
ap-652	382	58	cosines	cosine	NOUN
ap-652	382	59	from	from	ADP
ap-652	382	60	(	(	PUNCT
ap-652	382	61	43	43	NUM
ap-652	382	62	)	)	PUNCT
ap-652	382	63	,	,	PUNCT
ap-652	382	64	similarly	similarly	ADV
ap-652	382	65	as	as	ADP
ap-652	382	66	in	in	ADP
ap-652	382	67	section	section	NOUN
ap-652	382	68	3.2	3.2	NUM
ap-652	382	69	.	.	PUNCT
ap-652	383	1	now	now	ADV
ap-652	383	2	,	,	PUNCT
ap-652	383	3	due	due	ADP
ap-652	383	4	to	to	ADP
ap-652	383	5	the	the	DET
ap-652	383	6	orthogonality	orthogonality	NOUN
ap-652	383	7	of	of	ADP
ap-652	383	8	qj	qj	PROPN
ap-652	383	9	,	,	PUNCT
ap-652	383	10	the	the	DET
ap-652	383	11	sum	sum	NOUN
ap-652	383	12	of	of	ADP
ap-652	383	13	the	the	DET
ap-652	383	14	cosines	cosine	NOUN
ap-652	383	15	is	be	AUX
ap-652	383	16	equal	equal	ADJ
ap-652	383	17	to	to	ADP
ap-652	383	18	1	1	NUM
ap-652	383	19	,	,	PUNCT
ap-652	383	20	therefore	therefore	ADV
ap-652	383	21	g	g	PROPN
ap-652	383	22	s2	s2	PROPN
ap-652	383	23	9	9	NUM
ap-652	383	24	,	,	PUNCT
ap-652	383	25	*	*	PUNCT
ap-652	383	26	�	�	PROPN
ap-652	383	27	,	,	PUNCT
ap-652	383	28	if	if	SCONJ
ap-652	383	29	at	at	ADV
ap-652	383	30	least	least	ADV
ap-652	383	31	one	one	NUM
ap-652	383	32	optimal	optimal	ADJ
ap-652	383	33	medium	medium	NOUN
ap-652	383	34	exists	exist	NOUN
ap-652	383	35	,	,	PUNCT
ap-652	383	36	i.e.	i.e.	X
ap-652	383	37	if	if	SCONJ
ap-652	383	38	there	there	PRON
ap-652	383	39	can	can	AUX
ap-652	383	40	be	be	AUX
ap-652	383	41	found	find	VERB
ap-652	383	42	a	a	DET
ap-652	383	43	medium	medium	NOUN
ap-652	383	44	in	in	ADP
ap-652	383	45	which	which	PRON
ap-652	383	46	p	p	PRON
ap-652	383	47	0j	0j	NOUN
ap-652	383	48	j	j	PROPN
ap-652	383	49	�	�	PROPN
ap-652	383	50	�	�	PROPN
ap-652	383	51	�	�	PROPN
ap-652	383	52	1	1	NUM
ap-652	383	53	2	2	NUM
ap-652	383	54	3	3	NUM
ap-652	383	55	,	,	PUNCT
ap-652	383	56	,	,	PUNCT
ap-652	383	57	,	,	PUNCT
ap-652	383	58	(	(	PUNCT
ap-652	383	59	45–47	45–47	NOUN
ap-652	383	60	)	)	PUNCT
ap-652	383	61	hold	hold	VERB
ap-652	383	62	and	and	CCONJ
ap-652	383	63	no	no	DET
ap-652	383	64	zero	zero	NUM
ap-652	383	65	bars	bar	NOUN
ap-652	383	66	are	be	AUX
ap-652	383	67	contained	contain	VERB
ap-652	383	68	in	in	ADP
ap-652	383	69	it	it	PRON
ap-652	383	70	.	.	PUNCT
ap-652	384	1	the	the	DET
ap-652	384	2	requirement	requirement	NOUN
ap-652	384	3	p	p	PROPN
ap-652	384	4	0j	0j	VERB
ap-652	384	5	j	j	PROPN
ap-652	384	6	�	�	PROPN
ap-652	384	7	�	�	PROPN
ap-652	384	8	�	�	PROPN
ap-652	384	9	1	1	NUM
ap-652	384	10	2	2	NUM
ap-652	384	11	3	3	NUM
ap-652	384	12	,	,	PUNCT
ap-652	384	13	,	,	PUNCT
ap-652	384	14	is	be	AUX
ap-652	384	15	equivalent	equivalent	ADJ
ap-652	384	16	to	to	ADP
ap-652	384	17	the	the	DET
ap-652	384	18	condition	condition	NOUN
ap-652	384	19	under	under	ADP
ap-652	384	20	which	which	PRON
ap-652	384	21	&	&	CCONJ
ap-652	384	22	�	�	PROPN
ap-652	384	23	max	max	PROPN
ap-652	384	24	�	�	PROPN
ap-652	384	25	�	�	PROPN
ap-652	384	26	�	�	PROPN
ap-652	384	27	1,i	1,i	PROPN
ap-652	384	28	2,i	2,i	NUM
ap-652	384	29	3,i	3,i	PROPN
ap-652	384	30	(	(	PUNCT
ap-652	384	31	48	48	NUM
ap-652	384	32	)	)	PUNCT
ap-652	384	33	is	be	AUX
ap-652	384	34	obtained	obtain	VERB
ap-652	384	35	for	for	ADP
ap-652	384	36	each	each	DET
ap-652	384	37	i.	i.	NOUN
ap-652	384	38	solutions	solution	NOUN
ap-652	384	39	of	of	ADP
ap-652	384	40	(	(	PUNCT
ap-652	384	41	48	48	NUM
ap-652	384	42	)	)	PUNCT
ap-652	384	43	yield	yield	VERB
ap-652	384	44	four	four	NUM
ap-652	384	45	groups	group	NOUN
ap-652	384	46	of	of	ADP
ap-652	384	47	angles	angle	NOUN
ap-652	384	48	,	,	PUNCT
ap-652	384	49	as	as	SCONJ
ap-652	384	50	specified	specify	VERB
ap-652	384	51	in	in	ADP
ap-652	384	52	table	table	NOUN
ap-652	384	53	5	5	NUM
ap-652	384	54	,	,	PUNCT
ap-652	384	55	corresponding	correspond	VERB
ap-652	384	56	to	to	ADP
ap-652	384	57	the	the	DET
ap-652	384	58	main	main	ADJ
ap-652	384	59	diagonals	diagonal	NOUN
ap-652	384	60	of	of	ADP
ap-652	384	61	the	the	DET
ap-652	384	62	unit	unit	NOUN
ap-652	384	63	cube	cube	NOUN
ap-652	384	64	.	.	PUNCT
ap-652	385	1	it	it	PRON
ap-652	385	2	is	be	AUX
ap-652	385	3	not	not	PART
ap-652	385	4	convenient	convenient	ADJ
ap-652	385	5	to	to	PART
ap-652	385	6	choose	choose	VERB
ap-652	385	7	a	a	DET
ap-652	385	8	basic	basic	ADJ
ap-652	385	9	cell	cell	NOUN
ap-652	385	10	with	with	ADP
ap-652	385	11	eight	eight	NUM
ap-652	385	12	faces	face	NOUN
ap-652	385	13	(	(	PUNCT
ap-652	385	14	perpendicular	perpendicular	ADJ
ap-652	385	15	to	to	ADP
ap-652	385	16	the	the	DET
ap-652	385	17	directions	direction	NOUN
ap-652	385	18	of	of	ADP
ap-652	385	19	the	the	DET
ap-652	385	20	bars	bar	NOUN
ap-652	385	21	)	)	PUNCT
ap-652	385	22	,	,	PUNCT
ap-652	385	23	because	because	SCONJ
ap-652	385	24	a	a	DET
ap-652	385	25	regular	regular	ADJ
ap-652	385	26	octahedron	octahedron	NOUN
ap-652	385	27	does	do	AUX
ap-652	385	28	not	not	PART
ap-652	385	29	fill	fill	VERB
ap-652	385	30	the	the	DET
ap-652	385	31	space	space	NOUN
ap-652	385	32	.	.	PUNCT
ap-652	386	1	it	it	PRON
ap-652	386	2	is	be	AUX
ap-652	386	3	better	well	ADJ
ap-652	386	4	to	to	PART
ap-652	386	5	assume	assume	VERB
ap-652	386	6	a	a	DET
ap-652	386	7	rectangular	rectangular	ADJ
ap-652	386	8	cell	cell	NOUN
ap-652	386	9	according	accord	VERB
ap-652	386	10	to	to	ADP
ap-652	386	11	fig	fig	NOUN
ap-652	386	12	.	.	PUNCT
ap-652	387	1	6	6	NUM
ap-652	387	2	.	.	X
ap-652	387	3	conditions	condition	NOUN
ap-652	387	4	q	q	PROPN
ap-652	387	5	rj	rj	PROPN
ap-652	387	6	k	k	PROPN
ap-652	387	7	j	j	PROPN
ap-652	387	8	,	,	PUNCT
ap-652	387	9	k	k	PROPN
ap-652	387	10	1	1	NUM
ap-652	387	11	,	,	PUNCT
ap-652	387	12	2	2	NUM
ap-652	387	13	,	,	PUNCT
ap-652	387	14	3	3	NUM
ap-652	387	15	%	%	NOUN
ap-652	387	16	�	�	PROPN
ap-652	387	17	�	�	PROPN
ap-652	387	18	imply	imply	VERB
ap-652	387	19	,	,	PUNCT
ap-652	387	20	again	again	ADV
ap-652	387	21	,	,	PUNCT
ap-652	387	22	the	the	DET
ap-652	387	23	same	same	ADJ
ap-652	387	24	volume	volume	NOUN
ap-652	387	25	constraint	constraint	NOUN
ap-652	387	26	of	of	ADP
ap-652	387	27	the	the	DET
ap-652	387	28	bars	bar	NOUN
ap-652	387	29	within	within	ADP
ap-652	387	30	each	each	DET
ap-652	387	31	group	group	NOUN
ap-652	387	32	:	:	PUNCT
ap-652	387	33	l	l	X
ap-652	388	1	l	l	X
ap-652	388	2	l	l	NOUN
ap-652	388	3	li	li	PROPN
ap-652	389	1	i	i	PRON
ap-652	389	2	1.group	1.group	NUM
ap-652	389	3	j	j	PROPN
ap-652	390	1	j	j	PROPN
ap-652	391	1	2.group	2.group	NUM
ap-652	391	2	k	k	PROPN
ap-652	392	1	k	k	X
ap-652	392	2	3.group	3.group	NUM
ap-652	392	3	r	r	NOUN
ap-652	392	4	r	r	NOUN
ap-652	392	5	4.group	4.group	NUM
ap-652	392	6	a	a	DET
ap-652	392	7	a	a	DET
ap-652	392	8	a	a	DET
ap-652	392	9	a	a	DET
ap-652	392	10	�	�	PROPN
ap-652	392	11	�	�	PROPN
ap-652	392	12	�	�	PROPN
ap-652	392	13	�	�	PROPN
ap-652	392	14	�	�	PROPN
ap-652	392	15	�	�	PROPN
ap-652	392	16	�	�	PROPN
ap-652	392	17	,	,	PUNCT
ap-652	392	18	(	(	PUNCT
ap-652	392	19	49	49	NUM
ap-652	392	20	)	)	PUNCT
ap-652	392	21	which	which	PRON
ap-652	392	22	,	,	PUNCT
ap-652	392	23	in	in	ADP
ap-652	392	24	a	a	DET
ap-652	392	25	sequel	sequel	NOUN
ap-652	392	26	,	,	PUNCT
ap-652	392	27	guarantees	guarantee	VERB
ap-652	392	28	the	the	DET
ap-652	392	29	mutual	mutual	ADJ
ap-652	392	30	perpendicularity	perpendicularity	NOUN
ap-652	392	31	of	of	ADP
ap-652	392	32	q	q	PROPN
ap-652	392	33	j	j	PROPN
ap-652	392	34	j	j	PROPN
ap-652	392	35	1,2,3	1,2,3	NUM
ap-652	392	36	,	,	PUNCT
ap-652	392	37	�	�	PROPN
ap-652	392	38	,	,	PUNCT
ap-652	392	39	while	while	SCONJ
ap-652	392	40	(	(	PUNCT
ap-652	392	41	47	47	NUM
ap-652	392	42	)	)	PUNCT
ap-652	392	43	is	be	AUX
ap-652	392	44	satisfied	satisfied	ADJ
ap-652	392	45	directly	directly	ADV
ap-652	392	46	.	.	PUNCT
ap-652	393	1	it	it	PRON
ap-652	393	2	remains	remain	VERB
ap-652	393	3	to	to	PART
ap-652	393	4	ensure	ensure	VERB
ap-652	393	5	(	(	PUNCT
ap-652	393	6	45	45	NUM
ap-652	393	7	)	)	PUNCT
ap-652	393	8	and	and	CCONJ
ap-652	393	9	impose	impose	VERB
ap-652	393	10	conditions	condition	NOUN
ap-652	393	11	to	to	PART
ap-652	393	12	eliminate	eliminate	VERB
ap-652	393	13	zero	zero	NUM
ap-652	393	14	bars	bar	NOUN
ap-652	393	15	.	.	PUNCT
ap-652	394	1	let	let	VERB
ap-652	394	2	us	we	PRON
ap-652	394	3	take	take	VERB
ap-652	394	4	one	one	NUM
ap-652	394	5	bar	bar	NOUN
ap-652	394	6	from	from	ADP
ap-652	394	7	the	the	DET
ap-652	394	8	first	first	ADJ
ap-652	394	9	group	group	NOUN
ap-652	394	10	.	.	PUNCT
ap-652	395	1	from	from	ADP
ap-652	395	2	(	(	PUNCT
ap-652	395	3	45	45	NUM
ap-652	395	4	)	)	PUNCT
ap-652	395	5	it	it	PRON
ap-652	395	6	directly	directly	ADV
ap-652	395	7	follows	follow	VERB
ap-652	395	8	that	that	SCONJ
ap-652	395	9	in	in	ADP
ap-652	395	10	each	each	DET
ap-652	395	11	part	part	NOUN
ap-652	395	12	between	between	ADP
ap-652	395	13	the	the	DET
ap-652	395	14	joints	joint	NOUN
ap-652	395	15	of	of	ADP
ap-652	395	16	this	this	DET
ap-652	395	17	bar	bar	NOUN
ap-652	395	18	n	n	CCONJ
ap-652	395	19	ai	ai	VERB
ap-652	395	20	i	i	PRON
ap-652	395	21	�	�	PROPN
ap-652	395	22	(	(	PUNCT
ap-652	395	23	)	)	PUNCT
ap-652	395	24	�	�	PROPN
ap-652	395	25	�	�	PROPN
ap-652	395	26	�	�	PROPN
ap-652	395	27	1	1	NUM
ap-652	395	28	2	2	NUM
ap-652	395	29	3	3	NUM
ap-652	395	30	3	3	NUM
ap-652	395	31	holds	hold	NOUN
ap-652	395	32	.	.	PUNCT
ap-652	396	1	thus	thus	ADV
ap-652	396	2	the	the	DET
ap-652	396	3	normal	normal	ADJ
ap-652	396	4	forces	force	NOUN
ap-652	396	5	must	must	AUX
ap-652	396	6	be	be	AUX
ap-652	396	7	proportional	proportional	ADJ
ap-652	396	8	to	to	ADP
ap-652	396	9	the	the	DET
ap-652	396	10	cross	cross	NOUN
ap-652	396	11	sectional	sectional	ADJ
ap-652	396	12	areas	area	NOUN
ap-652	396	13	with	with	ADP
ap-652	396	14	the	the	DET
ap-652	396	15	same	same	ADJ
ap-652	396	16	coefficient	coefficient	NOUN
ap-652	396	17	of	of	ADP
ap-652	396	18	proportionality	proportionality	NOUN
ap-652	396	19	in	in	ADP
ap-652	396	20	each	each	DET
ap-652	396	21	group	group	NOUN
ap-652	396	22	,	,	PUNCT
ap-652	396	23	in	in	ADP
ap-652	396	24	other	other	ADJ
ap-652	396	25	words	word	NOUN
ap-652	396	26	,	,	PUNCT
ap-652	396	27	in	in	ADP
ap-652	396	28	the	the	DET
ap-652	396	29	bars	bar	NOUN
ap-652	396	30	of	of	ADP
ap-652	396	31	each	each	DET
ap-652	396	32	group	group	NOUN
ap-652	396	33	the	the	DET
ap-652	396	34	local	local	ADJ
ap-652	396	35	stresses	stress	NOUN
ap-652	396	36	must	must	AUX
ap-652	396	37	be	be	AUX
ap-652	396	38	the	the	DET
ap-652	396	39	same	same	ADJ
ap-652	396	40	:	:	PUNCT
ap-652	396	41	�	�	PROPN
ap-652	396	42	1	1	NUM
ap-652	396	43	,	,	PUNCT
ap-652	396	44	�	�	PROPN
ap-652	396	45	2	2	NUM
ap-652	396	46	,	,	PUNCT
ap-652	396	47	�	�	PROPN
ap-652	396	48	3	3	NUM
ap-652	396	49	,	,	PUNCT
ap-652	396	50	�	�	NOUN
ap-652	396	51	4	4	NUM
ap-652	396	52	,	,	PUNCT
ap-652	396	53	respectively	respectively	ADV
ap-652	396	54	.	.	PUNCT
ap-652	397	1	because	because	SCONJ
ap-652	397	2	four	four	NUM
ap-652	397	3	possible	possible	ADJ
ap-652	397	4	directions	direction	NOUN
ap-652	397	5	of	of	ADP
ap-652	397	6	the	the	DET
ap-652	397	7	bars	bar	NOUN
ap-652	397	8	exist	exist	VERB
ap-652	397	9	,	,	PUNCT
ap-652	397	10	it	it	PRON
ap-652	397	11	can	can	AUX
ap-652	397	12	not	not	PART
ap-652	397	13	be	be	AUX
ap-652	397	14	directly	directly	ADV
ap-652	397	15	concluded	conclude	VERB
ap-652	397	16	that	that	SCONJ
ap-652	397	17	due	due	ADP
ap-652	397	18	to	to	ADP
ap-652	397	19	the	the	DET
ap-652	397	20	equilibrium	equilibrium	NOUN
ap-652	397	21	in	in	ADP
ap-652	397	22	the	the	DET
ap-652	397	23	joints	joint	NOUN
ap-652	397	24	only	only	ADV
ap-652	397	25	continuous	continuous	ADJ
ap-652	397	26	bars	bar	NOUN
ap-652	397	27	are	be	AUX
ap-652	397	28	included	include	VERB
ap-652	397	29	in	in	ADP
ap-652	397	30	the	the	DET
ap-652	397	31	cell	cell	NOUN
ap-652	397	32	.	.	PUNCT
ap-652	398	1	however	however	ADV
ap-652	398	2	,	,	PUNCT
ap-652	398	3	this	this	DET
ap-652	398	4	statement	statement	NOUN
ap-652	398	5	can	can	AUX
ap-652	398	6	be	be	AUX
ap-652	398	7	justified	justify	VERB
ap-652	398	8	in	in	ADP
ap-652	398	9	the	the	DET
ap-652	398	10	following	following	ADJ
ap-652	398	11	way	way	NOUN
ap-652	398	12	.	.	PUNCT
ap-652	399	1	obviously	obviously	ADV
ap-652	399	2	�	�	PROPN
ap-652	399	3	�	�	PROPN
ap-652	399	4	�	�	PROPN
ap-652	399	5	�	�	PROPN
ap-652	399	6	�	�	PROPN
ap-652	399	7	�	�	PROPN
ap-652	399	8	�	�	PROPN
ap-652	399	9	�	�	PROPN
ap-652	399	10	�	�	PROPN
ap-652	399	11	�	�	PROPN
ap-652	399	12	�	�	PROPN
ap-652	399	13	�	�	PROPN
ap-652	399	14	�	�	PROPN
ap-652	399	15	1	1	NUM
ap-652	399	16	1	1	NUM
ap-652	399	17	2	2	NUM
ap-652	399	18	3	3	NUM
ap-652	399	19	2	2	NUM
ap-652	399	20	1	1	NUM
ap-652	399	21	2	2	NUM
ap-652	399	22	3	3	NUM
ap-652	399	23	3	3	NUM
ap-652	399	24	1	1	NUM
ap-652	399	25	2	2	NUM
ap-652	399	26	3	3	NUM
ap-652	399	27	3	3	NUM
ap-652	399	28	3	3	NUM
ap-652	399	29	3	3	NUM
ap-652	399	30	�	�	PROPN
ap-652	399	31	�	�	PROPN
ap-652	399	32	�	�	PROPN
ap-652	399	33	(	(	PUNCT
ap-652	399	34	)	)	PUNCT
ap-652	399	35	,	,	PUNCT
ap-652	399	36	(	(	PUNCT
ap-652	399	37	)	)	PUNCT
ap-652	399	38	,	,	PUNCT
ap-652	399	39	(	(	PUNCT
ap-652	399	40	)	)	PUNCT
ap-652	399	41	and	and	CCONJ
ap-652	399	42	4	4	NUM
ap-652	399	43	1	1	NUM
ap-652	399	44	2	2	NUM
ap-652	399	45	3	3	NUM
ap-652	399	46	3	3	NUM
ap-652	399	47	�	�	PROPN
ap-652	399	48	(	(	PUNCT
ap-652	399	49	)	)	PUNCT
ap-652	399	50	�	�	PROPN
ap-652	399	51	�	�	PROPN
ap-652	399	52	�	�	PROPN
ap-652	399	53	(	(	PUNCT
ap-652	399	54	50	50	NUM
ap-652	399	55	)	)	PUNCT
ap-652	399	56	hold	hold	NOUN
ap-652	399	57	.	.	PUNCT
ap-652	400	1	let	let	VERB
ap-652	400	2	us	we	PRON
ap-652	400	3	take	take	VERB
ap-652	400	4	a	a	DET
ap-652	400	5	joint	joint	NOUN
ap-652	400	6	and	and	CCONJ
ap-652	400	7	suppose	suppose	VERB
ap-652	400	8	that	that	SCONJ
ap-652	400	9	a	a	DET
ap-652	400	10	member	member	NOUN
ap-652	400	11	from	from	ADP
ap-652	400	12	each	each	DET
ap-652	400	13	group	group	NOUN
ap-652	400	14	is	be	AUX
ap-652	400	15	presented	present	VERB
ap-652	400	16	there	there	ADV
ap-652	400	17	as	as	ADP
ap-652	400	18	continuous	continuous	ADJ
ap-652	400	19	.	.	PUNCT
ap-652	401	1	contributions	contribution	NOUN
ap-652	401	2	to	to	ADP
ap-652	401	3	the	the	DET
ap-652	401	4	cell	cell	NOUN
ap-652	401	5	coordinate	coordinate	NOUN
ap-652	401	6	directions	direction	NOUN
ap-652	401	7	are	be	AUX
ap-652	401	8	given	give	VERB
ap-652	401	9	in	in	ADP
ap-652	401	10	table	table	NOUN
ap-652	401	11	6	6	NUM
ap-652	401	12	.	.	PUNCT
ap-652	402	1	consequently	consequently	ADV
ap-652	402	2	,	,	PUNCT
ap-652	402	3	the	the	DET
ap-652	402	4	equilibrium	equilibrium	NOUN
ap-652	402	5	in	in	ADP
ap-652	402	6	the	the	DET
ap-652	402	7	joint	joint	ADJ
ap-652	402	8	reads	read	NOUN
ap-652	402	9	as	as	ADP
ap-652	402	10	:	:	PUNCT
ap-652	402	11	�	�	PROPN
ap-652	402	12	�	�	PROPN
ap-652	402	13	�	�	PROPN
ap-652	402	14	�	�	PROPN
ap-652	402	15	1	1	NUM
ap-652	402	16	2	2	NUM
ap-652	402	17	3	3	NUM
ap-652	402	18	(	(	PUNCT
ap-652	402	19	)	)	PUNCT
ap-652	402	20	(	(	PUNCT
ap-652	402	21	)	)	PUNCT
ap-652	402	22	(	(	PUNCT
ap-652	402	23	)	)	PUNCT
ap-652	402	24	a	a	PRON
ap-652	403	1	a	a	DET
ap-652	403	2	a	a	DET
ap-652	403	3	a	a	DET
ap-652	403	4	a	a	DET
ap-652	403	5	a	a	DET
ap-652	403	6	1,m	1,m	NOUN
ap-652	403	7	1,m	1,m	NUM
ap-652	403	8	1	1	NUM
ap-652	403	9	2,n	2,n	NUM
ap-652	403	10	2,n	2,n	NUM
ap-652	403	11	1	1	NUM
ap-652	403	12	3,r	3,r	NUM
ap-652	403	13	3,r	3,r	NUM
ap-652	403	14	1	1	NUM
ap-652	403	15	4	4	NUM
ap-652	403	16	1	1	NUM
ap-652	403	17	2	2	NUM
ap-652	403	18	0	0	NUM
ap-652	403	19	(	(	PUNCT
ap-652	403	20	)	)	PUNCT
ap-652	403	21	,	,	PUNCT
ap-652	403	22	(	(	PUNCT
ap-652	403	23	)	)	PUNCT
ap-652	403	24	(	(	PUNCT
ap-652	403	25	)	)	PUNCT
ap-652	404	1	a	a	DET
ap-652	404	2	a	a	DET
ap-652	404	3	a	a	DET
ap-652	404	4	a	a	DET
ap-652	404	5	a	a	DET
ap-652	404	6	a	a	DET
ap-652	404	7	4,s	4,s	NUM
ap-652	404	8	4,s	4,s	NUM
ap-652	404	9	1	1	NUM
ap-652	404	10	1,m	1,m	NOUN
ap-652	404	11	1,m	1,m	NUM
ap-652	404	12	1	1	NUM
