ω =Π P We have Jiang function to see example 1 such that P We prove that there exist infinitely many primes P
|
|
- Georgia King
- 5 years ago
- Views:
Transcription
1 From Hardy-Lttlewood(9) To 04 All rme apers Are ot Eve Wrog (0Abel rze Is ot Eve Wrog,0Abel rze Is ot Eve Wrog) Chu-Xua Jag The Hardy-Lttlewood prme k-tuples cojecture[8,9,4] ad Erdos-Tura cojecture(every set of tegers of postve upper desty cotas arbtrarly log arthmetc progressos )[4,5,6,7,0,5] are ot eve wrog. Usg the crcle method ad the seve method oe do ot prove smplest tw prme cojecture( there exst ftely may pars of tw prmes) ad the smplest Goldbach cojecture (every eve umber >4 s the sum of of two prmes).therefore from Hardy-Lttlewood(9) to 04 all prme papers are ot eve wrog[-50].they do ot prove ay prme problems. 006Felds medal(gree-tao theorem[0]),007wolf prze(fursteberg theorem[5]) ad 0Abel prze(szemered theorem[4]) s ot eve wrog, they do ot uderstad arthmetc progressos. The correct arthmetc progressos s Example 8[6,p68-74].Isttute for Advaced study(math) has log bee recogzed as the leadg teratoal ceter of research pure mathematcs. A.of Math.publshed may wrog prme papers, for example:gree-tao[0,4],goldsto-tz-yldrm[8],wles-taylor[48,49], Zhag[8] ad other. Ther papers are related to the Hardy-Lttlewood wrog prme k-tuples cojecture[8,9,4,50].therefore ther papers are ot eve wrog. All Rema hypothess s ot eve wrog[5].all zeros of all zeta fuctos are ot eve wrog. 0Abel prze s ot eve wrog. But A.of Math reject Jag papers. Edtors of A.of Math do ot uderstad the prme theory ad wat to publsh wrog prme papers. Tw prmes theorem[6,p4]. = + We have Jag fucto to see example J ( ) ( ) 0 ω =Π We prove that there exst ftely may prmes such that + s prme.therefore we prove tw prmes theorem.
2 We have (,) = { : + = prme} ~ Π ( ) log Goldbach theorem[6,p4]. = + We have Jag fucto to see example J( ω) = Π( ) Π 0 We prove that every eve umber 6 s the sum of two prmes.therefore we prove Goldbach theorem. We have (,) = { : = prme} ~ Π ( ) Π log Usg above method we prove about 000 prme theorems[].ths paper s oly correct prme theory, other prme theores are wrog, because they do ot prove the smplest tw prmes theorem ad the smplest Goldbach theorem.the prme papers of ICM006,ICM00 ad ICM04 are wrog.if ICM do ot recogze ths paper,the the prme papers of ICM08 ad ICM0 also are wrog.tao does ot prove that every odd umber s the sum of fve prmes,hs proof s wrog[].i [6,p70-00] we establsh the theory of prme table.we prove that prmes tuples there exst ftely may prme solutos ad ftely may prme solutos. Let k be a gve prme,jp+k-j(j=,...,k-),there exst ftely may prme p such that each of jp+k-j s a prme[6].let k be a gve prme,jp^+k-j(j=,...,k-),we prove t has ftely may prme solutos ad ftely may prme solutos[7]. ********************************************************************* rme dstrbuto s regularty J ( ) + ω rather tha probablty /log to see formula(8)
3 ************************************* Jag s fucto J ( ) + ω prme dstrbuto Chu-Xua Jag 中国航天科工集团理论部. O. Box 94, Bejg 00854,. R. Cha jcxua@sa.com Abstract We defe that prme equatos f (,, ),, f (, ) (5) k are polyomals (wth teger coeffcets) rreducble over tegers, where,, are all the prme. If Jag s fucto J ( ) 0 + ω = the (5)has fte prme solutos. If J ( ) 0 + ω the there are ftely may prmes,, such that f, fk are prmes. We obta a ute prme formula prme dstrbuto k + (, + ) = {,, : f,, f k are k prmes} k k J+ ( ωω ) = (deg f ) ( + o()). (8) k k+ k+ (!) φ ( ω) log = Jag s fucto s accurate seve fucto. Usg Jag s fucto we prove about 600 prme theorems [6]. Jag s fucto provdes proofs of the prme theorems whch are smple eough to uderstad ad accurate eough to be useful. Mathematcas have tred va to dscover some order the sequece of prme umbers but we have every reaso to beleve that there are some mysteres whch the huma md wll ever peetrate. Leohard Euler
4 It wll be aother mllo years, at least, before we uderstad the prmes. aul Erdös Suppose that Euler totet fucto φω ( ) = Π( ) = as ω, () where ω = Π s called prmoral. Suppose that ( ω, h ) =, where =,, φω ( ). We have prme equatos = ω+,, = ω+ h () φω ( ) φω ( ) where = 0,,,. ()s called ftely may prme equatos (IME). Every equato has ftely may prme solutos. We have ( ) h = ( o()). = +, () φω ( ) h(mod ω) where h deotes the umber of prmes = ω+ h = 0,,,, ( ) the umber of prmes less tha or equal to. We replace sets of prme umbers by IME. () s the fudametal tool for provg the prme theorems prme dstrbuto. Let ω = 0 ad φ (0) = 8. From () we have eght prme equatos = 0+, = 0+ 7, = 0+, 4 = 0+, 5 = 0+ 7, 6 = 0+ 9, 7 = 0+, 8 = 0+ 9, = 0,,, (4) Every equato has ftely may prme solutos. THEOREM. We defe that prme equatos f (,, ),, f (,, ) (5) k are polyomals (wth teger coeffcets) rreducble over tegers, where,, are prmes. If Jag s fucto J + ( ω) = 0 the (5) has fte prme solutos. If J + ( ω) 0 the there exst ftely may prmes,, such that each f k s a prme. ROOF. Frstly, we have Jag s fucto [-] J ( ω) = Π[( ) χ( )], (6) + where χ ( ) s called seve costat ad deotes the umber of solutos for the followg specal cogruece k Π f ( q,, q ) 0 (mod ), (7) = where q =,,,, q =,,. J ( ) + ω deotes the umber of sets of,, prme equatos such that 4
