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PROPN iajs-948 7 13 for for ADP iajs-948 7 14 pure pure ADJ iajs-948 7 15 & & CCONJ iajs-948 7 16 appl appl PROPN iajs-948 7 17 . . PUNCT iajs-948 8 1 sci sci PROPN iajs-948 8 2 . . PUNCT iajs-948 9 1 vol.23 vol.23 PROPN iajs-948 9 2 ( ( PUNCT iajs-948 9 3 2 2 NUM iajs-948 9 4 ) ) PUNCT iajs-948 9 5 2010 2010 NUM iajs-948 9 6 direct direct ADJ iajs-948 9 7 and and CCONJ iajs-948 9 8 inverse inverse NOUN iajs-948 9 9 inequalities inequality NOUN iajs-948 9 10 for for ADP iajs-948 9 11 jackson jackson PROPN iajs-948 9 12 polynomials polynomial NOUN iajs-948 9 13 of of ADP iajs-948 9 14 2periodic 2periodic ADJ iajs-948 9 15 bounded bounded ADJ iajs-948 9 16 measurable measurable ADJ iajs-948 9 17 functions function NOUN iajs-948 9 18 in in ADP iajs-948 9 19 locally locally ADV iajs-948 9 20 clobal clobal ADJ iajs-948 9 21 norms norm NOUN iajs-948 9 22 s.k.jassim s.k.jassim NOUN iajs-948 9 23 , , PUNCT iajs-948 9 24 n.j.mohamed n.j.mohamed ADJ iajs-948 9 25 department department NOUN iajs-948 9 26 of of ADP iajs-948 9 27 mathematics mathematics PROPN iajs-948 9 28 , , PUNCT iajs-948 9 29 college college NOUN iajs-948 9 30 of of ADP iajs-948 9 31 science science NOUN iajs-948 9 32 , , PUNCT iajs-948 9 33 university university PROPN iajs-948 9 34 of of ADP iajs-948 9 35 al al PROPN iajs-948 9 36 - - PUNCT iajs-948 9 37 mustansirya mustansirya PROPN iajs-948 9 38 department department NOUN iajs-948 9 39 of of ADP iajs-948 9 40 mathematics mathematics PROPN iajs-948 9 41 - - PUNCT iajs-948 9 42 ibn ibn PROPN iajs-948 9 43 - - PUNCT iajs-948 9 44 al al PROPN iajs-948 9 45 - - PUNCT iajs-948 9 46 haitham haitham PROPN iajs-948 9 47 , , PUNCT iajs-948 9 48 college college NOUN iajs-948 9 49 of of ADP iajs-948 9 50 education education NOUN iajs-948 9 51 , , PUNCT iajs-948 9 52 university university NOUN iajs-948 9 53 of of ADP iajs-948 9 54 baghdad baghdad PROPN iajs-948 9 55 abstract abstract ADJ iajs-948 9 56 convergence convergence NOUN iajs-948 9 57 properties property NOUN iajs-948 9 58 of of ADP iajs-948 9 59 jackson jackson PROPN iajs-948 9 60 polynomials polynomial NOUN iajs-948 9 61 have have AUX iajs-948 9 62 been be AUX iajs-948 9 63 considered consider VERB iajs-948 9 64 by by ADP iajs-948 9 65 zugmund zugmund NOUN iajs-948 10 1 [ [ X iajs-948 10 2 1,ch.x 1,ch.x X iajs-948 10 3 ] ] PUNCT iajs-948 10 4 in in ADP iajs-948 10 5 ( ( PUNCT iajs-948 10 6 1959 1959 NUM iajs-948 10 7 ) ) PUNCT iajs-948 10 8 and and CCONJ iajs-948 10 9 j.szbados j.szbado VERB iajs-948 11 1 [ [ X iajs-948 11 2 2 2 NUM iajs-948 11 3 ] ] PUNCT iajs-948 11 4 , , PUNCT iajs-948 11 5 ( ( PUNCT iajs-948 11 6 p= p= NOUN iajs-948 11 7 ) ) PUNCT iajs-948 11 8 while while SCONJ iajs-948 11 9 in in ADP iajs-948 11 10 ( ( PUNCT iajs-948 11 11 1983 1983 NUM iajs-948 11 12 ) ) PUNCT iajs-948 11 13 v.a.popov v.a.popov NOUN iajs-948 11 14 and and CCONJ iajs-948 11 15 j.szabados j.szabado VERB iajs-948 11 16 [ [ X iajs-948 11 17 3 3 NUM iajs-948 11 18 ] ] X iajs-948 11 19 ( ( PUNCT iajs-948 11 20 1 1 NUM iajs-948 11 21   NOUN iajs-948 11 22 p p NOUN iajs-948 11 23   NUM iajs-948 11 24   NOUN iajs-948 11 25 ) ) PUNCT iajs-948 11 26 have have AUX iajs-948 11 27 proved prove VERB iajs-948 11 28 a a DET iajs-948 11 29 direct direct ADJ iajs-948 11 30 inequality inequality NOUN iajs-948 11 31 for for ADP iajs-948 11 32 jackson jackson PROPN iajs-948 11 33 polynomials polynomial NOUN iajs-948 11 34 in in ADP iajs-948 11 35 lp lp NOUN iajs-948 11 36 - - PUNCT iajs-948 11 37 space space NOUN iajs-948 11 38 of of ADP iajs-948 11 39 2periodic 2periodic ADJ iajs-948 11 40 bounded bounded ADJ iajs-948 11 41 riemann riemann PROPN iajs-948 11 42 integrable integrable PROPN iajs-948 11 43 functions function NOUN iajs-948 11 44 ( ( PUNCT iajs-948 11 45 f f PROPN iajs-948 11 46   PROPN iajs-948 11 47 r r NOUN iajs-948 11 48 ) ) PUNCT iajs-948 11 49 in in ADP iajs-948 11 50 terms term NOUN iajs-948 11 51 of of ADP iajs-948 11 52 some some DET iajs-948 11 53 modulus modulus NOUN iajs-948 11 54 of of ADP iajs-948 11 55 continuity continuity NOUN iajs-948 11 56 . . PUNCT iajs-948 12 1 in in ADP iajs-948 12 2 1991 1991 NUM iajs-948 12 3 s.k.jassim s.k.jassim NOUN iajs-948 12 4 proved prove VERB iajs-948 12 5 direct direct ADJ iajs-948 12 6 and and CCONJ iajs-948 12 7 inverse inverse ADJ iajs-948 12 8 inequality inequality NOUN iajs-948 12 9 for for ADP iajs-948 12 10 jackson jackson PROPN iajs-948 12 11 polynomials polynomial NOUN iajs-948 12 12 in in ADP iajs-948 12 13 locally locally ADV iajs-948 12 14 global global ADJ iajs-948 12 15 norms norm NOUN iajs-948 12 16 ( ( PUNCT iajs-948 12 17 l,p l,p PROPN iajs-948 12 18 ) ) PUNCT iajs-948 12 19 of of ADP iajs-948 12 20 2-periodic 2-periodic NUM iajs-948 12 21 bounded bounded ADJ iajs-948 12 22 measurable measurable ADJ iajs-948 12 23 functions function NOUN iajs-948 12 24 ( ( PUNCT iajs-948 12 25 f f PROPN iajs-948 12 26   PROPN iajs-948 12 27 l l NUM iajs-948 12 28 ) ) PUNCT iajs-948 12 29 in in ADP iajs-948 12 30 terms term NOUN iajs-948 12 31 of of ADP iajs-948 12 32 suitable suitable ADJ iajs-948 12 33 peetre peetre NOUN iajs-948 12 34 k k NOUN iajs-948 12 35 - - ADJ iajs-948 12 36 functional functional ADJ iajs-948 12 37 [ [ X iajs-948 12 38 4 4 NUM iajs-948 12 39 ] ] PUNCT iajs-948 12 40 . . 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PUNCT iajs-948 23 35 , , PUNCT iajs-948 23 36 n n CCONJ iajs-948 23 37 ) ) PUNCT iajs-948 23 38 , , PUNCT iajs-948 23 39 f f PROPN iajs-948 23 40 f f PROPN iajs-948 23 41 n n PROPN iajs-948 23 42 1 1 NUM iajs-948 23 43   NOUN iajs-948 23 44   NUM iajs-948 23 45   NUM iajs-948 23 46   PROPN iajs-948 23 47   ADJ iajs-948 23 48   X iajs-948 23 49   NOUN iajs-948 23 50 . . PUNCT iajs-948 24 1 now now ADV iajs-948 24 2 let let VERB iajs-948 24 3 us we PRON iajs-948 24 4 consider consider VERB iajs-948 24 5 the the DET iajs-948 24 6 dirich dirich NOUN iajs-948 24 7 let let VERB iajs-948 24 8 kernel kernel NOUN iajs-948 24 9 of of ADP iajs-948 24 10 degree degree NOUN iajs-948 24 11 n n DET iajs-948 24 12 4 4 NUM iajs-948 24 13 . . PUNCT iajs-948 25 1 n n CCONJ iajs-948 25 2 n n ADV iajs-948 25 3 v v NOUN iajs-948 25 4 1 1 NUM iajs-948 25 5 1 1 NUM iajs-948 25 6 d d PROPN iajs-948 25 7 ( ( PUNCT iajs-948 25 8 u u NOUN iajs-948 25 9 ) ) PUNCT iajs-948 25 10 cos(vu cos(vu NOUN iajs-948 25 11 ) ) PUNCT iajs-948 26 1 2 2 NUM iajs-948 26 2   NUM iajs-948 26 3   PROPN iajs-948 26 4   NOUN iajs-948 26 5   PROPN iajs-948 26 6 ur ur PROPN iajs-948 26 7 , , PUNCT iajs-948 26 8 n=0,1 n=0,1 ADV iajs-948 26 9 , , PUNCT iajs-948 26 10 … … PUNCT iajs-948 26 11 then then ADV iajs-948 26 12 it it PRON iajs-948 26 13 is be AUX iajs-948 26 14 easy easy ADJ iajs-948 26 15 to to PART iajs-948 26 16 get get VERB iajs-948 26 17 the the DET iajs-948 26 18 following following NOUN iajs-948 26 19 : : PUNCT iajs-948 26 20 ihjpas ihjpa VERB iajs-948 26 21 ibn ibn PROPN iajs-948 26 22 alhaitham alhaitham PROPN iajs-948 26 23 j. j. PROPN iajs-948 26 24 for for ADP iajs-948 26 25 pure pure ADJ iajs-948 26 26 & & CCONJ iajs-948 26 27 appl appl PROPN iajs-948 26 28 . . PUNCT iajs-948 27 1 sci sci PROPN iajs-948 27 2 . . PUNCT iajs-948 28 1 vol.23 vol.23 PROPN iajs-948 28 2 ( ( PUNCT iajs-948 28 3 2 2 NUM iajs-948 28 4 ) ) PUNCT iajs-948 28 5 2010 2010 NUM iajs-948 28 6 n n CCONJ iajs-948 28 7 1 1 NUM iajs-948 28 8 sin(n sin(n PROPN iajs-948 28 9 ) ) PUNCT iajs-948 28 10 u u NOUN iajs-948 28 11 2d 2d X iajs-948 28 12 ( ( PUNCT iajs-948 28 13 u u NOUN iajs-948 28 14 ) ) PUNCT iajs-948 28 15 u u NOUN iajs-948 28 16 2sin 2sin NOUN iajs-948 28 17 ( ( PUNCT iajs-948 28 18 ) ) PUNCT iajs-948 28 19 2 2 NUM iajs-948 28 20   ADP iajs-948 28 21   NUM iajs-948 28 22 and and CCONJ iajs-948 28 23 n n NUM iajs-948 29 1 1 1 NUM iajs-948 29 2 d d NOUN iajs-948 29 3 ( ( PUNCT iajs-948 29 4 u u NOUN iajs-948 29 5 ) ) PUNCT iajs-948 29 6 1 1 NUM iajs-948 29 7   PROPN iajs-948 29 8   PROPN iajs-948 29 9   ADJ iajs-948 29 10   NOUN iajs-948 29 11   PROPN iajs-948 29 12 . . PUNCT iajs-948 30 1 5 5 X iajs-948 30 2 . . X iajs-948 30 3 let let VERB iajs-948 30 4 n n NOUN iajs-948 30 5 0 0 NUM iajs-948 30 6 1 1 NUM iajs-948 30 7 n n NUM iajs-948 30 8 1 1 NUM iajs-948 30 9 k k X iajs-948 30 10 ( ( PUNCT iajs-948 30 11 u u NOUN iajs-948 30 12 ) ) PUNCT iajs-948 31 1 [ [ X iajs-948 31 2 d d X iajs-948 31 3 ( ( PUNCT iajs-948 31 4 u u NOUN iajs-948 31 5 ) ) PUNCT iajs-948 31 6 d d NOUN iajs-948 31 7 ( ( PUNCT iajs-948 31 8 u u NOUN iajs-948 31 9 ) ) PUNCT iajs-948 31 10 ... ... PUNCT iajs-948 32 1 d d X iajs-948 32 2 ( ( PUNCT iajs-948 32 3 u u NOUN iajs-948 32 4 ) ) PUNCT iajs-948 32 5 ] ] PUNCT iajs-948 32 6 n n CCONJ iajs-948 32 7 1 1 NUM iajs-948 32 8   PROPN iajs-948 32 9   ADV iajs-948 32 10   PUNCT iajs-948 32 11   PUNCT iajs-948 32 12   VERB iajs-948 32 13 be be AUX iajs-948 32 14 the the DET iajs-948 32 15 fejer fejer ADJ iajs-948 32 16 kernel kernel NOUN iajs-948 32 17 of of ADP iajs-948 32 18 degree degree NOUN iajs-948 32 19 not not PART iajs-948 32 20 grater grater NOUN iajs-948 32 21 than than ADP iajs-948 32 22 n n CCONJ iajs-948 32 23 , , PUNCT iajs-948 32 24 also also ADV iajs-948 32 25 it it PRON iajs-948 32 26 is be AUX iajs-948 32 27 easy easy ADJ iajs-948 32 28 to to PART iajs-948 32 29 get get VERB iajs-948 32 30 the the DET iajs-948 32 31 following following NOUN iajs-948 32 32 : : PUNCT iajs-948 32 33 2 2 NUM iajs-948 32 34 n n CCONJ iajs-948 32 35 n n CCONJ iajs-948 32 36 n n ADV iajs-948 32 37 2 2 NUM iajs-948 32 38 k k SYM iajs-948 32 39 1 1 NUM iajs-948 32 40 u u NOUN iajs-948 32 41 sin sin NOUN iajs-948 32 42 ( ( PUNCT iajs-948 32 43 n n NOUN iajs-948 32 44 1)1 1)1 NUM iajs-948 32 45 1 1 NUM iajs-948 32 46 12k 12k X iajs-948 32 47 ( ( PUNCT iajs-948 32 48 u u NOUN iajs-948 32 49 ) ) PUNCT iajs-948 32 50 , , PUNCT iajs-948 32 51 k k PROPN iajs-948 32 52 ( ( PUNCT iajs-948 32 53 u u NOUN iajs-948 32 54 ) ) PUNCT iajs-948 32 55 ( ( PUNCT iajs-948 32 56 n n X iajs-948 32 57 k k PROPN iajs-948 32 58 1)cos(ku 1)cos(ku X iajs-948 32 59 ) ) PUNCT iajs-948 32 60 u2(n u2(n PROPN iajs-948 32 61 1 1 NUM iajs-948 32 62 ) ) SYM iajs-948 32 63 2 2 NUM iajs-948 32 64 n n SYM iajs-948 32 65 1 1 NUM iajs-948 32 66 sin sin NOUN iajs-948 32 67 ( ( PUNCT iajs-948 32 68 ) ) PUNCT iajs-948 32 69 2 2 NUM iajs-948 32 70   NOUN iajs-948 32 71   ADV iajs-948 32 72   PROPN iajs-948 32 73   PROPN iajs-948 32 74   ADV iajs-948 32 75   PROPN iajs-948 32 76   ADV iajs-948 32 77   CCONJ iajs-948 32 78   PUNCT iajs-948 32 79   X iajs-948 32 80 and and CCONJ iajs-948 32 81 nk nk PROPN iajs-948 32 82 ( ( PUNCT iajs-948 32 83 u u NOUN iajs-948 32 84 ) ) PUNCT iajs-948 32 85 du du PROPN iajs-948 33 1 1 1 NUM iajs-948 33 2   PROPN iajs-948 33 3   ADV iajs-948 33 4   PROPN iajs-948 33 5 . . PUNCT iajs-948 34 1 6 6 NUM iajs-948 34 2 . . NUM iajs-948 34 3 n n CCONJ iajs-948 34 4 n n ADV iajs-948 34 5 k k NOUN iajs-948 34 6 , , PUNCT iajs-948 34 7 n n PROPN iajs-948 34 8 n n CCONJ iajs-948 34 9 k k NOUN iajs-948 34 10 , , PUNCT iajs-948 34 11 n n PROPN iajs-948 34 12 k k NOUN iajs-948 34 13 0 0 NUM iajs-948 34 14 2 2 NUM iajs-948 34 15 j j PROPN iajs-948 34 16 ( ( PUNCT iajs-948 34 17 f f PROPN iajs-948 34 18 , , PUNCT iajs-948 34 19 x x X iajs-948 34 20 ) ) PUNCT iajs-948 34 21 f f NOUN iajs-948 34 22 ( ( PUNCT iajs-948 34 23 x x X iajs-948 34 24 ) ) PUNCT iajs-948 34 25 k k NOUN iajs-948 34 26 ( ( PUNCT iajs-948 34 27 x x NOUN iajs-948 34 28 x x X iajs-948 34 29 ) ) PUNCT iajs-948 34 30 n n CCONJ iajs-948 34 31 2 2 NUM iajs-948 34 32   NUM iajs-948 34 33   PROPN iajs-948 34 34   PROPN iajs-948 34 35   PUNCT iajs-948 34 36   X iajs-948 34 37 is be AUX iajs-948 34 38 the the DET iajs-948 34 39 so so ADV iajs-948 34 40 called call VERB iajs-948 34 41 jackson jackson PROPN iajs-948 34 42 polynomial polynomial PROPN iajs-948 34 43 of of ADP iajs-948 34 44 function function PROPN iajs-948 35 1 f f PROPN iajs-948 35 2   NOUN iajs-948 36 1 l. l. PRON iajs-948 36 2 now now ADV iajs-948 36 3 we we PRON iajs-948 36 4 will will AUX iajs-948 36 5 use use VERB iajs-948 36 6 the the DET iajs-948 36 7 so so ADV iajs-948 36 8 called call VERB iajs-948 36 9 average average ADJ iajs-948 36 10 modulus modulus NOUN iajs-948 36 11 of of ADP iajs-948 36 12 continuity continuity NOUN iajs-948 36 13 to to PART iajs-948 36 14 solve solve VERB iajs-948 36 15 the the DET iajs-948 36 16 problem problem NOUN iajs-948 36 17 in in ADP iajs-948 36 18 locally locally ADV iajs-948 36 19 global global ADJ iajs-948 36 20 norm norm NOUN iajs-948 36 21 ( ( PUNCT iajs-948 36 22 l,p l,p PROPN iajs-948 36 23 ) ) PUNCT iajs-948 36 24 . . PUNCT iajs-948 37 1 the the DET iajs-948 37 2 locally locally ADV iajs-948 37 3 modulus modulus NOUN iajs-948 37 4 of of ADP iajs-948 37 5 continuity continuity NOUN iajs-948 37 6 for for ADP iajs-948 37 7 ( ( PUNCT iajs-948 37 8 f f PROPN iajs-948 37 9   PROPN iajs-948 37 10 l l NUM iajs-948 37 11 ) ) PUNCT iajs-948 37 12 is be AUX iajs-948 37 13 defined define VERB iajs-948 37 14 by by ADP iajs-948 37 15 7 7 NUM iajs-948 37 16 . . NUM iajs-948 37 17 n n CCONJ iajs-948 38 1 n n ADP iajs-948 38 2 h h NOUN iajs-948 38 3 h h NOUN iajs-948 38 4 ( ( PUNCT iajs-948 38 5 f f X iajs-948 38 6 , , PUNCT iajs-948 38 7 x x PROPN iajs-948 38 8 , , PUNCT iajs-948 38 9 h h NOUN iajs-948 38 10 ) ) PUNCT iajs-948 38 11 sup sup NOUN iajs-948 38 12 f f PROPN iajs-948 38 13 ( ( PUNCT iajs-948 38 14 x x NOUN iajs-948 38 15 ' ' NUM iajs-948 38 16 ) ) PUNCT iajs-948 38 17 f f NOUN iajs-948 38 18 ( ( PUNCT iajs-948 38 19 x x PROPN iajs-948 38 20 ) ) PUNCT iajs-948 38 21 , , PUNCT iajs-948 38 22 x x PRON iajs-948 38 23 ' ' NOUN iajs-948 38 24 , , PUNCT iajs-948 38 25 x x PUNCT iajs-948 38 26 x x X iajs-948 38 27 , , PUNCT iajs-948 38 28 x x SYM iajs-948 38 29 2 2 NUM iajs-948 38 30 2 2 NUM iajs-948 38 31   X iajs-948 38 32   ADP iajs-948 38 33   VERB iajs-948 38 34   VERB iajs-948 38 35   PROPN iajs-948 38 36   PROPN iajs-948 38 37   PROPN iajs-948 38 38   NOUN iajs-948 38 39   NOUN iajs-948 38 40   VERB iajs-948 39 1   DET iajs-948 39 2   ADJ iajs-948 39 3   PROPN iajs-948 39 4 , , PUNCT iajs-948 39 5 h h NOUN iajs-948 39 6 is be AUX iajs-948 39 7 a a DET iajs-948 39 8 constant constant ADJ iajs-948 39 9 number number NOUN iajs-948 39 10 while while SCONJ iajs-948 39 11 kth kth PROPN iajs-948 39 12 average average ADJ iajs-948 39 13 modulus modulus NOUN iajs-948 39 14 of of ADP iajs-948 39 15 smoothness smoothness NOUN iajs-948 39 16 for for ADP iajs-948 39 17 flp flp NOUN iajs-948 39 18 is be AUX iajs-948 39 19 defined define VERB iajs-948 39 20 by by ADP iajs-948 39 21 : : PUNCT iajs-948 39 22 8 8 NUM iajs-948 39 23 . . PUNCT iajs-948 40 1 p p X iajs-948 40 2 p p X iajs-948 40 3 k k PROPN iajs-948 40 4 l l PROPN iajs-948 41 1 k k X iajs-948 42 1 l l NOUN iajs-948 43 1 ( ( PUNCT iajs-948 43 2 f f PROPN iajs-948 43 3 , , PUNCT iajs-948 43 4 ) ) PUNCT iajs-948 43 5 ( ( PUNCT iajs-948 43 6 f f X iajs-948 43 7 , , PUNCT iajs-948 43 8 , , PUNCT iajs-948 43 9 ) ) PUNCT iajs-948 43 10   PROPN iajs-948 43 11   NUM iajs-948 43 12   X iajs-948 43 13   PROPN iajs-948 43 14   NOUN iajs-948 43 15   NUM iajs-948 43 16 1 1 NUM iajs-948 43 17   NOUN iajs-948 43 18 p p NOUN iajs-948 43 19   NUM iajs-948 43 20   NOUN iajs-948 43 21 , , PUNCT iajs-948 43 22   NUM iajs-948 43 23 > > X iajs-948 43 24 0 0 PROPN iajs-948 43 25 and and CCONJ iajs-948 43 26 k k PROPN iajs-948 43 27 . . PUNCT iajs-948 44 1 where where SCONJ iajs-948 44 2 the the DET iajs-948 44 3 kth kth PROPN iajs-948 44 4 modulus modulus NOUN iajs-948 44 5 of of ADP iajs-948 44 6 smoothness smoothness NOUN iajs-948 44 7 for for ADP iajs-948 44 8 flp flp NOUN iajs-948 44 9 , , PUNCT iajs-948 44 10 k k PROPN iajs-948 44 11 is be AUX iajs-948 44 12 defined define VERB iajs-948 44 13 by by ADP iajs-948 44 14 : : PUNCT iajs-948 44 15 9 9 NUM iajs-948 44 16 . . X iajs-948 45 1 k k PROPN iajs-948 46 1 k k PROPN iajs-948 46 2 h h PROPN iajs-948 47 1 k k PROPN iajs-948 47 2 k k PROPN iajs-948 47 3 ( ( PUNCT iajs-948 47 4 f f PROPN iajs-948 47 5 , , PUNCT iajs-948 47 6 x x NOUN iajs-948 47 7 , , PUNCT iajs-948 47 8 ) ) PUNCT iajs-948 47 9 sup sup NOUN iajs-948 47 10 f f PROPN iajs-948 47 11 ( ( PUNCT iajs-948 47 12 t t PROPN iajs-948 47 13 ) ) PUNCT iajs-948 47 14 : : PUNCT iajs-948 48 1 t t PROPN iajs-948 48 2 , , PUNCT iajs-948 48 3 t t PROPN iajs-948 48 4 kh kh PROPN iajs-948 48 5 x x X iajs-948 48 6 , , PUNCT iajs-948 48 7 x x PUNCT iajs-948 48 8 x x SYM iajs-948 48 9 2 2 NUM iajs-948 48 10 2 2 NUM iajs-948 48 11   NUM iajs-948 48 12   NUM iajs-948 48 13   PROPN iajs-948 48 14   NUM iajs-948 48 15   ADP iajs-948 48 16   PART iajs-948 48 17   NOUN iajs-948 48 18   NOUN iajs-948 48 19   NOUN iajs-948 48 20   VERB iajs-948 48 21   PROPN iajs-948 48 22   PROPN iajs-948 48 23   PUNCT iajs-948 48 24   PROPN iajs-948 48 25   VERB iajs-948 49 1   DET iajs-948 49 2   ADJ iajs-948 50 1   PROPN iajs-948 50 2 . . PUNCT iajs-948 51 1 now now ADV iajs-948 51 2 we we PRON iajs-948 51 3 set set VERB iajs-948 51 4 k k PROPN iajs-948 51 5 k k PROPN iajs-948 51 6 m m VERB iajs-948 51 7 k k NOUN iajs-948 51 8 m m VERB iajs-948 51 9 0h 0h PROPN iajs-948 51 10 k k PROPN iajs-948 51 11 ( ( PUNCT iajs-948 51 12 1 1 X iajs-948 51 13 ) ) PUNCT iajs-948 51 14 f(x f(x PROPN iajs-948 