ap-652	404	13	2,n	2,n	NUM
ap-652	404	14	2,n	2,n	NUM
ap-652	404	15	1	1	NUM
ap-652	404	16	�	�	PROPN
ap-652	404	17	�	�	PROPN
ap-652	404	18	�	�	PROPN
ap-652	404	19	�	�	PROPN
ap-652	404	20	�	�	PROPN
ap-652	404	21	�	�	PROPN
ap-652	404	22	3	3	NUM
ap-652	404	23	4	4	NUM
ap-652	404	24	1	1	NUM
ap-652	404	25	0	0	NUM
ap-652	404	26	(	(	PUNCT
ap-652	404	27	)	)	PUNCT
ap-652	404	28	(	(	PUNCT
ap-652	404	29	)	)	PUNCT
ap-652	404	30	,	,	PUNCT
ap-652	404	31	(	(	PUNCT
ap-652	404	32	)	)	PUNCT
ap-652	404	33	a	a	PRON
ap-652	404	34	a	a	DET
ap-652	404	35	a	a	DET
ap-652	404	36	a	a	DET
ap-652	404	37	a	a	DET
ap-652	404	38	a	a	DET
ap-652	404	39	3,r	3,r	NUM
ap-652	404	40	3,r	3,r	NUM
ap-652	404	41	1	1	NUM
ap-652	404	42	4,s	4,s	NUM
ap-652	404	43	4,s	4,s	NUM
ap-652	405	1	1	1	NUM
ap-652	405	2	1,m	1,m	NOUN
ap-652	405	3	1,m	1,m	NUM
ap-652	405	4	1	1	NUM
ap-652	405	5	�	�	PROPN
ap-652	405	6	�	�	PROPN
ap-652	405	7	�	�	PROPN
ap-652	405	8	�	�	PROPN
ap-652	405	9	2	2	NUM
ap-652	405	10	3	3	NUM
ap-652	405	11	4	4	NUM
ap-652	405	12	0	0	NUM
ap-652	405	13	(	(	PUNCT
ap-652	405	14	)	)	PUNCT
ap-652	405	15	(	(	PUNCT
ap-652	405	16	)	)	PUNCT
ap-652	405	17	(	(	PUNCT
ap-652	405	18	)	)	PUNCT
ap-652	405	19	a	a	PRON
ap-652	405	20	a	a	PRON
ap-652	405	21	a	a	DET
ap-652	405	22	a	a	DET
ap-652	405	23	a	a	DET
ap-652	405	24	a	a	DET
ap-652	405	25	2,n	2,n	NUM
ap-652	405	26	2,n	2,n	NUM
ap-652	405	27	1	1	NUM
ap-652	405	28	3,r	3,r	NUM
ap-652	405	29	3,r	3,r	NUM
ap-652	405	30	1	1	NUM
ap-652	405	31	4,s	4,s	NUM
ap-652	405	32	4,s	4,s	NUM
ap-652	405	33	1	1	NUM
ap-652	405	34	�	�	PROPN
ap-652	405	35	,	,	PUNCT
ap-652	405	36	(	(	PUNCT
ap-652	405	37	51	51	NUM
ap-652	405	38	)	)	PUNCT
ap-652	405	39	©	©	PROPN
ap-652	405	40	czech	czech	PROPN
ap-652	405	41	technical	technical	PROPN
ap-652	405	42	university	university	PROPN
ap-652	405	43	publishing	publishing	NOUN
ap-652	405	44	house	house	NOUN
ap-652	405	45	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	405	46	181	181	NUM
ap-652	405	47	acta	acta	PROPN
ap-652	405	48	polytechnica	polytechnica	PROPN
ap-652	405	49	vol	vol	NOUN
ap-652	405	50	.	.	PROPN
ap-652	405	51	44	44	NUM
ap-652	405	52	no.5–6/2004	no.5–6/2004	NOUN
ap-652	405	53	group	group	NOUN
ap-652	405	54	1	1	NUM
ap-652	405	55	.	.	NOUN
ap-652	405	56	2	2	NUM
ap-652	405	57	.	.	NOUN
ap-652	405	58	3	3	NUM
ap-652	405	59	.	.	NOUN
ap-652	405	60	4	4	NUM
ap-652	405	61	.	.	X
ap-652	405	62	spherical	spherical	ADJ
ap-652	405	63	angles	angle	NOUN
ap-652	405	64	cos	cos	NOUN
ap-652	405	65	;	;	PUNCT
ap-652	405	66	sin	sin	NOUN
ap-652	405	67	;	;	PUNCT
ap-652	405	68	cos	cos	X
ap-652	405	69	;	;	PUNCT
ap-652	405	70	sin	sin	PROPN
ap-652	405	71	�	�	PROPN
ap-652	405	72	�	�	PROPN
ap-652	405	73	1	1	NUM
ap-652	405	74	1	1	NUM
ap-652	405	75	1	1	NUM
ap-652	405	76	1	1	NUM
ap-652	405	77	1	1	NUM
ap-652	405	78	2	2	NUM
ap-652	405	79	1	1	NUM
ap-652	405	80	2	2	NUM
ap-652	405	81	1	1	NUM
ap-652	405	82	3	3	NUM
ap-652	405	83	2	2	NUM
ap-652	405	84	3	3	NUM
ap-652	405	85	�	�	PROPN
ap-652	405	86	�	�	PROPN
ap-652	405	87	�	�	PROPN
ap-652	405	88	�	�	PROPN
ap-652	405	89	cos	cos	PROPN
ap-652	405	90	;	;	PUNCT
ap-652	405	91	sin	sin	NOUN
ap-652	405	92	;	;	PUNCT
ap-652	405	93	cos	cos	X
ap-652	405	94	;	;	PUNCT
ap-652	405	95	sin	sin	PROPN
ap-652	405	96	�	�	PROPN
ap-652	405	97	�	�	PROPN
ap-652	405	98	2	2	NUM
ap-652	405	99	2	2	NUM
ap-652	405	100	2	2	NUM
ap-652	405	101	2	2	NUM
ap-652	405	102	1	1	NUM
ap-652	405	103	2	2	NUM
ap-652	405	104	1	1	NUM
ap-652	405	105	2	2	NUM
ap-652	405	106	1	1	NUM
ap-652	405	107	3	3	NUM
ap-652	405	108	2	2	NUM
ap-652	405	109	3	3	NUM
ap-652	405	110	�	�	PROPN
ap-652	405	111	�	�	PROPN
ap-652	405	112	�	�	PROPN
ap-652	405	113	�	�	PROPN
ap-652	405	114	cos	cos	PROPN
ap-652	405	115	;	;	PUNCT
ap-652	405	116	sin	sin	NOUN
ap-652	405	117	;	;	PUNCT
ap-652	405	118	cos	cos	X
ap-652	405	119	;	;	PUNCT
ap-652	405	120	sin	sin	PROPN
ap-652	405	121	�	�	PROPN
ap-652	405	122	�	�	PROPN
ap-652	405	123	3	3	NUM
ap-652	405	124	3	3	NUM
ap-652	405	125	3	3	NUM
ap-652	405	126	3	3	NUM
ap-652	405	127	1	1	NUM
ap-652	405	128	2	2	NUM
ap-652	405	129	1	1	NUM
ap-652	405	130	2	2	NUM
ap-652	405	131	1	1	NUM
ap-652	405	132	3	3	NUM
ap-652	405	133	2	2	NUM
ap-652	405	134	3	3	NUM
ap-652	405	135	�	�	PROPN
ap-652	405	136	�	�	PROPN
ap-652	405	137	�	�	PROPN
ap-652	405	138	�	�	PROPN
ap-652	405	139	cos	cos	PROPN
ap-652	405	140	;	;	PUNCT
ap-652	405	141	sin	sin	NOUN
ap-652	405	142	;	;	PUNCT
ap-652	405	143	cos	cos	X
ap-652	405	144	;	;	PUNCT
ap-652	405	145	sin	sin	PROPN
ap-652	405	146	�	�	PROPN
ap-652	405	147	�	�	PROPN
ap-652	405	148	4	4	NUM
ap-652	405	149	4	4	NUM
ap-652	405	150	4	4	NUM
ap-652	405	151	4	4	NUM
ap-652	405	152	1	1	NUM
ap-652	405	153	2	2	NUM
ap-652	405	154	1	1	NUM
ap-652	405	155	2	2	NUM
ap-652	405	156	1	1	NUM
ap-652	405	157	3	3	NUM
ap-652	405	158	2	2	NUM
ap-652	405	159	3	3	NUM
ap-652	405	160	�	�	PROPN
ap-652	405	161	�	�	PROPN
ap-652	405	162	�	�	PROPN
ap-652	405	163	�	�	PROPN
ap-652	405	164	values	value	NOUN
ap-652	405	165	of	of	ADP
ap-652	405	166	�	�	PROPN
ap-652	405	167	1	1	NUM
ap-652	405	168	,	,	PUNCT
ap-652	405	169	�	�	PROPN
ap-652	405	170	2	2	NUM
ap-652	405	171	,	,	PUNCT
ap-652	405	172	�	�	X
ap-652	405	173	3	3	NUM
ap-652	405	174	1/3	1/3	NUM
ap-652	405	175	,	,	PUNCT
ap-652	405	176	1/3	1/3	NUM
ap-652	405	177	,	,	PUNCT
ap-652	405	178	1/3	1/3	NUM
ap-652	405	179	1/3	1/3	NUM
ap-652	405	180	,	,	PUNCT
ap-652	405	181	1/3	1/3	NUM
ap-652	405	182	,	,	PUNCT
ap-652	405	183	1/3	1/3	NUM
ap-652	405	184	1/3	1/3	NUM
ap-652	405	185	,	,	PUNCT
ap-652	405	186	1/3	1/3	NUM
ap-652	405	187	,	,	PUNCT
ap-652	405	188	1/3	1/3	NUM
ap-652	405	189	1/3	1/3	NUM
ap-652	405	190	,	,	PUNCT
ap-652	405	191	1/3	1/3	NUM
ap-652	405	192	,	,	PUNCT
ap-652	405	193	1/3	1/3	NUM
ap-652	405	194	values	value	NOUN
ap-652	405	195	of	of	ADP
ap-652	405	196	�	�	PROPN
ap-652	405	197	1	1	NUM
ap-652	405	198	,	,	PUNCT
ap-652	405	199	�	�	PROPN
ap-652	405	200	2	2	NUM
ap-652	405	201	,	,	PUNCT
ap-652	405	202	�	�	X
ap-652	405	203	3	3	NUM
ap-652	405	204	1/3	1/3	NUM
ap-652	405	205	,	,	PUNCT
ap-652	405	206	1/3	1/3	NUM
ap-652	405	207	,	,	PUNCT
ap-652	405	208	1/3	1/3	NUM
ap-652	405	209	1/3	1/3	NUM
ap-652	405	210	,	,	PUNCT
ap-652	405	211	1/3	1/3	NUM
ap-652	405	212	,	,	PUNCT
ap-652	405	213	1/3	1/3	NUM
ap-652	405	214	1/3	1/3	NUM
ap-652	405	215	,	,	PUNCT
ap-652	405	216	1/3	1/3	NUM
ap-652	405	217	,	,	PUNCT
ap-652	405	218	1/3	1/3	NUM
ap-652	405	219	1/3	1/3	NUM
ap-652	405	220	,	,	PUNCT
ap-652	405	221	1/3	1/3	NUM
ap-652	405	222	,	,	PUNCT
ap-652	405	223	1/3	1/3	NUM
ap-652	405	224	table	table	NOUN
ap-652	405	225	5	5	NUM
ap-652	405	226	:	:	PUNCT
ap-652	405	227	characterization	characterization	NOUN
ap-652	405	228	of	of	ADP
ap-652	405	229	g2	g2	PROPN
ap-652	405	230	*	*	PUNCT
ap-652	405	231	-optimal	-optimal	ADJ
ap-652	405	232	media	medium	NOUN
ap-652	405	233	1y	1y	NOUN
ap-652	405	234	2y	2y	ADJ
ap-652	405	235	3y	3y	ADJ
ap-652	405	236	groups.2and.1	groups.2and.1	NOUN
ap-652	405	237	ofdirections	ofdirection	NOUN
ap-652	405	238	groups.4and.3	groups.4and.3	NOUN
ap-652	405	239	ofdirections	ofdirection	NOUN
ap-652	405	240	fig	fig	NOUN
ap-652	405	241	.	.	PUNCT
ap-652	406	1	6	6	NUM
ap-652	406	2	:	:	PUNCT
ap-652	406	3	rectangular	rectangular	ADJ
ap-652	406	4	cell	cell	NOUN
ap-652	406	5	for	for	ADP
ap-652	406	6	g2	g2	PROPN
ap-652	406	7	*	*	PUNCT
ap-652	406	8	-optimal	-optimal	ADJ
ap-652	406	9	media	medium	NOUN
ap-652	406	10	,	,	PUNCT
ap-652	406	11	top	top	ADJ
ap-652	406	12	view	view	NOUN
ap-652	406	13	where	where	SCONJ
ap-652	406	14	the	the	DET
ap-652	406	15	first	first	ADJ
ap-652	406	16	subscript	subscript	NOUN
ap-652	406	17	at	at	ADP
ap-652	406	18	the	the	DET
ap-652	406	19	cross	cross	NOUN
ap-652	406	20	sectional	sectional	ADJ
ap-652	406	21	areas	area	NOUN
ap-652	406	22	denotes	denote	VERB
ap-652	406	23	the	the	DET
ap-652	406	24	group	group	NOUN
ap-652	406	25	and	and	CCONJ
ap-652	406	26	the	the	DET
ap-652	406	27	second	second	ADJ
ap-652	406	28	one	one	NOUN
ap-652	406	29	expresses	express	VERB
ap-652	406	30	the	the	DET
ap-652	406	31	order	order	NOUN
ap-652	406	32	number	number	NOUN
ap-652	406	33	within	within	ADP
ap-652	406	34	the	the	DET
ap-652	406	35	group	group	NOUN
ap-652	406	36	.	.	PUNCT
ap-652	407	1	(	(	PUNCT
ap-652	407	2	51	51	NUM
ap-652	407	3	)	)	PUNCT
ap-652	407	4	must	must	AUX
ap-652	407	5	be	be	AUX
ap-652	407	6	satisfied	satisfied	ADJ
ap-652	407	7	for	for	ADP
ap-652	407	8	any	any	DET
ap-652	407	9	�	�	NOUN
ap-652	407	10	i	i	PRON
ap-652	407	11	i	i	PRON
ap-652	407	12	,	,	PUNCT
ap-652	407	13	,	,	PUNCT
ap-652	407	14	,	,	PUNCT
ap-652	407	15	,	,	PUNCT
ap-652	407	16	�	�	PROPN
ap-652	407	17	1	1	NUM
ap-652	407	18	2	2	NUM
ap-652	407	19	3	3	NUM
ap-652	407	20	4	4	NUM
ap-652	407	21	,	,	PUNCT
ap-652	407	22	consequently	consequently	ADV
ap-652	407	23	the	the	DET
ap-652	407	24	cross	cross	ADJ
ap-652	407	25	sectional	sectional	ADJ
ap-652	407	26	areas	area	NOUN
ap-652	407	27	must	must	AUX
ap-652	407	28	be	be	AUX
ap-652	407	29	either	either	CCONJ
ap-652	407	30	the	the	DET
ap-652	407	31	same	same	ADJ
ap-652	407	32	(	(	PUNCT
ap-652	407	33	resulting	result	VERB
ap-652	407	34	in	in	ADP
ap-652	407	35	a	a	DET
ap-652	407	36	continuous	continuous	ADJ
ap-652	407	37	bar	bar	NOUN
ap-652	407	38	with	with	ADP
ap-652	407	39	a	a	DET
ap-652	407	40	constant	constant	ADJ
ap-652	407	41	cross	cross	NOUN
ap-652	407	42	sectional	sectional	ADJ
ap-652	407	43	area	area	NOUN
ap-652	407	44	)	)	PUNCT
ap-652	407	45	or	or	CCONJ
ap-652	407	46	zero	zero	NUM
ap-652	407	47	(	(	PUNCT
ap-652	407	48	the	the	DET
ap-652	407	49	group	group	NOUN
ap-652	407	50	is	be	AUX
ap-652	407	51	not	not	PART
ap-652	407	52	contained	contain	VERB
ap-652	407	53	in	in	ADP
ap-652	407	54	the	the	DET
ap-652	407	55	joint	joint	NOUN
ap-652	407	56	)	)	PUNCT
ap-652	407	57	,	,	PUNCT
ap-652	407	58	which	which	PRON
ap-652	407	59	completes	complete	VERB
ap-652	407	60	the	the	DET
ap-652	407	61	justification	justification	NOUN
ap-652	407	62	.	.	PUNCT
ap-652	408	1	in	in	ADP
ap-652	408	2	summary	summary	NOUN
ap-652	408	3	,	,	PUNCT
ap-652	408	4	g	g	PROPN
ap-652	408	5	s2	s2	PROPN
ap-652	408	6	9	9	NUM
ap-652	408	7	,	,	PUNCT
ap-652	408	8	*	*	PUNCT
ap-652	408	9	�	�	PROPN
ap-652	408	10	and	and	CCONJ
ap-652	408	11	all	all	DET
ap-652	408	12	g2	g2	NOUN
ap-652	408	13	*	*	PUNCT
ap-652	408	14	-optimal	-optimal	ADJ
ap-652	408	15	media	medium	NOUN
ap-652	408	16	can	can	AUX
ap-652	408	17	be	be	AUX
ap-652	408	18	fully	fully	ADV
ap-652	408	19	geometrically	geometrically	ADV
ap-652	408	20	specified	specify	VERB
ap-652	408	21	in	in	ADP
ap-652	408	22	the	the	DET
ap-652	408	23	following	following	ADJ
ap-652	408	24	way	way	NOUN
ap-652	408	25	:	:	PUNCT
ap-652	408	26	g2	g2	PROPN
ap-652	408	27	*	*	PUNCT
ap-652	408	28	-optimal	-optimal	ADJ
ap-652	408	29	media	medium	NOUN
ap-652	408	30	are	be	AUX
ap-652	408	31	continuous	continuous	ADJ
ap-652	408	32	lattices	lattice	NOUN
ap-652	408	33	for	for	ADP
ap-652	408	34	which	which	PRON
ap-652	408	35	:	:	PUNCT
ap-652	408	36	�	�	PROPN
ap-652	408	37	a	a	DET
ap-652	408	38	rectangular	rectangular	ADJ
ap-652	408	39	basic	basic	ADJ
ap-652	408	40	cell	cell	NOUN
ap-652	408	41	,	,	PUNCT
ap-652	408	42	according	accord	VERB
ap-652	408	43	to	to	ADP
ap-652	408	44	fig	fig	NOUN
ap-652	408	45	.	.	PUNCT
ap-652	409	1	6	6	NUM
ap-652	409	2	,	,	PUNCT
ap-652	409	3	can	can	AUX
ap-652	409	4	be	be	AUX
ap-652	409	5	found	find	VERB
ap-652	409	6	,	,	PUNCT
ap-652	409	7	where	where	SCONJ
ap-652	409	8	only	only	ADV
ap-652	409	9	continuous	continuous	ADJ
ap-652	409	10	bars	bar	NOUN
ap-652	409	11	in	in	ADP
ap-652	409	12	the	the	DET
ap-652	409	13	four	four	NUM
ap-652	409	14	directions	direction	NOUN
ap-652	409	15	specified	specify	VERB
ap-652	409	16	by	by	ADP
ap-652	409	17	table	table	NOUN
ap-652	409	18	5	5	NUM
ap-652	409	19	are	be	AUX
ap-652	409	20	present	present	ADJ
ap-652	409	21	,	,	PUNCT
ap-652	409	22	�	�	PROPN
ap-652	409	23	each	each	DET
ap-652	409	24	continuous	continuous	ADJ
ap-652	409	25	bar	bar	NOUN
ap-652	409	26	has	have	VERB
ap-652	409	27	a	a	DET
ap-652	409	28	constant	constant	ADJ
ap-652	409	29	cross	cross	NOUN
ap-652	409	30	sectional	sectional	ADJ
ap-652	409	31	area	area	NOUN
ap-652	409	32	and	and	CCONJ
ap-652	409	33	(	(	PUNCT
ap-652	409	34	49	49	NUM
ap-652	409	35	)	)	PUNCT
ap-652	409	36	holds	hold	VERB
ap-652	409	37	.	.	PUNCT
ap-652	410	1	the	the	DET
ap-652	410	2	group	group	NOUN
ap-652	410	3	of	of	ADP
ap-652	410	4	media	medium	NOUN
ap-652	410	5	described	describe	VERB
ap-652	410	6	above	above	ADV
ap-652	410	7	is	be	AUX
ap-652	410	8	the	the	DET
ap-652	410	9	only	only	ADJ
ap-652	410	10	group	group	NOUN
ap-652	410	11	of	of	ADP
ap-652	410	12	g2	g2	PROPN
ap-652	410	13	*	*	PUNCT
ap-652	410	14	-optimal	-optimal	ADJ
ap-652	410	15	media	medium	NOUN
ap-652	410	16	.	.	PUNCT
ap-652	411	1	the	the	DET
ap-652	411	2	name	name	NOUN
ap-652	411	3	for	for	ADP
ap-652	411	4	such	such	ADJ
ap-652	411	5	media	medium	NOUN
ap-652	411	6	was	be	AUX
ap-652	411	7	introduced	introduce	VERB
ap-652	411	8	in	in	ADP
ap-652	411	9	dimitrovová	dimitrovová	PROPN
ap-652	411	10	and	and	CCONJ
ap-652	411	11	faria	faria	PROPN
ap-652	411	12	(	(	PUNCT
ap-652	411	13	1999	1999	NUM
ap-652	411	14	)	)	PUNCT
ap-652	411	15	as	as	ADP
ap-652	411	16	udl	udl	X
ap-652	411	17	(	(	PUNCT
ap-652	411	18	uniform	uniform	ADJ
ap-652	411	19	diagonal	diagonal	ADJ
ap-652	411	20	lattices	lattice	NOUN
ap-652	411	21	)	)	PUNCT
ap-652	411	22	.	.	PUNCT
ap-652	412	1	the	the	DET
ap-652	412	2	simplest	simple	ADJ
ap-652	412	3	example	example	NOUN
ap-652	412	4	from	from	ADP
ap-652	412	5	this	this	DET
ap-652	412	6	group	group	NOUN
ap-652	412	7	is	be	AUX
ap-652	412	8	the	the	DET
ap-652	412	9	regular	regular	ADJ
ap-652	412	10	cube	cube	NOUN
ap-652	412	11	-	-	PUNCT
ap-652	412	12	diagonal	diagonal	ADJ
ap-652	412	13	lattice	lattice	NOUN
ap-652	412	14	in	in	ADP
ap-652	412	15	fig	fig	NOUN
ap-652	412	16	.	.	PUNCT
ap-652	413	1	7	7	NUM
ap-652	413	2	.	.	SYM
ap-652	413	3	3.4	3.4	NUM
ap-652	413	4	shear	shear	NOUN
ap-652	413	5	modulus	modulus	NOUN
ap-652	413	6	g	g	PROPN
ap-652	413	7	*	*	PUNCT
ap-652	413	8	(	(	PUNCT
ap-652	413	9	for	for	ADP
ap-652	413	10	effective	effective	ADJ
ap-652	413	11	isotropy	isotropy	NOUN
ap-652	413	12	)	)	PUNCT
ap-652	413	13	in	in	ADP
ap-652	413	14	this	this	DET
ap-652	413	15	case	case	NOUN
ap-652	413	16	,	,	PUNCT
ap-652	413	17	the	the	DET
ap-652	413	18	conclusions	conclusion	NOUN
ap-652	413	19	from	from	ADP
ap-652	413	20	the	the	DET
ap-652	413	21	two	two	NUM
ap-652	413	22	previous	previous	ADJ
ap-652	413	23	sections	section	NOUN
ap-652	413	24	can	can	AUX
ap-652	413	25	be	be	AUX
ap-652	413	26	exploited	exploit	VERB
ap-652	413	27	.	.	PUNCT
ap-652	414	1	let	let	VERB
ap-652	414	2	us	we	PRON
ap-652	414	3	assume	assume	VERB
ap-652	414	4	that	that	SCONJ
ap-652	414	5	we	we	PRON
ap-652	414	6	already	already	ADV
ap-652	414	7	have	have	VERB
ap-652	414	8	a	a	DET
ap-652	414	9	g*-optimal	g*-optimal	ADJ
ap-652	414	10	medium	medium	NOUN
ap-652	414	11	.	.	PUNCT
ap-652	415	1	macroloads	macroload	NOUN
ap-652	415	2	�	�	PROPN
ap-652	415	3	1	1	NUM
ap-652	415	4	g	g	NOUN
ap-652	415	5	and	and	CCONJ
ap-652	415	6	�	�	PROPN
ap-652	415	7	2	2	NUM
ap-652	415	8	g	g	NOUN
ap-652	415	9	can	can	AUX
ap-652	415	10	be	be	AUX
ap-652	415	11	imposed	impose	VERB
ap-652	415	12	separately	separately	ADV
ap-652	415	13	on	on	ADP
ap-652	415	14	it	it	PRON
ap-652	415	15	and	and	CCONJ
ap-652	415	16	the	the	DET
ap-652	415	17	same	same	ADJ
ap-652	415	18	bounding	bounding	NOUN
ap-652	415	19	procedure	procedure	NOUN
ap-652	415	20	as	as	ADP
ap-652	415	21	in	in	ADP
ap-652	415	22	sections	section	NOUN
ap-652	415	23	3.3–4	3.3–4	NUM
ap-652	415	24	can	can	AUX
ap-652	415	25	be	be	AUX
ap-652	415	26	performed	perform	VERB
ap-652	415	27	.	.	PUNCT
ap-652	416	1	it	it	PRON
ap-652	416	2	is	be	AUX