5 f(,, ),, fk(,, ) are prme equatos. If J ( ) 0 + ω = the (5) has fte prme solutos. If J ( ) 0 + ω usg χ ( ) we sft out from () prme equatos whch ca ot be represeted,, the resdual prme equatos of () are,,, prme equatos such that f (,, ),, fk(,, ) are prme equatos. Therefore we prove that there exst ftely may prmes,, such that f(,, ),, fk(,, ) are prmes. Secodly, we have the best asymptotc formula [,,4,6] k + (, + ) = {,, : f,, f k are k prmes} k k J+ ( ωω ) = (deg f ) ( + o()). (8) k k+ k+ (!) φ ( ω) log = ( 8 ) s called a ute prme formula prme dstrbuto. Let =, k = 0, J ( ω) φω ( ) =. From (8) we have prme umber theorem (, ) = { : s prme } = ( + o()).. (9) log umber theorsts beleve that there are ftely may tw prmes, but they do ot have rgorous proof of ths old cojecture by ay method. All the prme theorems are cojectures except the prme umber theorem, because they do ot prove that prme equatos have ftely may prme solutos. We prove the followg cojectures by ths theorem. Example. Tw prmes +, (00BC). From (6) ad (7) we have Jag s fucto J ( ω) = Π( ) 0. (0) Sce J ( ) 0 ω () exst ftely may prme equatos such that + s a prme equato. Therefore we prove that there are ftely may prmes such that + s a prme. Let ω = 0 ad J (0) =. From (4) we have three prme equatos = 0+, = 0+ 7, = From (8) we have the best asymptotc formula J( ωω ) (, ) = { : + prme } = ( o()) φ ( ω) log + = Π ( o()). + ( ) log () 5
6 I 996 we proved tw prmes cojecture [] Remark. J ( ω ) deotes the umber of prme equatos, ω ( + o()) φ ( ω) log the umber of solutos of prmes for every prme equato. Example. Eve Goldbach s cojecture = +. Every eve umber 6 s the sum of two prmes. From (6) ad (7) we have Jag s fucto J( ω) = Π( ) Π 0. () Sce J ( ω) 0 as () exst ftely may prme equatos such that s a prme equato. Therefore we prove that every eve umber 6 s the sum of two prmes. From (8) we have the best asymptotc formula J( ωω ) (, ) = {, prme } = ( o()). φ ( ω) log + = Π ( o()) Π +. () ( ) log I 996 we proved eve Goldbach s cojecture [] Example. rme equatos, +, + 6. From (6) ad (7) we have Jag s fucto J ( ω) = Π( ) 0, 5 J ( ) ω s deotes the umber of prme equatos such that + ad + 6 are prme equatos. Sce J ( ) 0 ω () exst ftely may prme equatos such that + ad + 6 are prme equatos. Therefore we prove that there are ftely may prmes such that + ad + 6 are prmes. Let ω = 0, J(0) =. From (4) we have two prme equatos 5 = 0+, = From (8) we have the best asymptotc formula J ( ω) ω (,) = { : +, + 6are prmes} = ( + o()). (4) φ ( ω) log Example 4. Odd Goldbach s cojecture = + +. Every odd umber 9 s the sum of three prmes. From (6) ad (7) we have Jag s fucto 6
7 J( ω) = Π ( + ) ) Π 0. (5) + Sce J ( ω) 0 as () exst ftely may pars of ad prme equatos such that s a prme equato. Therefore we prove that every odd umber 9 s the sum of three prmes. From (8) we have the best asymptotc formula J( ωω ) (, ) = {, : prme } = ( o()) φ ( ω) log +. = Π + ( o()) Π +. (6) ( ) + log Usg very complex crcle method Helfgott deduces the Hardy-Lttlewood formula of three prme problem[0,],but Hardy-Lttlewood-Vogradov-Helfgott do ot prove that every odd umber >7 s the sum of three prme umbers.therefore ther proofs are wrog. Example 5. rme equato = +. From (6) ad (7) we have Jag s fucto ( ) J ( ω) = Π + 0 (7) J ( ω ) deotes the umber of pars of ad prme equatos such that s a prme equato. Sce J ( ω) 0 () exst ftely may pars of ad prme equatos such that s a prme equato. Therefore we prove that there are ftely may pars of prmes ad such that s a prme. From (8) we have the best asymptotc formula J( ωω ) (,) = {, : + prme } = ( o()). 4 φ ( ω) log + (8) ote. deg ( ) =. Example 6 []. rme equato = +. From (6) ad (7) we have Jag s fucto J, (9) ( ω) = Π ( ) χ( ) 0 where χ ( ) = ( ) f χ ( ) = otherwse. (mod ) ; χ ( ) = 0 f / (mod ) ; Sce J ( ω) 0 () there are ftely may pars of ad prme equatos such that s a prme equato. Therefore we prove that there are ftely may pars of prmes ad such that s a prme. 7
8 From (8) we have the best asymptotc formula ( J ( ω) ω,) = {, : + prme} = ( + o()). (0) 6φ ( ω) log 4 Example 7 []. rme equato = + ( + ). From (6) ad (7) we have Jag s fucto J( ω) = Π ( ) χ( ) 0 () where χ ( ) = ( ) f (mod 4) ; χ ( ) = ( ) f (mod 8) ; χ ( ) = 0 otherwse. Sce J ( ω) 0 () there are ftely may pars of ad prme equatos such that s a prme equato. Therefore we prove that there are ftely may pars of prmes ad such that s a prme. From (8) we have the best asymptotc formula J( ωω ) (,) = {, : prme } = ( o()). 8 φ ( ω) log + () Example 8 [4-0]. Arthmetc progressos cosstg oly of prmes. We defe the arthmetc progressos of legth k., = + d, = + d,, = + ( k ) d, ( d, ) =. () k From (8) we have the best asymptotc formula (,) = { :, + d,, + ( k ) d are prmes} ( ) k J ωω = ( + o()).. (4) k k φ ( ω) log If J ( ω ) = 0 the () has fte prme solutos. If J ( ) 0 ω the there are ftely may prmes such that,, k are prmes. To elmate d from () we have j =, = ( j ) ( j ), j k. (5) From (6) ad (7) we have Jag s fucto J ( ω) = Π ( ) Π( )( k+ ) 0 (6) < k k Sce J ( ω) 0 there are ftely may pars of ad prme equatos such that,, k are prme equatos. Therefore we prove that there are ftely may pars of prmes ad such that,, k are prmes. From (8) we have the best asymptotc formula { } k (,) =, : ( j ) ( j ) prme, j k 8
9 k J( ωω ) = ( + o()) k k k φ ( ω) log k k ( k+ ) = Π Π ( + o()). (7) k k k k < k ( ) k ( ) log Example 9. It s a well-kow cojecture that oe of,, + + s always dvsble by. To geeralze above to the k prmes, we prove the followg cojectures. Let be a square-free eve umber..,, + +, where ( + ). From (6) ad (7) we have J () = 0, hece oe of,, + + s always dvsble by. 4., +, +,, +, where 5 ( + b), b=,. 4 From (6) ad (7) we have J (5) = 0, hece oe of, +, +,, + s always dvsble by 5. 6., +, +,, +, where 7 ( + b), b=, 4. 6 From (6) ad (7) we have J (7) = 0, hece oe of, +, +,, + s always dvsble by , +, +,, +, where ( + b), b=,4,5,9. 0 From (6) ad (7) we have J () = 0, hece oe of, +, +,, + s always dvsble by. 5., +, +,, +, where ( + b), b=,6,7,. From (6) ad (7) we have J () = 0, hece oe of, +, +,, + s always dvsble by. 6 6., +, +,, +, where 7 ( + b), b=,5,6,7,0,,,4,5. 6 From (6) ad (7) we have J (7 ) = 0, hece oe of, +, +,, + s always dvsble by , +, +,, +, where 9 ( + b), b= 4,5,6,9, From (6) ad (7) we have J (9) = 0, hece oe of, +, +,, + s always dvsble by 9. Example 0. Let be a eve umber.., +, =,,5,,k+, 9