51 15 mh mh PROPN iajs-948 51 16 ) ) PUNCT iajs-948 51 17 if if SCONJ iajs-948 51 18 x x PRON iajs-948 51 19 or or CCONJ iajs-948 51 20 x x SYM iajs-948 51 21 h h NOUN iajs-948 51 22 x x X iajs-948 51 23 f f X iajs-948 51 24 ( ( PUNCT iajs-948 51 25 x x X iajs-948 51 26 ) ) PUNCT iajs-948 51 27 m m VERB iajs-948 51 28 0 0 NUM iajs-948 51 29 otherwise otherwise ADV iajs-948 51 30 . . PUNCT iajs-948 52 1   VERB iajs-948 52 2   PRON iajs-948 52 3   ADP iajs-948 52 4   NOUN iajs-948 52 5   PROPN iajs-948 52 6   PROPN iajs-948 52 7   PUNCT iajs-948 52 8   ADV iajs-948 52 9   PUNCT iajs-948 52 10   PROPN iajs-948 52 11   PROPN iajs-948 52 12   PROPN iajs-948 52 13   NUM iajs-948 52 14   PROPN iajs-948 52 15   NOUN iajs-948 52 16   PRON iajs-948 52 17   NUM iajs-948 52 18   X iajs-948 52 19 then then ADV iajs-948 52 20 we we PRON iajs-948 52 21 introduce introduce VERB iajs-948 52 22 the the DET iajs-948 52 23 definition definition NOUN iajs-948 52 24 of of ADP iajs-948 52 25 kth kth PROPN iajs-948 52 26 local local ADJ iajs-948 52 27 modulus modulus NOUN iajs-948 52 28 of of ADP iajs-948 52 29 lp lp NOUN iajs-948 52 30 - - NOUN iajs-948 52 31 continuity continuity NOUN iajs-948 52 32 for for ADP iajs-948 52 33 flp flp NOUN iajs-948 52 34 , , PUNCT iajs-948 52 35 ( ( PUNCT iajs-948 52 36 1p 1p NUM iajs-948 52 37 ) ) PUNCT iajs-948 52 38 and and CCONJ iajs-948 52 39 k k PROPN iajs-948 52 40 . . PUNCT iajs-948 53 1 10 10 NUM iajs-948 53 2 . . X iajs-948 53 3 1 1 NUM iajs-948 53 4 ( ( PUNCT iajs-948 53 5 x x NOUN iajs-948 53 6 ) ) PUNCT iajs-948 54 1 p p X iajs-948 54 2 p p X iajs-948 54 3 k k PROPN iajs-948 54 4 k k PROPN iajs-948 54 5 p p PROPN iajs-948 54 6 h h NOUN iajs-948 54 7 ( ( PUNCT iajs-948 54 8 x x X iajs-948 54 9 ) ) PUNCT iajs-948 54 10 1 1 NUM iajs-948 54 11 ( ( PUNCT iajs-948 54 12 f f PROPN iajs-948 54 13 , , PUNCT iajs-948 54 14 x x PROPN iajs-948 54 15 , , PUNCT iajs-948 54 16 ( ( PUNCT iajs-948 54 17 x x NOUN iajs-948 54 18 ) ) PUNCT iajs-948 54 19 ) ) PUNCT iajs-948 55 1 f f PROPN iajs-948 55 2 ( ( PUNCT iajs-948 55 3 x x X iajs-948 55 4 ) ) PUNCT iajs-948 55 5 dv dv PROPN iajs-948 55 6 2 2 NUM iajs-948 55 7 ( ( PUNCT iajs-948 55 8 x x X iajs-948 55 9 ) ) PUNCT iajs-948 55 10   NUM iajs-948 55 11   NUM iajs-948 55 12   PROPN iajs-948 55 13   NUM iajs-948 55 14   NUM iajs-948 55 15   PROPN iajs-948 55 16   PROPN iajs-948 55 17   NOUN iajs-948 55 18   PROPN iajs-948 55 19   PROPN iajs-948 55 20   PROPN iajs-948 55 21   PROPN iajs-948 55 22   PROPN iajs-948 55 23   PROPN iajs-948 55 24   PUNCT iajs-948 55 25 where where SCONJ iajs-948 55 26 (x (x NUM iajs-948 55 27 ) ) PUNCT iajs-948 55 28 is be AUX iajs-948 55 29 an an DET iajs-948 55 30 arbitrary arbitrary ADJ iajs-948 55 31 positive positive ADJ iajs-948 55 32 function function NOUN iajs-948 55 33 of of ADP iajs-948 55 34 x x PRON iajs-948 55 35 , , PUNCT iajs-948 55 36 but but CCONJ iajs-948 55 37 here here ADV iajs-948 55 38 we we PRON iajs-948 55 39 shall shall AUX iajs-948 55 40 consider consider VERB iajs-948 55 41 only only ADV iajs-948 55 42 the the DET iajs-948 55 43 case case NOUN iajs-948 55 44 (x (x NUM iajs-948 55 45 ) ) PUNCT iajs-948 55 46 is be AUX iajs-948 55 47 constant constant ADJ iajs-948 55 48 . . PUNCT iajs-948 56 1 the the DET iajs-948 56 2 k k PROPN iajs-948 56 3 th th X iajs-948 56 4 average average ADJ iajs-948 56 5 modulus modulus NOUN iajs-948 56 6 of of ADP iajs-948 56 7 smoothness smoothness NOUN iajs-948 56 8 was be AUX iajs-948 56 9 first first ADV iajs-948 56 10 introduced introduce VERB iajs-948 56 11 by by ADP iajs-948 56 12 b.sendov b.sendov NOUN iajs-948 56 13 in in ADP iajs-948 56 14 1983 1983 NUM iajs-948 56 15 and and CCONJ iajs-948 56 16 proved prove VERB iajs-948 56 17 to to PART iajs-948 56 18 be be AUX iajs-948 56 19 very very ADV iajs-948 56 20 useful useful ADJ iajs-948 56 21 in in ADP iajs-948 56 22 some some DET iajs-948 56 23 approximation approximation NOUN iajs-948 56 24 theoretical theoretical ADJ iajs-948 56 25 problems problem NOUN iajs-948 56 26 where where SCONJ iajs-948 56 27 the the DET iajs-948 56 28 ordinary ordinary ADJ iajs-948 56 29 modulus modulus NOUN iajs-948 56 30 of of ADP iajs-948 56 31 continuity continuity NOUN iajs-948 56 32 (f, (f, NOUN iajs-948 56 33 ) ) PUNCT iajs-948 56 34 is be AUX iajs-948 56 35 defined define VERB iajs-948 56 36 by by ADP iajs-948 56 37 the the DET iajs-948 56 38 following following NOUN iajs-948 56 39 : : PUNCT iajs-948 57 1 11 11 NUM iajs-948 57 2 . . X iajs-948 57 3 (f,)=sup{f(x (f,)=sup{f(x NOUN iajs-948 57 4 ' ' PUNCT iajs-948 57 5 ) ) PUNCT iajs-948 57 6 – – PUNCT iajs-948 57 7 f(x'') f(x'') NOUN iajs-948 57 8 , , PUNCT iajs-948 57 9 x x NOUN iajs-948 57 10 ' ' PUNCT iajs-948 57 11 – – PUNCT iajs-948 57 12 x" x" PROPN iajs-948 57 13   NUM iajs-948 57 14 , , PUNCT iajs-948 57 15 x x PRON iajs-948 57 16 ' ' NUM iajs-948 57 17 , , PUNCT iajs-948 57 18 x"x x"x NOUN iajs-948 57 19 } } PUNCT iajs-948 57 20 . . PUNCT iajs-948 58 1 while while SCONJ iajs-948 58 2 the the DET iajs-948 58 3 k k PROPN iajs-948 58 4 th th X iajs-948 58 5 ordinary ordinary ADJ iajs-948 58 6 modulus modulus NOUN iajs-948 58 7 of of ADP iajs-948 58 8 continuity continuity NOUN iajs-948 58 9 is be AUX iajs-948 58 10 defined define VERB iajs-948 58 11 by by ADP iajs-948 58 12 the the DET iajs-948 58 13 following following NOUN iajs-948 58 14 : : PUNCT iajs-948 59 1 12 12 NUM iajs-948 59 2 . . PUNCT iajs-948 60 1   NOUN iajs-948 60 2 k k NOUN iajs-948 60 3 k k PROPN iajs-948 60 4 h(f h(f X iajs-948 60 5 , , PUNCT iajs-948 60 6 ) ) PUNCT iajs-948 60 7 sup sup NOUN iajs-948 60 8 f f PROPN iajs-948 60 9 ( ( PUNCT iajs-948 60 10 x x NOUN iajs-948 60 11 ) ) PUNCT iajs-948 60 12 : : PUNCT iajs-948 61 1 h h NOUN iajs-948 61 2 , , PUNCT iajs-948 61 3 x x X iajs-948 61 4 , , PUNCT iajs-948 61 5 x x PROPN iajs-948 61 6 kh kh PROPN iajs-948 61 7 x x PROPN iajs-948 62 1   PROPN iajs-948 62 2   PROPN iajs-948 62 3   ADJ iajs-948 62 4   NOUN iajs-948 62 5   VERB iajs-948 62 6   NOUN iajs-948 62 7 . . PUNCT iajs-948 63 1 now now ADV iajs-948 63 2 let let VERB iajs-948 63 3 us we PRON iajs-948 63 4 consider consider VERB iajs-948 63 5 the the DET iajs-948 63 6 definition definition NOUN iajs-948 63 7 of of ADP iajs-948 63 8 ordinary ordinary ADJ iajs-948 63 9 lp lp ADJ iajs-948 63 10 - - PUNCT iajs-948 63 11 modulus modulus NOUN iajs-948 63 12 of of ADP iajs-948 63 13 continuity continuity NOUN iajs-948 63 14 ( ( PUNCT iajs-948 63 15 (f,)p (f,)p X iajs-948 63 16 ) ) PUNCT iajs-948 63 17 . . PUNCT iajs-948 64 1 ihjpas ihjpa VERB iajs-948 64 2 ibn ibn PROPN iajs-948 64 3 alhaitham alhaitham PROPN iajs-948 64 4 j. j. PROPN iajs-948 64 5 for for ADP iajs-948 64 6 pure pure ADJ iajs-948 64 7 & & CCONJ iajs-948 64 8 appl appl PROPN iajs-948 64 9 . . PUNCT iajs-948 65 1 sci sci PROPN iajs-948 65 2 . . PUNCT iajs-948 66 1 vol.23 vol.23 PROPN iajs-948 66 2 ( ( PUNCT iajs-948 66 3 2 2 NUM iajs-948 66 4 ) ) PUNCT iajs-948 66 5 2010 2010 NUM iajs-948 66 6 13 13 NUM iajs-948 66 7 . . PUNCT iajs-948 67 1 p p X iajs-948 67 2 p p X iajs-948 67 3 l l PROPN iajs-948 67 4 l l NOUN iajs-948 67 5 t t NOUN iajs-948 67 6 ( ( PUNCT iajs-948 67 7 f f PROPN iajs-948 67 8 , , PUNCT iajs-948 67 9 ) ) PUNCT iajs-948 67 10 sup sup NOUN iajs-948 67 11 f f PROPN iajs-948 67 12 ( ( PUNCT iajs-948 67 13 t t PROPN iajs-948 67 14 ) ) PUNCT iajs-948 67 15 f f PROPN iajs-948 67 16 ( ( PUNCT iajs-948 67 17 ) ) PUNCT iajs-948 67 18   NUM iajs-948 67 19   PROPN iajs-948 67 20   NUM iajs-948 67 21   NOUN iajs-948 67 22   ADJ iajs-948 67 23   PROPN iajs-948 67 24   PUNCT iajs-948 67 25   NOUN iajs-948 67 26   PROPN iajs-948 67 27 for for ADP iajs-948 67 28   NUM iajs-948 67 29 constant constant ADJ iajs-948 67 30 and and CCONJ iajs-948 67 31 14 14 NUM iajs-948 67 32 . . PUNCT iajs-948 68 1   PRON iajs-948 68 2 k k NOUN iajs-948 68 3 k k PROPN iajs-948 68 4 h h PROPN iajs-948 68 5 p p NOUN iajs-948 68 6 ( ( PUNCT iajs-948 68 7 f f PROPN iajs-948 68 8 , , PUNCT iajs-948 68 9 ) ) PUNCT iajs-948 68 10 sup sup NOUN iajs-948 68 11 f f PROPN iajs-948 68 12 ( ( PUNCT iajs-948 68 13 ) ) PUNCT iajs-948 68 14 : : PUNCT iajs-948 68 15 h h PROPN iajs-948 68 16   NUM iajs-948 68 17   PROPN iajs-948 68 18   ADJ iajs-948 68 19   DET iajs-948 68 20   NOUN iajs-948 68 21 also also ADV iajs-948 68 22 for for ADP iajs-948 68 23   NUM iajs-948 68 24 constant constant ADJ iajs-948 68 25 , , PUNCT iajs-948 68 26 be be AUX iajs-948 68 27 the the DET iajs-948 68 28 kth kth PROPN iajs-948 68 29 ordinary ordinary ADJ iajs-948 68 30 lp lp ADJ iajs-948 68 31 - - PUNCT iajs-948 68 32 modulus modulus NOUN iajs-948 68 33 of of ADP iajs-948 68 34 continuity continuity NOUN iajs-948 68 35 of of ADP iajs-948 68 36 flp flp NOUN iajs-948 68 37 . . PUNCT iajs-948 69 1 now now ADV iajs-948 69 2 for for ADP iajs-948 69 3 flp flp NOUN iajs-948 69 4 instead instead ADV iajs-948 69 5 of of ADP iajs-948 69 6 usual usual ADJ iajs-948 69 7 sup sup NOUN iajs-948 69 8 - - PUNCT iajs-948 69 9 norm norm NOUN iajs-948 69 10 , , PUNCT iajs-948 69 11 let let VERB iajs-948 69 12 us we PRON iajs-948 69 13 consider consider VERB iajs-948 69 14 the the DET iajs-948 69 15 family family NOUN iajs-948 69 16 of of ADP iajs-948 69 17 semi semi ADJ iajs-948 69 18 norm norm NOUN iajs-948 69 19 ( ( PUNCT iajs-948 69 20 locally locally ADV iajs-948 69 21 global global ADJ iajs-948 69 22 norm norm NOUN iajs-948 69 23 ) ) PUNCT iajs-948 69 24 for for ADP iajs-948 69 25   NUM iajs-948 69 26 > > X iajs-948 69 27 0 0 NUM iajs-948 69 28 , , PUNCT iajs-948 69 29 ( ( PUNCT iajs-948 69 30 1p 1p NUM iajs-948 69 31 ) ) PUNCT iajs-948 69 32 . . PUNCT iajs-948 70 1 15 15 NUM iajs-948 70 2 . . NOUN iajs-948 70 3 1 1 NUM iajs-948 70 4 p p NOUN iajs-948 70 5 p p NOUN iajs-948 70 6 , , PUNCT iajs-948 70 7 p p X iajs-948 70 8 x x X iajs-948 70 9 f f X iajs-948 70 10 f f PROPN iajs-948 70 11 ( ( PUNCT iajs-948 70 12 x x X iajs-948 70 13 ) ) PUNCT iajs-948 70 14 dx dx NOUN iajs-948 70 15   NOUN iajs-948 70 16   PROPN iajs-948 71 1   PROPN iajs-948 72 1   PROPN iajs-948 72 2   PROPN iajs-948 73 1   ADJ iajs-948 73 2   NOUN iajs-948 73 3   PUNCT iajs-948 73 4 , , PUNCT iajs-948 73 5 where where SCONJ iajs-948 73 6 f(x)=sup{f(t):tu(,x f(x)=sup{f(t):tu(,x NOUN iajs-948 73 7 ) ) PUNCT iajs-948 73 8 } } PUNCT iajs-948 73 9 and and CCONJ iajs-948 73 10 u(,x)={yx:x u(,x)={yx:x PROPN iajs-948 73 11 – – PUNCT iajs-948 73 12 y y NOUN iajs-948 73 13 } } PUNCT iajs-948 73 14 . . PUNCT iajs-948 74 1 the the DET iajs-948 74 2 main main ADJ iajs-948 74 3 property property NOUN iajs-948 74 4 of of ADP iajs-948 74 5 these these DET iajs-948 74 6 semi semi ADJ iajs-948 74 7 norm norm NOUN iajs-948 74 8 is be AUX iajs-948 74 9 that that SCONJ iajs-948 74 10 they they PRON iajs-948 74 11 do do AUX iajs-948 74 12 not not PART iajs-948 74 13 necessarily necessarily ADV iajs-948 74 14 vanish vanish VERB iajs-948 74 15 if if SCONJ iajs-948 74 16 f f PROPN iajs-948 74 17 = = SYM iajs-948 74 18 0 0 NUM iajs-948 74 19 lebesgue lebesgue NOUN iajs-948 74 20 almost almost ADV iajs-948 74 21 every every PRON iajs-948 74 22 where where SCONJ iajs-948 74 23 . . PUNCT iajs-948 75 1 let let VERB iajs-948 75 2 us we PRON iajs-948 75 3 denoted denote VERB iajs-948 75 4 by by ADP iajs-948 75 5 l,p l,p ADP iajs-948 75 6 the the DET iajs-948 75 7 set set NOUN iajs-948 75 8 of of ADP iajs-948 75 9 functions function NOUN iajs-948 75 10 from from ADP iajs-948 75 11 l l NUM iajs-948 75 12 which which PRON iajs-948 75 13 equipped equip VERB iajs-948 75 14 with with ADP iajs-948 75 15 semi semi ADJ iajs-948 75 16 norm norm NOUN iajs-948 75 17 , , PUNCT iajs-948 75 18 p p PROPN iajs-948 75 19   NOUN iajs-948 75 20 . . PUNCT iajs-948 76 1 by by ADP iajs-948 76 2 tn tn PROPN iajs-948 76 3 we we PRON iajs-948 76 4 denote denote VERB iajs-948 76 5 the the DET iajs-948 76 6 set set NOUN iajs-948 76 7 of of ADP iajs-948 76 8 all all DET iajs-948 76 9 trigonometric trigonometric ADJ iajs-948 76 10 polynomials polynomial NOUN iajs-948 76 11 in in ADP iajs-948 76 12 r r NOUN iajs-948 76 13 of of ADP iajs-948 76 14 degree degree NOUN iajs-948 76 15 not not PART iajs-948 76 16 greater great ADJ iajs-948 76 17 than than SCONJ iajs-948 76 18 n. n. VERB iajs-948 76 19 the the DET iajs-948 76 20 best good ADJ iajs-948 76 21 approximation approximation NOUN iajs-948 76 22 to to ADP iajs-948 76 23 a a DET iajs-948 76 24 given give VERB iajs-948 76 25 continuous continuous ADJ iajs-948 76 26 function function NOUN iajs-948 76 27 with with ADP iajs-948 76 28 trigonometric trigonometric ADJ iajs-948 76 29 polynomials polynomial NOUN iajs-948 76 30 from from ADP iajs-948 76 31 tn tn NOUN iajs-948 76 32 on on ADP iajs-948 76 33 the the DET iajs-948 76 34 interval interval NOUN iajs-948 76 35 x x PUNCT iajs-948 76 36 is be AUX iajs-948 76 37 given give VERB iajs-948 76 38 by by ADP iajs-948 76 39 : : PUNCT iajs-948 76 40 16 16 NUM iajs-948 76 41 . . PUNCT iajs-948 77 1   NOUN iajs-948 77 2 t t PROPN iajs-948 77 3 n n X iajs-948 77 4 ne ne X iajs-948 77 5 ( ( PUNCT iajs-948 77 6 f f X iajs-948 77 7 : : PUNCT iajs-948 77 8 x x X iajs-948 77 9 ) ) PUNCT iajs-948 77 10 inf inf PROPN iajs-948 77 11 f f PROPN iajs-948 77 12 ( ( PUNCT iajs-948 77 13 ) ) PUNCT iajs-948 77 14 t t PROPN iajs-948 77 15 ( ( PUNCT iajs-948 77 16 ) ) PUNCT iajs-948 77 17 : : PUNCT iajs-948 77 18 t t X iajs-948 77 19 t t NOUN iajs-948 77 20   VERB iajs-948 77 21   ADJ iajs-948 77 22   ADJ iajs-948 77 23   NOUN iajs-948 77 24   PROPN iajs-948 77 25   NOUN iajs-948 77 26 . . PUNCT iajs-948 78 1 while while SCONJ iajs-948 78 2 the the DET iajs-948 78 3 best good ADJ iajs-948 78 4 approximation approximation NOUN iajs-948 78 5 of of ADP iajs-948 78 6 a a DET iajs-948 78 7 function function NOUN iajs-948 78 8 flp(x flp(x PROPN iajs-948 78 9 ) ) PUNCT iajs-948 78 10 with with ADP iajs-948 78 11 trigonometric trigonometric ADJ iajs-948 78 12 polynomials polynomial NOUN iajs-948 78 13 from from ADP iajs-948 78 14 tn tn NOUN iajs-948 78 15 in in ADP iajs-948 78 16 the the DET iajs-948 78 17 metric metric NOUN iajs-948 78 18 of of ADP iajs-948 78 19 the the DET iajs-948 78 20 space space NOUN iajs-948 78 21 lp lp NOUN iajs-948 78 22 is be AUX iajs-948 78 23 given give VERB iajs-948 78 24 by by ADP iajs-948 78 25 : : PUNCT iajs-948 78 26 17 17 NUM iajs-948 78 27 . . PUNCT iajs-948 79 1   NOUN iajs-948 79 2 t t PROPN iajs-948 79 3 n n PROPN iajs-948 79 4 p p X iajs-948 79 5 np np INTJ iajs-948 79 6 e e X iajs-948 79 7 ( ( PUNCT iajs-948 79 8 f f PROPN iajs-948 79 9 ) ) PUNCT iajs-948 79 10 inf inf PROPN iajs-948 79 11 f f PROPN iajs-948 79 12 ( ( PUNCT iajs-948 79 13 ) ) PUNCT iajs-948 79 14 t t PROPN iajs-948 79 15 ( ( PUNCT iajs-948 79 16 ) ) PUNCT iajs-948 79 17 : : PUNCT iajs-948 79 18 t t X iajs-948 79 19 t t PROPN iajs-948 79 20   VERB iajs-948 79 21   PROPN iajs-948 79 22   PROPN iajs-948 79 23   NOUN iajs-948 79 24 . . PUNCT iajs-948 80 1 we we PRON iajs-948 80 2 also also ADV iajs-948 80 3 define define VERB iajs-948 80 4 the the DET iajs-948 80 5 best good ADJ iajs-948 80 6 approximation approximation NOUN iajs-948 80 7 of of ADP iajs-948 80 8 a a DET iajs-948 80 9 function function NOUN iajs-948 80 10 fl(x fl(x NOUN iajs-948 80 11 ) ) PUNCT iajs-948 80 12 with with ADP iajs-948 80 13 trigonometric trigonometric ADJ iajs-948 80 14 polynomials polynomial NOUN iajs-948 80 15 from from ADP iajs-948 80 16 tn tn NOUN iajs-948 80 17 in in ADP iajs-948 80 18 the the DET iajs-948 80 19 metric metric NOUN iajs-948 80 20 of of ADP iajs-948 80 21 the the DET iajs-948 80 22 spaces space NOUN iajs-948 80 23 lp lp ADV iajs-948 80 24 or or CCONJ iajs-948 80 25 l,p l,p PROPN iajs-948 80 26 are be AUX iajs-948 80 27 respectively respectively ADV iajs-948 80 28 given give VERB iajs-948 80 29 by by ADP iajs-948 80 30 : : PUNCT iajs-948 80 31 18 18 NUM iajs-948 80 32 . . X iajs-948 81 1   NOUN iajs-948 81 2 t t PROPN iajs-948 81 3 n n NOUN iajs-948 81 4 , , PUNCT iajs-948 81 5 p p NOUN iajs-948 81 6 n n NOUN iajs-948 81 7 , , PUNCT iajs-948 81 8 p p X iajs-948 81 9 ( ( PUNCT iajs-948 81 10 x x SYM iajs-948 81 11 ) ) PUNCT iajs-948 81 12 e e NOUN iajs-948 81 13 ( ( PUNCT iajs-948 81 14 f f PROPN iajs-948 81 15 ) ) PUNCT iajs-948 81 16 inf inf PROPN iajs-948 81 17 f f PROPN iajs-948 81 18 ( ( PUNCT iajs-948 81 19 ) ) PUNCT iajs-948 81 20 t t PROPN iajs-948 81 21 ( ( PUNCT iajs-948 81 22 ) ) PUNCT iajs-948 81 23 : : PUNCT iajs-948 81 24 t t X iajs-948 81 25 t t NUM iajs-948 82 1   NUM iajs-948 82 2   ADJ iajs-948 82 3   ADJ iajs-948 82 4   NOUN iajs-948 82 5   PROPN iajs-948 82 6   NOUN iajs-948 82 7 . . PUNCT iajs-948 83 1 the the DET iajs-948 83 2 best good ADJ iajs-948 83 3 one one NUM iajs-948 83 4 sided sided ADJ iajs-948 83 5 approximation approximation NOUN iajs-948 83 6 of of ADP iajs-948 83 7 a a DET iajs-948 83 8 function function NOUN iajs-948 83 9 fl(x fl(x NOUN iajs-948 83 10 ) ) PUNCT iajs-948 83 11 with with ADP iajs-948 83 12 trigonometric trigonometric ADJ iajs-948 83 13 polynomials polynomial NOUN iajs-948 83 14 from from ADP iajs-948 83 15 tn tn NOUN iajs-948 83 16 in in ADP iajs-948 83 17 the the DET iajs-948 83 18 metric metric NOUN iajs-948 83 19 of of ADP iajs-948 83 20 the the DET iajs-948 83 21 space space NOUN iajs-948 83 22 lp lp NOUN iajs-948 83 23 or or CCONJ iajs-948 83 