ap-652	416	3	only	only	ADV
ap-652	416	4	necessary	necessary	ADJ
ap-652	416	5	to	to	PART
ap-652	416	6	prevent	prevent	VERB
ap-652	416	7	a	a	DET
ap-652	416	8	geometrical	geometrical	ADJ
ap-652	416	9	specification	specification	NOUN
ap-652	416	10	which	which	PRON
ap-652	416	11	would	would	AUX
ap-652	416	12	enter	enter	VERB
ap-652	416	13	in	in	ADP
ap-652	416	14	contradiction	contradiction	NOUN
ap-652	416	15	with	with	ADP
ap-652	416	16	the	the	DET
ap-652	416	17	possibility	possibility	NOUN
ap-652	416	18	of	of	ADP
ap-652	416	19	effective	effective	ADJ
ap-652	416	20	isotropy	isotropy	NOUN
ap-652	416	21	of	of	ADP
ap-652	416	22	the	the	DET
ap-652	416	23	medium	medium	NOUN
ap-652	416	24	.	.	PUNCT
ap-652	417	1	thus	thus	ADV
ap-652	417	2	:	:	PUNCT
ap-652	417	3	g	g	PROPN
ap-652	417	4	s	s	PROPN
ap-652	417	5	*	*	PROPN
ap-652	417	6	�	�	PROPN
ap-652	417	7	�	�	PROPN
ap-652	417	8	4	4	NUM
ap-652	417	9	2	2	NUM
ap-652	417	10	2	2	NUM
ap-652	417	11	p	p	NOUN
ap-652	417	12	l	l	NOUN
ap-652	417	13	and	and	CCONJ
ap-652	417	14	g	g	PROPN
ap-652	417	15	s	s	PROPN
ap-652	417	16	*	*	PROPN
ap-652	417	17	�	�	PROPN
ap-652	417	18	�	�	PROPN
ap-652	417	19	6	6	NUM
ap-652	417	20	2	2	NUM
ap-652	417	21	2	2	NUM
ap-652	417	22	q	q	NOUN
ap-652	417	23	l	l	NOUN
ap-652	417	24	,	,	PUNCT
ap-652	417	25	(	(	PUNCT
ap-652	417	26	52	52	NUM
ap-652	417	27	)	)	PUNCT
ap-652	417	28	where	where	SCONJ
ap-652	417	29	the	the	DET
ap-652	417	30	subscripts	subscript	NOUN
ap-652	417	31	in	in	ADP
ap-652	417	32	p	p	NOUN
ap-652	417	33	and	and	CCONJ
ap-652	417	34	q	q	NOUN
ap-652	417	35	are	be	AUX
ap-652	417	36	omitted	omit	VERB
ap-652	417	37	for	for	ADP
ap-652	417	38	the	the	DET
ap-652	417	39	sake	sake	NOUN
ap-652	417	40	of	of	ADP
ap-652	417	41	simplicity	simplicity	NOUN
ap-652	417	42	.	.	PUNCT
ap-652	418	1	since	since	SCONJ
ap-652	418	2	the	the	DET
ap-652	418	3	maximum	maximum	NOUN
ap-652	418	4	in	in	ADP
ap-652	418	5	both	both	DET
ap-652	418	6	relations	relation	NOUN
ap-652	418	7	of	of	ADP
ap-652	418	8	(	(	PUNCT
ap-652	418	9	52	52	NUM
ap-652	418	10	)	)	PUNCT
ap-652	418	11	must	must	AUX
ap-652	418	12	be	be	AUX
ap-652	418	13	the	the	DET
ap-652	418	14	same	same	ADJ
ap-652	418	15	,	,	PUNCT
ap-652	418	16	p	p	PROPN
ap-652	418	17	q2	q2	NOUN
ap-652	418	18	22	22	NUM
ap-652	418	19	3	3	NUM
ap-652	418	20	�	�	PROPN
ap-652	418	21	and	and	CCONJ
ap-652	418	22	taking	take	VERB
ap-652	418	23	into	into	ADP
ap-652	418	24	account	account	NOUN
ap-652	418	25	the	the	DET
ap-652	418	26	last	last	ADJ
ap-652	418	27	expression	expression	NOUN
ap-652	418	28	of	of	ADP
ap-652	418	29	(	(	PUNCT
ap-652	418	30	26	26	NUM
ap-652	418	31	)	)	PUNCT
ap-652	418	32	,	,	PUNCT
ap-652	418	33	g	g	PROPN
ap-652	418	34	*	*	PROPN
ap-652	418	35	�	�	PROPN
ap-652	418	36	s/15	s/15	NOUN
ap-652	418	37	can	can	AUX
ap-652	418	38	finally	finally	ADV
ap-652	418	39	be	be	AUX
ap-652	418	40	obtained	obtain	VERB
ap-652	418	41	.	.	PUNCT
ap-652	419	1	therefore	therefore	ADV
ap-652	419	2	g	g	PROPN
ap-652	419	3	s	s	PROPN
ap-652	419	4	�	�	PROPN
ap-652	419	5	*	*	PROPN
ap-652	419	6	15	15	NUM
ap-652	419	7	,	,	PUNCT
ap-652	419	8	if	if	SCONJ
ap-652	419	9	at	at	ADV
ap-652	419	10	least	least	ADV
ap-652	419	11	one	one	NUM
ap-652	419	12	optimal	optimal	ADJ
ap-652	419	13	medium	medium	NOUN
ap-652	419	14	exists	exist	NOUN
ap-652	419	15	.	.	PUNCT
ap-652	420	1	the	the	DET
ap-652	420	2	necessary	necessary	ADJ
ap-652	420	3	maximality	maximality	NOUN
ap-652	420	4	and	and	CCONJ
ap-652	420	5	additional	additional	ADJ
ap-652	420	6	constraints	constraint	NOUN
ap-652	420	7	can	can	AUX
ap-652	420	8	be	be	AUX
ap-652	420	9	expressed	express	VERB
ap-652	420	10	by	by	ADP
ap-652	420	11	analogy	analogy	NOUN
ap-652	420	12	with	with	ADP
ap-652	420	13	sections	section	NOUN
ap-652	420	14	3.2–3	3.2–3	NUM
ap-652	420	15	as	as	ADP
ap-652	420	16	:	:	PUNCT
ap-652	420	17	n	n	CCONJ
ap-652	420	18	p	p	X
ap-652	420	19	q	q	PROPN
ap-652	420	20	�	�	PROPN
ap-652	420	21	�	�	PROPN
ap-652	420	22	�	�	PROPN
ap-652	420	23	�	�	PROPN
ap-652	420	24	j	j	PROPN
ap-652	420	25	j	j	PROPN
ap-652	421	1	k	k	PROPN
ap-652	422	1	k	k	PROPN
ap-652	423	1	j	j	PROPN
ap-652	424	1	k	k	PROPN
ap-652	424	2	,	,	PUNCT
ap-652	424	3	,	,	PUNCT
ap-652	424	4	,	,	PUNCT
ap-652	424	5	,	,	PUNCT
ap-652	424	6	1	1	NUM
ap-652	424	7	2	2	NUM
ap-652	424	8	3	3	NUM
ap-652	424	9	(	(	PUNCT
ap-652	424	10	53	53	NUM
ap-652	424	11	)	)	PUNCT
ap-652	424	12	and	and	CCONJ
ap-652	424	13	r	r	NOUN
ap-652	424	14	r	r	NOUN
ap-652	424	15	r	r	NOUN
ap-652	424	16	r	r	NOUN
ap-652	424	17	r	r	NOUN
ap-652	424	18	r	r	NOUN
ap-652	424	19	r	r	NOUN
ap-652	424	20	r	r	NOUN
ap-652	424	21	r	r	NOUN
ap-652	424	22	q	q	NOUN
ap-652	424	23	r	r	NOUN
ap-652	424	24	1	1	NUM
ap-652	424	25	2	2	NUM
ap-652	424	26	3	3	NUM
ap-652	424	27	1	1	NUM
ap-652	424	28	2	2	NUM
ap-652	424	29	2	2	NUM
ap-652	424	30	3	3	NUM
ap-652	424	31	3	3	NUM
ap-652	424	32	1	1	NUM
ap-652	424	33	�	�	PROPN
ap-652	424	34	�	�	PROPN
ap-652	424	35	�	�	PROPN
ap-652	424	36	�	�	PROPN
ap-652	424	37	%	%	NOUN
ap-652	424	38	�	�	PROPN
ap-652	424	39	,	,	PUNCT
ap-652	424	40	cos	cos	PROPN
ap-652	424	41	(	(	PUNCT
ap-652	424	42	,	,	PUNCT
ap-652	424	43	)	)	PUNCT
ap-652	424	44	cos	cos	PROPN
ap-652	424	45	(	(	PUNCT
ap-652	424	46	,	,	PUNCT
ap-652	424	47	)	)	PUNCT
ap-652	424	48	cos	cos	PROPN
ap-652	424	49	(	(	PUNCT
ap-652	424	50	,	,	PUNCT
ap-652	424	51	)	)	PUNCT
ap-652	424	52	;	;	PROPN
ap-652	424	53	j	j	PROPN
ap-652	424	54	k	k	PROPN
ap-652	424	55	j	j	PROPN
ap-652	424	56	,	,	PUNCT
ap-652	424	57	k	k	PROPN
ap-652	424	58	1	1	NUM
ap-652	424	59	3	3	NUM
ap-652	424	60	�	�	PROPN
ap-652	424	61	%	%	NOUN
ap-652	424	62	%	%	NOUN
ap-652	424	63	�	�	PROPN
ap-652	424	64	�	�	PROPN
ap-652	424	65	1	1	NUM
ap-652	424	66	2	2	NUM
ap-652	424	67	3	3	NUM
ap-652	424	68	2	2	NUM
ap-652	424	69	1	1	NUM
ap-652	424	70	2	2	NUM
ap-652	424	71	3	3	NUM
ap-652	424	72	,	,	PUNCT
ap-652	424	73	,	,	PUNCT
ap-652	425	1	;	;	PROPN
ap-652	425	2	;	;	VERB
ap-652	425	3	.q	.q	PROPN
ap-652	426	1	q	q	X
ap-652	427	1	q	q	X
ap-652	427	2	q	q	X
ap-652	427	3	q	q	X
ap-652	427	4	q	q	X
ap-652	427	5	(	(	PUNCT
ap-652	427	6	54	54	NUM
ap-652	427	7	)	)	PUNCT
ap-652	427	8	unfortunately	unfortunately	ADV
ap-652	427	9	,	,	PUNCT
ap-652	427	10	no	no	DET
ap-652	427	11	full	full	ADJ
ap-652	427	12	geometrical	geometrical	ADJ
ap-652	427	13	characterization	characterization	NOUN
ap-652	427	14	of	of	ADP
ap-652	427	15	g*-optimal	g*-optimal	ADJ
ap-652	427	16	media	medium	NOUN
ap-652	427	17	is	be	AUX
ap-652	427	18	possible	possible	ADJ
ap-652	427	19	.	.	PUNCT
ap-652	428	1	the	the	DET
ap-652	428	2	existence	existence	NOUN
ap-652	428	3	of	of	ADP
ap-652	428	4	at	at	ADV
ap-652	428	5	least	least	ADV
ap-652	428	6	one	one	NUM
ap-652	428	7	optimal	optimal	ADJ
ap-652	428	8	medium	medium	NOUN
ap-652	428	9	can	can	AUX
ap-652	428	10	be	be	AUX
ap-652	428	11	proven	prove	VERB
ap-652	428	12	by	by	ADP
ap-652	428	13	superposition	superposition	NOUN
ap-652	428	14	of	of	ADP
ap-652	428	15	the	the	DET
ap-652	428	16	results	result	NOUN
ap-652	428	17	,	,	PUNCT
ap-652	428	18	namely	namely	ADV
ap-652	428	19	by	by	ADP
ap-652	428	20	combining	combine	VERB
ap-652	428	21	of	of	ADP
ap-652	428	22	the	the	DET
ap-652	428	23	cells	cell	NOUN
ap-652	428	24	of	of	ADP
ap-652	428	25	the	the	DET
ap-652	428	26	simplestg1	simplestg1	NOUN
ap-652	428	27	*	*	PUNCT
ap-652	428	28	and	and	CCONJ
ap-652	428	29	g2	g2	PROPN
ap-652	428	30	*	*	PUNCT
ap-652	428	31	-optimal	-optimal	ADJ
ap-652	428	32	media	medium	NOUN
ap-652	428	33	,	,	PUNCT
ap-652	428	34	see	see	VERB
ap-652	428	35	dimitrovová	dimitrovová	NOUN
ap-652	428	36	and	and	CCONJ
ap-652	428	37	faria	faria	PROPN
ap-652	428	38	(	(	PUNCT
ap-652	428	39	1999	1999	NUM
ap-652	428	40	)	)	PUNCT
ap-652	428	41	for	for	ADP
ap-652	428	42	the	the	DET
ap-652	428	43	conditions	condition	NOUN
ap-652	428	44	under	under	ADP
ap-652	428	45	which	which	PRON
ap-652	428	46	such	such	DET
ap-652	428	47	a	a	DET
ap-652	428	48	superposition	superposition	NOUN
ap-652	428	49	can	can	AUX
ap-652	428	50	be	be	AUX
ap-652	428	51	performed	perform	VERB
ap-652	428	52	.	.	PUNCT
ap-652	429	1	let	let	VERB
ap-652	429	2	us	we	PRON
ap-652	429	3	denote	denote	VERB
ap-652	429	4	the	the	DET
ap-652	429	5	material	material	NOUN
ap-652	429	6	volume	volume	NOUN
ap-652	429	7	fractions	fraction	NOUN
ap-652	429	8	of	of	ADP
ap-652	429	9	the	the	DET
ap-652	429	10	simplest	simple	ADJ
ap-652	429	11	g1	g1	NOUN
ap-652	429	12	*	*	PUNCT
ap-652	429	13	and	and	CCONJ
ap-652	429	14	g2	g2	PROPN
ap-652	429	15	*	*	PUNCT
ap-652	429	16	-optimal	-optimal	ADJ
ap-652	429	17	media	medium	NOUN
ap-652	429	18	as	as	ADP
ap-652	429	19	s1	s1	PROPN
ap-652	429	20	g	g	PROPN
ap-652	429	21	and	and	CCONJ
ap-652	429	22	s2	s2	PROPN
ap-652	429	23	g	g	NOUN
ap-652	429	24	,	,	PUNCT
ap-652	429	25	respectively	respectively	ADV
ap-652	429	26	.	.	PUNCT
ap-652	430	1	it	it	PRON
ap-652	430	2	can	can	AUX
ap-652	430	3	be	be	AUX
ap-652	430	4	written	write	VERB
ap-652	430	5	:	:	PUNCT
ap-652	430	6	g	g	PROPN
ap-652	430	7	s	s	PROPN
ap-652	430	8	s	s	NOUN
ap-652	430	9	9	9	NUM
ap-652	430	10	1	1	NUM
ap-652	430	11	g	g	PROPN
ap-652	430	12	2	2	NUM
ap-652	430	13	g	g	NOUN
ap-652	430	14	*	*	PUNCT
ap-652	430	15	�	�	PROPN
ap-652	430	16	�	�	PROPN
ap-652	430	17	6	6	NUM
ap-652	430	18	,	,	PUNCT
ap-652	430	19	(	(	PUNCT
ap-652	430	20	55	55	NUM
ap-652	430	21	)	)	PUNCT
ap-652	430	22	yielding	yield	VERB
ap-652	430	23	s	s	PROPN
ap-652	430	24	s1	s1	NOUN
ap-652	430	25	g	g	NOUN
ap-652	430	26	2g	2g	NUM
ap-652	430	27	�	�	PROPN
ap-652	430	28	2	2	NUM
ap-652	430	29	3	3	NUM
ap-652	430	30	and	and	CCONJ
ap-652	430	31	consequently	consequently	ADV
ap-652	430	32	(	(	PUNCT
ap-652	430	33	s	s	NOUN
ap-652	430	34	=	=	NOUN
ap-652	430	35	s	s	NOUN
ap-652	430	36	s1	s1	NOUN
ap-652	430	37	g	g	ADJ
ap-652	430	38	2	2	NUM
ap-652	430	39	g	g	NOUN
ap-652	430	40	because	because	SCONJ
ap-652	430	41	the	the	DET
ap-652	430	42	bars	bar	NOUN
ap-652	430	43	of	of	ADP
ap-652	430	44	the	the	DET
ap-652	430	45	original	original	ADJ
ap-652	430	46	media	medium	NOUN
ap-652	430	47	do	do	AUX
ap-652	430	48	not	not	PART
ap-652	430	49	coincide)g	coincide)g	VERB
ap-652	430	50	s	s	PROPN
ap-652	430	51	*	*	PUNCT
ap-652	430	52	�	�	PROPN
ap-652	430	53	15	15	NUM
ap-652	430	54	for	for	ADP
ap-652	430	55	the	the	DET
ap-652	430	56	combined	combined	ADJ
ap-652	430	57	medium	medium	NOUN
ap-652	430	58	.	.	PUNCT
ap-652	431	1	as	as	ADP
ap-652	431	2	a	a	DET
ap-652	431	3	consequence	consequence	NOUN
ap-652	431	4	,	,	PUNCT
ap-652	431	5	the	the	DET
ap-652	431	6	relation	relation	NOUN
ap-652	431	7	between	between	ADP
ap-652	431	8	the	the	DET
ap-652	431	9	cross	cross	NOUN
ap-652	431	10	sectional	sectional	ADJ
ap-652	431	11	areas	area	NOUN
ap-652	431	12	can	can	AUX
ap-652	431	13	be	be	AUX
ap-652	431	14	derived	derive	VERB
ap-652	431	15	as	as	ADP
ap-652	431	16	a	a	DET
ap-652	431	17	a	a	DET
ap-652	431	18	91	91	NUM
ap-652	431	19	g	g	NOUN
ap-652	431	20	2g	2g	NUM
ap-652	431	21	�	�	NOUN
ap-652	431	22	8	8	NUM
ap-652	431	23	3	3	NUM
ap-652	431	24	,	,	PUNCT
ap-652	431	25	where	where	SCONJ
ap-652	431	26	,	,	PUNCT
ap-652	431	27	a1	a1	NOUN
ap-652	431	28	g	g	NOUN
ap-652	431	29	and	and	CCONJ
ap-652	431	30	a2	a2	PROPN
ap-652	431	31	g	g	PROPN
ap-652	431	32	stand	stand	NOUN
ap-652	431	33	for	for	ADP
ap-652	431	34	the	the	DET
ap-652	431	35	cross	cross	NOUN
ap-652	431	36	sections	section	NOUN
ap-652	431	37	of	of	ADP
ap-652	431	38	the	the	DET
ap-652	431	39	original	original	ADJ
ap-652	431	40	g1	g1	NOUN
ap-652	431	41	*	*	PUNCT
ap-652	431	42	and	and	CCONJ
ap-652	431	43	g2	g2	PROPN
ap-652	431	44	*	*	PUNCT
ap-652	431	45	-optimal	-optimal	ADJ
ap-652	431	46	media	medium	NOUN
ap-652	431	47	,	,	PUNCT
ap-652	431	48	respectively	respectively	ADV
ap-652	431	49	(	(	PUNCT
ap-652	431	50	figs	fig	NOUN
ap-652	431	51	.	.	X
ap-652	432	1	5	5	NUM
ap-652	432	2	and	and	CCONJ
ap-652	432	3	7	7	NUM
ap-652	432	4	)	)	PUNCT
ap-652	432	5	.	.	PUNCT
ap-652	433	1	it	it	PRON
ap-652	433	2	can	can	AUX
ap-652	433	3	be	be	AUX
ap-652	433	4	verified	verify	VERB
ap-652	433	5	that	that	SCONJ
ap-652	433	6	also	also	ADV
ap-652	433	7	in	in	ADP
ap-652	433	8	this	this	DET
ap-652	433	9	case	case	NOUN
ap-652	433	10	the	the	DET
ap-652	433	11	bending	bend	VERB
ap-652	433	12	effect	effect	NOUN
ap-652	433	13	can	can	AUX
ap-652	433	14	be	be	AUX
ap-652	433	15	superposed	superpose	VERB
ap-652	433	16	directly	directly	ADV
ap-652	433	17	,	,	PUNCT
ap-652	433	18	as	as	ADP
ap-652	433	19	in	in	ADP
ap-652	433	20	the	the	DET
ap-652	433	21	2d	2d	NUM
ap-652	433	22	analog	analog	NOUN
ap-652	433	23	,	,	PUNCT
ap-652	433	24	as	as	SCONJ
ap-652	433	25	shown	show	VERB
ap-652	433	26	in	in	ADP
ap-652	433	27	dimitrovová	dimitrovová	NOUN
ap-652	433	28	and	and	CCONJ
ap-652	433	29	faria	faria	PROPN
ap-652	433	30	(	(	PUNCT
ap-652	433	31	1999	1999	NUM
ap-652	433	32	)	)	PUNCT
ap-652	433	33	.	.	PUNCT
ap-652	434	1	4	4	NUM
ap-652	434	2	concluding	conclude	VERB
ap-652	434	3	remarks	remark	NOUN
ap-652	434	4	it	it	PRON
ap-652	434	5	was	be	AUX
ap-652	434	6	proven	prove	VERB
ap-652	434	7	that	that	SCONJ
ap-652	434	8	g1	g1	PROPN
ap-652	434	9	*	*	PUNCT
ap-652	434	10	and	and	CCONJ
ap-652	434	11	g2	g2	PROPN
ap-652	434	12	*	*	PUNCT
ap-652	434	13	-optimal	-optimal	ADJ
ap-652	434	14	media	medium	NOUN
ap-652	434	15	can	can	AUX
ap-652	434	16	be	be	AUX
ap-652	434	17	geometrically	geometrically	ADV
ap-652	434	18	fully	fully	ADV
ap-652	434	19	specified	specify	VERB
ap-652	434	20	.	.	PUNCT
ap-652	435	1	they	they	PRON
ap-652	435	2	are	be	AUX
ap-652	435	3	upl	upl	PROPN
ap-652	435	4	and	and	CCONJ
ap-652	435	5	udl	udl	PROPN
ap-652	435	6	,	,	PUNCT
ap-652	435	7	respectively	respectively	ADV
ap-652	435	8	.	.	PUNCT
ap-652	436	1	neither	neither	CCONJ
ap-652	436	2	for	for	ADP
ap-652	436	3	k*-optimal	k*-optimal	ADJ
ap-652	436	4	nor	nor	CCONJ
ap-652	436	5	for	for	ADP
ap-652	436	6	g*-optimal	g*-optimal	ADJ
ap-652	436	7	media	medium	NOUN
ap-652	436	8	can	can	AUX
ap-652	436	9	a	a	DET
ap-652	436	10	full	full	ADJ
ap-652	436	11	geometrical	geometrical	ADJ
ap-652	436	12	specification	specification	NOUN
ap-652	436	13	of	of	ADP
ap-652	436	14	their	their	PRON
ap-652	436	15	microstructure	microstructure	NOUN
ap-652	436	16	be	be	AUX
ap-652	436	17	given	give	VERB
ap-652	436	18	.	.	PUNCT
ap-652	437	1	182	182	NUM
ap-652	438	1	©	©	PROPN
ap-652	438	2	czech	czech	PROPN
ap-652	438	3	technical	technical	PROPN
ap-652	438	4	university	university	PROPN
ap-652	438	5	publishing	publishing	NOUN
ap-652	438	6	house	house	NOUN
ap-652	438	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	438	8	acta	acta	PROPN
ap-652	438	9	polytechnica	polytechnica	PROPN
ap-652	438	10	vol	vol	NOUN
ap-652	438	11	.	.	PROPN
ap-652	439	1	44	44	NUM
ap-652	439	2	no.5–6/2004	no.5–6/2004	PROPN
ap-652	439	3	1y	1y	NUM
ap-652	439	4	2y	2y	PROPN
ap-652	439	5	3y	3y	NUM
ap-652	439	6	g2a	g2a	PROPN
ap-652	439	7	fig	fig	NOUN
ap-652	439	8	.	.	PUNCT
ap-652	440	1	7	7	NUM
ap-652	440	2	:	:	PUNCT
ap-652	440	3	the	the	DET
ap-652	440	4	regular	regular	ADJ
ap-652	440	5	cube	cube	NOUN
ap-652	440	6	-	-	PUNCT
ap-652	440	7	diagonal	diagonal	ADJ
ap-652	440	8	lattice	lattice	NOUN
ap-652	440	9	�	�	PROPN
ap-652	440	10	1	1	NUM
ap-652	440	11	�	�	PROPN
ap-652	440	12	2	2	NUM
ap-652	440	13	�	�	PROPN
ap-652	440	14	3	3	NUM
ap-652	440	15	�	�	NOUN
ap-652	440	16	4	4	NUM
ap-652	440	17	y1	y1	NOUN
ap-652	440	18	1	1	NUM
ap-652	440	19	3	3	NUM
ap-652	440	20	1	1	NUM
ap-652	440	21	3	3	NUM
ap-652	440	22	1	1	NUM
ap-652	440	23	3	3	NUM
ap-652	440	24	1	1	NUM
ap-652	440	25	3	3	NUM
ap-652	440	26	y2	y2	NOUN
ap-652	440	27	1	1	NUM
ap-652	440	28	3	3	NUM
ap-652	440	29	1	1	NUM
ap-652	440	30	3	3	NUM
ap-652	440	31	1	1	NUM
ap-652	440	32	3	3	NUM
ap-652	440	33	1	1	NUM
ap-652	440	34	3	3	NUM
ap-652	440	35	y3	y3	NOUN
ap-652	440	36	1	1	NUM
ap-652	440	37	3	3	NUM
ap-652	440	38	1	1	NUM
ap-652	440	39	3	3	NUM