10 From (6) ad (7) we have J ( ) 0 ω. Therefore we prove that there exst ftely may prmes such that, + are prmes for ay k.., +, =, 4,6,, k. From (6) ad (7) we have J ( ) 0 ω. Therefore we prove that there exst ftely may prmes such that, + are prmes for ay k. Example. rme equato = + From (6) ad (7) we have Jag s fucto J ( ω) = Π( + ) 0. (8) Sce J ( ω) 0 () there are ftely may pars of ad prme equatos such that s prme equatos. Therefore we prove that there are ftely may pars of prmes ad such that s a prme. From (8) we have the best asymptotc formula J( ωω ) (,) = {, : prme } = ( o()). φ ( ω) log + (9) I the same way we ca prove = + whch has the same Jag s fucto. Jag s fucto s accurate seve fucto. Usg t we ca prove ay rreducble prme equatos prme dstrbuto. There are ftely may tw prmes but we do ot have rgorous proof of ths old cojecture by ay method []. As strog as the umercal evdece may be, we stll do ot eve kow whether there are ftely may pars of tw prmes []. All the prme theorems are cojectures except the prme umber theorem, because they do ot prove the smplest tw prmes. They cojecture that the prme dstrbuto s probablty[-8,-5,8-47]. Refereces [] Chu-Xua Jag, O the Yu-Goldbach prme theorem, Guagx Sceces (Chese) (996), 9-. [] Chu-Xua Jag, Foudatos of Satll s soumber theory, art I, Algebras Groups ad Geometres, 5(998), 5-9. [] ChuXua Jag, Foudatos of Satll s soumber theory, art II, Algebras Groups ad Geometres, 5(998), [4] Chu-Xua Jag, Foudatos Satll s soumber theory, I: Fudametal ope problems sceces at the ed of the mlleum, T. Gll, K. Lu ad E. Trell (Eds) Hadroc ress, USA, (999), [5] Chu-Xua Jag, roof of Schzel s hypothess, Algebras Groups ad Geometres, 8(00), [6] Chu-Xua Jag, Foudatos of Satll s somuber theory wth applcatos to ew cryptograms, Fermat s theorem ad Goldbach s cojecture, Iter. Acad. ress, 00, MR004c: 00, [7] Chu-Xua Jag, rme theorem Satll s soumber theory,algebras Groups ad Geometres, 9(00),
11 [8] Chu-Xua Jag, rme theorem Satll s soumber theory (II), Algebras Groups ad Geometres, 0(00), [9] Chu-Xua Jag, Dsproof s of Rema s hypothess, Algebras Groups ad Geometres, (005), Rema.pdf [0] Chu-Xua Jag, Fftee cosecutve tegers wth exactly k prme factors, Algebras Groups ad Geometres, (006), 9-4. [] Chu-Xua Jag, The smplest proofs of both arbtrarly log arthmetc progressos of prmes, preprt, 006. [] D. R. Heath-Brow, rmes represeted by -84. x + y, Acta Math., 86 (00), 4 [] J. Fredlader ad H. Iwaec, The polyomal x + y captures ts prmes, A. Of Math., 48(998), [4] E. Szemeréd, O sets of tegers cotag o k elemets arthmetc progressos, Acta Arth., 7(975), [5] H. Fursteberg, Ergodc behavor of dagoal measures ad a theorem of Szemeréd o arthmetc progressos, J. Aalyse Math., (997), [6] T. Gowers,Hypergraph regularty ad the multdmesoal Szemered theorem,a. of Math.,66(007), [7] T.Gowers,A ew proof of Szemered theorem,gafa,(997), [8] A.Odlyzko,M.Rubste ad M.Wolf,Jumpg Champos,Expermet Math.8,(999),07-8. [9] B. Kra, The Gree-Tao theorem o arthmetc progressos the prmes: A ergodc pot of vew, Bull. Amer. Math. Soc., 4(006), -. [0] B. Gree ad T. Tao, The prmes cota arbtrarly log arthmetc progressos, A.of Math., 67(08), [] T. Tao, The dchotomy betwee structure ad radomess, arthmetc progressos, ad the prmes, I: roceedgs of the teratoal cogress of mathematcas (Madrd. 006), Europ. Math. Soc. Vol , 007. [] B. Gree, Log arthmetc progressos of prmes, Clay Mathematcs roceedgs Vol. 7, 007, [] H. Iwace ad E. Kowalsk, Aalytc umber theory, Amer. Math. Soc., rovdece, RI, 004 [4] R. Cradall ad C. omerace, rme umbers a computatoal perspectve, Sprg-Verlag, ew York, 005. [5] B. Gree, Geeralsg the Hardy-Lttlewood method for prmes, I: roceedgs of the teratoal cogress of mathematcas (Madrd. 006), Europ. Math. Soc., Vol. II, 7-99, 007. [6] K. Soudararaja, Small gaps betwee prme umbers: The work of Goldsto-tz-Yldrm, Bull. Amer. Math. Soc., 44(007), -8. [7] A. Gravlle, Harald Cramér ad dstrbuto of prme umbers, Scad. Actuar. J, 995() (995), -8. [8] Ytag Zhag,Bouded gaps betwee prmes, A.of Math., 79(04)-74.
12 [9] Chu-Xua Jag,The Hardy-Lttlewood prme k-tuple cojecture s false. [0] H.A.Helfgott,Major arcs for Goldbach problem, [] H.A.Helfgott,Mor arcs for Goldbach problem, [] [] T.Tao,Every odd umber greater tha s the sum of at most fve prmes, Math.Comp 8(04), [4] G.H.Hardy ad J.E.Lttlewood,Some problems of artto umerorum ;III:O the expresso of a umber as a sum of prmes,acta Math.,44(9),-70. [5].Erdos ad.tura,o some sequeces of tegers,j.lodo Math.Soc.,(96),6-64. [6] Chu-Xua Jag,The ew prme theorem (5), [7] Chu-Xua Jag,The ew prme theorem (4), [8]D.Goldsto,J.tz ad C.Yldrm, rmes tuples I, A. of Math.,70(009), [9] D.Goldsto,Y.Motohash,J.tz,ad C.Yldrm,Small gaps betwee prmes exst,roc.japa Acad.Ser.A Math.Sc,8(006),6-65. [40] D.Goldsto,S.Graham,J.tz,ad Y.Yldrm,Small gaps betwee products of two prmes,roc Lodo Math.Soc.()98(009), [4] B.Gree ad T.Tao,Lear equatos prmes,a.of Math.,7(00), [4] J.Bourga,A.Gamburd ad.sarak,affe lear seve,expaders,ad sum-product,ivet Math,79(00), Bourga 获 00 年邵逸夫数学奖,Sarak 获 04 年邵逸夫数学奖. 这都是丘成桐推荐的 [4] M.I.Vogradov,Represetatos of a odd umber as a sum of three prmes,dokl.akad.auk SSSR 5(97),9-94. [44] T.Tao ad V.Vu,Addtve combatorcs, Cambrdge Uversty ress.cambrdge(006). [45] B.L.va der Waerde,Bewes eer Baudetsche Vermutug, euw Arch.Wsk.,5(97),-6. [46] B.Host ad B.Kra,Covergece of polyomal ergodc averages,israel J.Math,49(005),-9. [47]B.Host ad B.Kra,ocovetoal ergodc averages ad lmafolds,a of Math,6(005), [48] A.Wles,Modular ellptc curves ad Fermat last theorem, A.of Math.,4(995), [49] R.Taylor ad A.Wles,Rg-theoretc propertes of certa Hecke algebras,a of Math,4(995), [50]D.H.J.olymath,ew equdstrbuto estmates of Zhag type,ad bouded gaps