24 l,p l,p PROPN iajs-948 83 25 are be AUX iajs-948 83 26 respectively respectively ADV iajs-948 83 27 given give VERB iajs-948 83 28 by by ADP iajs-948 83 29 19 19 NUM iajs-948 83 30 . . PUNCT iajs-948 84 1   NOUN iajs-948 84 2 t t PROPN iajs-948 84 3 n n PROPN iajs-948 84 4 p p NOUN iajs-948 84 5 n n CCONJ iajs-948 84 6 n n NOUN iajs-948 84 7 np(x np(x NUM iajs-948 84 8 ) ) PUNCT iajs-948 84 9 e e NOUN iajs-948 84 10 ( ( PUNCT iajs-948 84 11 f f X iajs-948 84 12 ) ) PUNCT iajs-948 84 13 inf inf PROPN iajs-948 84 14 t t PROPN iajs-948 84 15 ( ( PUNCT iajs-948 84 16 ) ) PUNCT iajs-948 84 17 t t PROPN iajs-948 84 18 ( ( PUNCT iajs-948 84 19 ) ) PUNCT iajs-948 84 20 : : PUNCT iajs-948 84 21 t t PROPN iajs-948 84 22 t t PROPN iajs-948 84 23 , , PUNCT iajs-948 84 24 t t PROPN iajs-948 84 25 ( ( PUNCT iajs-948 84 26 x x X iajs-948 84 27 ) ) PUNCT iajs-948 84 28 f f PROPN iajs-948 84 29 ( ( PUNCT iajs-948 84 30 x x X iajs-948 84 31 ) ) PUNCT iajs-948 84 32 t t PROPN iajs-948 84 33 ( ( PUNCT iajs-948 84 34 x x NOUN iajs-948 84 35 ) ) PUNCT iajs-948 84 36 , , PUNCT iajs-948 84 37 x x SYM iajs-948 84 38 x x NOUN iajs-948 84 39   PROPN iajs-948 84 40   PROPN iajs-948 84 41   ADJ iajs-948 84 42   PROPN iajs-948 84 43   NOUN iajs-948 84 44   VERB iajs-948 84 45   NOUN iajs-948 84 46   NOUN iajs-948 84 47   NOUN iajs-948 84 48   NOUN iajs-948 84 49 . . PUNCT iajs-948 85 1 20 20 NUM iajs-948 85 2 . . PUNCT iajs-948 86 1   NOUN iajs-948 86 2 t t PROPN iajs-948 86 3 n n NOUN iajs-948 86 4 , , PUNCT iajs-948 86 5 p p NOUN iajs-948 86 6 n n CCONJ iajs-948 86 7 n n CCONJ iajs-948 86 8 n n CCONJ iajs-948 86 9 , , PUNCT iajs-948 86 10 p(x p(x PROPN iajs-948 86 11 ) ) PUNCT iajs-948 86 12 e e NOUN iajs-948 86 13 ( ( PUNCT iajs-948 86 14 f f PROPN iajs-948 86 15 ) ) PUNCT iajs-948 86 16 inf inf PROPN iajs-948 86 17 t t PROPN iajs-948 86 18 ( ( PUNCT iajs-948 86 19 ) ) PUNCT iajs-948 86 20 t t PROPN iajs-948 86 21 ( ( PUNCT iajs-948 86 22 ) ) PUNCT iajs-948 86 23 : : PUNCT iajs-948 86 24 t t PROPN iajs-948 86 25 t t PROPN iajs-948 86 26 , , PUNCT iajs-948 86 27 t t PROPN iajs-948 86 28 ( ( PUNCT iajs-948 86 29 x x X iajs-948 86 30 ) ) PUNCT iajs-948 86 31 f f PROPN iajs-948 86 32 ( ( PUNCT iajs-948 86 33 x x X iajs-948 86 34 ) ) PUNCT iajs-948 86 35 t t PROPN iajs-948 86 36 ( ( PUNCT iajs-948 86 37 x x NOUN iajs-948 86 38 ) ) PUNCT iajs-948 86 39 , , PUNCT iajs-948 86 40 x x PROPN iajs-948 86 41 x x PROPN iajs-948 86 42   NUM iajs-948 86 43   ADJ iajs-948 86 44   PROPN iajs-948 86 45   PROPN iajs-948 86 46   ADJ iajs-948 86 47   PROPN iajs-948 86 48   NOUN iajs-948 86 49   VERB iajs-948 86 50   NOUN iajs-948 86 51   NOUN iajs-948 86 52   NOUN iajs-948 86 53   NOUN iajs-948 86 54 . . PUNCT iajs-948 87 1 now now ADV iajs-948 87 2 let let VERB iajs-948 87 3 f f PRON iajs-948 87 4 be be AUX iajs-948 87 5 a a DET iajs-948 87 6 function function NOUN iajs-948 87 7 defined define VERB iajs-948 87 8 on on ADP iajs-948 87 9 a a DET iajs-948 87 10 domain domain NOUN iajs-948 88 1 d d NOUN iajs-948 88 2 then then ADV iajs-948 88 3 the the DET iajs-948 88 4 stecklov stecklov ADJ iajs-948 88 5 transformation transformation NOUN iajs-948 88 6 is be AUX iajs-948 88 7 given give VERB iajs-948 88 8 by by ADP iajs-948 88 9 21 21 NUM iajs-948 88 10 . . PUNCT iajs-948 89 1 1/ 1/ NUM iajs-948 89 2 n n CCONJ iajs-948 89 3 n n PROPN iajs-948 89 4 1/ 1/ NUM iajs-948 89 5 n n CCONJ iajs-948 89 6 n n NOUN iajs-948 89 7 f f PROPN iajs-948 89 8 ( ( PUNCT iajs-948 89 9 x x X iajs-948 89 10 ) ) PUNCT iajs-948 89 11 f f NOUN iajs-948 89 12 ( ( PUNCT iajs-948 89 13 x x X iajs-948 89 14 t)dt t)dt PROPN iajs-948 89 15 2 2 NUM iajs-948 89 16   NOUN iajs-948 89 17   NOUN iajs-948 89 18   PROPN iajs-948 89 19 . . PUNCT iajs-948 90 1 let let VERB iajs-948 90 2 f f PROPN iajs-948 90 3 and and CCONJ iajs-948 90 4 g g PROPN iajs-948 90 5 be be VERB iajs-948 90 6 two two NUM iajs-948 90 7 functions function NOUN iajs-948 90 8 then then ADV iajs-948 90 9 we we PRON iajs-948 90 10 say say VERB iajs-948 90 11 that that SCONJ iajs-948 90 12 f(x f(x PROPN iajs-948 90 13 ) ) PUNCT iajs-948 91 1 = = PUNCT iajs-948 91 2 o{g(x o{g(x NUM iajs-948 91 3 ) ) PUNCT iajs-948 91 4 } } PUNCT iajs-948 91 5 if if SCONJ iajs-948 91 6 f(x) > X iajs-948 100 64 0 0 NUM iajs-948 100 65 ) ) PUNCT iajs-948 100 66 , , PUNCT iajs-948 100 67 ( ( PUNCT iajs-948 100 68 1 1 NUM iajs-948 100 69   NOUN iajs-948 100 70 p p NOUN iajs-948 100 71   NOUN iajs-948 100 72   NOUN iajs-948 100 73 ) ) PUNCT iajs-948 100 74 . . PUNCT iajs-948 101 1 22 22 NUM iajs-948 101 2 . . PUNCT iajs-948 102 1   NOUN iajs-948 102 2 1 1 VERB iajs-948 102 3 1 1 NUM iajs-948 103 1 p p NOUN iajs-948 103 2 p p X iajs-948 103 3 pp pp ADP iajs-948 103 4 p p PROPN iajs-948 103 5 k(f k(f PROPN iajs-948 103 6 , , PUNCT iajs-948 103 7 t t PROPN iajs-948 103 8 , , PUNCT iajs-948 103 9 l l PROPN iajs-948 103 10 , , PUNCT iajs-948 103 11 w w PROPN iajs-948 103 12 ) ) PUNCT iajs-948 103 13 inf inf NOUN iajs-948 103 14 f f PROPN iajs-948 103 15 g g PROPN iajs-948 103 16 t t PROPN iajs-948 103 17 g g NOUN iajs-948 103 18 ' ' PUNCT iajs-948 103 19 : : PUNCT iajs-948 103 20 g g PROPN iajs-948 103 21 w w VERB iajs-948 103 22   PROPN iajs-948 103 23   PUNCT iajs-948 103 24   NOUN iajs-948 103 25 , , PUNCT iajs-948 103 26 23 23 NUM iajs-948 103 27 . . PUNCT iajs-948 104 1   NOUN iajs-948 104 2 1 1 VERB iajs-948 104 3 1 1 NUM iajs-948 104 4 t t PROPN iajs-948 104 5 , , PUNCT iajs-948 104 6 p p X iajs-948 104 7 p p X iajs-948 104 8 pt pt PROPN iajs-948 104 9 , , PUNCT iajs-948 104 10 p p X iajs-948 104 11 p p X iajs-948 104 12 k(f k(f PROPN iajs-948 104 13 ; ; PUNCT iajs-948 104 14 t t PROPN iajs-948 104 15 , , PUNCT iajs-948 104 16 l l PROPN iajs-948 104 17 , , PUNCT iajs-948 104 18 w w PROPN iajs-948 104 19 ) ) PUNCT iajs-948 104 20 inf inf NOUN iajs-948 104 21 f f PROPN iajs-948 104 22 g g PROPN iajs-948 104 23 t t PROPN iajs-948 104 24 g g NOUN iajs-948 104 25 ' ' PUNCT iajs-948 104 26 : : PUNCT iajs-948 104 27 g g PROPN iajs-948 104 28 w w VERB iajs-948 104 29   PROPN iajs-948 104 30   PUNCT iajs-948 104 31   NOUN iajs-948 104 32 , , PUNCT iajs-948 104 33 24 24 NUM iajs-948 104 34 . . PUNCT iajs-948 105 1   NOUN iajs-948 105 2 1 1 VERB iajs-948 105 3 1 1 NUM iajs-948 105 4 1 1 NUM iajs-948 105 5 1 1 NUM iajs-948 105 6 p p NOUN iajs-948 105 7 p p NOUN iajs-948 105 8 p p X iajs-948 105 9 p p NOUN iajs-948 106 1 pp pp ADP iajs-948 106 2 p p PROPN iajs-948 106 3 p p PROPN iajs-948 106 4 k(f k(f PROPN iajs-948 106 5 , , PUNCT iajs-948 106 6 t t PROPN iajs-948 106 7 , , PUNCT iajs-948 106 8 l l PROPN iajs-948 106 9 , , PUNCT iajs-948 106 10 w w PROPN iajs-948 106 11 , , PUNCT iajs-948 106 12 w w PROPN iajs-948 106 13 ) ) PUNCT iajs-948 106 14 inf inf NOUN iajs-948 107 1 f f PROPN iajs-948 107 2 g g PROPN iajs-948 107 3 t t PROPN iajs-948 107 4 g g PROPN iajs-948 107 5 ' ' PUNCT iajs-948 107 6 t t NOUN iajs-948 107 7 g g NOUN iajs-948 107 8 : : PUNCT iajs-948 107 9 g g PROPN iajs-948 107 10 w w PROPN iajs-948 107 11 w w VERB iajs-948 107 12   PROPN iajs-948 107 13   PUNCT iajs-948 107 14   PUNCT iajs-948 107 15   PROPN iajs-948 107 16   PROPN iajs-948 107 17   NOUN iajs-948 107 18 , , PUNCT iajs-948 107 19 25 25 NUM iajs-948 107 20 . . PUNCT iajs-948 108 1   NOUN iajs-948 108 2 1 1 VERB iajs-948 108 3 1 1 NUM iajs-948 108 4 1 1 NUM iajs-948 108 5 1 1 NUM iajs-948 108 6 t t NOUN iajs-948 108 7 , , PUNCT iajs-948 108 8 p p X iajs-948 108 9 p p X iajs-948 108 10 p p X iajs-948 108 11 p p X iajs-948 108 12 pt pt NOUN iajs-948 108 13 , , PUNCT iajs-948 108 14 p p X iajs-948 108 15 p p X iajs-948 108 16 p p X iajs-948 108 17 k(f k(f PROPN iajs-948 108 18 , , PUNCT iajs-948 108 19 t t PROPN iajs-948 108 20 , , PUNCT iajs-948 108 21 l l PROPN iajs-948 108 22 , , PUNCT iajs-948 108 23 w w PROPN iajs-948 108 24 , , PUNCT iajs-948 108 25 w w PROPN iajs-948 108 26 ) ) PUNCT iajs-948 108 27 inf inf NOUN iajs-948 109 1 f f PROPN iajs-948 109 2 g g PROPN iajs-948 109 3 t t PROPN iajs-948 109 4 g g PROPN iajs-948 109 5 ' ' PUNCT iajs-948 109 6 t t NOUN iajs-948 109 7 g g NOUN iajs-948 109 8 ' ' PUNCT iajs-948 109 9 : : PUNCT iajs-948 109 10 g g PROPN iajs-948 109 11 w w PROPN iajs-948 109 12 w w VERB iajs-948 109 13   PROPN iajs-948 109 14   PUNCT iajs-948 109 15   PUNCT iajs-948 109 16   NOUN iajs-948 109 17   NOUN iajs-948 109 18   NOUN iajs-948 109 19 . . PUNCT iajs-948 110 1 next next ADJ iajs-948 110 2 bernstein bernstein PROPN iajs-948 110 3 inequalities inequality NOUN iajs-948 110 4 are be AUX iajs-948 110 5 given give VERB iajs-948 110 6 since since SCONJ iajs-948 110 7 we we PRON iajs-948 110 8 use use VERB iajs-948 110 9 them they PRON iajs-948 110 10 further far ADV iajs-948 110 11 on on ADP iajs-948 110 12 26 26 NUM iajs-948 110 13 . . PUNCT iajs-948 110 14 ' ' PUNCT iajs-948 111 1 n n CCONJ iajs-948 111 2 n n CCONJ iajs-948 111 3 n n CCONJ iajs-948 111 4 npp npp PROPN iajs-948 111 5 t t PROPN iajs-948 111 6 n n PROPN iajs-948 111 7 t t PROPN iajs-948 111 8 , , PUNCT iajs-948 111 9 t t PROPN iajs-948 111 10 t t PROPN iajs-948 111 11 , , PUNCT iajs-948 111 12 1 1 NUM iajs-948 111 13 p p NOUN iajs-948 111 14 . . PUNCT iajs-948 112 1   NOUN iajs-948 112 2   NOUN iajs-948 112 3   NOUN iajs-948 112 4   VERB iajs-948 112 5 27 27 NUM iajs-948 112 6 . . PUNCT iajs-948 112 7 ' ' PUNCT iajs-948 113 1 n n CCONJ iajs-948 113 2 n n CCONJ iajs-948 113 3 n n CCONJ iajs-948 113 4 npp npp PROPN iajs-948 113 5 t t PROPN iajs-948 113 6 n n PROPN iajs-948 113 7 t t PROPN iajs-948 113 8 , , PUNCT iajs-948 113 9 t t PROPN iajs-948 113 10 t t PROPN iajs-948 113 11 , , PUNCT iajs-948 113 12 1 1 NUM iajs-948 113 13 p p NOUN iajs-948 113 14 . . PUNCT iajs-948 113 15   NOUN iajs-948 113 16   NUM iajs-948 113 17   NOUN iajs-948 113 18   PRON iajs-948 113 19 1assertions 1assertions PROPN iajs-948 113 20 1.1 1.1 NUM iajs-948 113 21 lemma lemma PROPN iajs-948 113 22 : : PUNCT iajs-948 113 23 [ [ X iajs-948 113 24 3 3 X iajs-948 113 25 ] ] X iajs-948 113 26 let let VERB iajs-948 113 27 f f PROPN iajs-948 113 28   PROPN iajs-948 113 29 lp lp ADP iajs-948 113 30 , , PUNCT iajs-948 113 31 then then ADV iajs-948 113 32 ( ( PUNCT iajs-948 113 33 1p 1p NUM iajs-948 113 34 ) ) PUNCT iajs-948 113 35 28 28 NUM iajs-948 113 36 . . PUNCT iajs-948 114 1 p p NOUN iajs-948 114 2 n n PROPN iajs-948 114 3 1 1 NUM iajs-948 114 4 n n NOUN iajs-948 114 5 pp pp ADJ iajs-948 114 6 n n ADV iajs-948 114 7 kp kp PROPN iajs-948 114 8 k k PROPN iajs-948 114 9 0 0 NUM iajs-948 114 10 1 1 NUM iajs-948 114 11 j j PROPN iajs-948 114 12 ( ( PUNCT iajs-948 114 13 f f PROPN iajs-948 114 14 , , PUNCT iajs-948 114 15 ) ) PUNCT iajs-948 114 16 o(1 o(1 PROPN iajs-948 114 17 ) ) PUNCT iajs-948 114 18 f f PROPN iajs-948 114 19 ( ( PUNCT iajs-948 114 20 t t PROPN iajs-948 114 21 ) ) PUNCT iajs-948 114 22 o o NOUN iajs-948 115 1 f f PROPN iajs-948 116 1 n n ADV iajs-948 116 2   VERB iajs-948 116 3   ADP iajs-948 117 1   NOUN iajs-948 117 2   PRON iajs-948 118 1   PROPN iajs-948 118 2   PROPN iajs-948 119 1   INTJ iajs-948 119 2   PROPN iajs-948 119 3   PROPN iajs-948 119 4   PROPN iajs-948 119 5   X iajs-948 119 6 . . PUNCT iajs-948 120 1 1.2 1.2 NUM iajs-948 120 2 lemma lemma PROPN iajs-948 120 3 : : PUNCT iajs-948 120 4 [ [ X iajs-948 120 5 5 5 NUM iajs-948 120 6 ] ] PUNCT iajs-948 120 7 let let VERB iajs-948 120 8 t t PROPN iajs-948 120 9   PROPN iajs-948 120 10 tn tn PROPN iajs-948 120 11 , , PUNCT iajs-948 120 12 then then ADV iajs-948 120 13 ( ( PUNCT iajs-948 120 14 1p 1p NUM iajs-948 120 15 ) ) PUNCT iajs-948 120 16 29 29 NUM iajs-948 120 17 . . PUNCT iajs-948 120 18 1 1 NUM iajs-948 120 19 p p NOUN iajs-948 120 20 , , PUNCT iajs-948 120 21 p p X iajs-948 120 22 ( ( PUNCT iajs-948 120 23 ) ) PUNCT iajs-948 120 24 p p X iajs-948 120 25 ( ( PUNCT iajs-948 120 26 ) ) PUNCT iajs-948 120 27 t t PROPN iajs-948 120 28 c(1 c(1 PROPN iajs-948 120 29 n n PROPN iajs-948 120 30 ) ) PUNCT iajs-948 120 31 t t PROPN iajs-948 121 1   NUM iajs-948 121 2   PROPN iajs-948 121 3   PROPN iajs-948 121 4   ADP iajs-948 121 5   NOUN iajs-948 121 6   PUNCT iajs-948 121 7 . . PUNCT iajs-948 122 1 1.3 1.3 NUM iajs-948 122 2 lemma lemma NOUN iajs-948 122 3 : : PUNCT iajs-948 123 1 [ [ X iajs-948 123 2 3 3 X iajs-948 123 3 ] ] PUNCT iajs-948 123 4 for for ADP iajs-948 123 5 f f PROPN iajs-948 123 6 , , PUNCT iajs-948 123 7 f f PROPN iajs-948 123 8 ' ' NUM iajs-948 123 9   NOUN iajs-948 123 10 lp lp INTJ iajs-948 123 11 we we PRON iajs-948 123 12 have have VERB iajs-948 123 13 ( ( PUNCT iajs-948 123 14 1p 1p NUM iajs-948 123 15 ) ) PUNCT iajs-948 123 16 30 30 NUM iajs-948 123 17 . . PUNCT iajs-948 124 1 p p X iajs-948 124 2 p p X iajs-948 124 3 l l NOUN iajs-948 124 4 ( ( PUNCT iajs-948 124 5 f f PROPN iajs-948 124 6 , , PUNCT iajs-948 124 7 h h NOUN iajs-948 124 8 ) ) PUNCT iajs-948 124 9 o(h o(h PROPN iajs-948 124 10 ) ) PUNCT iajs-948 124 11 f f NOUN iajs-948 125 1 ' ' PUNCT iajs-948 125 2   X iajs-948 125 3   NOUN iajs-948 125 4 , , PUNCT iajs-948 125 5 h h NOUN iajs-948 125 6 is be AUX iajs-948 125 7 constant constant ADJ iajs-948 125 8 . . PUNCT iajs-948 126 1 1.4 1.4 NUM iajs-948 126 2 lemma lemma PROPN iajs-948 126 3 : : PUNCT iajs-948 126 4 [ [ X iajs-948 126 5 6 6 NUM iajs-948 126 6 ] ] PUNCT iajs-948 126 7 let let VERB iajs-948 126 8 f f PROPN iajs-948 126 9   PROPN iajs-948 126 10 l l NUM iajs-948 126 11 , , PUNCT iajs-948 126 12 then then ADV iajs-948 126 13 we we PRON iajs-948 126 14 have have VERB iajs-948 126 15 ( ( PUNCT iajs-948 126 16 1p 1p NUM iajs-948 126 17 ) ) PUNCT iajs-948 126 18 31 31 NUM iajs-948 126 19 . . PUNCT iajs-948 127 1 1 1 NUM iajs-948 127 2 p p NOUN iajs-948 127 3 1 1 NUM iajs-948 127 4 p p NOUN iajs-948 127 5 1(f 1(f NUM iajs-948 127 6 , , PUNCT iajs-948 127 7 ) ) PUNCT iajs-948 127 8 ( ( PUNCT iajs-948 127 9 f f NOUN iajs-948 127 10 , , PUNCT iajs-948 127 11 ) ) PUNCT iajs-948 127 12 ( ( PUNCT iajs-948 127 13 f f NOUN iajs-948 127 14 , , PUNCT iajs-948 127 15 ) ) PUNCT iajs-948 127 16   PROPN iajs-948 127 17   NUM iajs-948 127 18   NOUN iajs-948 127 19   NUM iajs-948 127 20   PROPN iajs-948 127 21   NUM iajs-948 127 22   PROPN iajs-948 127 23   PROPN iajs-948 127 24 . . PUNCT iajs-948 128 1 1.5 1.5 NUM iajs-948 128 2 lemma lemma NOUN iajs-948 128 3 : : PUNCT iajs-948 128 4 [ [ X iajs-948 128 5 7 7 X iajs-948 128 6 ] ] X iajs-948 128 7 let let VERB iajs-948 128 8 f f PROPN iajs-948 128 9   PROPN iajs-948 128 10 l l NUM iajs-948 128 11 , , PUNCT iajs-948 128 12 then then ADV iajs-948 128 13 we we PRON iajs-948 128 14 have have VERB iajs-948 128 15 ( ( PUNCT iajs-948 128 16 1p 1p NUM iajs-948 128 17 ) ) PUNCT iajs-948 128 18 32 32 NUM iajs-948 128 19 . . PUNCT iajs-948 129 1 p p NOUN iajs-948 129 2 m m VERB iajs-948 129 3 1 1 NUM iajs-948 129 4 , , PUNCT iajs-948 129 5 p p NOUN iajs-948 129 6 m m NOUN iajs-948 129 7 f f NOUN iajs-948 129 8 c c PROPN iajs-948 129 9 f f NOUN iajs-948 129 10   ADJ iajs-948 129 11 , , PUNCT iajs-948 129 12 ( ( PUNCT iajs-948 129 13 m m NOUN iajs-948 129 14 = = SYM iajs-948 129 15 1 1 NUM iajs-948 129 16 , , PUNCT iajs-948 129 17 2 2 NUM iajs-948 129 18 , , PUNCT iajs-948 129 19 3 3 NUM iajs-948 129 20 , , PUNCT iajs-948 129 21 … … PUNCT iajs-948 129 22 ) ) PUNCT iajs-948 129 23 . . PUNCT iajs-948 130 1 1.6 1.6 NUM iajs-948 130 2 lemma lemma PROPN iajs-948 130 3 : : PUNCT iajs-948 130 4 [ [ X iajs-948 130 5 8 8 NUM iajs-948 130 6 ] ] PUNCT iajs-948 130 7 for for ADP iajs-948 130 8 f f PROPN iajs-948 130 9   PROPN iajs-948 130 10 l l NUM iajs-948 130 11 , , PUNCT iajs-948 130 12 we we PRON iajs-948 130 13 have have VERB iajs-948 130 14 33 33 NUM iajs-948 130 15 . . PUNCT iajs-948 131 1 p p X iajs-948 131 2 ( ( PUNCT iajs-948 131 3 ) ) PUNCT iajs-948 131 4 , , PUNCT iajs-948 131 5 p p X iajs-948 131 6 ( ( PUNCT iajs-948 131 7 ) ) PUNCT iajs-948 131 8 , , PUNCT iajs-948 131 9 ( ( PUNCT iajs-948 131 10 ) ) PUNCT iajs-948 131 11 ( ( PUNCT iajs-948 131 12 ) ) PUNCT iajs-948 131 13 f f PROPN iajs-948 132 1 f f X iajs-948 132 2 f f PROPN iajs-948 133 1 f f PROPN iajs-948 134 1   PROPN iajs-948 134 2   NUM iajs-948 134 3   PROPN iajs-948 134 4   PROPN iajs-948 134 5   ADP iajs-948 134 6   PROPN iajs-948 134 7   SYM iajs-948 134 8   NOUN iajs-948 134 9   NOUN iajs-948 134 10   NOUN iajs-948 134 11 . . PUNCT iajs-948 135 1 1.7 1.7 NUM iajs-948 135 2 lemma lemma PROPN iajs-948 135 3 : : PUNCT iajs-948 135 4 [ [ X iajs-948 135 5 6 6 NUM iajs-948 135 6 ] ] PUNCT iajs-948 135 7 let let VERB iajs-948 135 8 f f PROPN iajs-948 135 9   NOUN iajs-948 135 10 l l NUM iajs-948 135 11 and and CCONJ iajs-948 135 12 ( ( PUNCT iajs-948 135 13 1p 1p NUM iajs-948 135 14 ) ) PUNCT iajs-948 135 15 we we PRON iajs-948 135 16 have have AUX iajs-948 135 17 ihjpas ihjpa VERB iajs-948 135 18 ibn ibn PROPN iajs-948 135 19 alhaitham alhaitham PROPN iajs-948 135 20 j. j. PROPN iajs-948 135 21 for for ADP iajs-948 135 22 pure pure ADJ iajs-948 135 23 & & CCONJ iajs-948 135 24 appl appl PROPN iajs-948 135 25 . . PUNCT iajs-948 136 1 sci sci PROPN iajs-948 136 2 . . PUNCT iajs-948 137 1 vol.23 vol.23 PROPN iajs-948 137 2 ( ( PUNCT iajs-948 137 3 2 2 NUM iajs-948 137 4 ) ) PUNCT iajs-948 137 5 2010 2010 NUM iajs-948 137 6 34 34 NUM iajs-948 137 7 . . PUNCT iajs-948 138 1 p p X iajs-948 138 2 k k PROPN iajs-948 139 1 1 1 NUM iajs-948 139 2 k k NOUN iajs-948 139 3 p p X iajs-948 139 4 