ap-652	440	40	1	1	NUM
ap-652	440	41	3	3	NUM
ap-652	440	42	1	1	NUM
ap-652	440	43	3	3	NUM
ap-652	440	44	table	table	NOUN
ap-652	440	45	6	6	NUM
ap-652	440	46	:	:	PUNCT
ap-652	440	47	contributions	contribution	NOUN
ap-652	440	48	of	of	ADP
ap-652	440	49	the	the	DET
ap-652	440	50	local	local	ADJ
ap-652	440	51	stresses	stress	NOUN
ap-652	440	52	to	to	ADP
ap-652	440	53	the	the	DET
ap-652	440	54	coordinate	coordinate	NOUN
ap-652	440	55	directions	direction	NOUN
ap-652	440	56	it	it	PRON
ap-652	440	57	is	be	AUX
ap-652	440	58	easy	easy	ADJ
ap-652	440	59	to	to	PART
ap-652	440	60	verify	verify	VERB
ap-652	440	61	that	that	SCONJ
ap-652	440	62	g1	g1	PROPN
ap-652	440	63	*	*	PUNCT
ap-652	440	64	and	and	CCONJ
ap-652	440	65	k*-optimal	k*-optimal	ADJ
ap-652	440	66	media	medium	NOUN
ap-652	440	67	,	,	PUNCT
ap-652	440	68	assumed	assume	VERB
ap-652	440	69	either	either	CCONJ
ap-652	440	70	as	as	ADP
ap-652	440	71	micro	micro	NOUN
ap-652	440	72	-	-	NOUN
ap-652	440	73	trusses	truss	NOUN
ap-652	440	74	or	or	CCONJ
ap-652	440	75	as	as	ADP
ap-652	440	76	micro	micro	NOUN
ap-652	440	77	-	-	NOUN
ap-652	440	78	frames	frame	NOUN
ap-652	440	79	,	,	PUNCT
ap-652	440	80	respond	respond	VERB
ap-652	440	81	only	only	ADV
ap-652	440	82	axially	axially	ADV
ap-652	440	83	,	,	PUNCT
ap-652	440	84	while	while	SCONJ
ap-652	440	85	in	in	ADP
ap-652	440	86	g2	g2	PROPN
ap-652	440	87	*	*	PUNCT
ap-652	440	88	and	and	CCONJ
ap-652	440	89	g*-optimal	g*-optimal	PROPN
ap-652	440	90	micro	micro	NOUN
ap-652	440	91	-	-	NOUN
ap-652	440	92	frames	frame	NOUN
ap-652	440	93	,	,	PUNCT
ap-652	440	94	a	a	DET
ap-652	440	95	bending	bend	VERB
ap-652	440	96	response	response	NOUN
ap-652	440	97	is	be	AUX
ap-652	440	98	always	always	ADV
ap-652	440	99	presented	present	VERB
ap-652	440	100	.	.	PUNCT
ap-652	441	1	the	the	DET
ap-652	441	2	bending	bend	VERB
ap-652	441	3	contribution	contribution	NOUN
ap-652	441	4	is	be	AUX
ap-652	441	5	different	different	ADJ
ap-652	441	6	for	for	ADP
ap-652	441	7	different	different	ADJ
ap-652	441	8	g2	g2	NOUN
ap-652	441	9	*	*	PUNCT
ap-652	441	10	and	and	CCONJ
ap-652	441	11	g*-optimal	g*-optimal	PROPN
ap-652	441	12	media	medium	NOUN
ap-652	441	13	,	,	PUNCT
ap-652	441	14	therefore	therefore	ADV
ap-652	441	15	the	the	DET
ap-652	441	16	non	non	ADJ
ap-652	441	17	-	-	ADJ
ap-652	441	18	linear	linear	ADJ
ap-652	441	19	part	part	NOUN
ap-652	441	20	is	be	AUX
ap-652	441	21	rather	rather	ADV
ap-652	441	22	difficult	difficult	ADJ
ap-652	441	23	to	to	PART
ap-652	441	24	define	define	VERB
ap-652	441	25	.	.	PUNCT
ap-652	442	1	however	however	ADV
ap-652	442	2	,	,	PUNCT
ap-652	442	3	it	it	PRON
ap-652	442	4	can	can	AUX
ap-652	442	5	be	be	AUX
ap-652	442	6	stated	state	VERB
ap-652	442	7	that	that	SCONJ
ap-652	442	8	for	for	ADP
ap-652	442	9	low	low	ADJ
ap-652	442	10	-	-	PUNCT
ap-652	442	11	density	density	NOUN
ap-652	442	12	media	medium	NOUN
ap-652	442	13	this	this	DET
ap-652	442	14	non	non	ADJ
ap-652	442	15	-	-	ADJ
ap-652	442	16	linear	linear	ADJ
ap-652	442	17	part	part	NOUN
ap-652	442	18	is	be	AUX
ap-652	442	19	not	not	PART
ap-652	442	20	important	important	ADJ
ap-652	442	21	.	.	PUNCT
ap-652	443	1	the	the	DET
ap-652	443	2	bending	bend	VERB
ap-652	443	3	contribution	contribution	NOUN
ap-652	443	4	can	can	AUX
ap-652	443	5	be	be	AUX
ap-652	443	6	increased	increase	VERB
ap-652	443	7	by	by	ADP
ap-652	443	8	putting	put	VERB
ap-652	443	9	more	more	ADJ
ap-652	443	10	material	material	NOUN
ap-652	443	11	close	close	ADV
ap-652	443	12	to	to	ADP
ap-652	443	13	the	the	DET
ap-652	443	14	joints	joint	NOUN
ap-652	443	15	,	,	PUNCT
ap-652	443	16	because	because	SCONJ
ap-652	443	17	the	the	DET
ap-652	443	18	bending	bend	VERB
ap-652	443	19	moment	moment	NOUN
ap-652	443	20	distribution	distribution	NOUN
ap-652	443	21	is	be	AUX
ap-652	443	22	antisymmetric	antisymmetric	ADJ
ap-652	443	23	within	within	ADP
ap-652	443	24	each	each	DET
ap-652	443	25	beam	beam	NOUN
ap-652	443	26	(	(	PUNCT
ap-652	443	27	section	section	NOUN
ap-652	443	28	2.2	2.2	NUM
ap-652	443	29	)	)	PUNCT
ap-652	443	30	.	.	PUNCT
ap-652	444	1	however	however	ADV
ap-652	444	2	,	,	PUNCT
ap-652	444	3	this	this	DET
ap-652	444	4	change	change	NOUN
ap-652	444	5	would	would	AUX
ap-652	444	6	decrease	decrease	VERB
ap-652	444	7	the	the	DET
ap-652	444	8	axial	axial	ADJ
ap-652	444	9	contribution	contribution	NOUN
ap-652	444	10	(	(	PUNCT
ap-652	444	11	17–18	17–18	NUM
ap-652	444	12	)	)	PUNCT
ap-652	444	13	,	,	PUNCT
ap-652	444	14	and	and	CCONJ
ap-652	444	15	the	the	DET
ap-652	444	16	corresponding	corresponding	ADJ
ap-652	444	17	linearized	linearize	VERB
ap-652	444	18	bound	bind	VERB
ap-652	444	19	would	would	AUX
ap-652	444	20	decrease	decrease	VERB
ap-652	444	21	.	.	PUNCT
ap-652	445	1	then	then	ADV
ap-652	445	2	the	the	DET
ap-652	445	3	medium	medium	NOUN
ap-652	445	4	would	would	AUX
ap-652	445	5	no	no	ADV
ap-652	445	6	longer	long	ADV
ap-652	445	7	be	be	AUX
ap-652	445	8	optimal	optimal	ADJ
ap-652	445	9	according	accord	VERB
ap-652	445	10	to	to	ADP
ap-652	445	11	the	the	DET
ap-652	445	12	definition	definition	NOUN
ap-652	445	13	from	from	ADP
ap-652	445	14	section	section	NOUN
ap-652	445	15	2.2	2.2	NUM
ap-652	445	16	.	.	PUNCT
ap-652	446	1	it	it	PRON
ap-652	446	2	is	be	AUX
ap-652	446	3	useful	useful	ADJ
ap-652	446	4	to	to	PART
ap-652	446	5	remark	remark	VERB
ap-652	446	6	that	that	SCONJ
ap-652	446	7	the	the	DET
ap-652	446	8	directions	direction	NOUN
ap-652	446	9	of	of	ADP
ap-652	446	10	the	the	DET
ap-652	446	11	bars	bar	NOUN
ap-652	446	12	in	in	ADP
ap-652	446	13	optimal	optimal	ADJ
ap-652	446	14	micro	micro	NOUN
ap-652	446	15	-	-	NOUN
ap-652	446	16	trusses	truss	NOUN
ap-652	446	17	should	should	AUX
ap-652	446	18	be	be	AUX
ap-652	446	19	related	relate	VERB
ap-652	446	20	to	to	ADP
ap-652	446	21	the	the	DET
ap-652	446	22	principal	principal	ADJ
ap-652	446	23	directions	direction	NOUN
ap-652	446	24	of	of	ADP
ap-652	446	25	the	the	DET
ap-652	446	26	applied	apply	VERB
ap-652	446	27	macroload	macroload	NOUN
ap-652	446	28	according	accord	VERB
ap-652	446	29	to	to	ADP
ap-652	446	30	the	the	DET
ap-652	446	31	theory	theory	NOUN
ap-652	446	32	of	of	ADP
ap-652	446	33	michell	michell	PROPN
ap-652	446	34	trusses	truss	NOUN
ap-652	446	35	.	.	PUNCT
ap-652	447	1	this	this	PRON
ap-652	447	2	is	be	AUX
ap-652	447	3	directly	directly	ADV
ap-652	447	4	related	relate	VERB
ap-652	447	5	to	to	ADP
ap-652	447	6	the	the	DET
ap-652	447	7	impossibility	impossibility	NOUN
ap-652	447	8	of	of	ADP
ap-652	447	9	full	full	ADJ
ap-652	447	10	geometrical	geometrical	ADJ
ap-652	447	11	characterization	characterization	NOUN
ap-652	447	12	of	of	ADP
ap-652	447	13	k*and	k*and	NOUN
ap-652	447	14	g*-optimal	g*-optimal	ADJ
ap-652	447	15	media	medium	NOUN
ap-652	447	16	.	.	PUNCT
ap-652	448	1	for	for	ADP
ap-652	448	2	�	�	PROPN
ap-652	448	3	k	k	PROPN
ap-652	448	4	each	each	DET
ap-652	448	5	direction	direction	NOUN
ap-652	448	6	is	be	AUX
ap-652	448	7	a	a	DET
ap-652	448	8	principal	principal	ADJ
ap-652	448	9	direction	direction	NOUN
ap-652	448	10	.	.	PUNCT
ap-652	449	1	�	�	PROPN
ap-652	449	2	g	g	PROPN
ap-652	449	3	can	can	AUX
ap-652	449	4	be	be	AUX
ap-652	449	5	determined	determine	VERB
ap-652	449	6	by	by	ADP
ap-652	449	7	five	five	NUM
ap-652	449	8	non	non	ADJ
ap-652	449	9	-	-	ADJ
ap-652	449	10	zero	zero	ADJ
ap-652	449	11	and	and	CCONJ
ap-652	449	12	independent	independent	ADJ
ap-652	449	13	parameters	parameter	NOUN
ap-652	449	14	,	,	PUNCT
ap-652	449	15	and	and	CCONJ
ap-652	449	16	therefore	therefore	ADV
ap-652	449	17	each	each	DET
ap-652	449	18	direction	direction	NOUN
ap-652	449	19	can	can	AUX
ap-652	449	20	also	also	ADV
ap-652	449	21	be	be	AUX
ap-652	449	22	assumed	assume	VERB
ap-652	449	23	as	as	ADP
ap-652	449	24	a	a	DET
ap-652	449	25	principal	principal	ADJ
ap-652	449	26	one	one	NUM
ap-652	449	27	.	.	PUNCT
ap-652	450	1	the	the	DET
ap-652	450	2	directions	direction	NOUN
ap-652	450	3	of	of	ADP
ap-652	450	4	the	the	DET
ap-652	450	5	bars	bar	NOUN
ap-652	450	6	are	be	AUX
ap-652	450	7	precisely	precisely	ADV
ap-652	450	8	specified	specify	VERB
ap-652	450	9	in	in	ADP
ap-652	450	10	g1	g1	PROPN
ap-652	450	11	*	*	PUNCT
ap-652	450	12	and	and	CCONJ
ap-652	450	13	g2	g2	PROPN
ap-652	450	14	*	*	PUNCT
ap-652	450	15	-optimal	-optimal	ADJ
ap-652	450	16	media	medium	NOUN
ap-652	450	17	.	.	PUNCT
ap-652	451	1	in	in	ADP
ap-652	451	2	the	the	DET
ap-652	451	3	former	former	ADJ
ap-652	451	4	case	case	NOUN
ap-652	451	5	they	they	PRON
ap-652	451	6	coincide	coincide	VERB
ap-652	451	7	with	with	ADP
ap-652	451	8	the	the	DET
ap-652	451	9	principal	principal	ADJ
ap-652	451	10	directions	direction	NOUN
ap-652	451	11	of	of	ADP
ap-652	451	12	the	the	DET
ap-652	451	13	macroload	macroload	NOUN
ap-652	451	14	,	,	PUNCT
ap-652	451	15	which	which	PRON
ap-652	451	16	are	be	AUX
ap-652	451	17	in	in	ADP
ap-652	451	18	this	this	DET
ap-652	451	19	case	case	NOUN
ap-652	451	20	unique	unique	ADJ
ap-652	451	21	for	for	ADP
ap-652	451	22	any	any	DET
ap-652	451	23	�	�	PROPN
ap-652	451	24	1	1	NUM
ap-652	451	25	g	g	NOUN
ap-652	451	26	,	,	PUNCT
ap-652	451	27	but	but	CCONJ
ap-652	451	28	in	in	ADP
ap-652	451	29	the	the	DET
ap-652	451	30	latter	latter	ADJ
ap-652	451	31	case	case	NOUN
ap-652	451	32	the	the	DET
ap-652	451	33	directions	direction	NOUN
ap-652	451	34	of	of	ADP
ap-652	451	35	the	the	DET
ap-652	451	36	bars	bar	NOUN
ap-652	451	37	can	can	AUX
ap-652	451	38	hardly	hardly	ADV
ap-652	451	39	be	be	AUX
ap-652	451	40	determined	determine	VERB
ap-652	451	41	in	in	ADP
ap-652	451	42	such	such	DET
ap-652	451	43	a	a	DET
ap-652	451	44	way	way	NOUN
ap-652	451	45	.	.	PUNCT
ap-652	452	1	another	another	DET
ap-652	452	2	remark	remark	NOUN
ap-652	452	3	yields	yield	VERB
ap-652	452	4	from	from	ADP
ap-652	452	5	a	a	DET
ap-652	452	6	comparison	comparison	NOUN
ap-652	452	7	of	of	ADP
ap-652	452	8	the	the	DET
ap-652	452	9	additional	additional	ADJ
ap-652	452	10	constraints	constraint	NOUN
ap-652	452	11	(	(	PUNCT
ap-652	452	12	geometrical	geometrical	ADJ
ap-652	452	13	requirements	requirement	NOUN
ap-652	452	14	)	)	PUNCT
ap-652	452	15	for	for	ADP
ap-652	452	16	k*and	k*and	NOUN
ap-652	452	17	g*-optimal	g*-optimal	ADJ
ap-652	452	18	media	medium	NOUN
ap-652	452	19	,	,	PUNCT
ap-652	452	20	(	(	PUNCT
ap-652	452	21	33	33	NUM
ap-652	452	22	)	)	PUNCT
ap-652	452	23	and	and	CCONJ
ap-652	452	24	(	(	PUNCT
ap-652	452	25	54	54	NUM
ap-652	452	26	)	)	PUNCT
ap-652	452	27	,	,	PUNCT
ap-652	452	28	respectively	respectively	ADV
ap-652	452	29	.	.	PUNCT
ap-652	453	1	it	it	PRON
ap-652	453	2	can	can	AUX
ap-652	453	3	be	be	AUX
ap-652	453	4	shown	show	VERB
ap-652	453	5	,	,	PUNCT
ap-652	453	6	with	with	ADP
ap-652	453	7	the	the	DET
ap-652	453	8	help	help	NOUN
ap-652	453	9	of	of	ADP
ap-652	453	10	(	(	PUNCT
ap-652	453	11	24	24	NUM
ap-652	453	12	)	)	PUNCT
ap-652	453	13	and	and	CCONJ
ap-652	453	14	the	the	DET
ap-652	453	15	second	second	ADJ
ap-652	453	16	relation	relation	NOUN
ap-652	453	17	in	in	ADP
ap-652	453	18	(	(	PUNCT
ap-652	453	19	26	26	NUM
ap-652	453	20	)	)	PUNCT
ap-652	453	21	,	,	PUNCT
ap-652	453	22	that	that	SCONJ
ap-652	453	23	the	the	DET
ap-652	453	24	group	group	NOUN
ap-652	453	25	of	of	ADP
ap-652	453	26	media	medium	NOUN
ap-652	453	27	satisfying	satisfy	VERB
ap-652	453	28	(	(	PUNCT
ap-652	453	29	54	54	NUM
ap-652	453	30	)	)	PUNCT
ap-652	453	31	forms	form	VERB
ap-652	453	32	a	a	DET
ap-652	453	33	subgroup	subgroup	NOUN
ap-652	453	34	of	of	ADP
ap-652	453	35	microstructures	microstructure	NOUN
ap-652	453	36	for	for	ADP
ap-652	453	37	which	which	PRON
ap-652	453	38	(	(	PUNCT
ap-652	453	39	33	33	NUM
ap-652	453	40	)	)	PUNCT
ap-652	453	41	holds	hold	VERB
ap-652	453	42	.	.	PUNCT
ap-652	454	1	therefore	therefore	ADV
ap-652	454	2	each	each	DET
ap-652	454	3	k*-optimal	k*-optimal	PROPN
ap-652	454	4	medium	medium	NOUN
ap-652	454	5	already	already	ADV
ap-652	454	6	fulfills	fulfill	VERB
ap-652	454	7	additional	additional	ADJ
ap-652	454	8	constraints	constraint	NOUN
ap-652	454	9	for	for	ADP
ap-652	454	10	g*-optimal	g*-optimal	ADJ
ap-652	454	11	media	medium	NOUN
ap-652	454	12	,	,	PUNCT
ap-652	454	13	so	so	SCONJ
ap-652	454	14	that	that	SCONJ
ap-652	454	15	it	it	PRON
ap-652	454	16	is	be	AUX
ap-652	454	17	hard	hard	ADJ
ap-652	454	18	to	to	PART
ap-652	454	19	find	find	VERB
ap-652	454	20	a	a	DET
ap-652	454	21	g*-optimal	g*-optimal	ADJ
ap-652	454	22	medium	medium	NOUN
ap-652	454	23	which	which	PRON
ap-652	454	24	is	be	AUX
ap-652	454	25	not	not	PART
ap-652	454	26	k*-optimal	k*-optimal	ADJ
ap-652	454	27	.	.	PUNCT
ap-652	455	1	it	it	PRON
ap-652	455	2	is	be	AUX
ap-652	455	3	straightforward	straightforward	ADJ
ap-652	455	4	to	to	PART
ap-652	455	5	derive	derive	VERB
ap-652	455	6	bounds	bound	NOUN
ap-652	455	7	for	for	ADP
ap-652	455	8	young	young	ADJ
ap-652	455	9	’s	’s	PART
ap-652	455	10	modulus	modulus	NOUN
ap-652	455	11	for	for	ADP
ap-652	455	12	media	medium	NOUN
ap-652	455	13	with	with	ADP
ap-652	455	14	effective	effective	ADJ
ap-652	455	15	isotropy	isotropy	NOUN
ap-652	455	16	and	and	CCONJ
ap-652	455	17	cubic	cubic	ADJ
ap-652	455	18	symmetry	symmetry	NOUN
ap-652	455	19	,	,	PUNCT
ap-652	455	20	respectively	respectively	ADV
ap-652	455	21	,	,	PUNCT
ap-652	455	22	in	in	ADP
ap-652	455	23	the	the	DET
ap-652	455	24	forms	form	NOUN
ap-652	455	25	of	of	ADP
ap-652	455	26	e	e	PROPN
ap-652	455	27	k	k	PROPN
ap-652	455	28	g	g	PROPN
ap-652	456	1	k	k	PROPN
ap-652	456	2	g	g	PROPN
ap-652	456	3	s	s	PART
ap-652	456	4	s	s	NOUN
ap-652	456	5	s	s	X
ap-652	456	6	s	s	X
ap-652	456	7	s	s	NOUN
ap-652	456	8	is	be	AUX
ap-652	456	9	,	,	PUNCT
ap-652	456	10	�	�	PROPN
ap-652	456	11	�	�	PROPN
ap-652	456	12	�	�	PROPN
ap-652	456	13	�	�	PROPN
ap-652	456	14	*	*	PROPN
ap-652	456	15	*	*	PUNCT
ap-652	457	1	*	*	PUNCT
ap-652	457	2	*	*	PUNCT
ap-652	457	3	*	*	PUNCT
ap-652	457	4	,	,	PUNCT
ap-652	457	5	4	4	NUM
ap-652	457	6	4	4	NUM
ap-652	457	7	9	9	NUM
ap-652	457	8	15	15	NUM
ap-652	457	9	9	9	NUM
ap-652	457	10	15	15	NUM
ap-652	457	11	6	6	NUM
ap-652	457	12	(	(	PUNCT
ap-652	457	13	56a	56a	NUM
ap-652	457	14	)	)	PUNCT
ap-652	458	1	e	e	NOUN
ap-652	458	2	k	k	PROPN
ap-652	458	3	g	g	PROPN
ap-652	459	1	k	k	PROPN
ap-652	459	2	g	g	PROPN
ap-652	459	3	s	s	PART
ap-652	459	4	s	s	X
ap-652	459	5	s	s	NOUN
ap-652	459	6	s	s	NOUN
ap-652	459	7	4	4	NUM
ap-652	459	8	s	s	NOUN
ap-652	459	9	,	,	PUNCT
ap-652	459	10	cs	cs	X
ap-652	459	11	,	,	PUNCT
ap-652	459	12	�	�	PROPN
ap-652	459	13	�	�	PROPN
ap-652	459	14	�	�	PROPN
ap-652	459	15	�	�	PROPN
ap-652	459	16	*	*	PROPN
ap-652	459	17	*	*	PUNCT
ap-652	459	18	,	,	PUNCT
ap-652	459	19	*	*	PUNCT
ap-652	459	20	*	*	PUNCT
ap-652	459	21	,	,	PUNCT
ap-652	459	22	*	*	PUNCT
ap-652	459	23	4	4	NUM
ap-652	459	24	4	4	NUM
ap-652	459	25	9	9	NUM
ap-652	459	26	6	6	NUM
ap-652	459	27	9	9	NUM
ap-652	459	28	6	6	NUM
ap-652	459	29	15	15	NUM
ap-652	459	30	1	1	NUM
ap-652	459	31	1	1	NUM
ap-652	459	32	(	(	PUNCT
ap-652	459	33	56b	56b	NUM
ap-652	459	34	)	)	PUNCT
ap-652	459	35	but	but	CCONJ
ap-652	459	36	no	no	DET
ap-652	459	37	conclusions	conclusion	NOUN
ap-652	459	38	can	can	AUX
ap-652	459	39	be	be	AUX
ap-652	459	40	reached	reach	VERB
ap-652	459	41	on	on	ADP
ap-652	459	42	the	the	DET
ap-652	459	43	upper	upper	ADJ
ap-652	459	44	bounds	bound	NOUN
ap-652	459	45	on	on	ADP
ap-652	459	46	effective	effective	ADJ
ap-652	459	47	poisson	poisson	NOUN
ap-652	459	48	’s	’s	PART
ap-652	459	49	ratios	ratio	NOUN
ap-652	459	50	.	.	PUNCT
ap-652	460	1	it	it	PRON
ap-652	460	2	is	be	AUX
ap-652	460	3	only	only	ADV
ap-652	460	4	easy	easy	ADJ
ap-652	460	5	to	to	PART
ap-652	460	6	verify	verify	VERB
ap-652	460	7	that	that	SCONJ
ap-652	460	8	upl	upl	PROPN
ap-652	460	9	have	have	VERB
ap-652	460	10	zero	zero	NUM
ap-652	460	11	effective	effective	ADJ
ap-652	460	12	poisson	poisson	NOUN
ap-652	460	13	’s	’s	PART
ap-652	460	14	ratio	ratio	NOUN