13 betwee prmes, [5] Chu-Xua Jag,Dsproofs of Rema hypothess,algebras Groups ad Geometres,-6(005) 年我们用新方法证明了 tw prmes theorem ad Goldbach theorem[].995 年 0 月 8-0 日参加首届全国 [ 余新河数学题 ] 研讨会 我论文排在第一位, 中科院组织会议不允许我发言, 以后文集没我论文,996 年在 [ 广西科学 ] 上发表, 中科院去信不允许发表, 但文章巳印好, 最后在 [ 证明 ] 贴上 [ 探讨 ] 发表. 中国一篇划时代论文在中国这样悲惨遭遇. 以后在美国多次发表, 至今无人反驳和否定 从 (7) 我们使用一种特殊同余式 f(q) 三 0 (mod p) q=,...,p-; 不使用 q=,...,p-,p 共有 p 个元素, 这是过去所有数论中没有的, 这样我们创立新素数理论 这是 Euler fucto 推广, 因为 p 的 Euler 函数互素只有 p- 个,Jag fucto 作建立 ISO 数学, 中科院吓坏了, 用保存在 Euler fucto 中与研究素数方程有关的数,Euler fucto ad Jag fucto 都是研究素数的工具, 这一点是统一的 00 年 0 月 5 日科技日报头版报道蒋春暄证明哥德巴赫猜想, 证明费马大定理, 否定黎曼假设和改组科技日报, 下令不允许再报道蒋春暄工作. 蒋春暄母校北京航空航天大学校长沈士团于 00-- 和 召开两次会议邀请蒋春暄去北航成立数学小组, 展开蒋春暄开创工作研究工作, 新校长李未上台, 坚决反对蒋春暄去北航工作, 从北大中科院调干部去北航工作, 死死控制北航, 在北航成立华罗庚学习班. 这样完成整个中国对蒋春暄全面封杀. 中国只能宣传陈景润 +, 出书 [ 从哥德巴赫到陈景润 From Goldbach to Chejgru], 中国不承认蒋春暄正确素数理论, 外国也不承认蒋春暄正确素数理论 但他们都在读蒋春暄的书和论文 目前国内外数学杂志没有素数论文, 无人证明 tw prmes ad Goldbach cojecture. 这种不死不活场面还要继续下去, 我们继续宣传本文 从 Hardy(9) 到 94 年 90 年发表的素数论文都是错的 GY do ot prove that rmes tuples are admssble ad admssble.gy papers are 00% wrog, Ytag Zhag paper also s wrog[8]. O the sgular seres the Jag prme k-tuples theorem Chu-Xua Jag. O. Box 94, Bejg 00854,. R. Cha jcxua@sa.com Abstract
14 Usg Jag fucto we prove Jag prme k -tuples theorem.we fd true sgular seres. Usg the examples we prove the Hardy-Lttlewood prme k -tuples cojecture wth wrog sgular seres.. Jag prme k -tuples theorem wll replace the Hardy-Lttlewood prme k -tuples cojecture. (A) Jag prme k -tuples theorem wth true sgular seres[, ]. We defe the prme k -tuples equato p p+, (), where, =, k. we have Jag fucto [, ] J ( ) ( ( )) ω =Π χ, () where ω = Π, χ ( ) s the umber of solutos of the followg specal cogruece whch s true. k Π ( q+ ) 0 (mo d), q =,, p. () = If χ ( ) < the J ( ) 0 ω. There exst ftely may prmes such that each of + s prme. If χ ( ) = the J ( ) 0 ω =. There exst ftely may prmes such that each of + s prme. J ( ) ω s a subset of Euler fucto φω ( )[]. If J ( ) 0 ω, the we have the best asymptotc formula of the umber of prme [, ] (,) { : } ~ ( ) k J ωω k prme C( k) k k k = + = = (4) φ ( ω) log log φω ( ) =Π( ) + χ( ) Ck ( ) =Π s Jag true sgular seres. Example. Let k =,, +, tw prmes theorem. From () we have k (5) χ() = 0, χ( ) = f >, (6) Substtutg (6) to () we have 4
15 J ( ω) = Π( ) 0 (7) There exst ftely may prmes such that + s prme. Substtutg (7) to (4) we have the best asymptotc formula k (, ) = { : + = prme} ~ Π( ). ( ) log (8) Example. Let k =,, +, + 4. From () we have From () we have χ() = 0, χ() = (9) J ( ω ) = 0. (0) It has oly a soluto =, + = 5, + 4= 7. Oe of, +, + 4 s always dvsble by. Example. Let k= 4,, +, where =,6,8. From () we have Substtutg () to () we have χ( = )0, χ() =, χ( ) = f >. () J ( ω) = Π( 4) 0, () 5 There exst ftely may prmes such that each of + s prme. Substtutg () to (4) we have the best asymptotc formula 7 ( 4) 4(,) = { : + = prme} ~ Π 5 ( ) 4 log 4 () Example 4. Let k = 5,, +, where =,6,8,. From () we have Substtutg (4) to () we have χ( = )0, χ() =, χ(5) =, χ( ) = 4 f > 5 (4) J ( ω) = Π( 5) 0 (5) 7 There exst ftely may prmes such that each of + s prme. Substtutg (5) to (4) we have the best asymptotc formula ( 5) 5(,) = { : + = prme} ~ Π 7 ( ) 5 log 5 (6) 5
16 Example 5. Let k = 6,, +, where =,6,8,,4. From () ad () we have χ() = 0, χ() =, χ(5) = 4, J (5) = 0 (7) It has oly a soluto = 5, + = 7, + 6 =, + 8 =, + = 7, + 4 = 9. Oe of + s always dvsble by 5. (B)The Hardy-Lttlewood prme k -tuples cojecture wth wrog sgular seres[-6]. Ths cojecture s geerally beleved to be true, but has ot bee proved(odlyzko et al.jumpg champo,expermet math,8(999),07-8). We defe the prme k -tuples equato where, =,, k., + (8) I 9 Hardy ad Lttlewood cojectured the asymptotc formula where k(,) = { : + = prme} ~ H ( k), (9) log k ν ( ) Hk ( ) =Π s Hardy-Lttlewood wrog sgular seres, k (0) ν ( ) s the umber of solutos of cogruece whch s wrog. k Π ( q+ ) 0 (mo d), q=,,. () = From () we have ν ( ) < ad Hk ( ) 0. For ay prme k -tuples equato there exst ftely may prmes such that each of + s prme, whch s false. Cojecture. Let k =,, +, tw prmes theorem From () we have ν ( ) = () Substtutg () to (0) we have H () = Π () 6
17 Substtutg () to (9) we have the asymptotc formula (,) = { : + = prme} ~ Π log (4) whch s wrog see example. Cojecture. Let k =,, +, + 4. From () we have Substtutg (5) to (0) we have ν() =, ν( ) = f > (5) H () = 4 Π ( ) ( ) (6) Substtutg (6) to (9) we have asymptotc formula ( ) ( ) log (,) = { : + = prme, + 4 = prm} ~ 4 Π whch s wrog see example. Cojecture. Let k = 4,, +, where =,6,8. (7) From () we have ν( = ), ν() =, ν( ) = f > (8) Substtutg (8) to (0) we have H (4) = Π 7 ( ) > 4 ( ) (9) Substtutg (9) to (9) we have asymptotc formula 7 ( ) 4 = { + = prme} Π > 4 4 (,) : ~ ( ) log Whch s wrog see example. Cojecture 4. Let k = 5,, +, where =,6,8, (0) From () we have ν( = ), ν() =, ν(5) =, ν( ) = 4 f > 5 () Substtutg () to (0) we have ( 4) H (5) = Π 4 ( ) 5 > 5 5 () 7