k k PROPN iajs-948 139 5 l(f l(f PROPN iajs-948 139 6 , , PUNCT iajs-948 139 7 ) ) PUNCT iajs-948 139 8 ( ( PUNCT iajs-948 139 9 2 2 NUM iajs-948 139 10 ( ( PUNCT iajs-948 139 11 1 1 NUM iajs-948 139 12 ) ) PUNCT iajs-948 139 13 ) ) PUNCT iajs-948 140 1 ( ( PUNCT iajs-948 140 2 f f NOUN iajs-948 140 3 ; ; PUNCT iajs-948 140 4 ) ) PUNCT iajs-948 140 5 , , PUNCT iajs-948 140 6 0 0 NUM iajs-948 141 1   PROPN iajs-948 141 2   ADJ iajs-948 141 3   PROPN iajs-948 141 4   PROPN iajs-948 141 5   PROPN iajs-948 141 6   VERB iajs-948 141 7   PROPN iajs-948 141 8 . . PUNCT iajs-948 142 1 1.8 1.8 NUM iajs-948 142 2 lemma lemma NOUN iajs-948 142 3 : : PUNCT iajs-948 143 1 [ [ X iajs-948 143 2 6 6 NUM iajs-948 143 3 ] ] PUNCT iajs-948 143 4 for for ADP iajs-948 143 5 g g PROPN iajs-948 143 6 , , PUNCT iajs-948 143 7 g g PROPN iajs-948 143 8 ' ' PUNCT iajs-948 143 9   NOUN iajs-948 143 10 lp lp NOUN iajs-948 143 11 , , PUNCT iajs-948 143 12 we we PRON iajs-948 143 13 have have VERB iajs-948 143 14 ( ( PUNCT iajs-948 143 15 1p 1p NUM iajs-948 143 16 ) ) PUNCT iajs-948 143 17 35 35 NUM iajs-948 143 18 . . NOUN iajs-948 144 1 1 1 NUM iajs-948 144 2 p p NOUN iajs-948 144 3 p p X iajs-948 144 4 ( ( PUNCT iajs-948 144 5 g g NOUN iajs-948 144 6 , , PUNCT iajs-948 144 7 ) ) PUNCT iajs-948 144 8 , , PUNCT iajs-948 144 9 g' g' PROPN iajs-948 145 1   NUM iajs-948 145 2   NOUN iajs-948 145 3 . . PUNCT iajs-948 146 1 1.9 1.9 NUM iajs-948 146 2 lemma lemma PROPN iajs-948 146 3 : : PUNCT iajs-948 147 1 [ [ X iajs-948 147 2 5 5 NUM iajs-948 147 3 ] ] PUNCT iajs-948 147 4 for for ADP iajs-948 147 5 f f PROPN iajs-948 147 6   PROPN iajs-948 147 7 l l NUM iajs-948 147 8 and and CCONJ iajs-948 147 9 ( ( PUNCT iajs-948 147 10 1p 1p NUM iajs-948 147 11 ) ) PUNCT iajs-948 147 12 , , PUNCT iajs-948 147 13 we we PRON iajs-948 147 14 have have VERB iajs-948 147 15 36 36 NUM iajs-948 147 16 . . PUNCT iajs-948 148 1 n n CCONJ iajs-948 148 2 p p NOUN iajs-948 148 3 n n PROPN iajs-948 148 4 1 1 NUM iajs-948 148 5 n n NOUN iajs-948 148 6 p p NOUN iajs-948 148 7 , , PUNCT iajs-948 148 8 p p NOUN iajs-948 148 9 n n X iajs-948 148 10 e e X iajs-948 148 11 ( ( PUNCT iajs-948 148 12 f f PROPN iajs-948 148 13 ) ) PUNCT iajs-948 148 14 e e NOUN iajs-948 148 15 ( ( PUNCT iajs-948 148 16 f f PROPN iajs-948 148 17 ) ) PUNCT iajs-948 148 18 ce ce PROPN iajs-948 149 1 ( ( PUNCT iajs-948 149 2 f f PROPN iajs-948 149 3 ) ) PUNCT iajs-948 149 4   NOUN iajs-948 149 5   PROPN iajs-948 149 6   NOUN iajs-948 149 7 . . PUNCT iajs-948 150 1 1.10 1.10 NUM iajs-948 150 2 theorem theorem VERB iajs-948 150 3 : : PUNCT iajs-948 150 4 [ [ X iajs-948 150 5 6 6 NUM iajs-948 150 6 ] ] PUNCT iajs-948 150 7 for for ADP iajs-948 150 8 f f PROPN iajs-948 150 9   PROPN iajs-948 150 10 l( l( PROPN iajs-948 150 11 ) ) PUNCT iajs-948 150 12 , , PUNCT iajs-948 150 13 we we PRON iajs-948 150 14 have have VERB iajs-948 150 15 37 37 NUM iajs-948 150 16 . . PUNCT iajs-948 151 1 n n PRON iajs-948 152 1 p p NOUN iajs-948 152 2 k k PROPN iajs-948 152 3 k k PROPN iajs-948 152 4 p p X iajs-948 152 5 1 1 NUM iajs-948 152 6 e e NOUN iajs-948 152 7 ( ( PUNCT iajs-948 152 8 f f PROPN iajs-948 152 9 ) ) PUNCT iajs-948 152 10 c c NOUN iajs-948 152 11 ( ( PUNCT iajs-948 152 12 f f NOUN iajs-948 152 13 , , PUNCT iajs-948 152 14 ) ) PUNCT iajs-948 152 15 n n CCONJ iajs-948 152 16   PROPN iajs-948 152 17 , , PUNCT iajs-948 152 18 1p. 1p. NUM iajs-948 152 19 38 38 NUM iajs-948 152 20 . . PUNCT iajs-948 153 1 n n PROPN iajs-948 154 1 k k PROPN iajs-948 154 2 k k PROPN iajs-948 155 1 1 1 X iajs-948 156 1 k k NOUN iajs-948 157 1 p p X iajs-948 158 1 k k PROPN iajs-948 159 1 v v ADP iajs-948 159 2 p p NOUN iajs-948 159 3 v v NOUN iajs-948 159 4 0 0 NUM iajs-948 159 5 1 1 NUM iajs-948 159 6 ( ( PUNCT iajs-948 159 7 f f NOUN iajs-948 159 8 , , PUNCT iajs-948 159 9 ) ) PUNCT iajs-948 159 10 c c PROPN iajs-948 159 11 n n CCONJ iajs-948 159 12 ( ( PUNCT iajs-948 159 13 v v NOUN iajs-948 159 14 1 1 NUM iajs-948 159 15 ) ) PUNCT iajs-948 159 16 e e NOUN iajs-948 159 17 ( ( PUNCT iajs-948 159 18 f f PROPN iajs-948 159 19 ) ) PUNCT iajs-948 159 20 n n CCONJ iajs-948 159 21   PROPN iajs-948 159 22   PROPN iajs-948 159 23   PROPN iajs-948 159 24   NUM iajs-948 159 25   NOUN iajs-948 159 26   NOUN iajs-948 159 27   NOUN iajs-948 159 28 . . PUNCT iajs-948 160 1 1.11 1.11 NUM iajs-948 160 2 theorem theorem VERB iajs-948 160 3 : : PUNCT iajs-948 160 4 [ [ X iajs-948 160 5 3 3 X iajs-948 160 6 ] ] PUNCT iajs-948 160 7 for for ADP iajs-948 160 8 2-periodic 2-periodic NUM iajs-948 160 9 bounded bounded ADJ iajs-948 160 10 reimann reimann PROPN iajs-948 160 11 integrable integrable ADJ iajs-948 160 12 functions function NOUN iajs-948 160 13 we we PRON iajs-948 160 14 have have VERB iajs-948 160 15 the the DET iajs-948 160 16 following following NOUN iajs-948 160 17 : : PUNCT iajs-948 160 18 39 39 NUM iajs-948 160 19 . . PUNCT iajs-948 161 1 n n ADV iajs-948 161 2 1 1 NUM iajs-948 161 3 p p NOUN iajs-948 161 4 1 1 NUM iajs-948 161 5 pp pp ADP iajs-948 161 6 1 1 NUM iajs-948 161 7 1 1 NUM iajs-948 161 8 f f PROPN iajs-948 161 9 j j PROPN iajs-948 161 10 ( ( PUNCT iajs-948 161 11 f f PROPN iajs-948 161 12 , , PUNCT iajs-948 161 13 x x X iajs-948 161 14 ) ) PUNCT iajs-948 161 15 o(1 o(1 NOUN iajs-948 161 16 ) ) PUNCT iajs-948 161 17 ( ( PUNCT iajs-948 161 18 f f PROPN iajs-948 161 19 , , PUNCT iajs-948 161 20 ) ) PUNCT iajs-948 161 21 w w X iajs-948 161 22 ( ( PUNCT iajs-948 161 23 f f NOUN iajs-948 161 24 , , PUNCT iajs-948 161 25 ) ) PUNCT iajs-948 161 26 , , PUNCT iajs-948 162 1 p p NOUN iajs-948 162 2 1 1 NUM iajs-948 162 3 , , PUNCT iajs-948 162 4 n n CCONJ iajs-948 162 5 n n PRON iajs-948 162 6   NOUN iajs-948 162 7   PROPN iajs-948 162 8   NOUN iajs-948 162 9   PROPN iajs-948 162 10   PRON iajs-948 162 11   ADV iajs-948 162 12   PROPN iajs-948 162 13   PROPN iajs-948 162 14   PRON iajs-948 162 15   PROPN iajs-948 162 16   NOUN iajs-948 162 17 40 40 NUM iajs-948 162 18 . . PUNCT iajs-948 163 1 n n ADV iajs-948 163 2 1 1 NUM iajs-948 163 3 pp pp ADP iajs-948 163 4 1 1 NUM iajs-948 164 1 f f PROPN iajs-948 164 2 j j PROPN iajs-948 164 3 ( ( PUNCT iajs-948 164 4 f f PROPN iajs-948 164 5 , , PUNCT iajs-948 164 6 x x X iajs-948 164 7 ) ) PUNCT iajs-948 164 8 o(1 o(1 NOUN iajs-948 164 9 ) ) PUNCT iajs-948 164 10 ( ( PUNCT iajs-948 164 11 f f NOUN iajs-948 164 12 , , PUNCT iajs-948 164 13 ) ) PUNCT iajs-948 164 14 , , PUNCT iajs-948 164 15 1 1 NUM iajs-948 164 16 p p NOUN iajs-948 164 17 . . PUNCT iajs-948 165 1 n n CCONJ iajs-948 165 2   NUM iajs-948 165 3   PROPN iajs-948 165 4   PROPN iajs-948 165 5   PROPN iajs-948 165 6   VERB iajs-948 165 7 where where SCONJ iajs-948 165 8 f(x) f(x) PROPN iajs-948 165 9 is be AUX iajs-948 165 10 the the DET iajs-948 165 11 conjugate conjugate ADJ iajs-948 165 12 function function NOUN iajs-948 165 13 to to ADP iajs-948 165 14 f(x f(x PROPN iajs-948 165 15 ) ) PUNCT iajs-948 165 16 . . PUNCT iajs-948 166 1 1.12 1.12 NUM iajs-948 166 2 theorem theorem VERB iajs-948 166 3 : : PUNCT iajs-948 166 4 [ [ X iajs-948 166 5 4 4 X iajs-948 166 6 ] ] PUNCT iajs-948 166 7 for for ADP iajs-948 166 8 f f PROPN iajs-948 166 9   PROPN iajs-948 166 10 l l NUM iajs-948 166 11 , , PUNCT iajs-948 166 12 then then ADV iajs-948 166 13 41 41 NUM iajs-948 166 14 . . NOUN iajs-948 166 15 1 1 NUM iajs-948 166 16 1 1 NUM iajs-948 166 17 1 1 NUM iajs-948 166 18 p p NOUN iajs-948 166 19 p p NOUN iajs-948 166 20 1 1 NUM iajs-948 166 21 p p NOUN iajs-948 166 22 1 1 NUM iajs-948 166 23 , , PUNCT iajs-948 166 24 p p NOUN iajs-948 166 25 n n NOUN iajs-948 166 26 1 1 NUM iajs-948 166 27 1 1 NUM iajs-948 166 28 1 1 NUM iajs-948 166 29 k(f k(f PROPN iajs-948 166 30 , , PUNCT iajs-948 166 31 , , PUNCT iajs-948 166 32 l l NOUN iajs-948 166 33 , , PUNCT iajs-948 166 34 w w PROPN iajs-948 166 35 , , PUNCT iajs-948 166 36 w w PROPN iajs-948 166 37 ) ) PUNCT iajs-948 166 38 c c NOUN iajs-948 166 39 ( ( PUNCT iajs-948 166 40 f f PROPN iajs-948 166 41 , , PUNCT iajs-948 166 42 ) ) PUNCT iajs-948 166 43 w w X iajs-948 166 44 ( ( PUNCT iajs-948 166 45 f f PROPN iajs-948 166 46 , , PUNCT iajs-948 166 47 ) ) PUNCT iajs-948 166 48 , , PUNCT iajs-948 166 49 p p NOUN iajs-948 166 50 1 1 NUM iajs-948 166 51 , , PUNCT iajs-948 166 52 n n CCONJ iajs-948 166 53 n n CCONJ iajs-948 166 54 n n PRON iajs-948 166 55   NOUN iajs-948 166 56   PROPN iajs-948 166 57   ADJ iajs-948 166 58   NOUN iajs-948 166 59   ADV iajs-948 166 60   PROPN iajs-948 166 61   PROPN iajs-948 166 62   PRON iajs-948 166 63   PROPN iajs-948 166 64   PROPN iajs-948 166 65 . . PUNCT iajs-948 167 1 42 42 NUM iajs-948 167 2 . . NOUN iajs-948 167 3 1 1 NUM iajs-948 167 4 1 1 NUM iajs-948 167 5 1 1 NUM iajs-948 167 6 p p NOUN iajs-948 167 7 1 1 NUM iajs-948 167 8 p p NOUN iajs-948 167 9 p p NOUN iajs-948 167 10 1 1 NUM iajs-948 167 11 p p NOUN iajs-948 167 12 , , PUNCT iajs-948 167 13 p p NOUN iajs-948 167 14 n n NOUN iajs-948 167 15 1 1 NUM iajs-948 167 16 1 1 NUM iajs-948 167 17 1 1 NUM iajs-948 167 18 ( ( PUNCT iajs-948 167 19 f f PROPN iajs-948 167 20 , , PUNCT iajs-948 167 21 ) ) PUNCT iajs-948 167 22 k(f k(f PROPN iajs-948 167 23 ; ; PUNCT iajs-948 167 24 ; ; PUNCT iajs-948 167 25 l l NOUN iajs-948 167 26 , , PUNCT iajs-948 167 27 w w PROPN iajs-948 167 28 , , PUNCT iajs-948 167 29 w w PROPN iajs-948 167 30 ) ) PUNCT iajs-948 167 31 c c NOUN iajs-948 167 32 ( ( PUNCT iajs-948 167 33 f f NOUN iajs-948 167 34 , , PUNCT iajs-948 167 35 ) ) PUNCT iajs-948 167 36 1 1 NUM iajs-948 167 37 p p NOUN iajs-948 167 38 . . PUNCT iajs-948 168 1 n n CCONJ iajs-948 168 2 n n CCONJ iajs-948 168 3 n n PRON iajs-948 168 4   NOUN iajs-948 168 5   NOUN iajs-948 168 6   NOUN iajs-948 169 1   PROPN iajs-948 169 2   PROPN iajs-948 169 3   ADP iajs-948 169 4 1.13 1.13 NUM iajs-948 169 5 theorem theorem VERB iajs-948 169 6 : : PUNCT iajs-948 169 7 [ [ X iajs-948 169 8 9 9 NUM iajs-948 169 9 ] ] PUNCT iajs-948 169 10 for for ADP iajs-948 169 11 f f PROPN iajs-948 169 12   PROPN iajs-948 169 13 lp lp PROPN iajs-948 169 14 , , PUNCT iajs-948 169 15 we we PRON iajs-948 169 16 have have VERB iajs-948 169 17 43 43 NUM iajs-948 169 18 . . PUNCT iajs-948 170 1 n n CCONJ iajs-948 171 1 k k NOUN iajs-948 171 2 1 1 NUM iajs-948 172 1 k k NOUN iajs-948 172 2 p p X iajs-948 172 3 v v INTJ iajs-948 172 4 pk pk NOUN iajs-948 172 5 v v NOUN iajs-948 172 6 0 0 NUM iajs-948 172 7 1 1 NUM iajs-948 172 8 c(k c(k NOUN iajs-948 172 9 ) ) PUNCT iajs-948 173 1 w w NOUN iajs-948 173 2 ( ( PUNCT iajs-948 173 3 f f NOUN iajs-948 173 4 , , PUNCT iajs-948 173 5 ) ) PUNCT iajs-948 173 6 ( ( PUNCT iajs-948 173 7 1 1 NUM iajs-948 173 8 v v NOUN iajs-948 173 9 ) ) PUNCT iajs-948 174 1 e e NOUN iajs-948 174 2 ( ( PUNCT iajs-948 174 3 f f PROPN iajs-948 174 4 ) ) PUNCT iajs-948 174 5 n n CCONJ iajs-948 174 6 n n PRON iajs-948 174 7   VERB iajs-948 174 8   PROPN iajs-948 174 9   NOUN iajs-948 174 10   NOUN iajs-948 174 11 . . PUNCT iajs-948 175 1 2main 2main NUM iajs-948 175 2 results result VERB iajs-948 175 3 the the DET iajs-948 175 4 aim aim NOUN iajs-948 175 5 of of ADP iajs-948 175 6 his his PRON iajs-948 175 7 paper paper NOUN iajs-948 175 8 is be AUX iajs-948 175 9 to to PART iajs-948 175 10 find find VERB iajs-948 175 11 a a DET iajs-948 175 12 better well ADJ iajs-948 175 13 estimation estimation NOUN iajs-948 175 14 for for ADP iajs-948 175 15 the the DET iajs-948 175 16 rate rate NOUN iajs-948 175 17 of of ADP iajs-948 175 18 convergence convergence NOUN iajs-948 175 19 in in ADP iajs-948 175 20 l,p l,p ADJ iajs-948 175 21 space space NOUN iajs-948 175 22 of of ADP iajs-948 175 23 ( ( PUNCT iajs-948 175 24 f f PROPN iajs-948 175 25   PROPN iajs-948 175 26 l l NUM iajs-948 175 27 ) ) PUNCT iajs-948 175 28 by by ADP iajs-948 175 29 jackson jackson PROPN iajs-948 175 30 polynomials polynomial NOUN iajs-948 175 31 in in ADP iajs-948 175 32 terms term NOUN iajs-948 175 33 of of ADP iajs-948 175 34 some some DET iajs-948 175 35 modulus modulus NOUN iajs-948 175 36 of of ADP iajs-948 175 37 functions function NOUN iajs-948 175 38 . . PUNCT iajs-948 176 1 we we PRON iajs-948 176 2 shall shall AUX iajs-948 176 3 prove prove VERB iajs-948 176 4 direct direct ADJ iajs-948 176 5 and and CCONJ iajs-948 176 6 inverse inverse ADJ iajs-948 176 7 theorems theorem NOUN iajs-948 176 8 of of ADP iajs-948 176 9 ( ( PUNCT iajs-948 176 10 f f PROPN iajs-948 176 11   PROPN iajs-948 176 12 l l NUM iajs-948 176 13 ) ) PUNCT iajs-948 176 14 by by ADP iajs-948 176 15 jackson jackson PROPN iajs-948 176 16 polynomials polynomial NOUN iajs-948 176 17 in in ADP iajs-948 176 18 locally locally ADV iajs-948 176 19 global global ADJ iajs-948 176 20 norms norm NOUN iajs-948 176 21 in in ADP iajs-948 176 22 terms term NOUN iajs-948 176 23 of of ADP iajs-948 176 24 ordinary ordinary ADJ iajs-948 176 25 lp lp ADJ iajs-948 176 26 - - PUNCT iajs-948 176 27 modulus modulus NOUN iajs-948 176 28 of of ADP iajs-948 176 29 continuity continuity NOUN iajs-948 176 30 and and CCONJ iajs-948 176 31 average average ADJ iajs-948 176 32 modulus modulus NOUN iajs-948 176 33 of of ADP iajs-948 176 34 continuity continuity NOUN iajs-948 176 35 . . PUNCT iajs-948 177 1 ihjpas ihjpa VERB iajs-948 177 2 ibn ibn PROPN iajs-948 177 3 alhaitham alhaitham PROPN iajs-948 177 4 j. j. PROPN iajs-948 177 5 for for ADP iajs-948 177 6 pure pure ADJ iajs-948 177 7 & & CCONJ iajs-948 177 8 appl appl PROPN iajs-948 177 9 . . PUNCT iajs-948 178 1 sci sci PROPN iajs-948 178 2 . . PUNCT iajs-948 179 1 vol.23 vol.23 PROPN iajs-948 179 2 ( ( PUNCT iajs-948 179 3 2 2 NUM iajs-948 179 4 ) ) PUNCT iajs-948 179 5 2010 2010 NUM iajs-948 179 6 2.1 2.1 NUM iajs-948 179 7 theorem theorem VERB iajs-948 179 8 : : PUNCT iajs-948 179 9 ( ( PUNCT iajs-948 179 10 direct direct ADJ iajs-948 179 11 theorem theorem NOUN iajs-948 179 12 ) ) PUNCT iajs-948 179 13 let let VERB iajs-948 179 14 f f PROPN iajs-948 179 15   PROPN iajs-948 179 16 l l NUM iajs-948 179 17 , , PUNCT iajs-948 179 18 then then ADV iajs-948 179 19 1 1 NUM iajs-948 179 20 p p NOUN iajs-948 179 21 1 1 NUM iajs-948 179 22 p p NOUN iajs-948 179 23 1n 1n NUM iajs-948 179 24 , , PUNCT iajs-948 179 25 p p NOUN iajs-948 179 26 n n NOUN iajs-948 179 27 1 1 NUM iajs-948 179 28 p p NOUN iajs-948 179 29 1 1 NUM iajs-948 179 30 1 1 NUM iajs-948 179 31 c c NOUN iajs-948 179 32 ( ( PUNCT iajs-948 179 33 f f NOUN iajs-948 179 34 , , PUNCT iajs-948 179 35 ) ) PUNCT iajs-948 179 36 c c NOUN iajs-948 179 37 ( ( PUNCT iajs-948 179 38 f f PROPN iajs-948 179 39 , , PUNCT iajs-948 179 40 ) ) PUNCT iajs-948 179 41 , , PUNCT iajs-948 180 1 p p NOUN iajs-948 180 2 1 1 NUM iajs-948 180 3 , , PUNCT iajs-948 180 4 n n PROPN iajs-948 180 5 nf nf PROPN iajs-948 180 6 j j PROPN iajs-948 180 7 ( ( PUNCT iajs-948 180 8 f f PROPN iajs-948 180 9 ) ) PUNCT iajs-948 180 10 1 1 NUM iajs-948 180 11 c c NOUN iajs-948 180 12 ( ( PUNCT iajs-948 180 13 f f NOUN iajs-948 180 14 , , PUNCT iajs-948 180 15 ) ) PUNCT iajs-948 180 16 , , PUNCT iajs-948 180 17 1 1 NUM iajs-948 180 18 p p NOUN iajs-948 180 19 . . PUNCT iajs-948 181 1 n n CCONJ iajs-948 181 2   NOUN iajs-948 181 3   X iajs-948 181 4   PROPN iajs-948 181 5   ADV iajs-948 181 6   VERB iajs-948 181 7   PROPN iajs-948 181 8   PROPN iajs-948 181 9   NOUN iajs-948 181 10   NOUN iajs-948 181 11   NUM iajs-948 181 12   NUM iajs-948 181 13   PROPN iajs-948 181 14   PROPN iajs-948 181 15   VERB iajs-948 181 16   PROPN iajs-948 181 17   NOUN iajs-948 181 18 2.2 2.2 NUM iajs-948 181 19 theorem theorem VERB iajs-948 181 20 : : PUNCT iajs-948 181 21 ( ( PUNCT iajs-948 181 22 inverse inverse NOUN iajs-948 181 23 theorem theorem NOUN iajs-948 181 24 ) ) PUNCT iajs-948 181 25 let let VERB iajs-948 181 26 f f PROPN iajs-948 181 27   PROPN iajs-948 181 28 l l NUM iajs-948 181 29 , , PUNCT iajs-948 181 30 then then ADV iajs-948 181 31 n n CCONJ iajs-948 181 32 n n DET iajs-948 181 33 s(1/ s(1/ NOUN iajs-948 181 34 s s PART iajs-948 181 35 1),p 1),p NUM iajs-948 181 36 ( ( PUNCT iajs-948 181 37 1/ 1/ NUM iajs-948 181 38 s s NOUN iajs-948 181 39 1),p 1),p NUM iajs-948 181 40 1 1 NUM iajs-948 181 41 p p NOUN iajs-948 181 42 s s NOUN iajs-948 181 43 0 0 NUM iajs-948 181 44 s s PART iajs-948 181 45 ( ( PUNCT iajs-948 181 46 1/ 1/ NUM iajs-948 181 47 s s PART iajs-948 181 48 1),p 1),p PROPN iajs-948 181 49 f f PROPN iajs-948 181 50 j j PROPN iajs-948 181 51 ( ( PUNCT iajs-948 181 52 f f PROPN iajs-948 181 53 ) ) PUNCT iajs-948 182 1 f f PROPN iajs-948 182 2 j j PROPN iajs-948 182 3 ( ( PUNCT iajs-948 182 4 f f PROPN iajs-948 182 5 ) ) PUNCT iajs-948 182 6 , , PUNCT iajs-948 182 7 p p NOUN iajs-948 182 8 1,1 1,1 NUM iajs-948 182 9 c c NOUN iajs-948 182 10 ( ( PUNCT iajs-948 182 11 f f PROPN iajs-948 182 12 , , PUNCT iajs-948 182 13 ) ) PUNCT iajs-948 182 14 n n CCONJ iajs-948 182 15 n n PROPN iajs-948 182 16 f f PROPN iajs-948 182 17 j j PROPN iajs-948 182 18 ( ( PUNCT iajs-948 182 19 f f PROPN iajs-948 182 20 ) ) PUNCT iajs-948 182 21 , , PUNCT iajs-948 182 22 1 1 NUM iajs-948 182 23 p p NOUN iajs-948 182 24 . . PUNCT iajs-948 183 1   PROPN iajs-948 183 2   PROPN iajs-948 183 3   PROPN iajs-948 183 4   PROPN iajs-948 183 5   PUNCT iajs-948 183 6   ADP iajs-948 183 7   PROPN iajs-948 183 8   VERB iajs-948 183 9   VERB iajs-948 183 10   PROPN iajs-948 183 11   PROPN iajs-948 183 12   NUM iajs-948 183 13   NUM iajs-948 183 