ap-652	460	15	.	.	PUNCT
ap-652	461	1	k	k	X
ap-652	461	2	*	*	PUNCT
ap-652	461	3	&	&	CCONJ
ap-652	461	4	g*-optimal	g*-optimal	PROPN
ap-652	461	5	micro	micro	NOUN
ap-652	461	6	-	-	NOUN
ap-652	461	7	trusses	truss	NOUN
ap-652	461	8	have	have	VERB
ap-652	461	9	an	an	DET
ap-652	461	10	effective	effective	ADJ
ap-652	461	11	poisson	poisson	NOUN
ap-652	461	12	’s	’s	PART
ap-652	461	13	ratio	ratio	NOUN
ap-652	461	14	equal	equal	ADJ
ap-652	461	15	to	to	ADP
ap-652	461	16	1/4	1/4	NUM
ap-652	461	17	,	,	PUNCT
ap-652	461	18	as	as	SCONJ
ap-652	461	19	shown	show	VERB
ap-652	461	20	by	by	ADP
ap-652	461	21	bakhvalov	bakhvalov	PROPN
ap-652	461	22	and	and	CCONJ
ap-652	461	23	panasenko	panasenko	PROPN
ap-652	461	24	(	(	PUNCT
ap-652	461	25	1989	1989	NUM
ap-652	461	26	)	)	PUNCT
ap-652	461	27	.	.	PUNCT
ap-652	462	1	in	in	ADP
ap-652	462	2	optimal	optimal	ADJ
ap-652	462	3	micro	micro	NOUN
ap-652	462	4	-	-	NOUN
ap-652	462	5	trusses	truss	NOUN
ap-652	462	6	it	it	PRON
ap-652	462	7	is	be	AUX
ap-652	462	8	interesting	interesting	ADJ
ap-652	462	9	to	to	PART
ap-652	462	10	see	see	VERB
ap-652	462	11	what	what	PRON
ap-652	462	12	the	the	DET
ap-652	462	13	other	other	ADJ
ap-652	462	14	elastic	elastic	ADJ
ap-652	462	15	properties	property	NOUN
ap-652	462	16	are	be	AUX
ap-652	462	17	.	.	PUNCT
ap-652	463	1	a	a	DET
ap-652	463	2	summary	summary	NOUN
ap-652	463	3	is	be	AUX
ap-652	463	4	given	give	VERB
ap-652	463	5	in	in	ADP
ap-652	463	6	table	table	NOUN
ap-652	463	7	7	7	NUM
ap-652	463	8	.	.	PUNCT
ap-652	464	1	furthermore	furthermore	ADV
ap-652	464	2	,	,	PUNCT
ap-652	464	3	in	in	ADP
ap-652	464	4	table	table	NOUN
ap-652	464	5	8	8	NUM
ap-652	464	6	the	the	DET
ap-652	464	7	bounds	bound	NOUN
ap-652	464	8	for	for	ADP
ap-652	464	9	open	open	ADJ
ap-652	464	10	-	-	PUNCT
ap-652	464	11	cell	cell	NOUN
ap-652	464	12	foams	foam	NOUN
ap-652	464	13	proven	prove	VERB
ap-652	464	14	in	in	ADP
ap-652	464	15	this	this	DET
ap-652	464	16	paper	paper	NOUN
ap-652	464	17	are	be	AUX
ap-652	464	18	compared	compare	VERB
ap-652	464	19	with	with	ADP
ap-652	464	20	the	the	DET
ap-652	464	21	composite	composite	ADJ
ap-652	464	22	ones	one	NOUN
ap-652	464	23	.	.	PUNCT
ap-652	465	1	the	the	DET
ap-652	465	2	composite	composite	ADJ
ap-652	465	3	bounds	bound	NOUN
ap-652	465	4	for	for	ADP
ap-652	465	5	effectively	effectively	ADJ
ap-652	465	6	isotropic	isotropic	ADJ
ap-652	465	7	media	medium	NOUN
ap-652	465	8	are	be	AUX
ap-652	465	9	taken	take	VERB
ap-652	465	10	from	from	ADP
ap-652	465	11	hashin	hashin	NOUN
ap-652	465	12	and	and	CCONJ
ap-652	465	13	shtrikman	shtrikman	NOUN
ap-652	465	14	(	(	PUNCT
ap-652	465	15	1963	1963	NUM
ap-652	465	16	)	)	PUNCT
ap-652	465	17	and	and	CCONJ
ap-652	465	18	hashin	hashin	PROPN
ap-652	465	19	(	(	PUNCT
ap-652	465	20	1970	1970	NUM
ap-652	465	21	,	,	PUNCT
ap-652	465	22	1983	1983	NUM
ap-652	465	23	)	)	PUNCT
ap-652	465	24	and	and	CCONJ
ap-652	465	25	for	for	ADP
ap-652	465	26	media	medium	NOUN
ap-652	465	27	with	with	ADP
ap-652	465	28	effective	effective	ADJ
ap-652	465	29	cubic	cubic	ADJ
ap-652	465	30	symmetry	symmetry	NOUN
ap-652	465	31	they	they	PRON
ap-652	465	32	are	be	AUX
ap-652	465	33	taken	take	VERB
ap-652	465	34	from	from	ADP
ap-652	465	35	avellaneda	avellaneda	PROPN
ap-652	465	36	(	(	PUNCT
ap-652	465	37	1987	1987	NUM
ap-652	465	38	)	)	PUNCT
ap-652	465	39	.	.	PUNCT
ap-652	466	1	they	they	PRON
ap-652	466	2	are	be	AUX
ap-652	466	3	specified	specify	VERB
ap-652	466	4	to	to	ADP
ap-652	466	5	one	one	NUM
ap-652	466	6	void	void	ADJ
ap-652	466	7	phase	phase	NOUN
ap-652	466	8	and	and	CCONJ
ap-652	466	9	linearized	linearize	VERB
ap-652	466	10	with	with	ADP
ap-652	466	11	respect	respect	NOUN
ap-652	466	12	to	to	ADP
ap-652	466	13	the	the	DET
ap-652	466	14	material	material	NOUN
ap-652	466	15	volume	volume	NOUN
ap-652	466	16	fraction	fraction	NOUN
ap-652	466	17	.	.	PUNCT
ap-652	467	1	it	it	PRON
ap-652	467	2	can	can	AUX
ap-652	467	3	be	be	AUX
ap-652	467	4	seen	see	VERB
ap-652	467	5	that	that	SCONJ
ap-652	467	6	the	the	DET
ap-652	467	7	solid	solid	ADJ
ap-652	467	8	phase	phase	NOUN
ap-652	467	9	poisson	poisson	NOUN
ap-652	467	10	’s	’s	PART
ap-652	467	11	ratio	ratio	NOUN
ap-652	467	12	�	�	PROPN
ap-652	467	13	s	s	PART
ap-652	467	14	naturally	naturally	ADV
ap-652	467	15	appears	appear	VERB
ap-652	467	16	in	in	ADP
ap-652	467	17	the	the	DET
ap-652	467	18	linearized	linearize	VERB
ap-652	467	19	composite	composite	ADJ
ap-652	467	20	bounds	bound	NOUN
ap-652	467	21	(	(	PUNCT
ap-652	467	22	unlike	unlike	ADP
ap-652	467	23	the	the	DET
ap-652	467	24	2d	2d	NUM
ap-652	467	25	case	case	NOUN
ap-652	467	26	shown	show	VERB
ap-652	467	27	in	in	ADP
ap-652	467	28	dimitrovová	dimitrovová	NOUN
ap-652	467	29	and	and	CCONJ
ap-652	467	30	faria	faria	PROPN
ap-652	467	31	(	(	PUNCT
ap-652	467	32	1999	1999	NUM
ap-652	467	33	)	)	PUNCT
ap-652	467	34	)	)	PUNCT
ap-652	467	35	.	.	PUNCT
ap-652	468	1	this	this	PRON
ap-652	468	2	is	be	AUX
ap-652	468	3	because	because	SCONJ
ap-652	468	4	shell	shell	NOUN
ap-652	468	5	or	or	CCONJ
ap-652	468	6	plate	plate	NOUN
ap-652	468	7	parts	part	NOUN
ap-652	468	8	must	must	AUX
ap-652	468	9	be	be	AUX
ap-652	468	10	included	include	VERB
ap-652	468	11	in	in	ADP
ap-652	468	12	optimal	optimal	ADJ
ap-652	468	13	3d	3d	NUM
ap-652	468	14	media	medium	NOUN
ap-652	468	15	.	.	PUNCT
ap-652	469	1	�	�	PROPN
ap-652	469	2	and	and	CCONJ
ap-652	469	3	�	�	PROPN
ap-652	469	4	stand	stand	VERB
ap-652	469	5	for	for	ADP
ap-652	469	6	coefficients	coefficient	NOUN
ap-652	469	7	of	of	ADP
ap-652	469	8	the	the	DET
ap-652	469	9	bending	bend	VERB
ap-652	469	10	contribution	contribution	NOUN
ap-652	469	11	.	.	PUNCT
ap-652	470	1	finally	finally	ADV
ap-652	470	2	,	,	PUNCT
ap-652	470	3	let	let	VERB
ap-652	470	4	us	we	PRON
ap-652	470	5	make	make	VERB
ap-652	470	6	some	some	DET
ap-652	470	7	remarks	remark	NOUN
ap-652	470	8	about	about	ADP
ap-652	470	9	the	the	DET
ap-652	470	10	simplified	simplified	ADJ
ap-652	470	11	assumptions	assumption	NOUN
ap-652	470	12	adopted	adopt	VERB
ap-652	470	13	for	for	ADP
ap-652	470	14	the	the	DET
ap-652	470	15	strain	strain	ADJ
ap-652	470	16	energy	energy	NOUN
ap-652	470	17	contribution	contribution	NOUN
ap-652	470	18	.	.	PUNCT
ap-652	471	1	it	it	PRON
ap-652	471	2	is	be	AUX
ap-652	471	3	known	know	VERB
ap-652	471	4	that	that	SCONJ
ap-652	471	5	assuming	assume	VERB
ap-652	471	6	the	the	DET
ap-652	471	7	micro	micro	NOUN
ap-652	471	8	-	-	NOUN
ap-652	471	9	frame	frame	ADJ
ap-652	471	10	medium	medium	NOUN
ap-652	471	11	with	with	ADP
ap-652	471	12	theoretical	theoretical	ADJ
ap-652	471	13	lengths	length	NOUN
ap-652	471	14	makes	make	VERB
ap-652	471	15	the	the	DET
ap-652	471	16	medium	medium	NOUN
ap-652	471	17	softer	soft	ADJ
ap-652	471	18	than	than	SCONJ
ap-652	471	19	it	it	PRON
ap-652	471	20	really	really	ADV
ap-652	471	21	is	be	AUX
ap-652	471	22	.	.	PUNCT
ap-652	472	1	it	it	PRON
ap-652	472	2	is	be	AUX
ap-652	472	3	thus	thus	ADV
ap-652	472	4	better	well	ADJ
ap-652	472	5	to	to	PART
ap-652	472	6	use	use	VERB
ap-652	472	7	active	active	ADJ
ap-652	472	8	lengths	length	NOUN
ap-652	472	9	of	of	ADP
ap-652	472	10	the	the	DET
ap-652	472	11	beam	beam	NOUN
ap-652	472	12	and	and	CCONJ
ap-652	472	13	include	include	VERB
ap-652	472	14	the	the	DET
ap-652	472	15	deformation	deformation	NOUN
ap-652	472	16	of	of	ADP
ap-652	472	17	the	the	DET
ap-652	472	18	joints	joint	NOUN
ap-652	472	19	.	.	PUNCT
ap-652	473	1	moreover	moreover	ADV
ap-652	473	2	,	,	PUNCT
ap-652	473	3	the	the	DET
ap-652	473	4	strain	strain	NOUN
ap-652	473	5	energy	energy	NOUN
ap-652	473	6	density	density	NOUN
ap-652	473	7	corresponding	correspond	VERB
ap-652	473	8	to	to	ADP
ap-652	473	9	the	the	DET
ap-652	473	10	shear	shear	NOUN
ap-652	473	11	forces	force	NOUN
ap-652	473	12	can	can	AUX
ap-652	473	13	be	be	AUX
ap-652	473	14	included	include	VERB
ap-652	473	15	in	in	ADP
ap-652	473	16	w.	w.	PROPN
ap-652	473	17	obviously	obviously	ADV
ap-652	473	18	,	,	PUNCT
ap-652	473	19	such	such	ADJ
ap-652	473	20	improvements	improvement	NOUN
ap-652	473	21	do	do	AUX
ap-652	473	22	not	not	PART
ap-652	473	23	change	change	VERB
ap-652	473	24	the	the	DET
ap-652	473	25	linearized	linearize	VERB
ap-652	473	26	bounds	bound	NOUN
ap-652	473	27	since	since	SCONJ
ap-652	473	28	they	they	PRON
ap-652	473	29	do	do	AUX
ap-652	473	30	not	not	PART
ap-652	473	31	influence	influence	VERB
ap-652	473	32	expressions	expression	NOUN
ap-652	473	33	for	for	ADP
ap-652	473	34	the	the	DET
ap-652	473	35	axial	axial	ADJ
ap-652	473	36	response	response	NOUN
ap-652	473	37	of	of	ADP
ap-652	473	38	the	the	DET
ap-652	473	39	media	medium	NOUN
ap-652	473	40	.	.	PUNCT
ap-652	474	1	if	if	SCONJ
ap-652	474	2	,	,	PUNCT
ap-652	474	3	e.g.	e.g.	ADV
ap-652	474	4	,	,	PUNCT
ap-652	474	5	the	the	DET
ap-652	474	6	strain	strain	ADJ
ap-652	474	7	energy	energy	NOUN
ap-652	474	8	density	density	NOUN
ap-652	474	9	corresponding	correspond	VERB
ap-652	474	10	to	to	ADP
ap-652	474	11	the	the	DET
ap-652	474	12	shear	shear	NOUN
ap-652	474	13	forces	force	NOUN
ap-652	474	14	were	be	AUX
ap-652	474	15	to	to	PART
ap-652	474	16	be	be	AUX
ap-652	474	17	included	include	VERB
ap-652	474	18	,	,	PUNCT
ap-652	474	19	parameters	parameter	NOUN
ap-652	474	20	�	�	PROPN
ap-652	474	21	and	and	CCONJ
ap-652	474	22	�	�	PROPN
ap-652	474	23	from	from	ADP
ap-652	474	24	tab	tab	PROPN
ap-652	474	25	.	.	PUNCT
ap-652	474	26	8	8	NUM
ap-652	474	27	would	would	AUX
ap-652	474	28	decrease	decrease	VERB
ap-652	474	29	.	.	PUNCT
ap-652	475	1	in	in	ADP
ap-652	475	2	this	this	DET
ap-652	475	3	case	case	NOUN
ap-652	475	4	the	the	DET
ap-652	475	5	solid	solid	ADJ
ap-652	475	6	phase	phase	NOUN
ap-652	475	7	poisson	poisson	NOUN
ap-652	475	8	’s	’s	PART
ap-652	475	9	ratio	ratio	NOUN
ap-652	475	10	would	would	AUX
ap-652	475	11	appear	appear	VERB
ap-652	475	12	in	in	ADP
ap-652	475	13	the	the	DET
ap-652	475	14	final	final	ADJ
ap-652	475	15	result	result	NOUN
ap-652	475	16	.	.	PUNCT
ap-652	476	1	appendix	appendix	NOUN
ap-652	476	2	admitting	admit	VERB
ap-652	476	3	a	a	DET
ap-652	476	4	more	more	ADV
ap-652	476	5	general	general	ADJ
ap-652	476	6	solid	solid	ADJ
ap-652	476	7	material	material	ADJ
ap-652	476	8	behavior	behavior	NOUN
ap-652	476	9	it	it	PRON
ap-652	476	10	can	can	AUX
ap-652	476	11	be	be	AUX
ap-652	476	12	shown	show	VERB
ap-652	476	13	that	that	SCONJ
ap-652	476	14	open	open	ADJ
ap-652	476	15	-	-	PUNCT
ap-652	476	16	cell	cell	NOUN
ap-652	476	17	foam	foam	NOUN
ap-652	476	18	bounds	bound	NOUN
ap-652	476	19	coincide	coincide	VERB
ap-652	476	20	with	with	ADP
ap-652	476	21	the	the	DET
ap-652	476	22	voigt	voigt	PROPN
ap-652	476	23	bound	bind	VERB
ap-652	476	24	.	.	PUNCT
ap-652	477	1	for	for	ADP
ap-652	477	2	the	the	DET
ap-652	477	3	sake	sake	NOUN
ap-652	477	4	of	of	ADP
ap-652	477	5	simplicity	simplicity	NOUN
ap-652	477	6	let	let	VERB
ap-652	477	7	us	we	PRON
ap-652	477	8	assume	assume	VERB
ap-652	477	9	a	a	DET
ap-652	477	10	2d	2d	NUM
ap-652	477	11	medium	medium	NOUN
ap-652	477	12	,	,	PUNCT
ap-652	477	13	the	the	DET
ap-652	477	14	regular	regular	ADJ
ap-652	477	15	lattice	lattice	NOUN
ap-652	477	16	,	,	PUNCT
ap-652	477	17	which	which	PRON
ap-652	477	18	is	be	AUX
ap-652	477	19	k	k	NOUN
ap-652	477	20	*	*	PUNCT
ap-652	477	21	&	&	CCONJ
ap-652	477	22	g1	g1	NOUN
ap-652	477	23	*	*	PUNCT
ap-652	477	24	-optimal	-optimal	ADJ
ap-652	477	25	(	(	PUNCT
ap-652	477	26	dimitrovová	dimitrovová	NOUN
ap-652	477	27	and	and	CCONJ
ap-652	477	28	faria	faria	PROPN
ap-652	477	29	(	(	PUNCT
ap-652	477	30	1999	1999	NUM
ap-652	477	31	)	)	PUNCT
ap-652	477	32	)	)	PUNCT
ap-652	477	33	.	.	PUNCT
ap-652	478	1	k	k	X
ap-652	478	2	*	*	VERB
ap-652	478	3	stands	stand	VERB
ap-652	478	4	for	for	ADP
ap-652	478	5	2d	2d	NUM
ap-652	478	6	bulk	bulk	ADJ
ap-652	478	7	modulus	modulus	NOUN
ap-652	478	8	and	and	CCONJ
ap-652	478	9	has	have	VERB
ap-652	478	10	the	the	DET
ap-652	478	11	©	©	PROPN
ap-652	478	12	czech	czech	PROPN
ap-652	478	13	technical	technical	PROPN
ap-652	478	14	university	university	PROPN
ap-652	478	15	publishing	publishing	NOUN
ap-652	478	16	house	house	NOUN
ap-652	478	17	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	478	18	183	183	NUM
ap-652	478	19	acta	acta	PROPN
ap-652	478	20	polytechnica	polytechnica	PROPN
ap-652	478	21	vol	vol	NOUN
ap-652	478	22	.	.	PROPN
ap-652	479	1	44	44	NUM
ap-652	479	2	no.5–6/2004	no.5–6/2004	PROPN
ap-652	479	3	macro	macro	NOUN
ap-652	479	4	-	-	NOUN
ap-652	479	5	load	load	VERB
ap-652	479	6	optimal	optimal	ADJ
ap-652	479	7	micro	micro	NOUN
ap-652	479	8	-	-	NOUN
ap-652	479	9	trusses	truss	VERB
ap-652	479	10	other	other	ADJ
ap-652	479	11	elastic	elastic	ADJ
ap-652	479	12	properties	property	NOUN
ap-652	479	13	k	k	X
ap-652	480	1	*	*	PUNCT
ap-652	480	2	1	1	NUM
ap-652	480	3	g	g	NOUN
ap-652	480	4	*	*	PROPN
ap-652	480	5	2	2	NUM
ap-652	480	6	g	g	NOUN
ap-652	480	7	*	*	SYM
ap-652	480	8	g	g	PROPN
ap-652	480	9	*	*	PROPN
ap-652	480	10	�	�	PROPN
ap-652	480	11	k	k	PROPN
ap-652	480	12	upl	upl	PROPN
ap-652	480	13	,	,	PUNCT
ap-652	480	14	udl	udl	PROPN
ap-652	480	15	,	,	PUNCT
ap-652	480	16	other	other	ADJ
ap-652	480	17	media	medium	NOUN
ap-652	480	18	,	,	PUNCT
ap-652	480	19	which	which	PRON
ap-652	480	20	can	can	AUX
ap-652	480	21	not	not	PART
ap-652	480	22	be	be	AUX
ap-652	480	23	fully	fully	ADV
ap-652	480	24	geometrically	geometrically	ADV
ap-652	480	25	specified	specify	VERB
ap-652	480	26	k	k	PROPN
ap-652	480	27	*	*	PUNCT
ap-652	480	28	not	not	PART
ap-652	480	29	uniquely	uniquely	ADV
ap-652	480	30	defined	define	VERB
ap-652	480	31	not	not	PART
ap-652	480	32	uniquely	uniquely	ADV
ap-652	480	33	defined	define	VERB
ap-652	480	34	not	not	PART
ap-652	480	35	uniquely	uniquely	ADV
ap-652	480	36	defined	define	VERB
ap-652	480	37	�	�	NOUN
ap-652	480	38	1	1	NUM
ap-652	480	39	g	g	NOUN
ap-652	480	40	only	only	ADV
ap-652	480	41	upl	upl	PROPN
ap-652	480	42	k	k	PROPN
ap-652	480	43	*	*	PUNCT
ap-652	480	44	1	1	NUM
ap-652	480	45	g	g	NOUN
ap-652	480	46	*	*	PROPN
ap-652	480	47	0	0	NUM
ap-652	480	48	–	–	PUNCT
ap-652	480	49	�	�	NOUN
ap-652	480	50	2	2	NUM
ap-652	480	51	g	g	NOUN
ap-652	480	52	only	only	ADV
ap-652	480	53	udl	udl	PROPN
ap-652	480	54	k	k	PROPN
ap-652	480	55	*	*	PUNCT
ap-652	480	56	0	0	NUM
ap-652	480	57	2	2	NUM
ap-652	480	58	g	g	NOUN
ap-652	480	59	*	*	PUNCT
ap-652	480	60	–	–	PUNCT
ap-652	480	61	�	�	PROPN
ap-652	480	62	g	g	NOUN
ap-652	480	63	media	medium	NOUN
ap-652	480	64	,	,	PUNCT
ap-652	480	65	which	which	PRON
ap-652	480	66	can	can	AUX
ap-652	480	67	not	not	PART
ap-652	480	68	be	be	AUX
ap-652	480	69	fully	fully	ADV
ap-652	480	70	geometrically	geometrically	ADV
ap-652	480	71	specified	specify	VERB
ap-652	480	72	,	,	PUNCT
ap-652	480	73	but	but	CCONJ
ap-652	480	74	neither	neither	CCONJ
ap-652	480	75	upl	upl	PROPN
ap-652	480	76	nor	nor	CCONJ
ap-652	480	77	udl	udl	NOUN
ap-652	480	78	not	not	PART
ap-652	480	79	uniquely	uniquely	ADV
ap-652	480	80	defined	define	VERB
ap-652	480	81	g	g	NOUN
ap-652	480	82	*	*	PUNCT
ap-652	480	83	g	g	PROPN
ap-652	480	84	*	*	PUNCT
ap-652	480	85	g	g	NOUN
ap-652	480	86	*	*	PUNCT
ap-652	480	87	table	table	NOUN
ap-652	480	88	7	7	NUM
ap-652	480	89	:	:	PUNCT
ap-652	480	90	other	other	ADJ
ap-652	480	91	elastic	elastic	ADJ
ap-652	480	92	properties	property	NOUN
ap-652	480	93	in	in	ADP
ap-652	480	94	optimal	optimal	ADJ
ap-652	480	95	micro	micro	NOUN
ap-652	480	96	-	-	NOUN
ap-652	480	97	trusses	truss	NOUN
ap-652	480	98	same	same	ADJ
ap-652	480	99	meaning	meaning	NOUN
ap-652	480	100	as	as	ADP
ap-652	480	101	before	before	ADV
ap-652	480	102	.	.	PUNCT
ap-652	481	1	voigt	voigt	PROPN
ap-652	481	2	bounds	bound	VERB
ap-652	481	3	kv	kv	PROPN
ap-652	481	4	*	*	PUNCT
ap-652	481	5	and	and	CCONJ
ap-652	481	6	g1,v	g1,v	PROPN
ap-652	481	7	*	*	PUNCT
ap-652	481	8	for	for	ADP
ap-652	481	9	one	one	NUM