18 Substtutg () to (9) we have asymptotc formula ( 4) 5 = { + = prme} Π 5 > (,) : ~ 4 ( ) log Whch s wrog see example 4. Cojecture 5. Let k = 6,, +, where =,6,8,,4. () From () we have ν() =, ν() =, ν(5) = 4, ν( ) = 5 f > 5 (4) Substtutg (4) to (0) we have 5 ( 5) H (6) = Π 5 6 > ( ) 5 5 (5) Substtutg (5) to (9) we have asymptotc formula ( 5) 6(,) = { : + = prme} ~ Π > 5 ( ) 6 log 6 (6) whch s wrog see example 5. Cocluso.From Hardy-Lttlewood(9) to 04 all prme papers are wrog. The Jag prme k-tuples theorem has true sgular seres.the Hardy-Lttlewood prme k -tuples cojecture has wrog sgular seres. The tool of addtve prme umber theory s bascally the Hardy-Lttlewood wrog prme k-tuples cojecture [-5]. Usg Jag true sgular seres we prove almost all prme theorems. Jag prme k -tuples theorem wll replace Hardy-Lttlewood prme k -tuples cojecture. There caot be really moder prme theory wthout Jag fucto. Refereces [] Chu-Xua Jag, Foudatos of Satll s soumber theory wth applcatos to ew cryptograms, Fermat s theorem ad Goldbach s cojecture. Iter. Acad. ress, 00,MR004c:00,( ( pdf). [] Chu-Xua Jag, Jag s fucto J ( ) + ω prme dstrbuto. ( www. wbab. et/math/ xua. pdf) ( 8
19 [] G. H. Hardy ad J. E. Lttlewood, Some problems of artto umerorum, III: O the expresso of a umber as a sum of prmes, Acta Math, 44(9), -70. [4] B. Gree ad T. Tao, The prmes cota arbtrarly log arthmetc progressos, A. Math., 67(008), [5] D. A. Goldsto, S. W. Graham, J. tz ad C. Y. Yldrm, Small gaps betwee products of two prmes, roc. Lodo Math. Soc., () 98 (009) [6] D. A. Goldsto, S. W. Graham, J. tz ad C. Y. Yldrm, Small gaps betwee prmes or almost prmes, Tras. Amer. Math. Soc., 6(009) [7] D. A. Goldsto, J. tz ad C. Y. Yldrm, rmes tulpes I, A.of Math., 70(009) [8]. Rbebom, The ew book of prme umber records, rd edto, Sprger-Verlag, ew York, Y, [9] H.Halberstam ad H.-E.Rchert,Seve methods, Academc ress,974. [0] A.Schzel ad W.Serpsk, Sur certaes hypotheses cocerat les ombres premers,acta Arth.,4(958) [].T.Batema ad R.A.Hor,A heurstc asymptotc formula cocerg the dstrbuto of prme umbers,math.comp.,6(96)6-67 [] W.arkewcz,The developmet of prme umber theory,from Eucld to Hardy ad Lttlewood,Sprger-Verlag,ew York,Y,000,-5. [] B.Gree ad T.Tao,Lear equatos prmes, A.of Math.7(00) [4] T.Tao,Recet progress addtve prme umber theory, [5]Ytag Zhag,Bouded gaps betwee prmes,a.of Math.,.79(04)-74. [6] D.H.J.olymath,ew equdstrbuto estmates of Zhag type,ad bouded gaps betwee prmes. The ew rme theorem(5) 9
20 , j + k j( j =,, k ) Chu-Xua Jag. O. Box 94, Bejg 00854,. R. Cha jagchuxua@vp.sohu.com Abstract Usg Jag fucto we prove that there exst ftely may prmes such that each j + k j s a prme. Theorem. Let k be a gve prme., j + k j( j =,, k ) () There exst ftely may prmes such that each of j + k j s a prme. roof. We have Jag fucto[] where ω = Π, χ ( ) s the umber of solutos of cogruece q =,,. k j= J ( ) [ ( )] ω =Π χ, () Π ( jq + k j) 0 (mo d), () From () we have χ () = 0, f < k the χ ( ) =, χ ( k) =, f k < the χ ( ) = k. From () ad () we have J ( ) ( ) ( ) 0 ω = k Π k. (4) We prove that there exst ftely may prmes such that each of j + k j s a prme We have the asymptotc formula [] (,) { : } ~ ( ) k J ωω k = j + k j = prme, (5) k k φ ( ω) log k< where φω ( ) =Π ( ). Referece [] Chu-Xua Jag, Jag s fucto J ( ) + ω prme dstrbuto. wbab.et/math /xua. pdf. 0
21 All zeros of all zeta fuctos are wrog.0abel prze s wrog Rema s Hypothess ad Cojecture of Brch ad Swerto-Dyer are False Chu-Xua Jag. O. Box 94, Bejg Cha jcxua@sa.com Abstract All eyes are o the Rema s hypothess, zeta ad L-fuctos, whch are false, read ths paper. The Euler product coverges absolutely over the whole complex plae. Usg factorzato method we ca prove that Remam s hypothess ad cojecture of Brch ad Swerto-Dyer are false. All zero computatos are false, accurate to sx decmal places. Rema s zeta fuctos ad L fuctos are useless ad false mathematcal tools. Usg t oe caot prove ay problems umber theory. Euler totet fucto φ ( ) ad Jag s fucto J ( ) + ω wll replace zeta ad L fuctos.all Rema hypothess cludg Wel Rema hypothess are false.. Itroducto The fucto ζ () s defed by the absolute coverget seres ζ () s = s () complex half-plae Re () s > s called the Rema s zeta fucto. The Rema s zeta fucto has a smple pole wth the resdue at s = ad the fucto =
22 ζ () s s aalytcally cotued to whole complex plae. We the defe the ζ () s by the Euler product s, () ζ ( s) = ( ) where the product s take all prmes, s = σ + t, =, σ ad t are real. The Rema s zeta fucto ζ () s has o zeros Re () s >. The zeros of ζ () s 0 < Re () s < are called the otrval zeros. I 859 G. Rema cojectured that every zero of ζ () s would le o the le Re ( s ) = /. It s called the Reme s hypothess. [] We have We defe the ellptc curve [] where D s the cogruet umber. ζ( s = σ + t, σ ) 0 () ED : y x Dx =, (4) Assume that D s square-free. Let be a prme umber whch does ot dvde D. Let deote the umbers of pars ( xy, ) where x ad y ru over the tegers modulo, whch satsfy the cogruece ut y x Dx mod. (5) a = (6) We the defe the L fucto of E D by the Euler product s s (7) (, D) = LE (, s) = ( a + ) D where the product s take over all prmes whch do ot dvde D. The Euler product coverges absolutely over the half plae Re ( s ) > /, but t ca be aalytcally cotued over the whole complex plae. For ths fucto, t s the vertcal le Re () s = whch plays the aalogue of the le Re ( s ) = / for the Rema zeta fucto ad the Drchlet L fuctos. Of course, we beleve that every zero of LE ( D, s ) Re () s > 0 should le o the le Re () s =. It s called a cojecture of Brch ad Swerto-Dyer (BSD). We have. Rema s Hypothess s false L( E, s = σ + t, σ / ) 0 (8) D Theorem. Euler product coverges absolutely Re () s >. Let s 0 = /+ t, usg