14   NOUN iajs-948 183 15   PROPN iajs-948 183 16   PROPN iajs-948 184 1   PROPN iajs-948 184 2   PROPN iajs-948 184 3   X iajs-948 184 4   PROPN iajs-948 184 5 2.3 2.3 NUM iajs-948 184 6 lemma lemma PROPN iajs-948 184 7 : : PUNCT iajs-948 184 8 let let VERB iajs-948 184 9 n n PRON iajs-948 184 10 nt nt VERB iajs-948 184 11   NOUN iajs-948 184 12 such such ADJ iajs-948 184 13 that that SCONJ iajs-948 184 14 t t PROPN iajs-948 184 15 n n CCONJ iajs-948 184 16 p p NOUN iajs-948 184 17 n n CCONJ iajs-948 184 18 n n CCONJ iajs-948 184 19 p p NOUN iajs-948 184 20 e e X iajs-948 184 21 ( ( PUNCT iajs-948 184 22 f f PROPN iajs-948 184 23 ) ) PUNCT iajs-948 184 24 t t PROPN iajs-948 184 25 t t NUM iajs-948 184 26   ADJ iajs-948 184 27   NOUN iajs-948 184 28 , , PUNCT iajs-948 184 29 f f PROPN iajs-948 184 30   NOUN iajs-948 184 31 l l NUM iajs-948 184 32 and and CCONJ iajs-948 184 33 n n ADV iajs-948 184 34 nt not PART iajs-948 184 35 ( ( PUNCT iajs-948 184 36 x x X iajs-948 184 37 ) ) PUNCT iajs-948 184 38 f f PROPN iajs-948 184 39 ( ( PUNCT iajs-948 184 40 x x X iajs-948 184 41 ) ) PUNCT iajs-948 184 42 t t PROPN iajs-948 184 43 ( ( PUNCT iajs-948 184 44 x) x) PROPN iajs-948 184 45   PROPN iajs-948 184 46   NOUN iajs-948 184 47 then then ADV iajs-948 184 48 44 44 NUM iajs-948 184 49 . . PUNCT iajs-948 185 1 n n CCONJ iajs-948 185 2 n n ADV iajs-948 185 3 1 1 NUM iajs-948 186 1 p p NOUN iajs-948 186 2 1 1 NUM iajs-948 186 3 pp pp ADP iajs-948 186 4 1 1 NUM iajs-948 186 5 1 1 NUM iajs-948 186 6 t t NOUN iajs-948 186 7 ' ' PUNCT iajs-948 186 8 c c NOUN iajs-948 186 9 ( ( PUNCT iajs-948 186 10 f f NOUN iajs-948 186 11 , , PUNCT iajs-948 186 12 ) ) PUNCT iajs-948 186 13 ( ( PUNCT iajs-948 186 14 f f NOUN iajs-948 186 15 , , PUNCT iajs-948 186 16 ) ) PUNCT iajs-948 186 17 n n CCONJ iajs-948 186 18 n n PRON iajs-948 186 19   NOUN iajs-948 186 20   VERB iajs-948 186 21   PROPN iajs-948 186 22   ADJ iajs-948 186 23   NUM iajs-948 186 24   PROPN iajs-948 186 25   PROPN iajs-948 186 26   PROPN iajs-948 186 27   PROPN iajs-948 186 28 , , PUNCT iajs-948 186 29 1p. 1p. NUM iajs-948 186 30 proof proof NOUN iajs-948 186 31 : : PUNCT iajs-948 186 32 let let VERB iajs-948 186 33 n n PRON iajs-948 186 34 1 1 NUM iajs-948 186 35 2 2 NUM iajs-948 186 36 f f NOUN iajs-948 186 37 ( ( PUNCT iajs-948 186 38 x x NOUN iajs-948 186 39 ) ) PUNCT iajs-948 187 1 n n ADP iajs-948 187 2 f(x f(x PROPN iajs-948 187 3 u)du u)du PROPN iajs-948 188 1   PROPN iajs-948 188 2   PROPN iajs-948 188 3   NUM iajs-948 188 4 be be VERB iajs-948 188 5 the the DET iajs-948 188 6 stecklov stecklov ADJ iajs-948 188 7 transformation transformation NOUN iajs-948 188 8 n n CCONJ iajs-948 188 9 n n PROPN iajs-948 188 10 1 1 NUM iajs-948 188 11 h(x h(x PROPN iajs-948 188 12 ) ) PUNCT iajs-948 188 13 f f PROPN iajs-948 188 14 ( ( PUNCT iajs-948 188 15 x)d x)d X iajs-948 188 16 ( ( PUNCT iajs-948 188 17 t t NOUN iajs-948 188 18 ) ) PUNCT iajs-948 188 19 dt dt NOUN iajs-948 189 1   PROPN iajs-948 189 2   PROPN iajs-948 189 3   ADJ iajs-948 189 4   NOUN iajs-948 189 5   NUM iajs-948 189 6   AUX iajs-948 189 7 be be AUX iajs-948 189 8 a a DET iajs-948 189 9 trigonometric trigonometric ADJ iajs-948 189 10 polynomial polynomial NOUN iajs-948 189 11 of of ADP iajs-948 189 12 degree degree NOUN iajs-948 189 13 n n CCONJ iajs-948 189 14 , , PUNCT iajs-948 189 15 such such ADJ iajs-948 189 16 that that PRON iajs-948 189 17 dn(t dn(t NUM iajs-948 189 18 ) ) PUNCT iajs-948 189 19 is be AUX iajs-948 189 20 the the DET iajs-948 189 21 dirichlet dirichlet PROPN iajs-948 189 22 kernel kernel PROPN iajs-948 189 23 , , PUNCT iajs-948 189 24 then then ADV iajs-948 189 25 by by ADP iajs-948 189 26 using use VERB iajs-948 189 27 bernstein bernstein PROPN iajs-948 189 28 inequality inequality PROPN iajs-948 189 29 , , PUNCT iajs-948 189 30 we we PRON iajs-948 189 31 get get VERB iajs-948 189 32 n n PRON iajs-948 189 33 n n NOUN iajs-948 190 1 pp pp ADV iajs-948 191 1 p p PROPN iajs-948 192 1 n n PROPN iajs-948 193 1 pp pp ADV iajs-948 194 1 n n CCONJ iajs-948 195 1 n n CCONJ iajs-948 196 1 pp pp ADP iajs-948 196 2 p p PROPN iajs-948 196 3 t t PROPN iajs-948 196 4 ' ' PART iajs-948 196 5 n n NUM iajs-948 196 6 t t NOUN iajs-948 196 7 h h NOUN iajs-948 196 8 h h NOUN iajs-948 196 9 ' ' PUNCT iajs-948 196 10 n n NUM iajs-948 196 11 t t NOUN iajs-948 196 12 f f PROPN iajs-948 197 1 n n CCONJ iajs-948 197 2 f f PROPN iajs-948 197 3 h h NOUN iajs-948 197 4 h h NOUN iajs-948 197 5 ' ' PUNCT iajs-948 198 1 n n NUM iajs-948 198 2 t t PROPN iajs-948 198 3 t t PROPN iajs-948 199 1 n n CCONJ iajs-948 199 2 f f PROPN iajs-948 199 3 h h NOUN iajs-948 199 4 h h NOUN iajs-948 199 5 ' ' PUNCT iajs-948 199 6   ADV iajs-948 199 7   PROPN iajs-948 199 8   PUNCT iajs-948 199 9   PUNCT iajs-948 199 10   PROPN iajs-948 199 11   NOUN iajs-948 199 12   NOUN iajs-948 199 13   PUNCT iajs-948 199 14   NUM iajs-948 199 15   PROPN iajs-948 199 16   VERB iajs-948 199 17   PROPN iajs-948 199 18   ADV iajs-948 199 19   NUM iajs-948 199 20   PROPN iajs-948 199 21   VERB iajs-948 199 22   PROPN iajs-948 199 23   PUNCT iajs-948 199 24   PROPN iajs-948 199 25   PROPN iajs-948 199 26   PROPN iajs-948 199 27 now now ADV iajs-948 199 28 let let VERB iajs-948 199 29 us we PRON iajs-948 199 30 assume assume VERB iajs-948 199 31 that that SCONJ iajs-948 199 32 1p 1p NUM iajs-948 199 33 f f PROPN iajs-948 199 34 h h NOUN iajs-948 199 35 a a VERB iajs-948 199 36   NUM iajs-948 199 37 and and CCONJ iajs-948 199 38 2 2 NUM iajs-948 199 39 p p NOUN iajs-948 199 40 h h NOUN iajs-948 199 41 ' ' PUNCT iajs-948 199 42 a a NOUN iajs-948 199 43 then then ADV iajs-948 199 44 we we PRON iajs-948 199 45 get get VERB iajs-948 199 46 t t PROPN iajs-948 199 47 n n CCONJ iajs-948 199 48 n n NOUN iajs-948 199 49 p p NOUN iajs-948 199 50 1 1 NUM iajs-948 199 51 2p 2p NUM iajs-948 199 52 1 1 NUM iajs-948 199 53 n n NOUN iajs-948 200 1 np np NOUN iajs-948 200 2 p p NOUN iajs-948 200 3 1 1 NUM iajs-948 200 4 2 2 NUM iajs-948 200 5 n n ADP iajs-948 200 6 n n CCONJ iajs-948 200 7 n n ADV iajs-948 200 8 1 1 NUM iajs-948 200 9 2 2 NUM iajs-948 200 10 n n NOUN iajs-948 200 11 p p NOUN iajs-948 200 12 1 1 NUM iajs-948 200 13 2n 2n NUM iajs-948 200 14 n n CCONJ iajs-948 200 15 np np INTJ iajs-948 200 16 1 1 NUM iajs-948 200 17 2n 2n NUM iajs-948 200 18 t t PROPN iajs-948 200 19 ' ' PUNCT iajs-948 200 20 n n CCONJ iajs-948 200 21 ( ( PUNCT iajs-948 200 22 f f PROPN iajs-948 200 23 ) ) PUNCT iajs-948 200 24 na na ADP iajs-948 200 25 a a DET iajs-948 200 26 1 1 NUM iajs-948 200 27 a a DET iajs-948 200 28 f f NOUN iajs-948 200 29 h h NOUN iajs-948 201 1 [ [ X iajs-948 201 2 f f X iajs-948 201 3 ( ( PUNCT iajs-948 201 4 ) ) PUNCT iajs-948 201 5 f f PROPN iajs-948 201 6 ( ( PUNCT iajs-948 201 7 ) ) PUNCT iajs-948 201 8 ] ] PUNCT iajs-948 201 9 d d X iajs-948 201 10 ( ( PUNCT iajs-948 201 11 t)dt t)dt PROPN iajs-948 201 12 1 1 NUM iajs-948 201 13 n n NOUN iajs-948 201 14 [ [ X iajs-948 201 15 f f X iajs-948 201 16 ( ( PUNCT iajs-948 201 17 ) ) PUNCT iajs-948 201 18 f f PROPN iajs-948 201 19 ( ( PUNCT iajs-948 201 20 u)]dud u)]dud PROPN iajs-948 201 21 ( ( PUNCT iajs-948 201 22 t t PROPN iajs-948 201 23 ) ) PUNCT iajs-948 201 24 dt dt PROPN iajs-948 201 25 1 1 NUM iajs-948 201 26 n n PROPN iajs-948 201 27 f f PROPN iajs-948 201 28 ( ( PUNCT iajs-948 201 29 ) ) PUNCT iajs-948 201 30 f f PROPN iajs-948 201 31 ( ( PUNCT iajs-948 201 32 u u NOUN iajs-948 201 33 ) ) PUNCT iajs-948 201 34 dud dud NOUN iajs-948 201 35 ( ( PUNCT iajs-948 201 36 t)dt t)dt PROPN iajs-948 201 37   PROPN iajs-948 201 38   PROPN iajs-948 201 39   PROPN iajs-948 201 40   PROPN iajs-948 201 41   PROPN iajs-948 201 42   PROPN iajs-948 201 43   PROPN iajs-948 201 44   PROPN iajs-948 201 45   ADJ iajs-948 201 46   ADJ iajs-948 201 47   NOUN iajs-948 201 48   SYM iajs-948 201 49   PROPN iajs-948 201 50   NOUN iajs-948 201 51   ADJ iajs-948 201 52   PUNCT iajs-948 201 53   PUNCT iajs-948 202 1   PROPN iajs-948 202 2   PROPN iajs-948 202 3   ADJ iajs-948 202 4   PROPN iajs-948 202 5   NOUN iajs-948 202 6   NUM iajs-948 202 7   NUM iajs-948 202 8   ADJ iajs-948 202 9   NOUN iajs-948 202 10   VERB iajs-948 202 11   NOUN iajs-948 202 12   VERB iajs-948 202 13   NOUN iajs-948 202 14   NUM iajs-948 202 15   VERB iajs-948 202 16   PUNCT iajs-948 202 17   X iajs-948 202 18   X iajs-948 202 19   X iajs-948 202 20   X iajs-948 202 21   X iajs-948 202 22   NOUN iajs-948 202 23 this this PRON iajs-948 202 24 by by ADP iajs-948 202 25 using use VERB iajs-948 202 26 definition definition NOUN iajs-948 202 27 of of ADP iajs-948 202 28 average average ADJ iajs-948 202 29 modulus modulus NOUN iajs-948 202 30 of of ADP iajs-948 202 31 continuity continuity NOUN iajs-948 202 32 and and CCONJ iajs-948 202 33 by by ADP iajs-948 202 34 ( ( PUNCT iajs-948 202 35 34 34 NUM iajs-948 202 36 ) ) PUNCT iajs-948 202 37 , , PUNCT iajs-948 202 38 we we PRON iajs-948 202 39 get get VERB iajs-948 202 40 ihjpas ihjpa VERB iajs-948 202 41 ibn ibn PROPN iajs-948 202 42 alhaitham alhaitham PROPN iajs-948 202 43 j. j. PROPN iajs-948 202 44 for for ADP iajs-948 202 45 pure pure ADJ iajs-948 202 46 & & CCONJ iajs-948 202 47 appl appl PROPN iajs-948 202 48 . . PUNCT iajs-948 203 1 sci sci PROPN iajs-948 203 2 . . PUNCT iajs-948 204 1 vol.23 vol.23 PROPN iajs-948 204 2 ( ( PUNCT iajs-948 204 3 2 2 NUM iajs-948 204 4 ) ) PUNCT iajs-948 204 5 2010 2010 NUM iajs-948 204 6 1 1 NUM iajs-948 204 7 2 2 NUM iajs-948 204 8 2n 2n NUM iajs-948 204 9 1 1 NUM iajs-948 204 10 1 1 NUM iajs-948 204 11 p p NOUN iajs-948 204 12 n n NUM iajs-948 204 13 10 10 NUM iajs-948 204 14 2n 2n NUM iajs-948 204 15 2 2 NUM iajs-948 204 16 1 1 NUM iajs-948 204 17 p p NOUN iajs-948 204 18 n n NOUN iajs-948 204 19 1 1 NUM iajs-948 204 20 p p NOUN iajs-948 204 21 0 0 NUM iajs-948 204 22 1 1 NUM iajs-948 204 23 2n 2n NUM iajs-948 204 24 2 2 NUM iajs-948 204 25 n n NOUN iajs-948 204 26 p p NOUN iajs-948 204 27 1 1 NUM iajs-948 204 28 2n 2n NUM iajs-948 204 29 p p NOUN iajs-948 204 30 n n PROPN iajs-948 204 31 1 1 NUM iajs-948 204 32 1 1 NUM iajs-948 204 33 a a DET iajs-948 204 34 n n NOUN iajs-948 204 35 ( ( PUNCT iajs-948 204 36 f f PROPN iajs-948 204 37 , , PUNCT iajs-948 204 38 ) ) PUNCT iajs-948 204 39 dud dud PROPN iajs-948 204 40 ( ( PUNCT iajs-948 204 41 t)dt t)dt PROPN iajs-948 204 42 2n 2n NUM iajs-948 204 43 1 1 NUM iajs-948 204 44 1 1 NUM iajs-948 204 45 1 1 NUM iajs-948 204 46 ( ( PUNCT iajs-948 204 47 f f PROPN iajs-948 204 48 , , PUNCT iajs-948 204 49 ) ) PUNCT iajs-948 205 1 d d X iajs-948 205 2 ( ( PUNCT iajs-948 205 3 t)dt t)dt PROPN iajs-948 205 4 c c PROPN iajs-948 205 5 ( ( PUNCT iajs-948 205 6 f f PROPN iajs-948 205 7 , , PUNCT iajs-948 205 8 ) ) PUNCT iajs-948 205 9 2n 2n NUM iajs-948 205 10 2n 2n NUM iajs-948 205 11 1 1 NUM iajs-948 205 12 a a DET iajs-948 205 13 h h NOUN iajs-948 205 14 ' ' PUNCT iajs-948 205 15 n n PROPN iajs-948 205 16 f f NOUN iajs-948 205 17 ' ' PROPN iajs-948 205 18 ( ( PUNCT iajs-948 205 19 u)dud u)dud PROPN iajs-948 205 20 ( ( PUNCT iajs-948 205 21 t)dt t)dt PROPN iajs-948 205 22 1 1 NUM iajs-948 205 23 1 1 NUM iajs-948 205 24 1 1 NUM iajs-948 205 25 n n PROPN iajs-948 205 26 f f NOUN iajs-948 205 27 ' ' PROPN iajs-948 205 28 ( ( PUNCT iajs-948 205 29 ) ) PUNCT iajs-948 205 30 f f PROPN iajs-948 205 31 ( ( PUNCT iajs-948 205 32 ) ) PUNCT iajs-948 205 33 d d NOUN iajs-948 205 34 ( ( PUNCT iajs-948 205 35 t)dt t)dt PROPN iajs-948 205 36 2n 2n NUM iajs-948 205 37 2n 2n NUM iajs-948 205 38   PROPN iajs-948 205 39   PROPN iajs-948 205 40   PROPN iajs-948 205 41   PROPN iajs-948 205 42   ADJ iajs-948 205 43   ADJ iajs-948 205 44   NOUN iajs-948 205 45   NOUN iajs-948 205 46   NOUN iajs-948 205 47   NOUN iajs-948 205 48   PROPN iajs-948 205 49   PROPN iajs-948 205 50   ADJ iajs-948 205 51   NOUN iajs-948 205 52   PUNCT iajs-948 205 53   VERB iajs-948 205 54   NOUN iajs-948 205 55   NUM iajs-948 205 56   NUM iajs-948 205 57   NUM iajs-948 205 58   PROPN iajs-948 205 59   PROPN iajs-948 205 60   PUNCT iajs-948 205 61   NUM iajs-948 205 62   NUM iajs-948 205 63   PUNCT iajs-948 205 64   NOUN iajs-948 205 65   VERB iajs-948 205 66   NOUN iajs-948 205 67   NOUN iajs-948 205 68   X iajs-948 205 69   X iajs-948 205 70   NOUN iajs-948 205 71   X iajs-948 205 72   X iajs-948 205 73   X iajs-948 205 74   PROPN iajs-948 205 75   PROPN iajs-948 205 76   NOUN iajs-948 205 77 then then ADV iajs-948 205 78 by by ADP iajs-948 205 79 using use VERB iajs-948 205 80 definition definition NOUN iajs-948 205 81 of of ADP iajs-948 205 82 ordinary ordinary ADJ iajs-948 205 83 lp lp ADJ iajs-948 205 84 - - PUNCT iajs-948 205 85 modulus modulus NOUN iajs-948 205 86 of of ADP iajs-948 205 87 continuity continuity NOUN iajs-948 205 88 we we PRON iajs-948 205 89 get get VERB iajs-948 205 90 2 2 NUM iajs-948 205 91 2 2 NUM iajs-948 205 92 1 1 NUM iajs-948 205 93 p p NOUN iajs-948 205 94 1 1 NUM iajs-948 205 95 a a DET iajs-948 205 96 c c NOUN iajs-948 205 97 n n CCONJ iajs-948 205 98 ( ( PUNCT iajs-948 205 99 f f NOUN iajs-948 205 100 , , PUNCT iajs-948 205 101 ) ) PUNCT iajs-948 206 1 n n PROPN iajs-948 206 2   X iajs-948 206 3   X iajs-948 206 4 thus thus ADV iajs-948 206 5 t t PROPN iajs-948 206 6 n n CCONJ iajs-948 206 7 n n PROPN iajs-948 206 8 p p NOUN iajs-948 206 9 1 1 NUM iajs-948 206 10 1 1 NUM iajs-948 206 11 p p NOUN iajs-948 206 12 2 2 NUM iajs-948 206 13 pp pp ADP iajs-948 206 14 1 1 NUM iajs-948 206 15 1 1 NUM iajs-948 206 16 t t NOUN iajs-948 206 17 ' ' PUNCT iajs-948 206 18 n n CCONJ iajs-948 206 19 ( ( PUNCT iajs-948 206 20 f f PROPN iajs-948 206 21 ) ) PUNCT iajs-948 206 22 nc nc PROPN iajs-948 206 23 ( ( PUNCT iajs-948 206 24 f f PROPN iajs-948 206 25 , , PUNCT iajs-948 206 26 ) ) PUNCT iajs-948 206 27 c c PROPN iajs-948 207 1 n n PROPN iajs-948 207 2 ( ( PUNCT iajs-948 207 3 f f PROPN iajs-948 207 4 , , PUNCT iajs-948 207 5 ) ) PUNCT iajs-948 207 6 n n CCONJ iajs-948 207 7 n n PRON iajs-948 207 8   NOUN iajs-948 207 9   VERB iajs-948 207 10   NUM iajs-948 207 11   ADJ iajs-948 207 12   ADV iajs-948 207 13   PUNCT iajs-948 207 14   PROPN iajs-948 207 15   X iajs-948 207 16 by by ADP iajs-948 207 17 using use VERB iajs-948 207 18 ( ( PUNCT iajs-948 207 19 37 37 NUM iajs-948 207 20 ) ) PUNCT iajs-948 207 21 n n CCONJ iajs-948 207 22 n n ADV iajs-948 207 23 1 1 NUM iajs-948 207 24 p p NOUN iajs-948 207 25 1 1 NUM iajs-948 207 26 pp pp ADP iajs-948 207 27 1 1 NUM iajs-948 207 28 1 1 NUM iajs-948 207 29 t t NOUN iajs-948 207 30 ' ' PUNCT iajs-948 207 31 c c NOUN iajs-948 207 32 ( ( PUNCT iajs-948 207 33 f f NOUN iajs-948 207 34 , , PUNCT iajs-948 207 35 ) ) PUNCT iajs-948 207 36 ( ( PUNCT iajs-948 207 37 f f NOUN iajs-948 207 38 , , PUNCT iajs-948 207 39 ) ) PUNCT iajs-948 207 40 n n CCONJ iajs-948 207 41 n n PRON iajs-948 207 42   NOUN iajs-948 207 43   VERB iajs-948 207 44   PROPN iajs-948 207 45   ADJ iajs-948 207 46   NUM iajs-948 207 47   PROPN iajs-948 207 48   PROPN iajs-948 207 49   PROPN iajs-948 207 50   PROPN iajs-948 207 51 . . PUNCT iajs-948 208 1 2.4 2.4 NUM iajs-948 208 2 lemma lemma PROPN iajs-948 208 3 : : PUNCT iajs-948 208 4 let let VERB iajs-948 208 5 f f PROPN iajs-948 208 6   PROPN iajs-948 208 7 l l NUM iajs-948 208 8 then then ADV iajs-948 208 9 we we PRON iajs-948 208 10 have have VERB iajs-948 208 11 1p 1p NUM iajs-948 208 12 45 45 NUM iajs-948 208 13 . . NOUN iajs-948 208 14 1 1 NUM iajs-948 208 15 1n 1n NUM iajs-948 208 16 , , PUNCT iajs-948 208 17 p p NOUN iajs-948 208 18 , , PUNCT iajs-948 208 19 p p NOUN iajs-948 208 20 n n CCONJ iajs-948 208 21 n n PRON iajs-948 208 22 j j PROPN iajs-948 208 23 ( ( PUNCT iajs-948 208 24 f f PROPN iajs-948 208 25 ) ) PUNCT iajs-948 208 26 c c NOUN iajs-948 208 27 f f NOUN iajs-948 208 28 . . PUNCT iajs-948 209 1 proof proof NOUN iajs-948 209 2 : : PUNCT iajs-948 209 3 by by ADP iajs-948 209 4 using use VERB iajs-948 209 5 ( ( PUNCT iajs-948 209 6 29 29 NUM iajs-948 209 7 ) ) PUNCT iajs-948 209 8 , , PUNCT iajs-948 209 9 ( ( PUNCT iajs-948 209 10 28 28 NUM iajs-948 209 11 ) ) PUNCT iajs-948 209 12 and and CCONJ iajs-948 209 13 ( ( PUNCT iajs-948 209 14 32 32 NUM iajs-948 209 15 ) ) PUNCT iajs-948 209 16 , , PUNCT iajs-948 209 17 we we PRON iajs-948 209 18 get get VERB iajs-948 209 19 p p NOUN iajs-948 209 20 n n ADV iajs-948 209 21 1 1 NUM iajs-948 209 22 p p NOUN iajs-948 209 23 1n 1n NUM iajs-948 209 24 1 1 NUM iajs-948 209 25 n n CCONJ iajs-948 209 26 , , PUNCT iajs-948 209 27 p p PROPN iajs-948 209 28 p p PROPN iajs-948 209 29 n n CCONJ iajs-948 209 30 n n ADV iajs-948 209 31 2 2 NUM iajs-948 209 32 k k NOUN iajs-948 209 33 k k NOUN iajs-948 209 34 0 0 NUM iajs-948 209 35 3 3 NUM iajs-948 209 36 14 14 NUM iajs-948 209 37 , , PUNCT iajs-948 209 38 p p NOUN iajs-948 209 39 n n PROPN iajs-948 209 40 1 1 NUM iajs-948 209 41 j j PROPN iajs-948 209 42 ( ( PUNCT iajs-948 209 43 f f PROPN iajs-948 209 44 ) ) PUNCT iajs-948 209 45 c c NOUN iajs-948 209 46 ( ( PUNCT iajs-948 209 47 1 1 NUM iajs-948 209 48 n n NOUN iajs-948 209 49 ) ) PUNCT iajs-948 209 50 j j PROPN iajs-948 209 51 ( ( PUNCT iajs-948 209 52 f f PROPN iajs-948 209 53 ) ) PUNCT iajs-948 209 54 n n CCONJ iajs-948 209 55 1 1 NUM iajs-948 209 56 c c NOUN iajs-948 209 57 o(1 o(1 PROPN iajs-948 209 58 ) ) PUNCT iajs-948 209 59 f f PROPN iajs-948 209 60 ( ( PUNCT iajs-948 209 61 t t PROPN iajs-948 