ap-652	481	10	void	void	ADJ
ap-652	481	11	phase	phase	NOUN
ap-652	481	12	are	be	AUX
ap-652	481	13	(	(	PUNCT
ap-652	481	14	see	see	VERB
ap-652	481	15	hill	hill	NOUN
ap-652	481	16	(	(	PUNCT
ap-652	481	17	1963	1963	NUM
ap-652	481	18	)	)	PUNCT
ap-652	481	19	):	):	PUNCT
ap-652	482	1	k	k	PROPN
ap-652	482	2	s	s	PROPN
ap-652	482	3	g	g	PROPN
ap-652	482	4	s	s	PROPN
ap-652	482	5	v	v	NOUN
ap-652	482	6	*	*	PUNCT
ap-652	482	7	s	s	PART
ap-652	482	8	1,v	1,v	NUM
ap-652	482	9	*	*	SYM
ap-652	482	10	s	s	X
ap-652	482	11	�	�	PROPN
ap-652	482	12	�	�	PROPN
ap-652	482	13	2	2	NUM
ap-652	482	14	1	1	NUM
ap-652	482	15	2	2	NUM
ap-652	482	16	1	1	NUM
ap-652	482	17	(	(	PUNCT
ap-652	482	18	)	)	PUNCT
ap-652	482	19	,	,	PUNCT
ap-652	482	20	(	(	PUNCT
ap-652	482	21	)	)	PUNCT
ap-652	482	22	,	,	PUNCT
ap-652	482	23	�	�	PROPN
ap-652	482	24	�	�	PROPN
ap-652	482	25	where	where	SCONJ
ap-652	482	26	�	�	PROPN
ap-652	482	27	s	s	PART
ap-652	482	28	is	be	AUX
ap-652	482	29	the	the	DET
ap-652	482	30	solid	solid	ADJ
ap-652	482	31	phase	phase	NOUN
ap-652	482	32	poisson	poisson	NOUN
ap-652	482	33	’s	’s	PART
ap-652	482	34	ratio	ratio	NOUN
ap-652	482	35	.	.	PUNCT
ap-652	483	1	now	now	ADV
ap-652	483	2	deformation	deformation	NOUN
ap-652	483	3	of	of	ADP
ap-652	483	4	joints	joint	NOUN
ap-652	483	5	can	can	AUX
ap-652	483	6	not	not	PART
ap-652	483	7	be	be	AUX
ap-652	483	8	neglected	neglect	VERB
ap-652	483	9	,	,	PUNCT
ap-652	483	10	due	due	ADP
ap-652	483	11	to	to	ADP
ap-652	483	12	the	the	DET
ap-652	483	13	presence	presence	NOUN
ap-652	483	14	of	of	ADP
ap-652	483	15	�	�	PROPN
ap-652	483	16	s	s	PART
ap-652	483	17	,	,	PUNCT
ap-652	483	18	which	which	PRON
ap-652	483	19	is	be	AUX
ap-652	483	20	restricted	restrict	VERB
ap-652	483	21	to	to	ADP
ap-652	483	22	the	the	DET
ap-652	483	23	interval	interval	NOUN
ap-652	483	24	[	[	PUNCT
ap-652	483	25	1,1	1,1	NUM
ap-652	483	26	]	]	PUNCT
ap-652	483	27	.	.	PUNCT
ap-652	484	1	it	it	PRON
ap-652	484	2	is	be	AUX
ap-652	484	3	obvious	obvious	ADJ
ap-652	484	4	that	that	SCONJ
ap-652	484	5	the	the	DET
ap-652	484	6	strain	strain	NOUN
ap-652	484	7	field	field	NOUN
ap-652	484	8	inside	inside	ADP
ap-652	484	9	the	the	DET
ap-652	484	10	cell	cell	NOUN
ap-652	484	11	of	of	ADP
ap-652	484	12	the	the	DET
ap-652	484	13	regular	regular	ADJ
ap-652	484	14	lattice	lattice	NOUN
ap-652	484	15	would	would	AUX
ap-652	484	16	be	be	AUX
ap-652	484	17	fully	fully	ADV
ap-652	484	18	uniform	uniform	ADJ
ap-652	484	19	for	for	SCONJ
ap-652	484	20	�	�	PROPN
ap-652	484	21	k	k	PROPN
ap-652	484	22	macroload	macroload	VERB
ap-652	484	23	only	only	ADV
ap-652	484	24	if	if	SCONJ
ap-652	484	25	�	�	PROPN
ap-652	484	26	s	s	PART
ap-652	484	27	�	�	NOUN
ap-652	484	28	1	1	NUM
ap-652	484	29	giving	give	VERB
ap-652	484	30	k	k	PROPN
ap-652	484	31	sv	sv	PROPN
ap-652	484	32	*	*	PUNCT
ap-652	484	33	�	�	PROPN
ap-652	484	34	4	4	NUM
ap-652	484	35	and	and	CCONJ
ap-652	484	36	for	for	ADP
ap-652	484	37	�	�	PROPN
ap-652	484	38	1	1	NUM
ap-652	484	39	g	g	NOUN
ap-652	484	40	macroload	macroload	NOUN
ap-652	484	41	only	only	ADV
ap-652	484	42	if	if	SCONJ
ap-652	484	43	�	�	PROPN
ap-652	484	44	s	s	PART
ap-652	484	45	�	�	NOUN
ap-652	484	46	1	1	NUM
ap-652	484	47	yielding	yield	VERB
ap-652	484	48	g	g	PROPN
ap-652	484	49	s1,v	s1,v	PROPN
ap-652	484	50	*	*	PUNCT
ap-652	484	51	�	�	PROPN
ap-652	484	52	4	4	NUM
ap-652	484	53	,	,	PUNCT
ap-652	484	54	which	which	PRON
ap-652	484	55	are	be	AUX
ap-652	484	56	the	the	DET
ap-652	484	57	upper	upper	ADJ
ap-652	484	58	bounds	bound	NOUN
ap-652	484	59	on	on	ADP
ap-652	484	60	the	the	DET
ap-652	484	61	properties	property	NOUN
ap-652	484	62	of	of	ADP
ap-652	484	63	2d	2d	NUM
ap-652	484	64	cellular	cellular	ADJ
ap-652	484	65	media	medium	NOUN
ap-652	484	66	.	.	PUNCT
ap-652	485	1	references	reference	NOUN
ap-652	485	2	[	[	X
ap-652	485	3	1	1	NUM
ap-652	485	4	]	]	X
ap-652	485	5	allaire	allaire	PROPN
ap-652	485	6	g.	g.	PROPN
ap-652	485	7	,	,	PUNCT
ap-652	485	8	aubry	aubry	PROPN
ap-652	485	9	s.	s.	PROPN
ap-652	485	10	:	:	PUNCT
ap-652	485	11	“	"	PUNCT
ap-652	485	12	on	on	ADP
ap-652	485	13	optimal	optimal	ADJ
ap-652	485	14	microstructures	microstructure	NOUN
ap-652	485	15	for	for	ADP
ap-652	485	16	a	a	DET
ap-652	485	17	plane	plane	NOUN
ap-652	485	18	shape	shape	NOUN
ap-652	485	19	optimization	optimization	NOUN
ap-652	485	20	problem	problem	NOUN
ap-652	485	21	.	.	PUNCT
ap-652	485	22	”	"	PUNCT
ap-652	485	23	struct	struct	NOUN
ap-652	485	24	.	.	PUNCT
ap-652	486	1	opt	opt	PROPN
ap-652	486	2	.	.	PUNCT
ap-652	487	1	vol	vol	NOUN
ap-652	487	2	.	.	PROPN
ap-652	488	1	17	17	NUM
ap-652	488	2	(	(	PUNCT
ap-652	488	3	1999	1999	NUM
ap-652	488	4	)	)	PUNCT
ap-652	488	5	,	,	PUNCT
ap-652	489	1	p.	p.	NOUN
ap-652	489	2	86–94	86–94	NUM
ap-652	489	3	.	.	PUNCT
ap-652	490	1	[	[	X
ap-652	490	2	2	2	NUM
ap-652	490	3	]	]	X
ap-652	490	4	allaire	allaire	PROPN
ap-652	490	5	g.	g.	PROPN
ap-652	490	6	,	,	PUNCT
ap-652	490	7	kohn	kohn	PROPN
ap-652	490	8	r.	r.	PROPN
ap-652	490	9	v.	v.	PROPN
ap-652	490	10	:	:	PUNCT
ap-652	490	11	“	"	PUNCT
ap-652	490	12	optimal	optimal	ADJ
ap-652	490	13	design	design	NOUN
ap-652	490	14	for	for	ADP
ap-652	490	15	minimum	minimum	ADJ
ap-652	490	16	weight	weight	NOUN
ap-652	490	17	and	and	CCONJ
ap-652	490	18	compliance	compliance	NOUN
ap-652	490	19	in	in	ADP
ap-652	490	20	plane	plane	NOUN
ap-652	490	21	stress	stress	NOUN
ap-652	490	22	using	use	VERB
ap-652	490	23	extremal	extremal	ADJ
ap-652	490	24	microstructures	microstructure	NOUN
ap-652	490	25	.	.	PUNCT
ap-652	490	26	”	"	PUNCT
ap-652	491	1	eur	eur	PROPN
ap-652	491	2	.	.	PUNCT
ap-652	492	1	j.	j.	PROPN
ap-652	492	2	mech	mech	PROPN
ap-652	492	3	.	.	PROPN
ap-652	492	4	,	,	PUNCT
ap-652	492	5	a	a	DET
ap-652	492	6	/	/	SYM
ap-652	492	7	solids	solid	NOUN
ap-652	492	8	,	,	PUNCT
ap-652	492	9	vol	vol	NOUN
ap-652	492	10	.	.	PROPN
ap-652	492	11	12	12	NUM
ap-652	492	12	(	(	PUNCT
ap-652	492	13	1993	1993	NUM
ap-652	492	14	)	)	PUNCT
ap-652	492	15	,	,	PUNCT
ap-652	492	16	p.	p.	NOUN
ap-652	492	17	839–878	839–878	NUM
ap-652	492	18	.	.	PUNCT
ap-652	493	1	[	[	X
ap-652	493	2	3	3	X
ap-652	493	3	]	]	X
ap-652	493	4	avellaneda	avellaneda	PROPN
ap-652	493	5	m.	m.	PROPN
ap-652	493	6	:	:	PUNCT
ap-652	493	7	“	"	PUNCT
ap-652	493	8	optimal	optimal	ADJ
ap-652	493	9	bounds	bound	NOUN
ap-652	493	10	and	and	CCONJ
ap-652	493	11	microgeometries	microgeometrie	NOUN
ap-652	493	12	for	for	ADP
ap-652	493	13	elastic	elastic	ADJ
ap-652	493	14	two	two	NUM
ap-652	493	15	-	-	PUNCT
ap-652	493	16	phase	phase	NOUN
ap-652	493	17	composites	composite	NOUN
ap-652	493	18	.	.	PUNCT
ap-652	493	19	”	"	PUNCT
ap-652	494	1	j.	j.	PROPN
ap-652	494	2	appl	appl	PROPN
ap-652	494	3	.	.	PROPN
ap-652	494	4	math	math	PROPN
ap-652	494	5	.	.	PUNCT
ap-652	494	6	,	,	PUNCT
ap-652	494	7	siam	siam	PROPN
ap-652	494	8	,	,	PUNCT
ap-652	494	9	vol	vol	NOUN
ap-652	494	10	.	.	PUNCT
ap-652	495	1	47	47	NUM
ap-652	495	2	(	(	PUNCT
ap-652	495	3	1987	1987	NUM
ap-652	495	4	)	)	PUNCT
ap-652	495	5	,	,	PUNCT
ap-652	495	6	p.	p.	NOUN
ap-652	495	7	1216–1228	1216–1228	NUM
ap-652	495	8	.	.	PUNCT
ap-652	496	1	[	[	X
ap-652	496	2	4	4	NUM
ap-652	496	3	]	]	X
ap-652	496	4	bakhvalov	bakhvalov	X
ap-652	496	5	n.	n.	PROPN
ap-652	496	6	,	,	PUNCT
ap-652	496	7	panasenko	panasenko	PROPN
ap-652	496	8	g.	g.	PROPN
ap-652	496	9	:	:	PUNCT
ap-652	496	10	“	"	PUNCT
ap-652	496	11	homogenization	homogenization	NOUN
ap-652	496	12	:	:	PUNCT
ap-652	496	13	averaging	average	VERB
ap-652	496	14	processes	process	NOUN
ap-652	496	15	in	in	ADP
ap-652	496	16	periodic	periodic	ADJ
ap-652	496	17	media	medium	NOUN
ap-652	496	18	.	.	PUNCT
ap-652	496	19	”	"	PUNCT
ap-652	497	1	dordrecht	dordrecht	PROPN
ap-652	497	2	,	,	PUNCT
ap-652	497	3	boston	boston	PROPN
ap-652	497	4	,	,	PUNCT
ap-652	497	5	london	london	PROPN
ap-652	497	6	:	:	PUNCT
ap-652	497	7	kluwer	kluwer	NOUN
ap-652	497	8	academic	academic	ADJ
ap-652	497	9	publishers	publisher	NOUN
ap-652	497	10	,	,	PUNCT
ap-652	497	11	1989	1989	NUM
ap-652	497	12	.	.	PUNCT
ap-652	498	1	[	[	X
ap-652	498	2	5	5	NUM
ap-652	498	3	]	]	X
ap-652	498	4	bensoussan	bensoussan	PROPN
ap-652	498	5	a.	a.	NOUN
ap-652	498	6	,	,	PUNCT
ap-652	498	7	lions	lion	NOUN
ap-652	498	8	j.	j.	PROPN
ap-652	498	9	l.	l.	PROPN
ap-652	498	10	,	,	PUNCT
ap-652	498	11	papanicolau	papanicolau	PROPN
ap-652	498	12	g.	g.	PROPN
ap-652	498	13	:	:	PUNCT
ap-652	498	14	“	"	PUNCT
ap-652	498	15	asymptotic	asymptotic	ADJ
ap-652	498	16	analysis	analysis	NOUN
ap-652	498	17	for	for	ADP
ap-652	498	18	periodic	periodic	ADJ
ap-652	498	19	structures	structure	NOUN
ap-652	498	20	.	.	PUNCT
ap-652	498	21	”	"	PUNCT
ap-652	499	1	north	north	NOUN
ap-652	499	2	holland	holland	PROPN
ap-652	499	3	,	,	PUNCT
ap-652	499	4	amsterdam	amsterdam	PROPN
ap-652	499	5	,	,	PUNCT
ap-652	499	6	1978	1978	NUM
ap-652	499	7	.	.	PUNCT
ap-652	500	1	[	[	X
ap-652	500	2	6	6	NUM
ap-652	500	3	]	]	X
ap-652	500	4	christensen	christensen	PROPN
ap-652	500	5	r.	r.	PROPN
ap-652	500	6	m.	m.	PROPN
ap-652	500	7	:	:	PUNCT
ap-652	500	8	”	"	PUNCT
ap-652	500	9	heterogeneous	heterogeneous	ADJ
ap-652	500	10	material	material	NOUN
ap-652	500	11	mechanics	mechanic	NOUN
ap-652	500	12	at	at	ADP
ap-652	500	13	various	various	ADJ
ap-652	500	14	scales	scale	NOUN
ap-652	500	15	.	.	PUNCT
ap-652	500	16	”	"	PUNCT
ap-652	501	1	appl	appl	PROPN
ap-652	501	2	.	.	PROPN
ap-652	501	3	mech	mech	PROPN
ap-652	501	4	.	.	PUNCT
ap-652	502	1	rev	rev	PROPN
ap-652	502	2	.	.	PROPN
ap-652	502	3	,	,	PUNCT
ap-652	502	4	vol	vol	NOUN
ap-652	502	5	.	.	PUNCT
ap-652	503	1	47	47	NUM
ap-652	503	2	(	(	PUNCT
ap-652	503	3	1994	1994	NUM
ap-652	503	4	)	)	PUNCT
ap-652	503	5	,	,	PUNCT
ap-652	503	6	s20	s20	PROPN
ap-652	503	7	–	–	PUNCT
ap-652	503	8	s33	s33	NOUN
ap-652	503	9	.	.	PUNCT
ap-652	504	1	[	[	X
ap-652	504	2	7	7	X
ap-652	504	3	]	]	X
ap-652	504	4	christensen	christensen	PROPN
ap-652	504	5	r.	r.	PROPN
ap-652	504	6	m.	m.	PROPN
ap-652	504	7	:	:	PUNCT
ap-652	504	8	“	"	PUNCT
ap-652	504	9	the	the	DET
ap-652	504	10	hierarchy	hierarchy	NOUN
ap-652	504	11	of	of	ADP
ap-652	504	12	microstructures	microstructure	NOUN
ap-652	504	13	for	for	ADP
ap-652	504	14	low	low	ADJ
ap-652	504	15	density	density	NOUN
ap-652	504	16	materials	material	NOUN
ap-652	504	17	.	.	PUNCT
ap-652	504	18	”	"	PUNCT
ap-652	505	1	z.	z.	PROPN
ap-652	505	2	angew	angew	PROPN
ap-652	505	3	.	.	PUNCT
ap-652	506	1	math	math	NOUN
ap-652	506	2	.	.	PUNCT
ap-652	507	1	phys	phy	NOUN
ap-652	507	2	.	.	PUNCT
ap-652	507	3	,	,	PUNCT
ap-652	507	4	vol	vol	NOUN
ap-652	507	5	.	.	PROPN
ap-652	507	6	46	46	NUM
ap-652	507	7	(	(	PUNCT
ap-652	507	8	1995	1995	NUM
ap-652	507	9	)	)	PUNCT
ap-652	507	10	,	,	PUNCT
ap-652	507	11	p.	p.	NOUN
ap-652	507	12	s507	s507	PROPN
ap-652	507	13	–	–	PUNCT
ap-652	507	14	s521	s521	PROPN
ap-652	507	15	.	.	PUNCT
ap-652	508	1	[	[	X
ap-652	508	2	8	8	NUM
ap-652	508	3	]	]	X
ap-652	508	4	dimitrovová	dimitrovová	NOUN
ap-652	508	5	z.	z.	PROPN
ap-652	508	6	:	:	PUNCT
ap-652	508	7	“	"	PUNCT
ap-652	508	8	effective	effective	ADJ
ap-652	508	9	constitutive	constitutive	ADJ
ap-652	508	10	properties	property	NOUN
ap-652	508	11	of	of	ADP
ap-652	508	12	linear	linear	ADJ
ap-652	508	13	elastic	elastic	ADJ
ap-652	508	14	cellular	cellular	ADJ
ap-652	508	15	solids	solid	NOUN
ap-652	508	16	with	with	ADP
ap-652	508	17	randomly	randomly	ADV
ap-652	508	18	oriented	orient	VERB
ap-652	508	19	cells	cell	NOUN
ap-652	508	20	.	.	PUNCT
ap-652	508	21	”	"	PUNCT
ap-652	509	1	j.	j.	PROPN
ap-652	509	2	appl	appl	PROPN
ap-652	509	3	.	.	PROPN
ap-652	509	4	mech	mech	PROPN
ap-652	509	5	.	.	PROPN
ap-652	509	6	,	,	PUNCT
ap-652	509	7	asme	asme	PROPN
ap-652	509	8	,	,	PUNCT
ap-652	509	9	vol	vol	NOUN
ap-652	509	10	.	.	PROPN
ap-652	509	11	66	66	NUM
ap-652	509	12	(	(	PUNCT
ap-652	509	13	1999	1999	NUM
ap-652	509	14	)	)	PUNCT
ap-652	509	15	,	,	PUNCT
ap-652	509	16	p.	p.	NOUN
ap-652	509	17	918–915	918–915	NUM
ap-652	509	18	.	.	PUNCT
ap-652	510	1	[	[	X
ap-652	510	2	9	9	NUM
ap-652	510	3	]	]	X
ap-652	510	4	dimitrovová	dimitrovová	PROPN
ap-652	510	5	z.	z.	PROPN
ap-652	510	6	,	,	PUNCT
ap-652	510	7	faria	faria	PROPN
ap-652	510	8	l.	l.	PROPN
ap-652	510	9	:	:	PUNCT
ap-652	510	10	“	"	PUNCT
ap-652	510	11	new	new	ADJ
ap-652	510	12	methodology	methodology	NOUN
ap-652	510	13	to	to	PART
ap-652	510	14	establish	establish	VERB
ap-652	510	15	bounds	bound	NOUN
ap-652	510	16	on	on	ADP
ap-652	510	17	effective	effective	ADJ
ap-652	510	18	properties	property	NOUN
ap-652	510	19	of	of	ADP
ap-652	510	20	cellular	cellular	ADJ
ap-652	510	21	solids	solid	NOUN
ap-652	510	22	.	.	PUNCT
ap-652	510	23	”	"	PUNCT
ap-652	511	1	j.	j.	PROPN
ap-652	511	2	mech	mech	PROPN
ap-652	511	3	.	.	PUNCT
ap-652	512	1	compos	compos	PROPN
ap-652	512	2	.	.	PUNCT
ap-652	513	1	mater	mater	NOUN
ap-652	513	2	.	.	PUNCT
ap-652	513	3	struct	struct	NOUN
ap-652	513	4	.	.	PUNCT
ap-652	513	5	,	,	PUNCT
ap-652	514	1	vol	vol	NOUN
ap-652	514	2	.	.	PROPN
ap-652	514	3	6	6	NUM
ap-652	514	4	(	(	PUNCT
ap-652	514	5	1999	1999	NUM
ap-652	514	6	)	)	PUNCT
ap-652	514	7	,	,	PUNCT
ap-652	515	1	p.	p.	NOUN
ap-652	515	2	331–346	331–346	NUM
ap-652	515	3	.	.	PUNCT
ap-652	516	1	[	[	X
ap-652	516	2	10	10	NUM
ap-652	516	3	]	]	X
ap-652	516	4	duvaut	duvaut	PROPN
ap-652	516	5	g.	g.	PROPN
ap-652	516	6	:	:	PUNCT
ap-652	516	7	“	"	PUNCT
ap-652	516	8	homogenisation	homogenisation	NOUN
ap-652	516	9	et	et	NOUN
ap-652	516	10	materiaux	materiaux	NOUN
ap-652	516	11	composites	composite	NOUN
ap-652	516	12	.	.	PUNCT
ap-652	516	13	”	"	PUNCT
ap-652	517	1	in	in	ADP
ap-652	517	2	:	:	PUNCT
ap-652	517	3	“	"	PUNCT
ap-652	517	4	theoretical	theoretical	ADJ
ap-652	517	5	and	and	CCONJ
ap-652	517	6	applied	applied	ADJ
ap-652	517	7	mechanics	mechanic	NOUN
ap-652	517	8	.	.	PUNCT
ap-652	517	9	”	"	PUNCT
ap-652	518	1	ed	ed	NOUN
ap-652	518	2	.	.	PUNCT
ap-652	519	1	p.	p.	NOUN
ap-652	519	2	ciarlet	ciarlet	NOUN
ap-652	519	3	;	;	PUNCT
ap-652	519	4	m.	m.	NOUN
ap-652	519	5	rouseau	rouseau	PROPN
ap-652	519	6	,	,	PUNCT
ap-652	519	7	amsterdam	amsterdam	PROPN
ap-652	519	8	,	,	PUNCT
ap-652	519	9	north	north	NOUN
ap-652	519	10	-	-	PUNCT
ap-652	519	11	holland	holland	NOUN
ap-652	519	12	,	,	PUNCT
ap-652	519	13	1976	1976	NUM
ap-652	519	14	.	.	PUNCT
ap-652	520	1	[	[	X
ap-652	520	2	11	11	NUM
ap-652	520	3	]	]	X
ap-652	520	4	gibson	gibson	PROPN
ap-652	520	5	l.	l.	PROPN
ap-652	520	6	j.	j.	PROPN
ap-652	520	7	,	,	PUNCT
ap-652	520	8	ashby	ashby	PROPN
ap-652	520	9	m.	m.	PROPN
ap-652	520	10	f.	f.	PROPN
ap-652	520	11	:	:	PUNCT
ap-652	520	12	“	"	PUNCT
ap-652	520	13	cellular	cellular	ADJ
ap-652	520	14	solids	solid	NOUN
ap-652	520	15	.	.	PUNCT
ap-652	520	16	structure	structure	NOUN
ap-652	520	17	and	and	CCONJ
ap-652	520	18	properties	property	NOUN
ap-652	520	19	.	.	PUNCT
ap-652	520	20	”	"	PUNCT
ap-652	521	1	pergamon	pergamon	PROPN
ap-652	521	2	press	press	PROPN
ap-652	521	3	,	,	PUNCT
ap-652	521	4	oxford	oxford	NOUN
ap-652	521	5	,	,	PUNCT
ap-652	521	6	1988	1988	NUM
ap-652	521	7	.	.	PUNCT
ap-652	522	1	[	[	X
ap-652	522	2	12	12	NUM
ap-652	522	3	]	]	X
ap-652	522	4	gibianski	gibianski	PROPN
ap-652	522	5	l.	l.	PROPN
ap-652	522	6	v.	v.	PROPN
ap-652	522	7	,	,	PUNCT
ap-652	522	8	sigmund	sigmund	PROPN
ap-652	522	9	o.	o.	NOUN
ap-652	522	10	:	:	PUNCT
ap-652	522	11	“	"	PUNCT
ap-652	522	12	multiphase	multiphase	NOUN
ap-652	522	13	elastic	elastic	ADJ
ap-652	522	14	composites	composite	NOUN
ap-652	522	15	with	with	ADP
ap-652	522	16	extremal	extremal	ADJ
ap-652	522	17	bulk	bulk	ADJ
ap-652	522	18	modulus	modulus	NOUN
ap-652	522	19	.	.	PUNCT
ap-652	522	20	”	"	PUNCT
ap-652	523	1	j.	j.	PROPN
ap-652	523	2	mech	mech	PROPN
ap-652	523	3	.	.	PUNCT
ap-652	524	1	phys	phy	NOUN
ap-652	524	2	.	.	PUNCT
ap-652	525	1	solids	solid	NOUN
ap-652	525	2	,	,	PUNCT
ap-652	525	3	vol	vol	NOUN
ap-652	525	4	.	.	PUNCT
ap-652	526	1	48	48	NUM
ap-652	526	2	(	(	PUNCT
ap-652	526	3	2000	2000	NUM
ap-652	526	4	)	)	PUNCT