23 factorzato method we have ζ ( s = / + t) 0 (9) 0 roof. Let s= s0,. s0,.8 s0, s0, 4 s0, 5 s0, s 0 0 We have the followg Euler product equatos s0 ζ( s0) = ζ( s0) ( + ) 0, (0).s0.s 0 ζ(. s0) = ζ( s0) ( + ) 0, () s0.8s0.8s 0 ζ(.8 s0) = ζ( s0) ( + ) 0, () s0 ζ ζ ζ ζ, () 0 0 ( 0) ( 0) ( s s s = ζ s + + ) 0, (4) 0 0 (4 0) ( 0) ( s s s = ζ s + ) ( + ) 0, (5) (5 0) ( 0) ( s s s s ζ s s = ) 0 ( s 0 0) = ζ( s0) ( 0 ) s0 ( + + ) 0, (6) Sce the Euler product coverges absolutely Re () s >, the equato (0)-(6) are true. From (0)-(6) we obta ζ ( s ) 0 (9) 0 All zero computatos are false ad approxmate, accurate to sx decmal places. Usg three methods we proved the RH s false []. Usg the same Method we are able to prove that all Rema s hypotheses also are false. All L fuctos are false ad useless for umber theory.. The Cojecture of Brch ad Swerto-Dyer s false. Theorem. Euler product coverges absolutely Re ( s ) > /. Let s = + t. Usg factorzato method we have roof. Let s = s, s,4 s, we have the followg Euler product equatos. L( E, s = + t) 0 (7) D s s s ( a + ) + a LE ( D, s) = LE ( D, s) + 0 s s (, D) = a + (8)
24 s 4s 5s 4s a + a LE ( D, s) = LE ( D, s) + 0 s s (, D) = a + (9) 4s 6s 7s 6s a + a LE ( D,4 s) = LE ( D, s) + 0 s s (, D) = a + (0) Sce the Euler product coverges absolutely Re ( s ) > /, equatos (8)-(0) are true. From (8)-(0) we obta LE (, s) 0 (7) D All zero computatos are false ad approxmate. Usg the same method we are able to prove all LEs (, ) 0 whole complex plae. The ellptc curves are ot related wth the Dophate equatos ad umber theory [4]. Frey ad Rbet dd ot prove the lk betwee the ellptc curve ad Fermat s equato [4,5]. Wles proved Tayama-Shmura cojecture based o the works of Frey, Serre, Rbet, Mazuer ad Taylor, whch have othg to do wth Fermat s last theorem [6]. Tayama-Shmura cojecture was obscurty for about 0 years tll people serously started thkg about ellptc curves. Mathematcal proof does ot proceed by persoal abuse, but by show careful logcal argumet. Wles proof of Fermat s last theorem s false [7-9]. I 99 Jag proved drectly Fermat s last heorem [0,]. 4. Cocluso. The zero computatos of zeta fuctos ad L fuctos are false. Rema s zeta fuctos ad L fuctos are useless ad false mathematcal tools. Usg t oe caot prove ay problems umber theory []. The heart of Laglads program(l) s the L fuctos []. Therefore L s false. Wles proof of Fermat last theorem s the frst step L. Usg L oe caot prove ay problems umber theory, for example Fermat s last theorem [6]. Euler totet fucto φ ( ) ad Jag s fucto J ( ) + ω wll replace Rema s zeta fuctos ad L fuctos [-5]. Refereces [] B. Rema, Uber de Azahl der rmzahle uder eer gegebeer GrÖsse, Moatsber. Akad. Berl (859) [] Joh Coates, umber theory, Acet ad Moder, I: ICCM 007. vol. I, -. [] Chu-Xua Jag, Dsproofs of Rema s hypothess. Algebras, Groups ad Geometres,, -6(005) [4] G. Frey, Lks betwee stable ellptc curves ad certa dophate equatos, Aales Uverstats Saravess (986), -40. [5] K. A. Rbet, O modular represetatos of Gal ( Q/ Q ) arsg from modular forms, Ivet. 4
25 Math. 00 (990), [6] A. Wles, Modular ellptc curves ad Fermat s last theorem, A. of Math. 4(995), [7] G. erelma, erelma dsproves Wles proof of Fermat s theorem. [8] Y. G. Zhvotov, Fermat s last theorem ad Keeth Rbet s mstakes, html. [9] Y. G. Zhvotov, Fermat s last theorem ad mstakes of Adrew Wles, [0] Chu-Xua Jag, Automorphc fucto ad Fermat s last theorem () [] Chu-Xua Jag, Automorphc fucto ad Fermat s last theorem ()(Fermat s proof of FLT), [] Arthur, et al., edtors, O certa L fuctos. AMS, CMI. 0. volume. [] S. Gelbart, A elemetary troducto to the Laglads program, Bull, of AMS. 0(984) [4] Chu-Xua Jag, The Hardy-Lttlewood prme k tuple cojecture s false. ( ( [5] Chu-Xua Jag, Jag s fucto J ( ) + ω prme dstrbuto, ( ( [6] Chu-Xua Jag, Foudatos of Satll s soumber theory wth applcatos to ew cryptograms, Fermat s theorem ad Goldbach s cojecture, Iter. Acad. ress, 00. MR004c:/00. ( ( 最后说明 Euler product 是绝对收敛的 方程 (0) (6) 和 (8) (0) 是绝对正确的 0 世纪数论上没有重大突破, 主要大家集中力量研究黎曼假设 (RH) 利用 RH 来研究数论问题 RH 所有零点计算都是错误的, 因为无穷 ` 级数无法计算精确值, 这些错误零点计算使 00 年来所有数学家都相信 RH 是正确的, 顶尖数学家都集中力量证明 RH, 并指出 RH 是 世纪最大要解决问题 所有 RH 专家都集中在 IAS Isttute of advaced study was the udsputed Mecca of the Rema hypothess. 0 世纪所有伟大数学家都研究 RH 例如 Hbert. Hardy, Wel, If I were to awake after havg stept for fve hudred years, my frst questo would be: Has the Rema hypothess bee prove? (Davd Hbert) 如果没有蒋春暄否定 RH, 那末再过 500 年 RH 仍不能解决.RH 是数论的基础 利用 RH 许多数学家证明上千个定理, 这些定理都是错的 RH 零点是错的, 那末 L fuctos 零点也是错的 利用 zeta 函数和 5
26 L fuctos 不能证明数论中任何问题 从 RH 出发利用 L 函数和椭圆曲线 R. L. Laglads 提出 Laglads program(l) 把许多没有关系数学问题统一联系起来 利用中国成语 张冠李戴 办法解决所有数学问题, 怀尔斯证明费马大定理就是 L 第一次应用最大成果, 怀尔斯失败, 身败名裂, 也是 L 失败 蒋春暄否定 RH 在 AIM, CLAYMA, IAS, THES, MIM, MSRI 已无人研究 RH 和数论 但是他们仍抓住 L 函数和椭圆曲线不放继续研究, 所以他们集中力量研究 BSD 猜想 目前国内外数论专家下岗或改行 但他们对蒋春暄开创数论新时代, 他们都不讲话, 因为中国对蒋春暄数论成果不承认, 定为伪科学 以 RH 开创数论时代已结束 一个新的数论时代将开始 0 年由卢昌海著王元序 [ 黎曼猜想漫谈 The Rema hypothess(rh)] 到 04 年由清华大学出版社巳印了三次, 大力宣传 RH, 不承认蒋春暄否定 RH. 王元又在中国宣传陈氏定理 +, 不承认蒋春暄 996 年证明 +. 中华民族就这么落后. 又如何成为世界科学强国. reprt (Jauary 994). After Wles was about to aouce hs proof of FLT to the world o Jue, 99. Jag wrote ths paper. Tepper Gll, Kex Lu, ad Erc Trell, Edtors Fudametal Ope roblems Scece at the Ed of the Mleum roceedgs of the Bejg Workshop, August 997 Hadroc ress, alm Harbor, FL , U. S. A ISB , pp Fermat Last Theorem was roved 99 Jag, Chu-xua. O. Box 94, Bejg,. R. Cha We foud out a ew method for provg Fermat last theorem (FLT) o the afteroo of 6