209 62 ) ) PUNCT iajs-948 209 63 n n PROPN iajs-948 210 1 c c NOUN iajs-948 210 2 f f PROPN iajs-948 210 3 c c PROPN iajs-948 210 4 f f PROPN iajs-948 211 1   PROPN iajs-948 211 2   PROPN iajs-948 211 3   PUNCT iajs-948 211 4   NOUN iajs-948 211 5   NOUN iajs-948 211 6   NOUN iajs-948 211 7   X iajs-948 211 8   VERB iajs-948 211 9 2.5 2.5 NUM iajs-948 211 10 lemma lemma PROPN iajs-948 211 11 : : PUNCT iajs-948 211 12 let let VERB iajs-948 211 13 f f PROPN iajs-948 211 14   PROPN iajs-948 211 15 l l NUM iajs-948 211 16 then then ADV iajs-948 211 17 we we PRON iajs-948 211 18 have have VERB iajs-948 211 19 1p 1p NUM iajs-948 211 20 46 46 NUM iajs-948 211 21 . . PUNCT iajs-948 212 1 k k PROPN iajs-948 213 1 p p X iajs-948 213 2 p p X iajs-948 213 3 ( ( PUNCT iajs-948 213 4 f f PROPN iajs-948 213 5 , , PUNCT iajs-948 213 6 ) ) PUNCT iajs-948 214 1 c c PROPN iajs-948 215 1 f f PROPN iajs-948 215 2 . . PROPN iajs-948 216 1   NUM iajs-948 216 2   NOUN iajs-948 216 3 proof proof NOUN iajs-948 216 4 : : PUNCT iajs-948 216 5 by by ADP iajs-948 216 6 using use VERB iajs-948 216 7 definition definition NOUN iajs-948 216 8 of of ADP iajs-948 216 9 average average ADJ iajs-948 216 10 modulus modulus NOUN iajs-948 216 11 of of ADP iajs-948 216 12 continuity continuity NOUN iajs-948 216 13 , , PUNCT iajs-948 216 14 we we PRON iajs-948 216 15 get get VERB iajs-948 216 16 k k PROPN iajs-948 216 17 k k PROPN iajs-948 216 18 p p X iajs-948 216 19 k k PROPN iajs-948 216 20 hp hp PROPN iajs-948 217 1 p p PROPN iajs-948 217 2 k k PROPN iajs-948 218 1 i i NOUN iajs-948 218 2 0 0 PUNCT iajs-948 219 1 p p X iajs-948 219 2 p p X iajs-948 219 3 k k PROPN iajs-948 219 4 k k X iajs-948 219 5 ( ( PUNCT iajs-948 219 6 f f PROPN iajs-948 219 7 , , PUNCT iajs-948 219 8 ) ) PUNCT iajs-948 219 9 ( ( PUNCT iajs-948 219 10 f f NOUN iajs-948 219 11 , , PUNCT iajs-948 219 12 ) ) PUNCT iajs-948 219 13 sup sup NOUN iajs-948 219 14 f f PROPN iajs-948 219 15 ( ( PUNCT iajs-948 219 16 t t PROPN iajs-948 219 17 ) ) PUNCT iajs-948 219 18 ; ; PUNCT iajs-948 219 19 t t PROPN iajs-948 219 20 , , PUNCT iajs-948 219 21 t t PROPN iajs-948 219 22 kh kh PROPN iajs-948 219 23 x x X iajs-948 219 24 , , PUNCT iajs-948 219 25 x x SYM iajs-948 219 26 x x SYM iajs-948 219 27 2 2 NUM iajs-948 219 28 2 2 NUM iajs-948 219 29 k k NOUN iajs-948 219 30 k k PROPN iajs-948 220 1 k k PROPN iajs-948 220 2 sup sup PROPN iajs-948 220 3 f f PROPN iajs-948 220 4 ( ( PUNCT iajs-948 220 5 ih ih NOUN iajs-948 220 6 ) ) PUNCT iajs-948 220 7 ; ; PUNCT iajs-948 220 8 t t PROPN iajs-948 220 9 , , PUNCT iajs-948 220 10 t t PROPN iajs-948 220 11 kh kh PROPN iajs-948 220 12 x x X iajs-948 220 13 , , PUNCT iajs-948 220 14 x x PUNCT iajs-948 220 15 x x X iajs-948 220 16 i i NOUN iajs-948 220 17 2 2 NUM iajs-948 220 18 2 2 NUM iajs-948 220 19 c c NOUN iajs-948 220 20 f f PROPN iajs-948 221 1   PROPN iajs-948 221 2   NUM iajs-948 221 3   NOUN iajs-948 221 4   NUM iajs-948 221 5   PROPN iajs-948 221 6   NUM iajs-948 221 7   PROPN iajs-948 221 8   ADJ iajs-948 221 9   NOUN iajs-948 221 10   ADJ iajs-948 221 11   ADP iajs-948 221 12   NOUN iajs-948 221 13   PUNCT iajs-948 221 14   NOUN iajs-948 221 15   NOUN iajs-948 221 16   NOUN iajs-948 221 17   VERB iajs-948 221 18   PROPN iajs-948 221 19   PROPN iajs-948 221 20   PUNCT iajs-948 221 21   PROPN iajs-948 221 22   VERB iajs-948 221 23   DET iajs-948 221 24   PROPN iajs-948 222 1   PROPN iajs-948 222 2   NOUN iajs-948 222 3   NOUN iajs-948 222 4   PROPN iajs-948 222 5   ADJ iajs-948 222 6   PROPN iajs-948 222 7   PUNCT iajs-948 222 8   PUNCT iajs-948 222 9   PROPN iajs-948 222 10   PROPN iajs-948 222 11   ADV iajs-948 222 12   VERB iajs-948 222 13   X iajs-948 222 14   VERB iajs-948 222 15   ADJ iajs-948 222 16   NOUN iajs-948 222 17   NOUN iajs-948 222 18   NUM iajs-948 222 19   NUM iajs-948 222 20 2.6 2.6 NUM iajs-948 222 21 lemma lemma PROPN iajs-948 222 22 : : PUNCT iajs-948 222 23 ihjpas ihjpa VERB iajs-948 222 24 ibn ibn PROPN iajs-948 222 25 alhaitham alhaitham PROPN iajs-948 222 26 j. j. PROPN iajs-948 222 27 for for ADP iajs-948 222 28 pure pure ADJ iajs-948 222 29 & & CCONJ iajs-948 222 30 appl appl PROPN iajs-948 222 31 . . PUNCT iajs-948 223 1 sci sci PROPN iajs-948 223 2 . . PUNCT iajs-948 224 1 vol.23 vol.23 PROPN iajs-948 224 2 ( ( PUNCT iajs-948 224 3 2 2 NUM iajs-948 224 4 ) ) PUNCT iajs-948 224 5 2010 2010 NUM iajs-948 224 6 let let VERB iajs-948 224 7 t t PROPN iajs-948 224 8 > > X iajs-948 224 9 0 0 PROPN iajs-948 224 10 , , PUNCT iajs-948 224 11 f f PROPN iajs-948 224 12   PROPN iajs-948 224 13 l l NUM iajs-948 224 14 , , PUNCT iajs-948 224 15 we we PRON iajs-948 224 16 have have VERB iajs-948 224 17 1p 1p NUM iajs-948 224 18 47 47 NUM iajs-948 224 19 . . PUNCT iajs-948 225 1 1 1 NUM iajs-948 225 2 1 1 NUM iajs-948 225 3 1 1 NUM iajs-948 225 4 1 1 NUM iajs-948 225 5 p p NOUN iajs-948 225 6 p p PROPN iajs-948 225 7 p p PROPN iajs-948 225 8 t t NOUN iajs-948 225 9 , , PUNCT iajs-948 225 10 p p PROPN iajs-948 225 11 p p NOUN iajs-948 225 12 pk(f pk(f PUNCT iajs-948 225 13 ; ; PUNCT iajs-948 225 14 t t X iajs-948 225 15 ; ; PUNCT iajs-948 225 16 l l NOUN iajs-948 225 17 , , PUNCT iajs-948 225 18 w w PROPN iajs-948 225 19 , , PUNCT iajs-948 225 20 w w PROPN iajs-948 225 21 ) ) PUNCT iajs-948 225 22 k(f k(f NOUN iajs-948 225 23 ; ; PUNCT iajs-948 225 24 t;l t;l INTJ iajs-948 225 25 , , PUNCT iajs-948 225 26 w w NOUN iajs-948 225 27 , , PUNCT iajs-948 225 28 w w PROPN iajs-948 225 29 ) ) PUNCT iajs-948 225 30   PROPN iajs-948 225 31   NOUN iajs-948 225 32 proof proof NOUN iajs-948 225 33 : : PUNCT iajs-948 225 34 by by ADP iajs-948 225 35 using use VERB iajs-948 225 36 definition definition NOUN iajs-948 225 37 of of ADP iajs-948 225 38 peetre peetre NOUN iajs-948 225 39 k k NOUN iajs-948 225 40 - - ADJ iajs-948 225 41 functional functional ADJ iajs-948 225 42 and and CCONJ iajs-948 225 43 ( ( PUNCT iajs-948 225 44 33 33 NUM iajs-948 225 45 ) ) PUNCT iajs-948 225 46 , , PUNCT iajs-948 225 47 we we PRON iajs-948 225 48 get get VERB iajs-948 225 49   PROPN iajs-948 225 50   PROPN iajs-948 225 51   PROPN iajs-948 225 52   PROPN iajs-948 225 53 1 1 NUM iajs-948 225 54 1 1 NUM iajs-948 225 55 1 1 NUM iajs-948 225 56 1 1 NUM iajs-948 225 57 p p NOUN iajs-948 225 58 p p NOUN iajs-948 225 59 p p X iajs-948 225 60 p p NOUN iajs-948 226 1 pp pp ADP iajs-948 227 1 p p PROPN iajs-948 228 1 p p NOUN iajs-948 229 1 1 1 NUM iajs-948 229 2 1 1 NUM iajs-948 229 3 p p NOUN iajs-948 229 4 pt pt NOUN iajs-948 229 5 , , PUNCT iajs-948 229 6 p p X iajs-948 229 7 p p X iajs-948 229 8 p p NOUN iajs-948 229 9 1 1 NUM iajs-948 229 10 1 1 NUM iajs-948 229 11 t t NOUN iajs-948 229 12 , , PUNCT iajs-948 229 13 p p X iajs-948 229 14 p p X iajs-948 229 15 p p X iajs-948 229 16 k(f k(f PROPN iajs-948 229 17 ; ; PUNCT iajs-948 229 18 t;l t;l INTJ iajs-948 229 19 , , PUNCT iajs-948 229 20 w w NOUN iajs-948 229 21 , , PUNCT iajs-948 229 22 w w PROPN iajs-948 229 23 ) ) PUNCT iajs-948 229 24 inf inf NOUN iajs-948 229 25 f f PROPN iajs-948 229 26 g g PROPN iajs-948 229 27 t t PROPN iajs-948 229 28 g g PROPN iajs-948 229 29 ' ' PUNCT iajs-948 229 30 t t PROPN iajs-948 229 31 g g NOUN iajs-948 229 32 ' ' PUNCT iajs-948 229 33 , , PUNCT iajs-948 229 34 g g PROPN iajs-948 229 35 w w PROPN iajs-948 229 36 w w PROPN iajs-948 229 37 inf inf PROPN iajs-948 229 38 f f PROPN iajs-948 229 39 g g PROPN iajs-948 229 40 t t PROPN iajs-948 229 41 g g PROPN iajs-948 229 42 ' ' PUNCT iajs-948 229 43 t t PROPN iajs-948 229 44 g g NOUN iajs-948 229 45 ' ' PUNCT iajs-948 229 46 , , PUNCT iajs-948 229 47 g g PROPN iajs-948 229 48 w w PROPN iajs-948 229 49 w w PROPN iajs-948 229 50 k(f k(f PROPN iajs-948 229 51 ; ; PUNCT iajs-948 229 52 t;l t;l INTJ iajs-948 229 53 , , PUNCT iajs-948 229 54 w w NOUN iajs-948 229 55 , , PUNCT iajs-948 229 56 w w PROPN iajs-948 229 57 ) ) PUNCT iajs-948 229 58   PROPN iajs-948 229 59   PROPN iajs-948 229 60   ADV iajs-948 229 61   PUNCT iajs-948 229 62   NOUN iajs-948 229 63   PUNCT iajs-948 229 64   NUM iajs-948 229 65   NOUN iajs-948 229 66   PUNCT iajs-948 229 67   PUNCT iajs-948 229 68   NOUN iajs-948 229 69   PUNCT iajs-948 229 70   NUM iajs-948 229 71   NOUN iajs-948 229 72   X iajs-948 229 73   PROPN iajs-948 229 74   PROPN iajs-948 229 75 2.7 2.7 NUM iajs-948 229 76 lemma lemma PROPN iajs-948 229 77 : : PUNCT iajs-948 229 78 let let VERB iajs-948 229 79 f f X iajs-948 229 80 , , PUNCT iajs-948 229 81 g g PROPN iajs-948 229 82 be be AUX iajs-948 229 83 two two NUM iajs-948 229 84 function function NOUN iajs-948 229 85 define define VERB iajs-948 229 86 on on ADP iajs-948 229 87 the the DET iajs-948 229 88 same same ADJ iajs-948 229 89 domain domain NOUN iajs-948 229 90 then then ADV iajs-948 229 91 for for ADP iajs-948 229 92 1p 1p NUM iajs-948 229 93 , , PUNCT iajs-948 229 94 we we PRON iajs-948 229 95 have have VERB iajs-948 229 96 48 48 NUM iajs-948 229 97 . . PUNCT iajs-948 230 1 k k PROPN iajs-948 231 1 p p X iajs-948 232 1 k k PROPN iajs-948 233 1 p p X iajs-948 234 1 k k PROPN iajs-948 234 2 p p X iajs-948 234 3 1 1 NUM iajs-948 234 4 1 1 NUM iajs-948 234 5 1 1 NUM iajs-948 234 6 ( ( PUNCT iajs-948 234 7 f f NOUN iajs-948 234 8 , , PUNCT iajs-948 234 9 ) ) PUNCT iajs-948 234 10 ( ( PUNCT iajs-948 234 11 f f NOUN iajs-948 234 12 g g PROPN iajs-948 234 13 , , PUNCT iajs-948 234 14 ) ) PUNCT iajs-948 234 15 ( ( PUNCT iajs-948 234 16 g g NOUN iajs-948 234 17 , , PUNCT iajs-948 234 18 ) ) PUNCT iajs-948 234 19 n n CCONJ iajs-948 234 20 n n CCONJ iajs-948 234 21 n n PRON iajs-948 234 22   NOUN iajs-948 234 23   NOUN iajs-948 234 24   NOUN iajs-948 234 25   PROPN iajs-948 234 26   PUNCT iajs-948 234 27 . . PUNCT iajs-948 235 1 proof proof NOUN iajs-948 235 2 : : PUNCT iajs-948 235 3 the the DET iajs-948 235 4 proof proof NOUN iajs-948 235 5 follows follow VERB iajs-948 235 6 from from ADP iajs-948 235 7 the the DET iajs-948 235 8 definition definition NOUN iajs-948 235 9 of of ADP iajs-948 235 10 k(f,)p k(f,)p PROPN iajs-948 235 11 . . PROPN iajs-948 236 1 2.8 2.8 NUM iajs-948 236 2 lemma lemma PROPN iajs-948 236 3 : : PUNCT iajs-948 236 4 for for ADP iajs-948 236 5 t t PROPN iajs-948 236 6 > > X iajs-948 236 7 0 0 PROPN iajs-948 236 8 , , PUNCT iajs-948 236 9 f f PROPN iajs-948 236 10   PROPN iajs-948 236 11 l l NUM iajs-948 236 12 , , PUNCT iajs-948 236 13 we we PRON iajs-948 236 14 have have VERB iajs-948 236 15 49 49 NUM iajs-948 236 16 . . PUNCT iajs-948 237 1 1 1 NUM iajs-948 237 2 1 1 NUM iajs-948 237 3 1 1 NUM iajs-948 237 4 p p NOUN iajs-948 237 5 p p NOUN iajs-948 237 6 p p PROPN iajs-948 237 7 p p NOUN iajs-948 237 8 pk(f pk(f PUNCT iajs-948 237 9 ; ; PUNCT iajs-948 237 10 t t X iajs-948 237 11 ; ; PUNCT iajs-948 237 12 l l NOUN iajs-948 237 13 , , PUNCT iajs-948 237 14 w w PROPN iajs-948 237 15 ) ) PUNCT iajs-948 237 16 k(f k(f NOUN iajs-948 237 17 ; ; PUNCT iajs-948 237 18 t;l t;l INTJ iajs-948 237 19 , , PUNCT iajs-948 237 20 w w NOUN iajs-948 237 21 , , PUNCT iajs-948 237 22 w w NOUN iajs-948 237 23 ) ) PUNCT iajs-948 237 24   PROPN iajs-948 237 25   NOUN iajs-948 237 26 proof proof NOUN iajs-948 237 27 : : PUNCT iajs-948 237 28 by by ADP iajs-948 237 29 using use VERB iajs-948 237 30 definition definition NOUN iajs-948 237 31 of of ADP iajs-948 237 32 peetre peetre NOUN iajs-948 237 33 k k NOUN iajs-948 237 34 - - ADJ iajs-948 237 35 functional functional ADJ iajs-948 237 36   PROPN iajs-948 237 37   PROPN iajs-948 237 38   PROPN iajs-948 237 39   PROPN iajs-948 237 40 1 1 NUM iajs-948 237 41 1 1 NUM iajs-948 237 42 p p NOUN iajs-948 237 43 p p NOUN iajs-948 238 1 pp pp ADP iajs-948 238 2 p p NOUN iajs-948 238 3 1 1 NUM iajs-948 238 4 1 1 NUM iajs-948 238 5 p p NOUN iajs-948 238 6 pp pp ADP iajs-948 238 7 p p PROPN iajs-948 238 8 p p NOUN iajs-948 238 9 1 1 NUM iajs-948 238 10 1 1 NUM iajs-948 238 11 p p NOUN iajs-948 238 12 p p X iajs-948 238 13 p p X iajs-948 238 14 k(f k(f PROPN iajs-948 238 15 ; ; PUNCT iajs-948 238 16 t t PROPN iajs-948 238 17 ; ; PUNCT iajs-948 238 18 l l NOUN iajs-948 238 19 , , PUNCT iajs-948 238 20 w w PROPN iajs-948 238 21 ) ) PUNCT iajs-948 238 22 inf inf NOUN iajs-948 238 23 f f PROPN iajs-948 238 24 g g PROPN iajs-948 238 25 t t PROPN iajs-948 238 26 g g PROPN iajs-948 238 27 ' ' PUNCT iajs-948 238 28 ; ; PUNCT iajs-948 238 29 g g PROPN iajs-948 238 30 w w PROPN iajs-948 238 31 inf inf PROPN iajs-948 238 32 f f PROPN iajs-948 238 33 g g PROPN iajs-948 238 34 t t PROPN iajs-948 238 35 g g PROPN iajs-948 238 36 ' ' PUNCT iajs-948 238 37 t t PROPN iajs-948 238 38 g g NOUN iajs-948 238 39 ' ' PUNCT iajs-948 238 40 ; ; PUNCT iajs-948 238 41 g g PROPN iajs-948 238 42 w w PROPN iajs-948 238 43 w w PROPN iajs-948 238 44 k(f k(f PROPN iajs-948 238 45 ; ; PUNCT iajs-948 238 46 t;l t;l INTJ iajs-948 238 47 , , PUNCT iajs-948 238 48 w w NOUN iajs-948 238 49 , , PUNCT iajs-948 238 50 w w PROPN iajs-948 238 51 ) ) PUNCT iajs-948 239 1   PROPN iajs-948 239 2   PROPN iajs-948 239 3   PUNCT iajs-948 239 4   NOUN iajs-948 239 5   NUM iajs-948 239 6   PROPN iajs-948 239 7   PUNCT iajs-948 239 8   PUNCT iajs-948 239 9   NOUN iajs-948 239 10   PUNCT iajs-948 239 11   NUM iajs-948 239 12   PROPN iajs-948 239 13   PROPN iajs-948 239 14 2.9 2.9 NUM iajs-948 239 15 lemma lemma PROPN iajs-948 239 16 : : PUNCT iajs-948 239 17 let let VERB iajs-948 239 18 f f PROPN iajs-948 239 19   PROPN iajs-948 239 20 l l NUM iajs-948 239 21 , , PUNCT iajs-948 239 22 1p 1p NUM iajs-948 239 23 , , PUNCT iajs-948 239 24 then then ADV iajs-948 239 25 we we PRON iajs-948 239 26 have have VERB iajs-948 239 27 50 50 NUM iajs-948 239 28 . . PUNCT iajs-948 240 1 t t PROPN iajs-948 240 2 t t PROPN iajs-948 240 3 n n PROPN iajs-948 240 4 s s PROPN iajs-948 240 5 ( ( PUNCT iajs-948 240 6 1/ 1/ NUM iajs-948 240 7 s s NOUN iajs-948 240 8 1),p 1),p NUM iajs-948 240 9 s s X iajs-948 240 10 ( ( PUNCT iajs-948 240 11 1/ 1/ NUM iajs-948 240 12 s s NOUN iajs-948 240 13 1),p1 1),p1 NUM iajs-948 240 14 1 1 NUM iajs-948 241 1 p p NOUN iajs-948 241 2 p p X iajs-948 241 3 p p X iajs-948 241 4 t t PROPN iajs-948 241 5 s s PROPN iajs-948 241 6 0 0 NUM iajs-948 241 7 s s PART iajs-948 241 8 ( ( PUNCT iajs-948 241 9 1/ 1/ NUM iajs-948 241 10 s s NOUN iajs-948 241 11 1),p 1),p NUM iajs-948 241 12 ( ( PUNCT iajs-948 241 13 f f PROPN iajs-948 241 14 ) ) PUNCT iajs-948 241 15 ( ( PUNCT iajs-948 241 16 f f PROPN iajs-948 241 17 ) ) PUNCT iajs-948 241 18 , , PUNCT iajs-948 241 19 p p NOUN iajs-948 241 20 1,1 1,1 NUM iajs-948 241 21 c c X iajs-948 241 22 k(f k(f X iajs-948 241 23 ; ; PUNCT iajs-948 241 24 ; ; PUNCT iajs-948 241 25 l l NOUN iajs-948 241 26 , , PUNCT iajs-948 241 27 w w PROPN iajs-948 241 28 , , PUNCT iajs-948 241 29 w w PROPN iajs-948 241 30 ) ) PUNCT iajs-948 241 31 n n CCONJ iajs-948 241 32 n n PROPN iajs-948 241 33 ( ( PUNCT iajs-948 241 34 f f PROPN iajs-948 241 35 ) ) PUNCT iajs-948 241 36 , , PUNCT iajs-948 241 37 1 1 NUM iajs-948 241 38 p p NOUN iajs-948 241 39   VERB iajs-948 241 40   PROPN iajs-948 241 41   PROPN iajs-948 241 42   PROPN iajs-948 241 43   PROPN iajs-948 241 44   VERB iajs-948 241 45   PROPN iajs-948 241 46   PROPN iajs-948 241 47   PROPN iajs-948 241 48   NUM iajs-948 241 49   NUM iajs-948 241 50   ADJ iajs-948 241 51   PROPN iajs-948 241 52   PROPN iajs-948 242 1   PROPN iajs-948 242 2   X iajs-948 242 3   X iajs-948 242 4   NOUN iajs-948 242 5 proof proof NOUN iajs-948 242 6 : : PUNCT iajs-948 242 7 by by ADP iajs-948 242 8 using use VERB iajs-948 242 9 ( ( PUNCT iajs-948 242 10 49 49 NUM iajs-948 242 11 ) ) PUNCT iajs-948 242 12 , , PUNCT iajs-948 242 13 ( ( PUNCT iajs-948 242 14 41 41 NUM iajs-948 242 15 ) ) PUNCT iajs-948 242 16 , , PUNCT iajs-948 242 17 ( ( PUNCT iajs-948 242 18 49 49 NUM iajs-948 242 19 ) ) PUNCT iajs-948 242 20 , , PUNCT iajs-948 242 21 ( ( PUNCT iajs-948 242 22 38 38 NUM iajs-948 242 23 ) ) PUNCT iajs-948 242 24 , , PUNCT iajs-948 242 25 ( ( PUNCT iajs-948 242 26 43 43 NUM iajs-948 242 27 ) ) PUNCT iajs-948 242 28 , , PUNCT iajs-948 242 29 ( ( PUNCT iajs-948 242 30 36 36 NUM iajs-948 242 31 ) ) PUNCT iajs-948 242 32 and and CCONJ iajs-948 242 33 ( ( PUNCT iajs-948 242 34 33 33 NUM iajs-948 242 35 ) ) PUNCT iajs-948 242 36 , , PUNCT iajs-948 242 37 we we PRON iajs-948 242 38 get get VERB iajs-948 242 39 1 1 NUM iajs-948 242 40 1 1 NUM iajs-948 242 41 1 1 NUM iajs-948 242 42 1 1 NUM iajs-948 242 43 p p NOUN iajs-948 242 44 p p X iajs-948 242 45 p p X iajs-948 242 46 ( ( PUNCT iajs-948 242 47 1 1 NUM iajs-948 242 48 / / SYM iajs-948 242 49 n),p n),p PROPN iajs-948 242 50 p p NOUN iajs-948 242 51 p p NOUN iajs-948 242 52 1 1 NUM iajs-948 242 53 1 1 NUM iajs-948 242 54 p p NOUN iajs-948 242 55 1 1 NUM iajs-948 242 56 p p NOUN iajs-948 242 57 2 2 NUM iajs-948 242 58 1 1 NUM iajs-948 242 59 p p NOUN iajs-948 242 60 ' ' PUNCT iajs-948 242 61 ' ' NUM iajs-948 242 62 n n NUM iajs-948 242 63 t t NOUN iajs-948 242 64 t1 t1 NOUN iajs-948 242 65 1 1 NUM iajs-948 242 66 1 1 NUM iajs-948 242 67 s s NOUN iajs-948 242 68 p p NOUN iajs-948 242 69 1 1 NUM iajs-948 242 70 s s PART iajs-948 242 71 p p NOUN iajs-948 242 72 s s NOUN iajs-948 242 73 0 0 NUM iajs-948 242 74 ' ' PUNCT iajs-948 242 75 n n NUM iajs-948 242 76 t1 t1 NOUN iajs-948 242 77 2 2 NUM iajs-948 242 78 s s VERB iajs-948 242 79 p p NOUN iajs-948 242 80 s s NOUN iajs-948 242 81 0 0 NUM iajs-948 242 82 t t NOUN iajs-948 242 83 s s