ap-652	526	5	,	,	PUNCT
ap-652	527	1	p.	p.	NOUN
ap-652	527	2	461–498	461–498	NUM
ap-652	527	3	.	.	PUNCT
ap-652	528	1	[	[	X
ap-652	528	2	13	13	NUM
ap-652	528	3	]	]	PUNCT
ap-652	528	4	grenestedt	grenestedt	NOUN
ap-652	528	5	j.	j.	PROPN
ap-652	528	6	l.	l.	PROPN
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ap-652	528	8	“	"	PUNCT
ap-652	528	9	effective	effective	ADJ
ap-652	528	10	elastic	elastic	ADJ
ap-652	528	11	behavior	behavior	NOUN
ap-652	528	12	of	of	ADP
ap-652	528	13	some	some	DET
ap-652	528	14	models	model	NOUN
ap-652	528	15	for	for	ADP
ap-652	528	16	‘	'	PUNCT
ap-652	528	17	perfect	perfect	ADJ
ap-652	528	18	’	'	PUNCT
ap-652	528	19	cellular	cellular	ADJ
ap-652	528	20	solids	solid	NOUN
ap-652	528	21	.	.	PUNCT
ap-652	528	22	”	"	PUNCT
ap-652	529	1	int	int	NOUN
ap-652	529	2	.	.	PUNCT
ap-652	530	1	j.	j.	PROPN
ap-652	530	2	solids	solids	PROPN
ap-652	530	3	struct	struct	NOUN
ap-652	530	4	.	.	PUNCT
ap-652	530	5	,	,	PUNCT
ap-652	530	6	vol	vol	NOUN
ap-652	530	7	.	.	PROPN
ap-652	530	8	36	36	NUM
ap-652	530	9	(	(	PUNCT
ap-652	530	10	1999	1999	NUM
ap-652	530	11	)	)	PUNCT
ap-652	530	12	,	,	PUNCT
ap-652	530	13	p.	p.	NOUN
ap-652	530	14	1471–1501	1471–1501	NUM
ap-652	530	15	.	.	PUNCT
ap-652	531	1	[	[	X
ap-652	531	2	14	14	NUM
ap-652	531	3	]	]	PUNCT
ap-652	531	4	guedes	guede	NOUN
ap-652	531	5	j.	j.	PROPN
ap-652	531	6	m.	m.	PROPN
ap-652	531	7	,	,	PUNCT
ap-652	531	8	rodrigues	rodrigues	PROPN
ap-652	531	9	h.	h.	PROPN
ap-652	531	10	c.	c.	PROPN
ap-652	531	11	,	,	PUNCT
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ap-652	531	13	m.	m.	PROPN
ap-652	531	14	p.	p.	NOUN
ap-652	531	15	:	:	PUNCT
ap-652	531	16	“	"	PUNCT
ap-652	531	17	a	a	DET
ap-652	531	18	material	material	NOUN
ap-652	531	19	optimization	optimization	NOUN
ap-652	531	20	model	model	NOUN
ap-652	531	21	to	to	PART
ap-652	531	22	approximate	approximate	VERB
ap-652	531	23	energy	energy	NOUN
ap-652	531	24	bounds	bound	NOUN
ap-652	531	25	for	for	ADP
ap-652	531	26	cellular	cellular	ADJ
ap-652	531	27	materials	material	NOUN
ap-652	531	28	under	under	ADP
ap-652	531	29	multiload	multiload	NOUN
ap-652	531	30	conditions	condition	NOUN
ap-652	531	31	.	.	PUNCT
ap-652	531	32	”	"	PUNCT
ap-652	531	33	struct	struct	NOUN
ap-652	531	34	.	.	PUNCT
ap-652	532	1	opt	opt	PROPN
ap-652	532	2	.	.	PUNCT
ap-652	532	3	,	,	PUNCT
ap-652	533	1	vol	vol	NOUN
ap-652	533	2	.	.	PROPN
ap-652	534	1	25	25	NUM
ap-652	534	2	(	(	PUNCT
ap-652	534	3	2003	2003	NUM
ap-652	534	4	)	)	PUNCT
ap-652	534	5	,	,	PUNCT
ap-652	534	6	p.	p.	NOUN
ap-652	534	7	446–452	446–452	NUM
ap-652	534	8	.	.	PUNCT
ap-652	535	1	[	[	X
ap-652	535	2	15	15	NUM
ap-652	535	3	]	]	X
ap-652	535	4	hashin	hashin	PROPN
ap-652	535	5	z.	z.	PROPN
ap-652	535	6	:	:	PUNCT
ap-652	535	7	“	"	PUNCT
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ap-652	535	9	elastic	elastic	ADJ
ap-652	535	10	moduli	modulus	NOUN
ap-652	535	11	of	of	ADP
ap-652	535	12	heterogeneous	heterogeneous	ADJ
ap-652	535	13	materials	material	NOUN
ap-652	535	14	.	.	PUNCT
ap-652	535	15	”	"	PUNCT
ap-652	536	1	j.	j.	PROPN
ap-652	536	2	appl	appl	PROPN
ap-652	536	3	.	.	PROPN
ap-652	536	4	mech	mech	PROPN
ap-652	536	5	.	.	PROPN
ap-652	536	6	,	,	PUNCT
ap-652	536	7	asme	asme	PROPN
ap-652	536	8	,	,	PUNCT
ap-652	536	9	vol	vol	NOUN
ap-652	536	10	.	.	PROPN
ap-652	536	11	29	29	NUM
ap-652	536	12	(	(	PUNCT
ap-652	536	13	1962	1962	NUM
ap-652	536	14	)	)	PUNCT
ap-652	536	15	,	,	PUNCT
ap-652	537	1	p.	p.	NOUN
ap-652	537	2	143–150	143–150	NUM
ap-652	537	3	.	.	PUNCT
ap-652	538	1	[	[	X
ap-652	538	2	16	16	NUM
ap-652	538	3	]	]	X
ap-652	538	4	hashin	hashin	PROPN
ap-652	538	5	z.	z.	PROPN
ap-652	538	6	:	:	PUNCT
ap-652	538	7	“	"	PUNCT
ap-652	538	8	theory	theory	NOUN
ap-652	538	9	of	of	ADP
ap-652	538	10	composite	composite	ADJ
ap-652	538	11	materials	material	NOUN
ap-652	538	12	.	.	PUNCT
ap-652	538	13	”	"	PUNCT
ap-652	539	1	in	in	ADP
ap-652	539	2	:	:	PUNCT
ap-652	539	3	”	"	PUNCT
ap-652	539	4	mechanics	mechanic	NOUN
ap-652	539	5	of	of	ADP
ap-652	539	6	composite	composite	ADJ
ap-652	539	7	materials	material	NOUN
ap-652	539	8	.	.	PUNCT
ap-652	539	9	”	"	PUNCT
ap-652	539	10	ed	ed	NOUN
ap-652	539	11	.	.	PUNCT
ap-652	539	12	f.	f.	PROPN
ap-652	539	13	w.	w.	PROPN
ap-652	539	14	wendt	wendt	PROPN
ap-652	539	15	,	,	PUNCT
ap-652	539	16	h.	h.	PROPN
ap-652	539	17	liebowitz	liebowitz	PROPN
ap-652	539	18	,	,	PUNCT
ap-652	539	19	n.	n.	PROPN
ap-652	539	20	perrone	perrone	PROPN
ap-652	539	21	.	.	PUNCT
ap-652	540	1	pergamon	pergamon	PROPN
ap-652	540	2	press	press	PROPN
ap-652	540	3	,	,	PUNCT
ap-652	540	4	oxford	oxford	PROPN
ap-652	540	5	,	,	PUNCT
ap-652	540	6	(	(	PUNCT
ap-652	540	7	1970	1970	NUM
ap-652	540	8	)	)	PUNCT
ap-652	540	9	.	.	PUNCT
ap-652	541	1	[	[	X
ap-652	541	2	17	17	NUM
ap-652	541	3	]	]	X
ap-652	541	4	hashin	hashin	PROPN
ap-652	541	5	z.	z.	PROPN
ap-652	541	6	:	:	PUNCT
ap-652	541	7	“	"	PUNCT
ap-652	541	8	analysis	analysis	NOUN
ap-652	541	9	of	of	ADP
ap-652	541	10	composite	composite	ADJ
ap-652	541	11	materials	material	NOUN
ap-652	541	12	-	-	PUNCT
ap-652	541	13	a	a	DET
ap-652	541	14	survey	survey	NOUN
ap-652	541	15	.	.	PUNCT
ap-652	541	16	”	"	PUNCT
ap-652	542	1	j.	j.	PROPN
ap-652	542	2	appl	appl	PROPN
ap-652	542	3	.	.	PROPN
ap-652	542	4	mech	mech	PROPN
ap-652	542	5	.	.	PROPN
ap-652	542	6	,	,	PUNCT
ap-652	542	7	asme	asme	PROPN
ap-652	542	8	,	,	PUNCT
ap-652	542	9	vol	vol	NOUN
ap-652	542	10	.	.	PROPN
ap-652	542	11	50	50	NUM
ap-652	542	12	(	(	PUNCT
ap-652	542	13	1983	1983	NUM
ap-652	542	14	)	)	PUNCT
ap-652	542	15	,	,	PUNCT
ap-652	543	1	p.	p.	NOUN
ap-652	543	2	481–505	481–505	NUM
ap-652	543	3	.	.	PUNCT
ap-652	544	1	[	[	X
ap-652	544	2	18	18	NUM
ap-652	544	3	]	]	X
ap-652	544	4	hashin	hashin	PROPN
ap-652	544	5	z.	z.	PROPN
ap-652	544	6	,	,	PUNCT
ap-652	544	7	shtrikman	shtrikman	PROPN
ap-652	544	8	s.	s.	PROPN
ap-652	544	9	:	:	PUNCT
ap-652	544	10	“	"	PUNCT
ap-652	544	11	a	a	DET
ap-652	544	12	variational	variational	ADJ
ap-652	544	13	approach	approach	NOUN
ap-652	544	14	to	to	ADP
ap-652	544	15	the	the	DET
ap-652	544	16	theory	theory	NOUN
ap-652	544	17	of	of	ADP
ap-652	544	18	the	the	DET
ap-652	544	19	elastic	elastic	ADJ
ap-652	544	20	behavior	behavior	NOUN
ap-652	544	21	of	of	ADP
ap-652	544	22	polycrystals	polycrystal	NOUN
ap-652	544	23	.	.	PUNCT
ap-652	544	24	”	"	PUNCT
ap-652	545	1	j.	j.	PROPN
ap-652	545	2	mech	mech	PROPN
ap-652	545	3	.	.	PUNCT
ap-652	546	1	phys	phy	NOUN
ap-652	546	2	.	.	PUNCT
ap-652	547	1	solids	solid	NOUN
ap-652	547	2	,	,	PUNCT
ap-652	547	3	vol	vol	NOUN
ap-652	547	4	.	.	PROPN
ap-652	548	1	10	10	NUM
ap-652	548	2	(	(	PUNCT
ap-652	548	3	1962	1962	NUM
ap-652	548	4	)	)	PUNCT
ap-652	548	5	,	,	PUNCT
ap-652	549	1	p.	p.	NOUN
ap-652	549	2	343–352	343–352	NUM
ap-652	549	3	.	.	PUNCT
ap-652	550	1	184	184	NUM
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ap-652	550	4	technical	technical	PROPN
ap-652	550	5	university	university	PROPN
ap-652	550	6	publishing	publishing	NOUN
ap-652	550	7	house	house	NOUN
ap-652	550	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	550	9	acta	acta	PROPN
ap-652	550	10	polytechnica	polytechnica	PROPN
ap-652	550	11	vol	vol	NOUN
ap-652	550	12	.	.	PROPN
ap-652	551	1	44	44	NUM
ap-652	551	2	no.5–6/2004	no.5–6/2004	NOUN
ap-652	551	3	bounds	bound	VERB
ap-652	551	4	comparison	comparison	NOUN
ap-652	551	5	composite	composite	ADJ
ap-652	551	6	bounds	bound	NOUN
ap-652	552	1	k	k	PROPN
ap-652	552	2	�	�	PROPN
ap-652	552	3	*	*	PUNCT
ap-652	552	4	(	(	PUNCT
ap-652	552	5	(	(	PUNCT
ap-652	552	6	)	)	PUNCT
ap-652	552	7	(	(	PUNCT
ap-652	552	8	)	)	PUNCT
ap-652	552	9	)	)	PUNCT
ap-652	552	10	2	2	NUM
ap-652	552	11	3	3	NUM
ap-652	552	12	3	3	NUM
ap-652	552	13	1	1	NUM
ap-652	552	14	1	1	NUM
ap-652	552	15	s	s	PART
ap-652	552	16	ss	ss	PROPN
ap-652	552	17	s	s	PROPN
ap-652	552	18	�	�	PROPN
ap-652	552	19	�	�	PROPN
ap-652	552	20	g	g	PROPN
ap-652	552	21	�	�	PROPN
ap-652	552	22	*	*	PUNCT
ap-652	552	23	)	)	PUNCT
ap-652	552	24	(	(	PUNCT
ap-652	552	25	)	)	PUNCT
ap-652	552	26	(	(	PUNCT
ap-652	552	27	(	(	PUNCT
ap-652	552	28	)	)	PUNCT
ap-652	552	29	(	(	PUNCT
ap-652	552	30	)	)	PUNCT
ap-652	552	31	)	)	PUNCT
ap-652	553	1	s(7	s(7	ADJ
ap-652	553	2	5	5	NUM
ap-652	553	3	s	s	NOUN
ap-652	553	4	s	s	NOUN
ap-652	553	5	s	s	X
ap-652	553	6	s	s	X
ap-652	553	7	s	s	X
ap-652	553	8	�	�	PROPN
ap-652	553	9	�	�	PROPN
ap-652	553	10	�	�	PROPN
ap-652	553	11	�	�	PROPN
ap-652	553	12	2	2	NUM
ap-652	553	13	1	1	NUM
ap-652	553	14	15	15	NUM
ap-652	553	15	1	1	NUM
ap-652	553	16	2	2	NUM
ap-652	553	17	4	4	NUM
ap-652	553	18	5	5	NUM
ap-652	553	19	1	1	NUM
ap-652	553	20	g	g	PROPN
ap-652	553	21	�	�	PROPN
ap-652	553	22	�	�	PROPN
ap-652	553	23	*	*	PUNCT
ap-652	553	24	)	)	PUNCT
ap-652	553	25	(	(	PUNCT
ap-652	553	26	)	)	PUNCT
ap-652	553	27	(	(	PUNCT
ap-652	553	28	(	(	PUNCT
ap-652	553	29	)	)	PUNCT
ap-652	553	30	(	(	PUNCT
ap-652	553	31	)	)	PUNCT
ap-652	553	32	)	)	PUNCT
ap-652	554	1	s(2	s(2	NOUN
ap-652	554	2	s	s	NOUN
ap-652	554	3	s	s	NOUN
ap-652	554	4	s	s	X
ap-652	554	5	s	s	X
ap-652	554	6	s	s	X
ap-652	554	7	�	�	PROPN
ap-652	554	8	�	�	PROPN
ap-652	554	9	�	�	PROPN
ap-652	554	10	�	�	PROPN
ap-652	554	11	2	2	NUM
ap-652	554	12	1	1	NUM
ap-652	554	13	1	1	NUM
ap-652	554	14	3	3	NUM
ap-652	554	15	1	1	NUM
ap-652	554	16	1	1	NUM
ap-652	554	17	2	2	NUM
ap-652	554	18	2	2	NUM
ap-652	554	19	g	g	NOUN
ap-652	554	20	�	�	PROPN
ap-652	554	21	*	*	PUNCT
ap-652	554	22	)	)	PUNCT
ap-652	554	23	(	(	PUNCT
ap-652	554	24	)	)	PUNCT
ap-652	554	25	(	(	PUNCT
ap-652	554	26	(	(	PUNCT
ap-652	554	27	)	)	PUNCT
ap-652	554	28	(	(	PUNCT
ap-652	554	29	)	)	PUNCT
ap-652	554	30	)	)	PUNCT
ap-652	555	1	s(5	s(5	NOUN
ap-652	555	2	3	3	NUM
ap-652	555	3	s	s	NOUN
ap-652	555	4	s	s	NOUN
ap-652	555	5	s	s	X
ap-652	555	6	s	s	X
ap-652	555	7	s	s	X
ap-652	555	8	�	�	PROPN
ap-652	555	9	�	�	PROPN
ap-652	555	10	�	�	PROPN
ap-652	555	11	�	�	PROPN
ap-652	555	12	2	2	NUM
ap-652	555	13	1	1	NUM
ap-652	555	14	9	9	NUM
ap-652	555	15	1	1	NUM
ap-652	555	16	2	2	NUM
ap-652	555	17	2	2	NUM
ap-652	555	18	3	3	NUM
ap-652	555	19	k	k	NOUN
ap-652	555	20	*	*	PUNCT
ap-652	555	21	1	1	NUM
ap-652	555	22	g	g	NOUN
ap-652	555	23	*	*	NUM
ap-652	555	24	2	2	NUM
ap-652	555	25	g	g	NOUN
ap-652	555	26	*	*	SYM
ap-652	555	27	g	g	NOUN
ap-652	555	28	*	*	PUNCT
ap-652	555	29	linearized	linearize	VERB
ap-652	555	30	form	form	NOUN
ap-652	555	31	2	2	NUM
ap-652	555	32	s	s	NOUN
ap-652	555	33	s9	s9	NOUN
ap-652	555	34	1	1	NUM
ap-652	555	35	(	(	PUNCT
ap-652	555	36	)	)	PUNCT
ap-652	555	37	�	�	PROPN
ap-652	555	38	2	2	NUM
ap-652	555	39	ss	ss	NOUN
ap-652	555	40	s	s	PROPN
ap-652	555	41	�	�	PROPN
ap-652	555	42	�	�	PROPN
ap-652	555	43	6	6	NUM
ap-652	555	44	1	1	NUM
ap-652	555	45	2	2	NUM
ap-652	555	46	(	(	PUNCT
ap-652	555	47	)	)	PUNCT
ap-652	555	48	5	5	NUM
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ap-652	555	51	3	3	NUM
ap-652	555	52	18	18	NUM
ap-652	555	53	1	1	NUM
ap-652	555	54	2	2	NUM
ap-652	555	55	�	�	PROPN
ap-652	555	56	�	�	PROPN
ap-652	555	57	(	(	PUNCT
ap-652	555	58	)	)	PUNCT
ap-652	555	59	7	7	NUM
ap-652	555	60	ss	ss	NOUN
ap-652	555	61	s	s	NOUN
ap-652	555	62	5	5	NUM
ap-652	555	63	30	30	NUM
ap-652	555	64	1	1	NUM
ap-652	555	65	2	2	NUM
ap-652	555	66	�	�	PROPN
ap-652	555	67	�	�	PROPN
ap-652	555	68	(	(	PUNCT
ap-652	555	69	)	)	PUNCT
ap-652	555	70	previous	previous	ADJ
ap-652	555	71	form	form	NOUN
ap-652	555	72	with	with	ADP
ap-652	555	73	�	�	PROPN
ap-652	555	74	s	s	PART
ap-652	555	75	�	�	NOUN
ap-652	555	76	0	0	ADJ
ap-652	555	77	2s	2s	NUM
ap-652	555	78	9	9	NUM
ap-652	555	79	s	s	NOUN
ap-652	555	80	3	3	NUM
ap-652	555	81	5s	5s	NUM
ap-652	555	82	18	18	NUM
ap-652	555	83	7s	7	NOUN
ap-652	555	84	30	30	NUM
ap-652	555	85	bound	bind	VERB
ap-652	555	86	for	for	ADP
ap-652	555	87	open	open	ADJ
ap-652	555	88	-	-	PUNCT
ap-652	555	89	cell	cell	NOUN
ap-652	555	90	foams	foam	NOUN
ap-652	555	91	from	from	ADP
ap-652	555	92	this	this	DET
ap-652	555	93	article	article	NOUN
ap-652	555	94	s	s	PART
ap-652	555	95	9	9	NUM
ap-652	555	96	s	s	NUM
ap-652	555	97	6	6	NUM
ap-652	555	98	s	s	PART
ap-652	555	99	s2	s2	NOUN
ap-652	555	100	9	9	NUM
ap-652	555	101	�	�	PROPN
ap-652	555	102	s	s	PART
ap-652	555	103	s2	s2	PROPN
ap-652	555	104	15	15	NUM
ap-652	555	105	�	�	PROPN
ap-652	555	106	optimal	optimal	ADJ
ap-652	555	107	media	medium	NOUN
ap-652	555	108	are	be	AUX
ap-652	555	109	…	…	PUNCT
ap-652	555	110	determined	determine	VERB
ap-652	555	111	by	by	ADP
ap-652	555	112	necessary	necessary	ADJ
ap-652	555	113	and	and	CCONJ
ap-652	555	114	sufficient	sufficient	ADJ
ap-652	555	115	conditions	condition	NOUN
ap-652	555	116	fully	fully	ADV
ap-652	555	117	geometrically	geometrically	ADV
ap-652	555	118	specified	specify	VERB
ap-652	555	119	fully	fully	ADV
ap-652	555	120	geometrically	geometrically	ADV
ap-652	555	121	specified	specify	VERB
ap-652	555	122	determined	determine	VERB
ap-652	555	123	by	by	ADP
ap-652	555	124	necessary	necessary	ADJ
ap-652	555	125	and	and	CCONJ
ap-652	555	126	sufficient	sufficient	ADJ
ap-652	555	127	conditions	condition	NOUN
ap-652	555	128	table	table	VERB
ap-652	555	129	8	8	NUM
ap-652	555	130	:	:	PUNCT
ap-652	555	131	:	:	PUNCT
ap-652	555	132	composite	composite	ADJ
ap-652	555	133	bounds	bound	NOUN
ap-652	555	134	,	,	PUNCT
ap-652	555	135	bounds	bound	VERB
ap-652	555	136	for	for	ADP
ap-652	555	137	open	open	ADJ
ap-652	555	138	-	-	PUNCT
ap-652	555	139	cell	cell	NOUN
ap-652	555	140	foams	foam	NOUN
ap-652	555	141	and	and	CCONJ
ap-652	555	142	characterization	characterization	NOUN
ap-652	555	143	of	of	ADP
ap-652	555	144	the	the	DET
ap-652	555	145	optimal	optimal	ADJ
ap-652	555	146	media	medium	NOUN
ap-652	555	147	[	[	X
ap-652	555	148	19	19	NUM
ap-652	555	149	]	]	X
ap-652	555	150	hashin	hashin	PROPN
ap-652	555	151	z.	z.	PROPN
ap-652	555	152	,	,	PUNCT
ap-652	555	153	shtrikman	shtrikman	PROPN
ap-652	555	154	s.	s.	PROPN
ap-652	555	155	:	:	PUNCT
ap-652	555	156	“	"	PUNCT
ap-652	555	157	a	a	DET
ap-652	555	158	variational	variational	ADJ
ap-652	555	159	approach	approach	NOUN
ap-652	555	160	to	to	ADP
ap-652	555	161	the	the	DET
ap-652	555	162	theory	theory	NOUN
ap-652	555	163	of	of	ADP
ap-652	555	164	the	the	DET
ap-652	555	165	elastic	elastic	ADJ
ap-652	555	166	behavior	behavior	NOUN
ap-652	555	167	of	of	ADP
ap-652	555	168	multiphase	multiphase	NOUN
ap-652	555	169	materials	material	NOUN
ap-652	555	170	.	.	PUNCT
ap-652	555	171	”	"	PUNCT
ap-652	556	1	j.	j.	PROPN
ap-652	556	2	mech	mech	PROPN
ap-652	556	3	.	.	PUNCT
ap-652	557	1	phys	phy	NOUN
ap-652	557	2	.	.	PUNCT
ap-652	558	1	solids	solid	NOUN
ap-652	558	2	,	,	PUNCT
ap-652	558	3	vol	vol	NOUN
ap-652	558	4	.	.	PROPN
ap-652	558	5	11	11	NUM
ap-652	558	6	(	(	PUNCT
ap-652	558	7	1963	1963	NUM
ap-652	558	8	)	)	PUNCT
ap-652	558	9	,	,	PUNCT
ap-652	559	1	p.	p.	NOUN
ap-652	559	2	127–140	127–140	NUM
ap-652	559	3	.	.	PUNCT
ap-652	560	1	[	[	X
ap-652	560	2	20	20	NUM
ap-652	560	3	]	]	PUNCT
ap-652	560	4	hill	hill	PROPN
ap-652	560	5	r.	r.	PROPN
ap-652	560	6	:	:	PUNCT
ap-652	560	7	“	"	PUNCT
ap-652	560	8	elastic	elastic	ADJ
ap-652	560	9	properties	property	NOUN
ap-652	560	10	of	of	ADP
ap-652	560	11	reinforced	reinforce	VERB
ap-652	560	12	solids	solid	NOUN
ap-652	560	13	:	:	PUNCT
ap-652	560	14	some	some	DET
ap-652	560	15	theoretical	theoretical	ADJ
ap-652	560	16	principles	principle	NOUN
ap-652	560	17	.	.	PUNCT
ap-652	560	18	”	"	PUNCT
ap-652	561	1	j.	j.	PROPN
ap-652	561	2	mech	mech	PROPN
ap-652	561	3	.	.	PUNCT
ap-652	562	1	phys	phy	NOUN
ap-652	562	2	.	.	PUNCT
ap-652	563	1	solids	solid	NOUN
ap-652	563	2	,	,	PUNCT
ap-652	563	3	vol	vol	NOUN
ap-652	563	4	.	.	PROPN
ap-652	563	5	11	11	NUM
ap-652	563	6	(	(	PUNCT
ap-652	563	7	1963	1963	NUM
ap-652	563	8	)	)	PUNCT
ap-652	563	9	,	,	PUNCT
ap-652	563	10	p.	p.	NOUN
ap-652	563	11	357–372	357–372	NUM
ap-652	563	12	.	.	PUNCT
ap-652	564	1	[	[	X
ap-652	564	2	21	21	NUM
ap-652	564	3	]	]	X
ap-652	564	4	kraynik	kraynik	PROPN