27 October 5, 99. We proved FLT at oe stroke for all prme expoets p >, It led to the dscovery to calculate = 5,,5,05,. To ths date, o oe dsprove ths proof. Ayoe ca ot dey t, because t s a smple ad marvelous proof. It ca ft the marg of Fermat book. I 974 we foud out Euler formula of the cyclotomc real umbers the cyclotomc felds []. exp tj = SJ, () = = where J deotes a - th root of uty, J =, s a odd umber, t are the real umbers. S s called the complex hyperbolc fuctos of order wth varables, where A ( ) j B j θ j j = ( ) j S = [ e + ( ) e cos( + ( ) )], () α j α j A= t, B = t ( ) cos, = ( ) t ( ) s α j j+ α j α j α θ j α α= α= α=, A+ B = 0. () = Usg () the cyclostomes theory may exted to totally real umber felds. It s called the hypercomplex varable theory []. () may be wrtte the matrx form 0 0 A S ( ) e cos s s B S e cosθ ( ) B S s cos s s e θ =, S exp( B )s( θ ) ( ) ( ) ( ) cos s s (4) where ( ) / s a eve umber. From (4) we may obta ts verse trasformato 7
28 A e ( ) cos cos cos S B e cosθ S B e sθ ( ) = 0 s s s S exp( B )s( θ ) S 0 s s s ( ) ( ) ( ) From (5) we have A j j e = S, e cos = S + S ( ) cos e B j θ j + = =, j s ( ) ( ) s. (6) B j j+ θ j = S + j = I () ad (6) t ad S have the same formulas such that every factor of has a Fermat equato. Assume S 0, S 0, S = 0 where =, 4,, S=. 0 are determate equatos wth varables. From (6) we have A B j j j e = S+ S, e = S + S + SS ( ) cos. (7) From () ad (7) we may obta the Fermat equato (5). exp j j A+ B j = ( S+ S) ( S + S + SS ( ) cos ) = S + S =. j= j= (8) Theorem. Fermat last theorem has o ratoal solutos wth SS 0 for all odd expoets. roof. The proof of FLT s dffcult whe s a odd prme. We cosder s a composte umber. Let = Π, where rages over all odd umber. From () we have f f f f (9) j j= f α = exp( A+ B ) = [exp( t α )] From (7) we have f f f (0) j j= f exp( A+ B ) = S + S where f s a factor of. From (9) ad (0) we may obta Fermat equato 8
29 f f f f f f j j= f α = () exp( A+ B ) = S + S = [exp( t α )] Every factor of has a Fermat equato. From () we have f =, B = B = 0, e = S + S = exp( t α ) () A 0 α = 0 j = f= t, = t = 0, exp( A+ B) = S + S = () α = f =,exp( A+ B ) = S + S = [exp( t α )] (4) If S =, S = 0 ad S = 0, S =, the A= B j = 0. Euler proved (), therefore () has o ratoal solutos wth SS 0 (ad so o teger solutos wth SS 0 ) for all odd expoets f. () ad () ca ft the marg of Fermat book. Let = p where p s a odd prme. From () ad (7) we may derve Fermat equtatos p p p p p j (5) = exp( A+ B ) = S + S = ( S ) + ( S ) = p α = exp( A+ Bp ) = S + S = [exp t α )] (6) p p p j p p p (7) = exp( A+ B ) = S + S = [exp( t + t )] Euler proved (5) ad (6), therefore (7) have o ratoal solutos wth SS 0 (ad so o teger solutos wth SS 0 ) for ay odd prme p >. (5)-(7) ca ft the marg Let = 5 p where p s a odd prme. From () ad (7) we may derve Fermat eqatos 5p 5p 5p j (8) j= exp( A+ B ) = S + S = p p 5 α = exp( A+ Bp + B ) = S + S = [exp t α )] (9) p 4 p p p 5j p j= α = (0) exp( A+ B ) = S + S = [exp( t α )] 9
30 (8)-(0) ca ft the marg. Let = 7 p where p s a odd prme. From () ad (7) we may derve Fermat equatos 7p 7p 7p j () = exp( A+ B ) = S + S = p p p p 7 α = exp( A+ B + B + B ) = S + S = [exp t α )] () p 6 p p p 7 j p = α = () exp( A+ B ) = S + S = [exp t α )] ()-() ca also ft the marg. Usg ths method we proved FLT 99 [-5]. a Refereces. Jag, Chu-xua. Hypercomplex varable theory, reprts, Jag, Chu-xua. Fermat last theorem has bee proved (Chese, Eglsh summary) Qa Kexue, (99)7-0. reprts (Eglsh), December, 99. (It s suffcet to prove S S + = for FLT of odd expoets).. Jag, Chu-xua. More tha 00 years ago Fermat last theorem was proved (Chese, Eglsh summary). Qa Kexue, 6(99) 8-0. (It s suffcet to prove S 4 4 S = for FLT.) 4. Jag, Chu-xua. Fermat proof for FLT. reprts (Eglsh), March, Jag, Chu-xua. Factorzato theorem for Fermat equato. reprts (Eglsh), May, 99. ote. Let oe kew the mportat results, we gave out about 600 preprts There were my preprts rceto, Harvard, Berkeley, MIT, Uchcago, Columba, Marylad, Oho, Wscos, Yale,, Eglad, Caada, Japa, olad, Germay, Frace, Flad,, A. Math., Mathematka, J. umber Theory, Glasgow Math. J., Lodo Math. Soc., I. J. Math. Math. Sc., Acta Arth., Ca. Math. Bull. (They refused the publcatos of my papers). Both papers were publshed Chese. FLT s as smple as ythagorea theorem. Ths proof ca ft the marg of Fermat book. We thk the game s up. We set dept of math (rceto Uversty) a preprt o Ja. 5, 99. Wles clams the secod proof of FLT Eglad (ot U. S. A.) after two years. We wsh Wles ad hs supporters dsprove my proof, otherwse Wles work s oly the secod ad complex proof of FLT. We beleve that the rceto s the farest Uversty ad hstory wll pass the farest judgmet o proofs of FLT ad other problems. We are watg for word from the experts who are studyg ths paper. 0
Riemann s Hypothesis and Conjecture of Birch and Swinnerton-Dyer are False
Riemann s Hypothesis and Conjecture of Birch and Swinnerton-yer are False Chun-Xuan Jiang. O. Box 3924, Beijing 854 China jcxuan@sina.com Abstract All eyes are on the Riemann s hypothesis, zeta and L-functions,
More informationFrom Hardy-Littlewood(1923) To 2013 All Prime Papers Are Wrong
From Hardy-Lttlewood(19) To 01 All rme apers Are Wrong The Hardy-Lttlewood prme -tuples conjecture[18,9,4] and Erdos-Turan conjecture(every set of ntegers of postve upper densty contans arbtrarly long
More informationThe Hardy-Littlewood prime k-tuple conjecture is false
The Hardy-Lttlewood prme -tuple conjecture s false Chun-Xuan Jang. O. Box 9, Bejng 008,. R. Chna Jangchunxuan@vp.sohu.com Abstract Usng Jang functon we prove Jang prme -tuple theorem. We prove that the
More information素数分布中蒋函数 蒋春暄. 应该是 ν (log N ) k, 不是 ν 2 (log N ) k 他们 66 页论文没有直接讨论素
素数分布中蒋函数 蒋春暄 777 年最伟大数学家 Euler 说 : 数学家还没有发现素数序列中的一些规则 我们有理由相信它是一个人类智慧尚未洞悉的奥秘 0 世纪最伟大数学家 Erdös 说 : 至少还需要 00 万年, 我们才能真正理解素数 说明素数研究多么困难! 多么复杂! 但是我的兴趣就是要研究没有人研究的问题 用我的思路 我的方法进行研究 不管这个问题多么困难 这篇论文是把我过去对素数研究作一个总结,
More informationd) There is a Web page that includes links to both Web page A and Web page B.