PART iajs-948 242 84 ( ( PUNCT iajs-948 242 85 1/ 1/ NUM iajs-948 242 86 s s NOUN iajs-948 242 87 1 1 NUM iajs-948 242 88 1 1 NUM iajs-948 242 89 k(f k(f PROPN iajs-948 242 90 ; ; PUNCT iajs-948 242 91 ; ; PUNCT iajs-948 242 92 l l X iajs-948 242 93 , , PUNCT iajs-948 242 94 w w PROPN iajs-948 242 95 , , PUNCT iajs-948 242 96 w w PROPN iajs-948 242 97 ) ) PUNCT iajs-948 242 98 k(f k(f PROPN iajs-948 242 99 ; ; PUNCT iajs-948 242 100 ; ; PUNCT iajs-948 242 101 l l X iajs-948 242 102 , , PUNCT iajs-948 242 103 w w PROPN iajs-948 242 104 , , PUNCT iajs-948 242 105 w w PROPN iajs-948 242 106 ) ) PUNCT iajs-948 242 107 n n CCONJ iajs-948 242 108 n n ADV iajs-948 242 109 1 1 NUM iajs-948 242 110 1 1 NUM iajs-948 242 111 c c X iajs-948 242 112 ( ( PUNCT iajs-948 242 113 f f PROPN iajs-948 242 114 , , PUNCT iajs-948 242 115 ) ) PUNCT iajs-948 242 116 ( ( PUNCT iajs-948 242 117 f f NOUN iajs-948 242 118 , , PUNCT iajs-948 242 119 ) ) PUNCT iajs-948 242 120 , , PUNCT iajs-948 242 121 p p NOUN iajs-948 242 122 1 1 NUM iajs-948 242 123 , , PUNCT iajs-948 242 124 n n CCONJ iajs-948 242 125 n n CCONJ iajs-948 242 126 1 1 NUM iajs-948 242 127 c c X iajs-948 242 128 ( ( PUNCT iajs-948 242 129 f f PROPN iajs-948 242 130 , , PUNCT iajs-948 242 131 ) ) PUNCT iajs-948 242 132 , , PUNCT iajs-948 242 133 1 1 NUM iajs-948 242 134 p p NOUN iajs-948 242 135 . . PUNCT iajs-948 243 1 n n PROPN iajs-948 243 2 c c NOUN iajs-948 243 3 c c NOUN iajs-948 243 4 c c X iajs-948 243 5 e e X iajs-948 243 6 ( ( PUNCT iajs-948 243 7 f f PROPN iajs-948 243 8 ) ) PUNCT iajs-948 244 1 c c PROPN iajs-948 244 2 e e X iajs-948 244 3 ( ( PUNCT iajs-948 244 4 f f PROPN iajs-948 244 5 ) ) PUNCT iajs-948 244 6 , , PUNCT iajs-948 244 7 p p NOUN iajs-948 244 8 1 1 NUM iajs-948 244 9 , , PUNCT iajs-948 244 10 n n CCONJ iajs-948 244 11 n n NOUN iajs-948 244 12 c c NOUN iajs-948 244 13 c c X iajs-948 244 14 e e X iajs-948 244 15 ( ( PUNCT iajs-948 244 16 f f PROPN iajs-948 244 17 ) ) PUNCT iajs-948 244 18 , , PUNCT iajs-948 244 19 1 1 NUM iajs-948 244 20 p p NOUN iajs-948 244 21 . . PUNCT iajs-948 245 1 n n CCONJ iajs-948 245 2 ( ( PUNCT iajs-948 245 3 f f X iajs-948 245 4 ) ) PUNCT iajs-948 245 5 c c NOUN iajs-948 245 6 n n NOUN iajs-948 245 7   NOUN iajs-948 245 8   X iajs-948 245 9   NOUN iajs-948 245 10   PROPN iajs-948 245 11   PROPN iajs-948 245 12   ADJ iajs-948 245 13   NOUN iajs-948 245 14   ADP iajs-948 246 1   PROPN iajs-948 246 2   NOUN iajs-948 246 3   PROPN iajs-948 247 1   PROPN iajs-948 247 2   PROPN iajs-948 247 3   NOUN iajs-948 247 4   NOUN iajs-948 247 5   NUM iajs-948 247 6   NOUN iajs-948 247 7   PROPN iajs-948 247 8   NUM iajs-948 247 9   NUM iajs-948 247 10   PRON iajs-948 247 11   NOUN iajs-948 247 12   PROPN iajs-948 247 13   PROPN iajs-948 247 14   NOUN iajs-948 247 15   VERB iajs-948 247 16   NOUN iajs-948 247 17   X iajs-948 247 18   NOUN iajs-948 247 19   PROPN iajs-948 248 1   PROPN iajs-948 248 2   PROPN iajs-948 248 3   NUM iajs-948 248 4   NOUN iajs-948 248 5   NUM iajs-948 248 6   NUM iajs-948 248 7   PROPN iajs-948 248 8   PROPN iajs-948 248 9   VERB iajs-948 248 10   PROPN iajs-948 248 11   ADJ iajs-948 248 12   PROPN iajs-948 248 13   X iajs-948 248 14   X iajs-948 249 1   PROPN iajs-948 249 2   PROPN iajs-948 249 3   PROPN iajs-948 249 4   PROPN iajs-948 249 5   PROPN iajs-948 249 6   PROPN iajs-948 249 7 tn tn PROPN iajs-948 249 8 1),p 1),p PROPN iajs-948 249 9 s s X iajs-948 249 10 ( ( PUNCT iajs-948 249 11 1 1 NUM iajs-948 249 12 /s /s PUNCT iajs-948 249 13 1),p 1),p NUM iajs-948 249 14 t t NOUN iajs-948 249 15 s s PART iajs-948 249 16 0 0 NUM iajs-948 249 17 s s PART iajs-948 249 18 ( ( PUNCT iajs-948 249 19 1/ 1/ NUM iajs-948 249 20 s s NOUN iajs-948 249 21 1),p 1),p NUM iajs-948 249 22 ( ( PUNCT iajs-948 249 23 f f PROPN iajs-948 249 24 ) ) PUNCT iajs-948 249 25 , , PUNCT iajs-948 249 26 p p NOUN iajs-948 249 27 1 1 NUM iajs-948 249 28 , , PUNCT iajs-948 249 29 ( ( PUNCT iajs-948 249 30 f f PROPN iajs-948 249 31 ) ) PUNCT iajs-948 249 32 , , PUNCT iajs-948 249 33 1 1 NUM iajs-948 249 34 p p NOUN iajs-948 249 35   ADV iajs-948 249 36   PROPN iajs-948 249 37   PUNCT iajs-948 249 38   ADP iajs-948 249 39   PROPN iajs-948 249 40   ADJ iajs-948 249 41   PROPN iajs-948 249 42   PROPN iajs-948 250 1   NUM iajs-948 250 2   ADJ iajs-948 250 3   PROPN iajs-948 250 4   PROPN iajs-948 251 1   PROPN iajs-948 251 2   PROPN iajs-948 251 3   PROPN iajs-948 251 4 ihjpas ihjpa VERB iajs-948 251 5 ibn ibn PROPN iajs-948 251 6 alhaitham alhaitham PROPN iajs-948 251 7 j. j. PROPN iajs-948 251 8 for for ADP iajs-948 251 9 pure pure ADJ iajs-948 251 10 & & CCONJ iajs-948 251 11 appl appl PROPN iajs-948 251 12 . . PUNCT iajs-948 252 1 sci sci PROPN iajs-948 252 2 . . PUNCT iajs-948 253 1 vol.23 vol.23 PROPN iajs-948 253 2 ( ( PUNCT iajs-948 253 3 2 2 NUM iajs-948 253 4 ) ) PUNCT iajs-948 253 5 2010 2010 NUM iajs-948 253 6 proof proof NOUN iajs-948 253 7 of of ADP iajs-948 253 8 theorem theorem ADJ iajs-948 253 9 2.1 2.1 NUM iajs-948 253 10 ( ( PUNCT iajs-948 253 11 direct direct ADJ iajs-948 253 12 theorem theorem NOUN iajs-948 253 13 ) ) PUNCT iajs-948 253 14 let let VERB iajs-948 253 15 nt nt PROPN iajs-948 253 16 tn tn PUNCT iajs-948 253 17 such such ADJ iajs-948 253 18 that that SCONJ iajs-948 253 19 t t PROPN iajs-948 253 20 n n CCONJ iajs-948 253 21 p p NOUN iajs-948 253 22 n n CCONJ iajs-948 253 23 n n CCONJ iajs-948 253 24 p p NOUN iajs-948 253 25 e e X iajs-948 253 26 ( ( PUNCT iajs-948 253 27 f f PROPN iajs-948 253 28 ) ) PUNCT iajs-948 253 29 t t PROPN iajs-948 253 30 t t PROPN iajs-948 253 31   ADJ iajs-948 253 32   NOUN iajs-948 253 33 then then ADV iajs-948 253 34 by by ADP iajs-948 253 35 using use VERB iajs-948 253 36 linearity linearity NOUN iajs-948 253 37 of of ADP iajs-948 253 38 jackson jackson PROPN iajs-948 253 39 polynomials polynomials PROPN iajs-948 253 40 , , PUNCT iajs-948 253 41 ( ( PUNCT iajs-948 253 42 45 45 NUM iajs-948 253 43 ) ) PUNCT iajs-948 253 44 , , PUNCT iajs-948 253 45 ( ( PUNCT iajs-948 253 46 29 29 NUM iajs-948 253 47 ) ) PUNCT iajs-948 253 48 , , PUNCT iajs-948 253 49 ( ( PUNCT iajs-948 253 50 39 39 NUM iajs-948 253 51 ) ) PUNCT iajs-948 253 52 , , PUNCT iajs-948 253 53 ( ( PUNCT iajs-948 253 54 40 40 NUM iajs-948 253 55 ) ) PUNCT iajs-948 253 56 , , PUNCT iajs-948 253 57 ( ( PUNCT iajs-948 253 58 30 30 NUM iajs-948 253 59 ) ) PUNCT iajs-948 253 60 , , PUNCT iajs-948 253 61 ( ( PUNCT iajs-948 253 62 44 44 NUM iajs-948 253 63 ) ) PUNCT iajs-948 253 64 and and CCONJ iajs-948 253 65 ( ( PUNCT iajs-948 253 66 46 46 NUM iajs-948 253 67 ) ) PUNCT iajs-948 253 68 n n CCONJ iajs-948 253 69 n n CCONJ iajs-948 253 70 n n CCONJ iajs-948 253 71 n n CCONJ iajs-948 253 72 n n CCONJ iajs-948 253 73 n n CCONJ iajs-948 253 74 n(1/ n(1/ PROPN iajs-948 253 75 n),p n),p PROPN iajs-948 253 76 ( ( PUNCT iajs-948 253 77 1/ 1/ NUM iajs-948 253 78 n n CCONJ iajs-948 253 79 ) ) PUNCT iajs-948 253 80 , , PUNCT iajs-948 253 81 p p X iajs-948 253 82 ( ( PUNCT iajs-948 253 83 1/ 1/ NUM iajs-948 253 84 n),p n),p PROPN iajs-948 253 85 ( ( PUNCT iajs-948 253 86 1/ 1/ NUM iajs-948 253 87 n),p n),p PROPN iajs-948 253 88 n n CCONJ iajs-948 253 89 n n CCONJ iajs-948 253 90 n n CCONJ iajs-948 253 91 n n CCONJ iajs-948 253 92 n n CCONJ iajs-948 253 93 1 1 NUM iajs-948 253 94 n n PRON iajs-948 253 95 n(1/ n(1/ PROPN iajs-948 253 96 n n NUM iajs-948 253 97 ) ) PUNCT iajs-948 253 98 , , PUNCT iajs-948 253 99 p p X iajs-948 253 100 ( ( PUNCT iajs-948 253 101 1/ 1/ NUM iajs-948 253 102 n),p n),p PROPN iajs-948 253 103 ( ( PUNCT iajs-948 253 104 1/ 1/ NUM iajs-948 253 105 n),p n),p PROPN iajs-948 253 106 t t PROPN iajs-948 253 107 2 2 NUM iajs-948 253 108 n n NOUN iajs-948 253 109 p p NOUN iajs-948 253 110 3 3 NUM iajs-948 253 111 n n CCONJ iajs-948 253 112 n n CCONJ iajs-948 253 113 n n NOUN iajs-948 253 114 p p NOUN iajs-948 253 115 1 1 NUM iajs-948 253 116 n n NOUN iajs-948 253 117 p p NOUN iajs-948 253 118 1 1 NUM iajs-948 253 119 n n PROPN iajs-948 253 120 p p NOUN iajs-948 253 121 t t PROPN iajs-948 253 122 2 2 NUM iajs-948 253 123 n n NOUN iajs-948 253 124 p p NOUN iajs-948 253 125 3 3 NUM iajs-948 253 126 1 1 NUM iajs-948 253 127 n n PROPN iajs-948 253 128 f f PROPN iajs-948 253 129 j j PROPN iajs-948 253 130 ( ( PUNCT iajs-948 253 131 f f PROPN iajs-948 253 132 ) ) PUNCT iajs-948 254 1 f f PROPN iajs-948 254 2 t t PROPN iajs-948 254 3 t t PROPN iajs-948 254 4 j j PROPN iajs-948 254 5 ( ( PUNCT iajs-948 254 6 t t PROPN iajs-948 254 7 ) ) PUNCT iajs-948 254 8 j j PROPN iajs-948 254 9 ( ( PUNCT iajs-948 254 10 t t PROPN iajs-948 254 11 f f X iajs-948 254 12 ) ) PUNCT iajs-948 254 13 t t PROPN iajs-948 254 14 t t PROPN iajs-948 254 15 t t PROPN iajs-948 254 16 j j PROPN iajs-948 254 17 ( ( PUNCT iajs-948 254 18 t t PROPN iajs-948 254 19 ) ) PUNCT iajs-948 255 1 c c PROPN iajs-948 255 2 t t PROPN iajs-948 255 3 t t X iajs-948 255 4 c c X iajs-948 255 5 e e X iajs-948 255 6 ( ( PUNCT iajs-948 255 7 f f PROPN iajs-948 255 8 ) ) PUNCT iajs-948 255 9 c c PROPN iajs-948 255 10 t t PROPN iajs-948 255 11 j j PROPN iajs-948 255 12 ( ( PUNCT iajs-948 255 13 t t PROPN iajs-948 255 14 ) ) PUNCT iajs-948 255 15 1 1 NUM iajs-948 255 16 1 1 NUM iajs-948 255 17 o(1 o(1 NOUN iajs-948 255 18 ) ) PUNCT iajs-948 255 19 ( ( PUNCT iajs-948 255 20 t t PROPN iajs-948 255 21 , , PUNCT iajs-948 255 22 ) ) PUNCT iajs-948 255 23 ( ( PUNCT iajs-948 255 24 t t NOUN iajs-948 255 25 , , PUNCT iajs-948 255 26 ) ) PUNCT iajs-948 255 27 , , PUNCT iajs-948 255 28 p p NOUN iajs-948 255 29 1 1 NUM iajs-948 255 30 , , PUNCT iajs-948 255 31 n n X iajs-948 255 32 nc nc PROPN iajs-948 255 33 e e PROPN iajs-948 255 34 ( ( PUNCT iajs-948 255 35 f f X iajs-948 255 36 ) ) PUNCT iajs-948 255 37 c c NOUN iajs-948 255 38 1 1 NUM iajs-948 255 39 o(1 o(1 NOUN iajs-948 255 40 ) ) PUNCT iajs-948 255 41 ( ( PUNCT iajs-948 255 42 t t NOUN iajs-948 255 43 , , PUNCT iajs-948 255 44   PROPN iajs-948 255 45   PROPN iajs-948 255 46   PROPN iajs-948 255 47   ADV iajs-948 255 48   VERB iajs-948 255 49   PUNCT iajs-948 255 50   PUNCT iajs-948 255 51   PROPN iajs-948 255 52   PROPN iajs-948 255 53   PROPN iajs-948 255 54   PUNCT iajs-948 255 55   PUNCT iajs-948 255 56   PROPN iajs-948 255 57   PROPN iajs-948 255 58   PROPN iajs-948 255 59   PROPN iajs-948 255 60   PUNCT iajs-948 255 61   PUNCT iajs-948 255 62   PROPN iajs-948 255 63   NOUN iajs-948 255 64   PROPN iajs-948 255 65   PUNCT iajs-948 255 66   PROPN iajs-948 255 67   PUNCT iajs-948 255 68   PROPN iajs-948 255 69   NOUN iajs-948 255 70   PROPN iajs-948 255 71   PUNCT iajs-948 255 72   PROPN iajs-948 255 73   VERB iajs-948 255 74   PROPN iajs-948 255 75   PROPN iajs-948 255 76   ADV iajs-948 255 77   PROPN iajs-948 255 78   VERB iajs-948 255 79   PROPN iajs-948 255 80   VERB iajs-948 255 81   NUM iajs-948 255 82   ADJ iajs-948 255 83   ADJ iajs-948 255 84   PROPN iajs-948 255 85   NOUN iajs-948 255 86 p p PROPN iajs-948 255 87 4 4 NUM iajs-948 255 88 1 1 NUM iajs-948 255 89 n n NOUN iajs-948 255 90 p p NOUN iajs-948 255 91 4 4 NUM iajs-948 255 92 n n PROPN iajs-948 255 93 p p NOUN iajs-948 255 94 t t PROPN iajs-948 255 95 2 2 NUM iajs-948 255 96 n n NOUN iajs-948 255 97 p p NOUN iajs-948 255 98 4 4 NUM iajs-948 255 99 1 1 NUM iajs-948 255 100 n n NOUN iajs-948 255 101 p p NOUN iajs-948 255 102 4 4 NUM iajs-948 255 103 4 4 NUM iajs-948 255 104 1 1 NUM iajs-948 255 105 n n NOUN iajs-948 255 106 p p NOUN iajs-948 255 107 4 4 NUM iajs-948 255 108 1 1 NUM iajs-948 255 109 p p NOUN iajs-948 255 110 t t PROPN iajs-948 255 111 2 2 NUM iajs-948 255 112 n n NOUN iajs-948 255 113 p p NOUN iajs-948 255 114 5 5 NUM iajs-948 255 115 1 1 NUM iajs-948 255 116 p p NOUN iajs-948 255 117 1 1 NUM iajs-948 255 118 p p NOUN iajs-948 255 119 n n PRON iajs-948 255 120 p p NOUN iajs-948 255 121 4 4 NUM iajs-948 255 122 1 1 NUM iajs-948 255 123 n n NOUN iajs-948 255 124 p p NOUN iajs-948 255 125 4 4 NUM iajs-948 255 126 1 1 NUM iajs-948 255 127 p p NOUN iajs-948 255 128 ) ) PUNCT iajs-948 255 129 , , PUNCT iajs-948 255 130 1 1 NUM iajs-948 255 131 p p NOUN iajs-948 255 132 n n NUM iajs-948 255 133 1 1 NUM iajs-948 255 134 1 1 NUM iajs-948 255 135 c c NOUN iajs-948 255 136 ( ( PUNCT iajs-948 255 137 t t PROPN iajs-948 255 138 , , PUNCT iajs-948 255 139 ) ) PUNCT iajs-948 255 140 c c NOUN iajs-948 256 1 o o NOUN iajs-948 256 2 ( ( PUNCT iajs-948 256 3 ) ) PUNCT iajs-948 256 4 t t NOUN iajs-948 256 5 , , PUNCT iajs-948 256 6 p p PROPN iajs-948 256 7 1 1 NUM iajs-948 256 8 , , PUNCT iajs-948 256 9 n n X iajs-948 256 10 nc nc PROPN iajs-948 256 11 e e PROPN iajs-948 256 12 ( ( PUNCT iajs-948 256 13 f f X iajs-948 256 14 ) ) PUNCT iajs-948 256 15 1 1 NUM iajs-948 256 16 c c NOUN iajs-948 256 17 ( ( PUNCT iajs-948 256 18 t t PROPN iajs-948 256 19 , , PUNCT iajs-948 256 20 ) ) PUNCT iajs-948 256 21 , , PUNCT iajs-948 256 22 1 1 NUM iajs-948 256 23 p p NOUN iajs-948 256 24 n n X iajs-948 256 25 c1 c1 NOUN iajs-948 256 26 1 1 NUM iajs-948 256 27 c c PROPN iajs-948 256 28 ( ( PUNCT iajs-948 256 29 t t NOUN iajs-948 256 30 f f PROPN iajs-948 256 31 , , PUNCT iajs-948 256 32 ) ) PUNCT iajs-948 256 33 c c NOUN iajs-948 257 1 ( ( PUNCT iajs-948 257 2 f f PROPN iajs-948 257 3 , , PUNCT iajs-948 257 4 ) ) PUNCT iajs-948 258 1 o o NOUN iajs-948 258 2 ( ( PUNCT iajs-948 258 3 ) ) PUNCT iajs-948 258 4 n n CCONJ iajs-948 258 5 n n CCONJ iajs-948 258 6 n n ADV iajs-948 258 7 1 1 NUM iajs-948 258 8 1 1 NUM iajs-948 258 9 c c NOUN iajs-948 258 10 e e X iajs-948 258 11 ( ( PUNCT iajs-948 258 12 f f X iajs-948 258 13 ) ) PUNCT iajs-948 258 14 c c NOUN iajs-948 258 15 ( ( PUNCT iajs-948 258 16 f f PROPN iajs-948 258 17 , , PUNCT iajs-948 258 18 ) ) PUNCT iajs-948 258 19 ( ( PUNCT iajs-948 258 20 f f X iajs-948 258 21 , , PUNCT iajs-948 258 22 ) ) PUNCT iajs-948 258 23 t t NOUN iajs-948 258 24 , , PUNCT iajs-948 258 25 p p PROPN iajs-948 258 26 1 1 NUM iajs-948 258 27 , , PUNCT iajs-948 258 28 n n CCONJ iajs-948 258 29 n n ADV iajs-948 258 30 1 1 NUM iajs-948 258 31 1 1 NUM iajs-948 258 32 c c NOUN iajs-948 258 33 ( ( PUNCT iajs-948 258 34 t t NOUN iajs-948 258 35 f f PROPN iajs-948 258 36 , , PUNCT iajs-948 258 37 ) ) PUNCT iajs-948 259 1 c c NOUN iajs-948 259 2 ( ( PUNCT iajs-948 259 3 f f PROPN iajs-948 259 4 , , PUNCT iajs-948 259 5 ) ) PUNCT iajs-948 259 6 , , PUNCT iajs-948 259 7 1 1 NUM iajs-948 259 8 n n ADP iajs-948 259 9 n n DET iajs-948 259 10   NOUN iajs-948 259 11   NOUN iajs-948 259 12   NOUN iajs-948 259 13   NOUN iajs-948 259 14   ADV iajs-948 259 15   ADJ iajs-948 259 16   NOUN iajs-948 259 17   PROPN iajs-948 259 18   ADV iajs-948 259 19   PROPN iajs-948 259 20   PROPN iajs-948 259 21   PROPN iajs-948 259 22   PUNCT iajs-948 259 23   PUNCT iajs-948 259 24   ADP iajs-948 260 1   PROPN iajs-948 260 2   NUM iajs-948 260 3   NOUN iajs-948 260 4   NUM iajs-948 260 5   NUM iajs-948 260 6   NOUN iajs-948 260 7   NUM iajs-948 260 8   PROPN iajs-948 260 9   PROPN iajs-948 260 10   VERB iajs-948 260 11   PRON iajs-948 260 12   PROPN iajs-948 260 13   PROPN iajs-948 260 14   ADP iajs-948 260 15   PROPN iajs-948 260 16   PROPN iajs-948 260 17   PROPN iajs-948 260 18   NOUN iajs-948 260 19   VERB iajs-948 260 20   NUM iajs-948 260 21   NUM iajs-948 260 22   PROPN iajs-948 260 23   PROPN iajs-948 260 24   VERB iajs-948 260 25   PROPN iajs-948 260 26   PROPN iajs-948 260 27   PART iajs-948 260 28   PROPN iajs-948 260 29   ADV iajs-948 260 30   PUNCT iajs-948 260 31   PROPN iajs-948 260 32   PROPN iajs-948 260 33   PROPN iajs-948 260 34   SYM iajs-948 260 35   X iajs-948 260 36   PROPN iajs-948 260 37   PROPN iajs-948 260 38   VERB iajs-948 260 39 6 6 NUM iajs-948 260 40 n n NOUN iajs-948 260 41 7 7 NUM iajs-948 260 42 1 1 NUM iajs-948 260 43 p p NOUN iajs-948 260 44 8 8 NUM iajs-948 260 45 1 1 NUM iajs-948 260 46 pp pp ADP iajs-948 260 47 t t PROPN iajs-948 260 48 2 2 NUM iajs-948 260 49 n n NOUN iajs-948 260 50 p p NOUN iajs-948 260 51 6 6 NUM iajs-948 260 52 n n NUM iajs-948 260 53 4 4 NUM iajs-948 260 54 1 1 NUM iajs-948 260 55 pp pp ADP iajs-948 260 56 p p NOUN iajs-948 260 57 1 1 NUM iajs-948 260 58 1 1 NUM iajs-948 260 59 c c NOUN iajs-948 260 60 t t NOUN iajs-948 260 61 f f X iajs-948 260 62 c c PROPN iajs-948 260 63 ( ( PUNCT iajs-948 260 64 f f PROPN iajs-948 260 65 , , PUNCT iajs-948 260 66 ) ) PUNCT iajs-948 260 67 c c NOUN iajs-948 260 68 ( ( PUNCT iajs-948 260 69 f f NOUN iajs-948 260 70 , , PUNCT iajs-948 260 71 ) ) PUNCT iajs-948 260 72 , , PUNCT iajs-948 261 1 p p NOUN iajs-948 261 2 1 1 NUM iajs-948 261 3 , , PUNCT iajs-948 261 4 n n X iajs-948 261 5 nc nc PROPN iajs-948 261 6 e e PROPN iajs-948 261 7 ( ( PUNCT iajs-948 261 8 f f X iajs-948 261 9 ) ) PUNCT iajs-948 261 10 1 1 NUM iajs-948 261 11 c c NOUN iajs-948 261 12 t t NOUN iajs-948 261 13 f f X iajs-948 261 14 c c PROPN iajs-948 261 15 ( ( PUNCT iajs-948 261 16 f f PROPN iajs-948 261 17 , , PUNCT iajs-948 261 18 ) ) PUNCT iajs-948 261 19 , , PUNCT iajs-948 261 20 1 1 NUM iajs-948 261 21 p p NOUN iajs-948 261 22 n n DET iajs-948 261 23   NOUN iajs-948 261 24   PROPN iajs-948 261 25   PROPN iajs-948 261 26   ADV iajs-948 261 27   VERB iajs-948 261 28   ADP iajs-948 261 29   NUM iajs-948 261 30   NUM iajs-948 261 31   NUM iajs-948 261 32   NUM iajs-948 261 33   NUM iajs-948 261 34   NUM iajs-948 261 35   PROPN iajs-948 261 36   PROPN iajs-948 262 1   INTJ iajs-948 263 1   