ap-652	564	5	a.	a.	PROPN
ap-652	564	6	m.	m.	PROPN
ap-652	564	7	,	,	PUNCT
ap-652	564	8	warren	warren	PROPN
ap-652	564	9	w.	w.	PROPN
ap-652	564	10	e.	e.	PROPN
ap-652	564	11	:	:	PUNCT
ap-652	564	12	“	"	PUNCT
ap-652	564	13	the	the	DET
ap-652	564	14	elastic	elastic	ADJ
ap-652	564	15	behavior	behavior	NOUN
ap-652	564	16	of	of	ADP
ap-652	564	17	low	low	ADJ
ap-652	564	18	-	-	PUNCT
ap-652	564	19	density	density	NOUN
ap-652	564	20	cellular	cellular	ADJ
ap-652	564	21	plastics	plastic	NOUN
ap-652	564	22	.	.	PUNCT
ap-652	564	23	”	"	PUNCT
ap-652	565	1	in	in	ADP
ap-652	565	2	:	:	PUNCT
ap-652	565	3	“	"	PUNCT
ap-652	565	4	low	low	ADJ
ap-652	565	5	density	density	NOUN
ap-652	565	6	cellular	cellular	ADJ
ap-652	565	7	plastics	plastic	NOUN
ap-652	565	8	:	:	PUNCT
ap-652	565	9	physical	physical	ADJ
ap-652	565	10	basis	basis	NOUN
ap-652	565	11	of	of	ADP
ap-652	565	12	behavior	behavior	NOUN
ap-652	565	13	.	.	PUNCT
ap-652	565	14	”	"	PUNCT
ap-652	566	1	ed	ed	NOUN
ap-652	566	2	.	.	PUNCT
ap-652	566	3	n.	n.	PROPN
ap-652	566	4	c.	c.	PROPN
ap-652	566	5	hilyard	hilyard	PROPN
ap-652	566	6	,	,	PUNCT
ap-652	566	7	a.	a.	PROPN
ap-652	566	8	cunningham	cunningham	PROPN
ap-652	566	9	.	.	PUNCT
ap-652	567	1	chapman	chapman	PROPN
ap-652	567	2	&	&	CCONJ
ap-652	567	3	hall	hall	PROPN
ap-652	567	4	,	,	PUNCT
ap-652	567	5	london	london	PROPN
ap-652	567	6	,	,	PUNCT
ap-652	567	7	1994	1994	NUM
ap-652	567	8	,	,	PUNCT
ap-652	567	9	p.	p.	NOUN
ap-652	567	10	217	217	NUM
ap-652	567	11	.	.	PUNCT
ap-652	568	1	[	[	X
ap-652	568	2	22	22	NUM
ap-652	568	3	]	]	PUNCT
ap-652	568	4	lekhnitskii	lekhnitskii	PROPN
ap-652	568	5	s.	s.	PROPN
ap-652	568	6	g.	g.	PROPN
ap-652	568	7	:	:	PUNCT
ap-652	568	8	“	"	PUNCT
ap-652	568	9	theory	theory	NOUN
ap-652	568	10	of	of	ADP
ap-652	568	11	elasticity	elasticity	NOUN
ap-652	568	12	of	of	ADP
ap-652	568	13	an	an	DET
ap-652	568	14	anisotropic	anisotropic	NOUN
ap-652	568	15	body	body	NOUN
ap-652	568	16	.	.	PUNCT
ap-652	568	17	”	"	PUNCT
ap-652	569	1	mir	mir	PROPN
ap-652	569	2	publishers	publisher	NOUN
ap-652	569	3	,	,	PUNCT
ap-652	569	4	moscow	moscow	PROPN
ap-652	569	5	,	,	PUNCT
ap-652	569	6	1981	1981	NUM
ap-652	569	7	.	.	PUNCT
ap-652	570	1	[	[	X
ap-652	570	2	23	23	NUM
ap-652	570	3	]	]	X
ap-652	570	4	li	li	PROPN
ap-652	570	5	k.	k.	PROPN
ap-652	570	6	,	,	PUNCT
ap-652	570	7	gao	gao	PROPN
ap-652	570	8	x.-l	x.-l	PROPN
ap-652	570	9	.	.	PUNCT
ap-652	570	10	,	,	PUNCT
ap-652	570	11	roy	roy	PROPN
ap-652	570	12	a.	a.	PROPN
ap-652	570	13	k.	k.	PROPN
ap-652	570	14	:	:	PUNCT
ap-652	570	15	“	"	PUNCT
ap-652	570	16	micromechanics	micromechanic	NOUN
ap-652	570	17	model	model	NOUN
ap-652	570	18	for	for	ADP
ap-652	570	19	three	three	NUM
ap-652	570	20	-	-	PUNCT
ap-652	570	21	dimensional	dimensional	ADJ
ap-652	570	22	open	open	ADJ
ap-652	570	23	-	-	PUNCT
ap-652	570	24	cell	cell	NOUN
ap-652	570	25	foams	foam	NOUN
ap-652	570	26	using	use	VERB
ap-652	570	27	a	a	DET
ap-652	570	28	tetrakaidecahedral	tetrakaidecahedral	ADJ
ap-652	570	29	unit	unit	NOUN
ap-652	570	30	cell	cell	NOUN
ap-652	570	31	and	and	CCONJ
ap-652	570	32	castigliano	castigliano	PROPN
ap-652	570	33	’s	’s	PART
ap-652	570	34	second	second	ADJ
ap-652	570	35	theorem	theorem	NOUN
ap-652	570	36	.	.	PUNCT
ap-652	570	37	”	"	PUNCT
ap-652	571	1	compos	compos	PROPN
ap-652	571	2	.	.	PUNCT
ap-652	572	1	sci	sci	PROPN
ap-652	572	2	.	.	PUNCT
ap-652	572	3	techn	techn	PROPN
ap-652	572	4	.	.	PROPN
ap-652	572	5	,	,	PUNCT
ap-652	572	6	vol	vol	NOUN
ap-652	572	7	.	.	PROPN
ap-652	572	8	63	63	NUM
ap-652	572	9	(	(	PUNCT
ap-652	572	10	2003	2003	NUM
ap-652	572	11	)	)	PUNCT
ap-652	572	12	,	,	PUNCT
ap-652	572	13	p.1769–1781	p.1769–1781	VERB
ap-652	572	14	.	.	PUNCT
ap-652	573	1	[	[	X
ap-652	573	2	24	24	NUM
ap-652	573	3	]	]	PUNCT
ap-652	573	4	nemat	nemat	NOUN
ap-652	573	5	-	-	PUNCT
ap-652	573	6	nasser	nasser	PROPN
ap-652	573	7	s.	s.	PROPN
ap-652	573	8	,	,	PUNCT
ap-652	573	9	hori	hori	PROPN
ap-652	573	10	m.	m.	PROPN
ap-652	573	11	:	:	PUNCT
ap-652	573	12	”	"	PUNCT
ap-652	573	13	micromechanics	micromechanic	NOUN
ap-652	573	14	:	:	PUNCT
ap-652	573	15	overall	overall	ADJ
ap-652	573	16	properties	property	NOUN
ap-652	573	17	of	of	ADP
ap-652	573	18	heterogeneous	heterogeneous	ADJ
ap-652	573	19	materials	material	NOUN
ap-652	573	20	.	.	PUNCT
ap-652	573	21	”	"	PUNCT
ap-652	574	1	north	north	NOUN
ap-652	574	2	-	-	PUNCT
ap-652	574	3	holland	holland	PROPN
ap-652	574	4	series	series	NOUN
ap-652	574	5	in	in	ADP
ap-652	574	6	applied	applied	ADJ
ap-652	574	7	mathematics	mathematic	NOUN
ap-652	574	8	and	and	CCONJ
ap-652	574	9	mechanics	mechanic	NOUN
ap-652	574	10	,	,	PUNCT
ap-652	574	11	vol	vol	NOUN
ap-652	574	12	.	.	PROPN
ap-652	574	13	37	37	NUM
ap-652	574	14	,	,	PUNCT
ap-652	574	15	ed	ed	NOUN
ap-652	574	16	.	.	PUNCT
ap-652	575	1	j.	j.	PROPN
ap-652	575	2	achenbach	achenbach	PROPN
ap-652	575	3	,	,	PUNCT
ap-652	575	4	b.	b.	PROPN
ap-652	575	5	budiansky	budiansky	PROPN
ap-652	575	6	,	,	PUNCT
ap-652	575	7	h.a	h.a	PROPN
ap-652	575	8	.	.	PROPN
ap-652	575	9	lauwerier	lauwerier	PROPN
ap-652	575	10	,	,	PUNCT
ap-652	575	11	p.g	p.g	PROPN
ap-652	575	12	.	.	PROPN
ap-652	575	13	saffman	saffman	PROPN
ap-652	575	14	,	,	PUNCT
ap-652	575	15	l.	l.	PROPN
ap-652	575	16	van	van	PROPN
ap-652	575	17	wijngaarden	wijngaarden	PROPN
ap-652	575	18	,	,	PUNCT
ap-652	575	19	j.r	j.r	PROPN
ap-652	575	20	.	.	PROPN
ap-652	575	21	willis	willis	PROPN
ap-652	575	22	,	,	PUNCT
ap-652	575	23	north	north	NOUN
ap-652	575	24	-	-	PUNCT
ap-652	575	25	holland	holland	PROPN
ap-652	575	26	-	-	PUNCT
ap-652	575	27	amsterdam	amsterdam	PROPN
ap-652	575	28	,	,	PUNCT
ap-652	575	29	london	london	PROPN
ap-652	575	30	,	,	PUNCT
ap-652	575	31	new	new	PROPN
ap-652	575	32	york	york	PROPN
ap-652	575	33	,	,	PUNCT
ap-652	575	34	tokyo	tokyo	PROPN
ap-652	575	35	,	,	PUNCT
ap-652	575	36	1993	1993	NUM
ap-652	575	37	.	.	PUNCT
ap-652	576	1	[	[	X
ap-652	576	2	25	25	NUM
ap-652	576	3	]	]	PUNCT
ap-652	576	4	neves	neve	NOUN
ap-652	576	5	m.	m.	PROPN
ap-652	576	6	m	m	PROPN
ap-652	576	7	,	,	PUNCT
ap-652	576	8	guedes	guedes	PROPN
ap-652	576	9	j.	j.	PROPN
ap-652	576	10	m.	m.	PROPN
ap-652	576	11	,	,	PUNCT
ap-652	576	12	rodrigues	rodrigues	PROPN
ap-652	576	13	h.	h.	PROPN
ap-652	576	14	:	:	PUNCT
ap-652	576	15	“	"	PUNCT
ap-652	576	16	optimal	optimal	ADJ
ap-652	576	17	design	design	NOUN
ap-652	576	18	of	of	ADP
ap-652	576	19	periodic	periodic	ADJ
ap-652	576	20	linear	linear	ADJ
ap-652	576	21	elastic	elastic	ADJ
ap-652	576	22	microstructures	microstructure	NOUN
ap-652	576	23	.	.	PUNCT
ap-652	576	24	”	"	PUNCT
ap-652	577	1	comput	comput	NOUN
ap-652	577	2	.	.	PUNCT
ap-652	577	3	&	&	CCONJ
ap-652	577	4	struct	struct	PROPN
ap-652	577	5	.	.	PUNCT
ap-652	577	6	,	,	PUNCT
ap-652	577	7	vol	vol	NOUN
ap-652	577	8	.	.	PROPN
ap-652	578	1	76	76	NUM
ap-652	578	2	(	(	PUNCT
ap-652	578	3	2000	2000	NUM
ap-652	578	4	)	)	PUNCT
ap-652	578	5	,	,	PUNCT
ap-652	579	1	p.	p.	NOUN
ap-652	579	2	421–429	421–429	NUM
ap-652	579	3	.	.	PUNCT
ap-652	580	1	[	[	X
ap-652	580	2	26	26	NUM
ap-652	580	3	]	]	X
ap-652	580	4	noor	noor	PROPN
ap-652	580	5	a.	a.	PROPN
ap-652	580	6	k.	k.	PROPN
ap-652	580	7	:	:	PUNCT
ap-652	580	8	“	"	PUNCT
ap-652	580	9	continuum	continuum	ADJ
ap-652	580	10	modeling	modeling	NOUN
ap-652	580	11	for	for	ADP
ap-652	580	12	repetitive	repetitive	ADJ
ap-652	580	13	lattice	lattice	NOUN
ap-652	580	14	structures	structure	NOUN
ap-652	580	15	.	.	PUNCT
ap-652	580	16	”	"	PUNCT
ap-652	581	1	appl	appl	PROPN
ap-652	581	2	.	.	PROPN
ap-652	581	3	mech	mech	PROPN
ap-652	581	4	.	.	PUNCT
ap-652	582	1	rev	rev	PROPN
ap-652	582	2	.	.	PROPN
ap-652	582	3	,	,	PUNCT
ap-652	582	4	vol	vol	NOUN
ap-652	582	5	.	.	PROPN
ap-652	582	6	41	41	NUM
ap-652	582	7	(	(	PUNCT
ap-652	582	8	1988	1988	NUM
ap-652	582	9	)	)	PUNCT
ap-652	582	10	,	,	PUNCT
ap-652	582	11	p.	p.	NOUN
ap-652	582	12	285–296	285–296	NUM
ap-652	582	13	.	.	PUNCT
ap-652	583	1	[	[	X
ap-652	583	2	27	27	NUM
ap-652	583	3	]	]	X
ap-652	583	4	sigmund	sigmund	NOUN
ap-652	583	5	o.	o.	NOUN
ap-652	583	6	:	:	PUNCT
ap-652	583	7	“	"	PUNCT
ap-652	583	8	materials	material	NOUN
ap-652	583	9	with	with	ADP
ap-652	583	10	prescribed	prescribe	VERB
ap-652	583	11	constitutive	constitutive	ADJ
ap-652	583	12	parameters	parameter	NOUN
ap-652	583	13	:	:	PUNCT
ap-652	583	14	an	an	DET
ap-652	583	15	inverse	inverse	ADJ
ap-652	583	16	homogenization	homogenization	NOUN
ap-652	583	17	problem	problem	NOUN
ap-652	583	18	.	.	PUNCT
ap-652	583	19	”	"	PUNCT
ap-652	584	1	int	int	NOUN
ap-652	584	2	.	.	PUNCT
ap-652	585	1	j.	j.	PROPN
ap-652	585	2	solids	solids	PROPN
ap-652	585	3	struct	struct	NOUN
ap-652	585	4	.	.	PUNCT
ap-652	585	5	,	,	PUNCT
ap-652	585	6	vol	vol	NOUN
ap-652	585	7	.	.	PROPN
ap-652	585	8	31	31	NUM
ap-652	585	9	(	(	PUNCT
ap-652	585	10	1994	1994	NUM
ap-652	585	11	)	)	PUNCT
ap-652	585	12	,	,	PUNCT
ap-652	585	13	p.	p.	NOUN
ap-652	585	14	2313–2329	2313–2329	NUM
ap-652	585	15	.	.	PUNCT
ap-652	586	1	[	[	X
ap-652	586	2	28	28	NUM
ap-652	586	3	]	]	X
ap-652	586	4	suquet	suquet	NOUN
ap-652	586	5	p.	p.	NOUN
ap-652	586	6	m.	m.	NOUN
ap-652	586	7	:	:	PUNCT
ap-652	586	8	“	"	PUNCT
ap-652	586	9	elements	element	NOUN
ap-652	586	10	of	of	ADP
ap-652	586	11	homogenization	homogenization	NOUN
ap-652	586	12	for	for	ADP
ap-652	586	13	inelastic	inelastic	ADJ
ap-652	586	14	solid	solid	ADJ
ap-652	586	15	mechanics	mechanic	NOUN
ap-652	586	16	.	.	PUNCT
ap-652	586	17	”	"	PUNCT
ap-652	587	1	in	in	ADP
ap-652	587	2	:	:	PUNCT
ap-652	587	3	“	"	PUNCT
ap-652	587	4	homogenization	homogenization	NOUN
ap-652	587	5	techniques	technique	NOUN
ap-652	587	6	for	for	ADP
ap-652	587	7	composite	composite	ADJ
ap-652	587	8	media	medium	NOUN
ap-652	587	9	.	.	PUNCT
ap-652	587	10	”	"	PUNCT
ap-652	588	1	ed	ed	NOUN
ap-652	588	2	.	.	PUNCT
ap-652	588	3	e.	e.	PROPN
ap-652	588	4	sanchez	sanchez	PROPN
ap-652	588	5	-	-	PUNCT
ap-652	588	6	palencia	palencia	PROPN
ap-652	588	7	,	,	PUNCT
ap-652	588	8	a.	a.	NOUN
ap-652	588	9	zaoui	zaoui	PROPN
ap-652	588	10	,	,	PUNCT
ap-652	588	11	lecture	lecture	NOUN
ap-652	588	12	notes	note	NOUN
ap-652	588	13	in	in	ADP
ap-652	588	14	physics	physics	NOUN
ap-652	588	15	,	,	PUNCT
ap-652	588	16	272	272	NUM
ap-652	588	17	,	,	PUNCT
ap-652	588	18	springer	springer	NOUN
ap-652	588	19	-	-	PUNCT
ap-652	588	20	verlag	verlag	PROPN
ap-652	588	21	,	,	PUNCT
ap-652	588	22	1985	1985	NUM
ap-652	588	23	,	,	PUNCT
ap-652	588	24	p.	p.	NOUN
ap-652	588	25	193	193	NUM
ap-652	588	26	-	-	SYM
ap-652	588	27	278	278	NUM
ap-652	588	28	.	.	PUNCT
ap-652	589	1	[	[	X
ap-652	589	2	29	29	NUM
ap-652	589	3	]	]	X
ap-652	589	4	warren	warren	PROPN
ap-652	589	5	w.	w.	PROPN
ap-652	589	6	e.	e.	PROPN
ap-652	589	7	,	,	PUNCT
ap-652	589	8	kraynik	kraynik	PROPN
ap-652	589	9	a.	a.	NOUN
ap-652	589	10	m.	m.	PROPN
ap-652	589	11	:	:	PUNCT
ap-652	589	12	“	"	PUNCT
ap-652	589	13	the	the	DET
ap-652	589	14	linear	linear	ADJ
ap-652	589	15	elastic	elastic	ADJ
ap-652	589	16	properties	property	NOUN
ap-652	589	17	of	of	ADP
ap-652	589	18	open	open	ADJ
ap-652	589	19	-	-	PUNCT
ap-652	589	20	cell	cell	NOUN
ap-652	589	21	foams	foam	NOUN
ap-652	589	22	.	.	PUNCT
ap-652	589	23	”	"	PUNCT
ap-652	590	1	j.	j.	PROPN
ap-652	590	2	appl	appl	PROPN
ap-652	590	3	.	.	PROPN
ap-652	590	4	mech	mech	PROPN
ap-652	590	5	.	.	PROPN
ap-652	590	6	,	,	PUNCT
ap-652	590	7	asme	asme	PROPN
ap-652	590	8	,	,	PUNCT
ap-652	590	9	vol	vol	NOUN
ap-652	590	10	.	.	PUNCT
ap-652	591	1	55	55	NUM
ap-652	591	2	(	(	PUNCT
ap-652	591	3	1988	1988	NUM
ap-652	591	4	)	)	PUNCT
ap-652	591	5	,	,	PUNCT
ap-652	591	6	p.	p.	NOUN
ap-652	591	7	341–346	341–346	NUM
ap-652	591	8	.	.	PUNCT
ap-652	592	1	[	[	X
ap-652	592	2	30	30	NUM
ap-652	592	3	]	]	X
ap-652	592	4	warren	warren	PROPN
ap-652	592	5	w.	w.	PROPN
ap-652	592	6	e.	e.	PROPN
ap-652	592	7	,	,	PUNCT
ap-652	592	8	kraynik	kraynik	PROPN
ap-652	592	9	a.	a.	PROPN
ap-652	592	10	m.	m.	PROPN
ap-652	592	11	:	:	PUNCT
ap-652	592	12	“	"	PUNCT
ap-652	592	13	linear	linear	ADJ
ap-652	592	14	elastic	elastic	ADJ
ap-652	592	15	behavior	behavior	NOUN
ap-652	592	16	of	of	ADP
ap-652	592	17	a	a	DET
ap-652	592	18	low	low	ADJ
ap-652	592	19	-	-	PUNCT
ap-652	592	20	density	density	NOUN
ap-652	592	21	kelvin	kelvin	PROPN
ap-652	592	22	foam	foam	PROPN
ap-652	592	23	with	with	ADP
ap-652	592	24	open	open	ADJ
ap-652	592	25	cells	cell	NOUN
ap-652	592	26	.	.	PUNCT
ap-652	592	27	”	"	PUNCT
ap-652	593	1	j.	j.	PROPN
ap-652	593	2	appl	appl	PROPN
ap-652	593	3	.	.	PROPN
ap-652	593	4	mech	mech	PROPN
ap-652	593	5	.	.	PROPN
ap-652	593	6	,	,	PUNCT
ap-652	593	7	asme	asme	PROPN
ap-652	593	8	,	,	PUNCT
ap-652	593	9	vol	vol	NOUN
ap-652	593	10	.	.	PROPN
ap-652	593	11	64	64	NUM
ap-652	593	12	(	(	PUNCT
ap-652	593	13	1997	1997	NUM
ap-652	593	14	)	)	PUNCT
ap-652	593	15	,	,	PUNCT
ap-652	593	16	p.	p.	NOUN
ap-652	593	17	787–794	787–794	NUM
ap-652	593	18	.	.	PUNCT
ap-652	594	1	[	[	X
ap-652	594	2	31	31	NUM
ap-652	594	3	]	]	X
ap-652	594	4	zhu	zhu	PROPN
ap-652	594	5	h.	h.	PROPN
ap-652	594	6	x.	x.	PROPN
ap-652	594	7	,	,	PUNCT
ap-652	594	8	knott	knott	PROPN
ap-652	594	9	j.	j.	PROPN
ap-652	594	10	f.	f.	PROPN
ap-652	594	11	,	,	PUNCT
ap-652	594	12	mills	mills	PROPN
ap-652	594	13	n.	n.	PROPN
ap-652	594	14	j.	j.	PROPN
ap-652	594	15	:	:	PUNCT
ap-652	594	16	“	"	PUNCT
ap-652	594	17	analysis	analysis	NOUN
ap-652	594	18	of	of	ADP
ap-652	594	19	the	the	DET
ap-652	594	20	elastic	elastic	ADJ
ap-652	594	21	properties	property	NOUN
ap-652	594	22	of	of	ADP
ap-652	594	23	open	open	ADJ
ap-652	594	24	-	-	PUNCT
ap-652	594	25	cell	cell	NOUN
ap-652	594	26	foams	foam	NOUN
ap-652	594	27	with	with	ADP
ap-652	594	28	tetrakaidecahedral	tetrakaidecahedral	ADJ
ap-652	594	29	cells	cell	NOUN
ap-652	594	30	.	.	PUNCT
ap-652	594	31	”	"	PUNCT
ap-652	595	1	j.	j.	PROPN
ap-652	595	2	mech	mech	PROPN
ap-652	595	3	.	.	PUNCT
ap-652	596	1	phys	phy	NOUN
ap-652	596	2	.	.	PUNCT
ap-652	597	1	solids	solid	NOUN
ap-652	597	2	,	,	PUNCT
ap-652	597	3	vol	vol	NOUN
ap-652	597	4	.	.	PROPN
ap-652	598	1	45	45	NUM
ap-652	598	2	(	(	PUNCT
ap-652	598	3	1997	1997	NUM
ap-652	598	4	)	)	PUNCT
ap-652	598	5	,	,	PUNCT
ap-652	599	1	p.	p.	NOUN
ap-652	599	2	319–343	319–343	NUM
ap-652	599	3	.	.	PUNCT
ap-652	600	1	zuzana	zuzana	PROPN
ap-652	600	2	dimitrovová	dimitrovová	PROPN
ap-652	600	3	phone	phone	PROPN
ap-652	600	4	:	:	PUNCT
ap-652	600	5	+351	+351	PROPN
ap-652	600	6	218419462	218419462	NUM
ap-652	600	7	fax	fax	NOUN
ap-652	600	8	:	:	PUNCT
ap-652	600	9	+351	+351	NUM
ap-652	600	10	218417915	218417915	NUM
ap-652	600	11	e	e	NOUN
ap-652	600	12	-	-	NOUN
ap-652	600	13	mail	mail	NOUN
ap-652	600	14	:	:	PUNCT
ap-652	600	15	zdimitro@dem.ist.utl.pt	zdimitro@dem.ist.utl.pt	NOUN
ap-652	600	16	/	/	SYM
ap-652	600	17	zuzana@dem.isel.ipl.pt	zuzana@dem.isel.ipl.pt	NOUN
ap-652	600	18	dem	dem	ADJ
ap-652	600	19	/	/	SYM
ap-652	600	20	isel	isel	ADJ
ap-652	600	21	idmec	idmec	ADJ
ap-652	600	22	/	/	SYM
ap-652	600	23	ist	ist	PROPN
ap-652	600	24	instituto	instituto	PROPN
ap-652	600	25	superior	superior	PROPN
ap-652	600	26	técnico	técnico	PROPN
ap-652	600	27	av	av	PROPN
ap-652	600	28	.	.	PUNCT
ap-652	601	1	rovisco	rovisco	PROPN
ap-652	601	2	pais	pais	PROPN
ap-652	601	3	,	,	PUNCT
ap-652	601	4	1	1	NUM
ap-652	601	5	1049	1049	NUM
ap-652	601	6	-	-	PUNCT
ap-652	601	7	001	001	NUM
ap-652	601	8	lisbon	lisbon	PROPN
ap-652	601	9	,	,	PUNCT
ap-652	601	10	portugal	portugal	PROPN
ap-652	601	11	©	©	PROPN
ap-652	601	12	czech	czech	PROPN
ap-652	601	13	technical	technical	PROPN
ap-652	601	14	university	university	PROPN
ap-652	601	15	publishing	publishing	NOUN
ap-652	601	16	house	house	NOUN
ap-652	601	17	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-652	601	18	185	185	NUM
ap-652	601	19	acta	acta	PROPN
ap-652	601	20	polytechnica	polytechnica	PROPN
ap-652	601	21	vol	vol	NOUN
ap-652	601	22	.	.	PROPN
ap-652	602	1	44	44	NUM
ap-652	602	2	no.5–6/2004	no.5–6/2004	NOUN