PROPN iajs-948 263 2   ADP iajs-948 263 3   PROPN iajs-948 263 4   VERB iajs-948 263 5   PUNCT iajs-948 263 6   PROPN iajs-948 263 7   PROPN iajs-948 263 8   NOUN iajs-948 263 9   VERB iajs-948 263 10   NUM iajs-948 263 11   NUM iajs-948 263 12   NOUN iajs-948 263 13   ADV iajs-948 263 14   PROPN iajs-948 263 15   PROPN iajs-948 263 16   VERB iajs-948 263 17   PROPN iajs-948 263 18   PROPN iajs-948 263 19   PROPN iajs-948 263 20 6 6 NUM iajs-948 263 21 n n NOUN iajs-948 263 22 n n ADV iajs-948 264 1 7 7 NUM iajs-948 264 2 1 1 NUM iajs-948 264 3 p p NOUN iajs-948 264 4 8 8 NUM iajs-948 264 5 1 1 NUM iajs-948 264 6 ppt ppt NOUN iajs-948 264 7 n n CCONJ iajs-948 264 8 2 2 NUM iajs-948 264 9 n n NOUN iajs-948 264 10 p(1/ p(1/ VERB iajs-948 264 11 n),p n),p PROPN iajs-948 264 12 6 6 NUM iajs-948 264 13 n n NOUN iajs-948 264 14 n n ADV iajs-948 264 15 4 4 NUM iajs-948 264 16 1 1 NUM iajs-948 264 17 pp pp ADP iajs-948 264 18 t t PROPN iajs-948 264 19 6 6 NUM iajs-948 264 20 n n NOUN iajs-948 264 21 p p NOUN iajs-948 264 22 7 7 NUM iajs-948 264 23 1 1 NUM iajs-948 264 24 p p NOUN iajs-948 264 25 8 8 NUM iajs-948 264 26 1 1 NUM iajs-948 264 27 p p NOUN iajs-948 264 28 t t PROPN iajs-948 264 29 2 2 NUM iajs-948 264 30 n n PROPN iajs-948 264 31 p p X iajs-948 264 32 t t PROPN iajs-948 264 33 6 6 NUM iajs-948 264 34 n n NOUN iajs-948 264 35 p p NOUN iajs-948 264 36 4 4 NUM iajs-948 264 37 1 1 NUM iajs-948 264 38 p p NOUN iajs-948 264 39 t t NOUN iajs-948 264 40 9 9 NUM iajs-948 264 41 n n NOUN iajs-948 264 42 1 1 NUM iajs-948 264 43 1 1 NUM iajs-948 264 44 c c NOUN iajs-948 264 45 t t NOUN iajs-948 264 46 t t X iajs-948 264 47 c c X iajs-948 264 48 ( ( PUNCT iajs-948 264 49 f f NOUN iajs-948 264 50 , , PUNCT iajs-948 264 51 ) ) PUNCT iajs-948 264 52 c c NOUN iajs-948 264 53 ( ( PUNCT iajs-948 264 54 f f PROPN iajs-948 264 55 , , PUNCT iajs-948 264 56 ) ) PUNCT iajs-948 264 57 , , PUNCT iajs-948 265 1 p p NOUN iajs-948 265 2 1 1 NUM iajs-948 265 3 , , PUNCT iajs-948 265 4 n n CCONJ iajs-948 265 5 n n PROPN iajs-948 265 6 f f PROPN iajs-948 265 7 j j PROPN iajs-948 265 8 ( ( PUNCT iajs-948 265 9 f f PROPN iajs-948 265 10 ) ) PUNCT iajs-948 265 11 c c PROPN iajs-948 265 12 e e X iajs-948 265 13 ( ( PUNCT iajs-948 265 14 f f PROPN iajs-948 265 15 ) ) PUNCT iajs-948 265 16 1 1 NUM iajs-948 265 17 c c NOUN iajs-948 265 18 t t NOUN iajs-948 265 19 t t X iajs-948 265 20 c c X iajs-948 265 21 ( ( PUNCT iajs-948 265 22 f f NOUN iajs-948 265 23 , , PUNCT iajs-948 265 24 ) ) PUNCT iajs-948 265 25 , , PUNCT iajs-948 265 26 1 1 NUM iajs-948 265 27 p p NOUN iajs-948 265 28 n n NUM iajs-948 265 29 1 1 NUM iajs-948 265 30 1 1 NUM iajs-948 265 31 c c NOUN iajs-948 265 32 e e X iajs-948 265 33 ( ( PUNCT iajs-948 265 34 f f PROPN iajs-948 265 35 ) ) PUNCT iajs-948 265 36 c c NOUN iajs-948 265 37 ( ( PUNCT iajs-948 265 38 f f NOUN iajs-948 265 39 , , PUNCT iajs-948 265 40 ) ) PUNCT iajs-948 265 41 c c NOUN iajs-948 265 42 ( ( PUNCT iajs-948 265 43 f f PROPN iajs-948 265 44 , , PUNCT iajs-948 265 45 ) ) PUNCT iajs-948 265 46 , , PUNCT iajs-948 265 47 p p NOUN iajs-948 265 48 1 1 NUM iajs-948 265 49 , , PUNCT iajs-948 265 50 n n X iajs-948 265 51 nc nc PROPN iajs-948 265 52 e e PROPN iajs-948 265 53 ( ( PUNCT iajs-948 265 54 f f PROPN iajs-948 265 55 ) ) PUNCT iajs-948 265 56 1 1 NUM iajs-948 265 57 c c NOUN iajs-948 265 58 e e X iajs-948 265 59 ( ( PUNCT iajs-948 265 60 f f PROPN iajs-948 265 61 ) ) PUNCT iajs-948 265 62 c c NOUN iajs-948 265 63 ( ( PUNCT iajs-948 265 64 f f NOUN iajs-948 265 65 , , PUNCT iajs-948 265 66 ) ) PUNCT iajs-948 265 67 , , PUNCT iajs-948 265 68 1 1 NUM iajs-948 265 69 p p NOUN iajs-948 265 70 n n PROPN iajs-948 265 71 c c NOUN iajs-948 265 72 e e X iajs-948 265 73 ( ( PUNCT iajs-948 265 74 f f PROPN iajs-948 265 75 ) ) PUNCT iajs-948 265 76   PROPN iajs-948 266 1   PROPN iajs-948 266 2   NOUN iajs-948 266 3   VERB iajs-948 266 4   PROPN iajs-948 266 5   PROPN iajs-948 266 6   ADV iajs-948 266 7   PROPN iajs-948 266 8   VERB iajs-948 266 9   X iajs-948 266 10   ADP iajs-948 266 11   PROPN iajs-948 266 12   VERB iajs-948 266 13   PUNCT iajs-948 266 14   PROPN iajs-948 266 15   PROPN iajs-948 266 16   PROPN iajs-948 266 17   NOUN iajs-948 266 18   VERB iajs-948 266 19   NUM iajs-948 266 20   NUM iajs-948 266 21   NOUN iajs-948 266 22   ADV iajs-948 266 23   PROPN iajs-948 266 24   PROPN iajs-948 266 25   VERB iajs-948 266 26   PROPN iajs-948 266 27   ADP iajs-948 266 28   PROPN iajs-948 266 29   PROPN iajs-948 266 30   PROPN iajs-948 266 31   PROPN iajs-948 266 32   NOUN iajs-948 266 33   ADJ iajs-948 266 34   NUM iajs-948 266 35   NUM iajs-948 266 36   ADV iajs-948 266 37   PROPN iajs-948 266 38   PROPN iajs-948 266 39   VERB iajs-948 266 40   PROPN iajs-948 266 41   NUM iajs-948 266 42   ADJ iajs-948 266 43   X iajs-948 266 44   PROPN iajs-948 266 45   PROPN iajs-948 266 46   PROPN iajs-948 266 47   NOUN iajs-948 266 48 1 1 NUM iajs-948 266 49 p p NOUN iajs-948 266 50 8 8 NUM iajs-948 266 51 1 1 NUM iajs-948 266 52 p p NOUN iajs-948 266 53 p p PROPN iajs-948 266 54 10 10 NUM iajs-948 266 55 1 1 NUM iajs-948 266 56 p p NOUN iajs-948 266 57 1 1 NUM iajs-948 266 58 p p NOUN iajs-948 266 59 1 1 NUM iajs-948 266 60 p p NOUN iajs-948 266 61 1 1 NUM iajs-948 266 62 p p NOUN iajs-948 266 63 1 1 NUM iajs-948 266 64 1 1 NUM iajs-948 266 65 ( ( PUNCT iajs-948 266 66 f f NOUN iajs-948 266 67 , , PUNCT iajs-948 266 68 ) ) PUNCT iajs-948 266 69 c c NOUN iajs-948 266 70 ( ( PUNCT iajs-948 266 71 f f PROPN iajs-948 266 72 , , PUNCT iajs-948 266 73 ) ) PUNCT iajs-948 266 74 , , PUNCT iajs-948 267 1 p p NOUN iajs-948 267 2 1 1 NUM iajs-948 267 3 , , PUNCT iajs-948 267 4 n n X iajs-948 267 5 nc nc PROPN iajs-948 267 6 1 1 NUM iajs-948 267 7 ( ( PUNCT iajs-948 267 8 f f NOUN iajs-948 267 9 , , PUNCT iajs-948 267 10 ) ) PUNCT iajs-948 267 11 , , PUNCT iajs-948 267 12 1 1 NUM iajs-948 267 13 p p NOUN iajs-948 267 14 n n NUM iajs-948 267 15 1 1 NUM iajs-948 267 16 1 1 NUM iajs-948 267 17 ( ( PUNCT iajs-948 267 18 f f PROPN iajs-948 267 19 , , PUNCT iajs-948 267 20 ) ) PUNCT iajs-948 267 21 ( ( PUNCT iajs-948 267 22 f f NOUN iajs-948 267 23 , , PUNCT iajs-948 267 24 ) ) PUNCT iajs-948 267 25 , , PUNCT iajs-948 267 26 p p NOUN iajs-948 267 27 1 1 NUM iajs-948 267 28 , , PUNCT iajs-948 267 29 n n X iajs-948 267 30 nc nc PROPN iajs-948 267 31 1 1 NUM iajs-948 267 32 ( ( PUNCT iajs-948 267 33 f f PROPN iajs-948 267 34 , , PUNCT iajs-948 267 35 ) ) PUNCT iajs-948 267 36 , , PUNCT iajs-948 267 37 1 1 NUM iajs-948 267 38 p p NOUN iajs-948 267 39 n n DET iajs-948 267 40   NOUN iajs-948 267 41   X iajs-948 267 42   NOUN iajs-948 267 43   VERB iajs-948 267 44   X iajs-948 267 45   PROPN iajs-948 267 46   ADV iajs-948 267 47   PROPN iajs-948 268 1   PROPN iajs-948 268 2   PROPN iajs-948 268 3   ADV iajs-948 268 4   NUM iajs-948 268 5   NUM iajs-948 268 6   PROPN iajs-948 268 7   PROPN iajs-948 268 8   VERB iajs-948 268 9   PROPN iajs-948 268 10   ADP iajs-948 268 11   PROPN iajs-948 268 12   PROPN iajs-948 268 13   ADJ iajs-948 268 14   NOUN iajs-948 268 15   NUM iajs-948 268 16   NUM iajs-948 268 17   PROPN iajs-948 268 18   PROPN iajs-948 268 19   VERB iajs-948 268 20   PROPN iajs-948 268 21   PROPN iajs-948 268 22   PROPN iajs-948 268 23 ihjpas ihjpa VERB iajs-948 268 24 ibn ibn PROPN iajs-948 268 25 alhaitham alhaitham PROPN iajs-948 268 26 j. j. PROPN iajs-948 268 27 for for ADP iajs-948 268 28 pure pure ADJ iajs-948 268 29 & & CCONJ iajs-948 268 30 appl appl PROPN iajs-948 268 31 . . PUNCT iajs-948 269 1 sci sci PROPN iajs-948 269 2 . . PUNCT iajs-948 270 1 vol.23 vol.23 PROPN iajs-948 270 2 ( ( PUNCT iajs-948 270 3 2 2 NUM iajs-948 270 4 ) ) PUNCT iajs-948 270 5 2010 2010 NUM iajs-948 270 6 proof proof NOUN iajs-948 270 7 of of ADP iajs-948 270 8 theorem theorem ADJ iajs-948 270 9 2.2 2.2 NUM iajs-948 270 10 let let VERB iajs-948 270 11 g g PROPN iajs-948 270 12 1 1 NUM iajs-948 270 13 pw pw NOUN iajs-948 270 14 then then ADV iajs-948 270 15 by by ADP iajs-948 270 16 using use VERB iajs-948 270 17 the the DET iajs-948 270 18 following follow VERB iajs-948 270 19 ( ( PUNCT iajs-948 270 20 48 48 NUM iajs-948 270 21 ) ) PUNCT iajs-948 270 22 , , PUNCT iajs-948 270 23 ( ( PUNCT iajs-948 270 24 46 46 NUM iajs-948 270 25 ) ) PUNCT iajs-948 270 26 , , PUNCT iajs-948 270 27 ( ( PUNCT iajs-948 270 28 35 35 NUM iajs-948 270 29 ) ) PUNCT iajs-948 270 30 , , PUNCT iajs-948 270 31 ( ( PUNCT iajs-948 270 32 47 47 NUM iajs-948 270 33 ) ) PUNCT iajs-948 270 34 and and CCONJ iajs-948 270 35 ( ( PUNCT iajs-948 270 36 50 50 NUM iajs-948 270 37 ) ) PUNCT iajs-948 270 38 , , PUNCT iajs-948 270 39 we we PRON iajs-948 270 40 get get VERB iajs-948 270 41 1 1 NUM iajs-948 270 42 p p NOUN iajs-948 270 43 1 1 NUM iajs-948 270 44 p p NOUN iajs-948 270 45 1 1 NUM iajs-948 270 46 p p NOUN iajs-948 270 47 1 1 NUM iajs-948 270 48 p p NOUN iajs-948 270 49 p p NOUN iajs-948 270 50 p p NOUN iajs-948 270 51 1 1 NUM iajs-948 270 52 1 1 NUM iajs-948 270 53 1 1 NUM iajs-948 270 54 ( ( PUNCT iajs-948 270 55 f f PROPN iajs-948 270 56 , , PUNCT iajs-948 270 57 ) ) PUNCT iajs-948 270 58 ( ( PUNCT iajs-948 270 59 ( ( PUNCT iajs-948 270 60 f f NOUN iajs-948 270 61 g g NOUN iajs-948 270 62 ) ) PUNCT iajs-948 270 63 , , PUNCT iajs-948 270 64 ) ) PUNCT iajs-948 271 1 ( ( PUNCT iajs-948 271 2 f f X iajs-948 271 3 , , PUNCT iajs-948 271 4 ) ) PUNCT iajs-948 271 5 n n CCONJ iajs-948 271 6 n n CCONJ iajs-948 271 7 n n ADV iajs-948 271 8 1 1 NUM iajs-948 271 9 1 1 NUM iajs-948 271 10 c c NOUN iajs-948 271 11 f f PROPN iajs-948 271 12 g g PROPN iajs-948 271 13 g g PROPN iajs-948 271 14 ' ' PUNCT iajs-948 271 15 g g NOUN iajs-948 271 16 ' ' PUNCT iajs-948 271 17 n n CCONJ iajs-948 271 18 n n PRON iajs-948 271 19   NOUN iajs-948 271 20   NOUN iajs-948 271 21   NOUN iajs-948 271 22   PROPN iajs-948 271 23   VERB iajs-948 271 24   ADP iajs-948 271 25   PROPN iajs-948 271 26   NOUN iajs-948 271 27   NOUN iajs-948 271 28   VERB iajs-948 271 29   VERB iajs-948 271 30   ADJ iajs-948 271 31   PROPN iajs-948 271 32   PROPN iajs-948 271 33   ADV iajs-948 271 34 now now ADV iajs-948 271 35 if if SCONJ iajs-948 271 36 we we PRON iajs-948 271 37 take take VERB iajs-948 271 38 the the DET iajs-948 271 39 infimum infimum NOUN iajs-948 271 40 of of ADP iajs-948 271 41 g g PROPN iajs-948 271 42 1 1 NUM iajs-948 271 43 pw pw PROPN iajs-948 271 44   NOUN iajs-948 271 45 1 1 NUM iajs-948 271 46 pw pw PROPN iajs-948 271 47   NOUN iajs-948 271 48 , , PUNCT iajs-948 271 49 we we PRON iajs-948 271 50 obtain obtain VERB iajs-948 271 51 1 1 NUM iajs-948 271 52 1 1 NUM iajs-948 271 53 1 1 NUM iajs-948 271 54 p p NOUN iajs-948 271 55 1 1 NUM iajs-948 272 1 p p NOUN iajs-948 272 2 p p NOUN iajs-948 272 3 p p NOUN iajs-948 272 4 1 1 NUM iajs-948 272 5 1 1 NUM iajs-948 272 6 1 1 NUM iajs-948 272 7 ( ( PUNCT iajs-948 272 8 1/ 1/ NUM iajs-948 272 9 n),p n),p PROPN iajs-948 272 10 p p X iajs-948 272 11 p p X iajs-948 272 12 t t PROPN iajs-948 272 13 t t PROPN iajs-948 272 14 n n X iajs-948 272 15 s s X iajs-948 272 16 ( ( PUNCT iajs-948 272 17 1/ 1/ NUM iajs-948 272 18 s s NOUN iajs-948 272 19 1),p 1),p NUM iajs-948 272 20 s s X iajs-948 272 21 ( ( PUNCT iajs-948 272 22 1 1 NUM iajs-948 272 23 / / SYM iajs-948 272 24 s s NOUN iajs-948 272 25 1),p2 1),p2 NUM iajs-948 272 26 1 1 NUM iajs-948 272 27 t t NOUN iajs-948 272 28 s s NOUN iajs-948 272 29 0 0 NUM iajs-948 272 30 s s PART iajs-948 272 31 ( ( PUNCT iajs-948 272 32 1/ 1/ NUM iajs-948 272 33 s s PART iajs-948 272 34 1),p 1),p NUM iajs-948 272 35 s s NOUN iajs-948 272 36 s(1/ s(1/ NOUN iajs-948 272 37 s s PART iajs-948 272 38 1),p 1),p NUM iajs-948 272 39 ( ( PUNCT iajs-948 272 40 1/ 1/ NUM iajs-948 272 41 s s NOUN iajs-948 272 42 1),p 1),p NUM iajs-948 272 43 s s X iajs-948 272 44 ( ( PUNCT iajs-948 272 45 1/ 1/ NUM iajs-948 272 46 s s NOUN iajs-948 272 47 1),p 1),p NUM iajs-948 272 48 1 1 NUM iajs-948 272 49 1 1 NUM iajs-948 272 50 ( ( PUNCT iajs-948 272 51 f f PROPN iajs-948 272 52 , , PUNCT iajs-948 272 53 ) ) PUNCT iajs-948 272 54 c c PROPN iajs-948 272 55 k(f k(f PROPN iajs-948 272 56 ; ; PUNCT iajs-948 272 57 , , PUNCT iajs-948 272 58 l l NOUN iajs-948 272 59 , , PUNCT iajs-948 272 60 w w PROPN iajs-948 272 61 , , PUNCT iajs-948 272 62 w w PROPN iajs-948 272 63 ) ) PUNCT iajs-948 272 64 n n CCONJ iajs-948 272 65 n n ADV iajs-948 272 66 1 1 NUM iajs-948 272 67 c c X iajs-948 272 68 k(f k(f X iajs-948 272 69 ; ; PUNCT iajs-948 272 70 , , PUNCT iajs-948 272 71 l l NOUN iajs-948 272 72 , , PUNCT iajs-948 272 73 w w PROPN iajs-948 272 74 , , PUNCT iajs-948 272 75 w w PROPN iajs-948 272 76 ) ) PUNCT iajs-948 272 77 n n X iajs-948 272 78 e e X iajs-948 272 79 ( ( PUNCT iajs-948 272 80 f f PROPN iajs-948 272 81 ) ) PUNCT iajs-948 272 82 e e NOUN iajs-948 272 83 ( ( PUNCT iajs-948 272 84 f f PROPN iajs-948 272 85 ) ) PUNCT iajs-948 272 86 , , PUNCT iajs-948 272 87 p p NOUN iajs-948 272 88 1,c 1,c NOUN iajs-948 272 89 c c NOUN iajs-948 272 90 n n ADP iajs-948 272 91 e e X iajs-948 272 92 ( ( PUNCT iajs-948 272 93 f f PROPN iajs-948 272 94 ) ) PUNCT iajs-948 272 95 , , PUNCT iajs-948 273 1 1 1 NUM iajs-948 273 2 p p X iajs-948 273 3 f f PROPN iajs-948 273 4 j j PROPN iajs-948 273 5 ( ( PUNCT iajs-948 273 6 f f X iajs-948 273 7 ) ) PUNCT iajs-948 274 1 f f PROPN iajs-948 275 1 j j PROPN iajs-948 275 2 ( ( PUNCT iajs-948 275 3 f f PROPN iajs-948 275 4 ) ) PUNCT iajs-948 275 5 , , PUNCT iajs-948 275 6 p p PRON iajs-948 275 7 1,c 1,c NOUN iajs-948 275 8 n n CCONJ iajs-948 275 9 f f PROPN iajs-948 275 10 j j PROPN iajs-948 275 11 ( ( PUNCT iajs-948 275 12 f f PROPN iajs-948 275 13 ) ) PUNCT iajs-948 275 14 , , PUNCT iajs-948 275 15 1 1 NUM iajs-948 275 16 p p NOUN iajs-948 275 17 . . PUNCT iajs-948 276 1   PROPN iajs-948 276 2   PROPN iajs-948 276 3   PROPN iajs-948 276 4   PROPN iajs-948 276 5   PROPN iajs-948 276 6   PUNCT iajs-948 276 7   PUNCT iajs-948 276 8   PUNCT iajs-948 276 9   NUM iajs-948 276 10   NOUN iajs-948 276 11   ADP iajs-948 276 12   PROPN iajs-948 276 13   PROPN iajs-948 276 14   PROPN iajs-948 276 15   NUM iajs-948 276 16   NUM iajs-948 276 17   PROPN iajs-948 276 18   PROPN iajs-948 277 1   PROPN iajs-948 277 2   PROPN iajs-948 277 3   VERB iajs-948 277 4   VERB iajs-948 277 5   NOUN iajs-948 277 6   VERB iajs-948 277 7   NOUN iajs-948 277 8   NOUN iajs-948 277 9   PROPN iajs-948 277 10   PROPN iajs-948 277 11   VERB iajs-948 277 12   X iajs-948 277 13   X iajs-948 277 14   PROPN iajs-948 277 15   NOUN iajs-948 277 16 n n PUNCT iajs-948 277 17 s s VERB iajs-948 277 18 0 0 NUM iajs-948 277 19   NOUN iajs-948 277 20   NUM iajs-948 277 21   NUM iajs-948 277 22   NOUN iajs-948 277 23   PROPN iajs-948 277 24 references reference NOUN iajs-948 277 25 1 1 NUM iajs-948 277 26 . . PUNCT iajs-948 278 1 zugmund zugmund PROPN iajs-948 278 2 , , PUNCT iajs-948 278 3 a. a. NOUN iajs-948 278 4 ( ( PUNCT iajs-948 278 5 1959 1959 NUM iajs-948 278 6 ) ) PUNCT iajs-948 278 7 , , PUNCT iajs-948 278 8 trigonometric trigonometric ADJ iajs-948 278 9 series series NOUN iajs-948 278 10 , , PUNCT iajs-948 278 11 i i PRON iajs-948 278 12 , , PUNCT iajs-948 278 13 ii ii PROPN iajs-948 278 14 cambridge cambridge PROPN iajs-948 278 15 . . PUNCT iajs-948 279 1 2 2 X iajs-948 279 2 . . X iajs-948 279 3 zabados zabados PROPN iajs-948 279 4 , , PUNCT iajs-948 279 5 j.s j.s PROPN iajs-948 279 6 . . 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X iajs-948 283 3 popov popov PROPN iajs-948 283 4 , , PUNCT iajs-948 283 5 v.a v.a PROPN iajs-948 283 6 . . PROPN iajs-948 283 7 and and CCONJ iajs-948 283 8 szabados szabado NOUN iajs-948 283 9 , , PUNCT iajs-948 283 10 ( ( PUNCT iajs-948 283 11 1984 1984 NUM iajs-948 283 12 ) ) PUNCT iajs-948 283 13 , , PUNCT iajs-948 283 14 on on ADP iajs-948 283 15 the the DET iajs-948 283 16 convergence convergence NOUN iajs-948 283 17 and and CCONJ iajs-948 283 18 saturation saturation NOUN iajs-948 283 19 of of ADP iajs-948 283 20 the the DET iajs-948 283 21 jackson jackson PROPN iajs-948 283 22 on on ADP iajs-948 283 23 polynomials polynomial NOUN iajs-948 283 24 in in ADP iajs-948 283 25 lp lp ADJ iajs-948 283 26 - - PUNCT iajs-948 283 27 spaces space NOUN iajs-948 283 28 approximation approximation NOUN iajs-948 283 29 theory theory NOUN iajs-948 283 30 and and CCONJ iajs-948 283 31 it it PRON iajs-948 283 32 's be AUX iajs-948 283 33 appl appl ADJ iajs-948 283 34 . . PROPN iajs-948 283 35 , , PUNCT iajs-948 283 36 1 1 NUM iajs-948 283 37 , , PUNCT iajs-948 283 38 1 1 NUM iajs-948 283 39 - - SYM iajs-948 283 40 10 10 NUM iajs-948 283 41 . . PUNCT iajs-948 284 1 4 4 NUM iajs-948 284 2 . . X iajs-948 284 3 jassim jassim PROPN iajs-948 284 4 , , PUNCT iajs-948 284 5 s.k s.k PROPN iajs-948 284 6 . . PROPN iajs-948 284 7 ( ( PUNCT iajs-948 284 8 1990 1990 NUM iajs-948 284 9 ) ) PUNCT iajs-948 284 10 , , PUNCT iajs-948 284 11 direct direct ADJ iajs-948 284 12 and and CCONJ iajs-948 284 13 inverse inverse ADJ iajs-948 284 14 inequalities inequality NOUN iajs-948 284 15 for for ADP iajs-948 284 16 some some DET iajs-948 284 17 discrete discrete NOUN iajs-948 284 18 of of ADP iajs-948 284 19 bounded bounded ADJ iajs-948 284 20 measurable measurable ADJ iajs-948 284 21 functions function NOUN iajs-948 284 22 , , PUNCT iajs-948 284 23 serdica serdica NOUN iajs-948 284 24 . . 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