P403-406 5. Determine whether the relation R on the set of all eb pages is reflexive( 自反 ), symmetric( 对 称 ), antisymmetric( 反对称 ), and/or transitive( 传递 ), where (a, b) R if and only if a) Everyone who
More informationThe dynamic N1-methyladenosine methylome in eukaryotic messenger RNA 报告人 : 沈胤
The dynamic N1-methyladenosine methylome in eukaryotic messenger RNA 报告人 : 沈胤 2016.12.26 研究背景 RNA 甲基化作为表观遗传学研究的重要内容之一, 是指发生在 RNA 分子上不同位置的甲基化修饰现象 RNA 甲基化在调控基因表达 剪接 RNA 编辑 RNA 稳定性 控制 mrna 寿命和降解等方面可能扮演重要角色
More informationThere are only 92 stable elements in nature
There are only stable elements in nature Jiang Chun-xuan P. O. Box, Beijing 0, P. R. China jcxxxx@.com Abstract Using mathematical method we prove that there are only stable elements in nature and obtain
More informationA New Sifting function J ( ) n+ 1. prime distribution. Chun-Xuan Jiang P. O. Box 3924, Beijing , P. R. China
A New Siftig fuctio J ( ) + ω i prime distributio Chu-Xua Jiag. O. Box 94, Beijig 00854,. R. Chia jiagchuxua@vip.sohu.com Abstract We defie that prime equatios f (, L, ), L, f (, L ) (5) are polyomials
More informationFermat Last Theorem And Riemann Hypothesis(3) Automorphic Functions And Fermat s Last Theorem(3) (Fermat s Proof of FLT)
Fermat Last Theorem Ad Rema Hypothess(3) Automorphc Fuctos Ad Fermat s Last Theorem(3) (Fermat s Proof of FLT) Chu-Xua Jag P. O. Box 394, Beg 854, P. R. Cha agchuxua@sohu.com Abstract I 637 Fermat wrote:
More information( N) Chun-Xuan Jiang. P. O. Box 3924, Beijing , P. R. China
ang s functon n ( ) n prme dstrbuton Chun-Xuan ang P O Box 94, Bejng 00854, P R Chna jcxuan@snacom Abstract: We defne that prme equatons f( P,, Pn ),, f ( P, Pn ) (5)are polynomals (wth nteger coeffcents)
More informationThe Hardy-Littlewood prime k-tuple conjecture is false
The Hardy-Lttlewood prme k-tuple conjecture s false Chun-Xuan Jang. O. Box 9, Bejng 008,. R. Chna Jangchunxuan@vp.sohu.com Abstract Usng Jang functon we prove Jang prme k -tuple theorem. We prove that
More informationOn the singular series in the Jiang prime k-tuple theorem
On the sngular seres n the Jang prme k-tuple theorem Chun-Xuan Jang. O. Box 9, Bejng 1008,. R. Chna jcxuan@sna.com Abstract Usng Jang functon we prove Jang prme k -tuple theorem.we fnd true sngular seres.
More informationOn the singular series in the Jiang prime k-tuple theorem
On the sngular seres n the Jang prme -tuple theorem Chun-Xuan Jang. O. Box 94, Bejng 10084,. R. Chna jcxuan@sna.com Abstract Usng Jang functon we prove Jang prme -tuple theorem.we fnd true sngular seres.
More informationOn the Quark model based on virtual spacetime and the origin of fractional charge
On the Quark model based on virtual spacetime and the origin of fractional charge Zhi Cheng No. 9 Bairong st. Baiyun District, Guangzhou, China. 510400. gzchengzhi@hotmail.com Abstract: The quark model
More informationA proof of the 3x +1 conjecture
A proof of he 3 + cojecure (Xjag, Cha Rado ad Televso Uversy) (23..) Su-fawag Absrac: Fd a soluo o 3 + cojecures a mahemacal ool o fd ou he codo 3 + cojecures gve 3 + cojecure became a proof. Keywords:
More informationSource mechanism solution
Source mechanism solution Contents Source mechanism solution 1 1. A general introduction 1 2. A step-by-step guide 1 Step-1: Prepare data files 1 Step-2: Start GeoTaos or GeoTaos_Map 2 Step-3: Convert
More information偏微分方程及其应用国际会议在数学科学学院举行
1 偏微分方程及其应用国际会议在数学科学学院举行 2007 年 5 月 28 日至 31 日, 偏微分方程及其应用国际会议 (International Conference on PDEs and Applications) 在北京师范大学数学科学学院举行 国际著名数学家, 世界数学家大会一小时报告人, 美国科学院院士,University of Texas at Austin 教授 Luis Caffarelli
More information2012 AP Calculus BC 模拟试卷
0 AP Calculus BC 模拟试卷 北京新东方罗勇 luoyong@df.cn 0-3- 说明 : 请严格按照实际考试时间进行模拟, 考试时间共 95 分钟 Multiple-Choice section A 部分 : 无计算器 B 部分 : 有计算器 Free-response section A 部分 : 有计算器 B 部分 : 无计算器 总计 45 题 /05 分钟 8 题,55 分钟
More informationUSTC SNST 2014 Autumn Semester Lecture Series
USTC SNST 2014 Autumn Semester Lecture Series Title: Introduction to Tokamak Fusion Energy Nuclear Science and Technology Research and Development (R&D) L8 A: Putting it all together: the box and thinking
More informationThe Lagrange Mean Value Theorem Of Functions of n Variables
陕西师范大学学士学位论文 The Lagrage Mea Value Theorem Of Fuctios of Variables 作 者 单 位 数学与信息科学学院 指 导 老 师 曹怀 信 作 者 姓 名 李 碧 专 业 班 级数学与应用数学专业 4 级 班 The Lagrage Mea Value Theorem of a Fuctio of Variables LI i lass, Grade
More information( 选出不同类别的单词 ) ( 照样子完成填空 ) e.g. one three
Contents 目录 TIPS: 对于数量的问答 - How many + 可数名词复数 + have you/i/we/they got? has he/she/it/kuan got? - I/You/We/They have got + 数字 (+ 可数名词复数 ). He/She/It/Kuan has got + 数字 (+ 可数名词复数 ). e.g. How many sweets
More informationGRE 精确 完整 数学预测机经 发布适用 2015 年 10 月考试
智课网 GRE 备考资料 GRE 精确 完整 数学预测机经 151015 发布适用 2015 年 10 月考试 20150920 1. n is an integer. : (-1)n(-1)n+2 : 1 A. is greater. B. is greater. C. The two quantities are equal D. The relationship cannot be determined
More informationConcurrent Engineering Pdf Ebook Download >>> DOWNLOAD
1 / 6 Concurrent Engineering Pdf Ebook Download >>> DOWNLOAD 2 / 6 3 / 6 Rozenfeld, WEversheim, HKroll - Springer.US - 1998 WDuring 2005 年 3 月 1 日 - For.the.journal,.see.Conc urrent.engineering.(journal)verhagen
More informationQTM - QUALITY TOOLS' MANUAL.
1 2.4.1 Design Of Experiments (DOE) 1. Definition Experimentation is a systematic approach to answer questions and more specifically; how do changes to a system actually affect the quality function or
More information沙强 / 讲师 随时欢迎对有机化学感兴趣的同学与我交流! 理学院化学系 从事专业 有机化学. 办公室 逸夫楼 6072 实验室 逸夫楼 6081 毕业院校 南京理工大学 电子邮箱 研 究 方 向 催化不对称合成 杂环骨架构建 卡宾化学 生物活性分子设计
沙强 / 讲师 随时欢迎对有机化学感兴趣的同学与我交流! 院系 理学院化学系 从事专业 有机化学 学历 博士研究生 学位 博士 办公室 逸夫楼 6072 实验室 逸夫楼 6081 毕业院校 南京理工大学 电子邮箱 qsha@njau.edu.cn 研 究 方 向 催化不对称合成 杂环骨架构建 卡宾化学 生物活性分子设计 研究方向汇总图个人简介 2010 年毕业于南京理工大学制药工程专业, 获得工学学士学位,
More informationAdrien-Marie Legendre
Adrien-Marie Legendre Born: 18 Sept 1752 in Paris, France Died: 10 Jan 1833 in Paris, France 法国数学家 毕业于巴扎林学院 曾任军事学院和巴黎高师的数学教授, 并担任过政府许多部门的顾问, 后来担任艺术学院的学生监督, 直至 1833 年逝世 1783 年与 1787 年, 他先后被选为法兰西科学院院士和伦敦皇家学会会员
More informationChapter 2 the z-transform. 2.1 definition 2.2 properties of ROC 2.3 the inverse z-transform 2.4 z-transform properties
Chapter 2 the -Transform 2.1 definition 2.2 properties of ROC 2.3 the inverse -transform 2.4 -transform properties 2.1 definition One motivation for introducing -transform is that the Fourier transform
More information系统生物学. (Systems Biology) 马彬广
系统生物学 (Systems Biology) 马彬广 通用建模工具 ( 第十四讲 ) 梗概 (Synopsis) 通用建模工具 ( 数学计算软件 ) 专用建模工具 ( 细胞生化体系建模 ) 通用建模工具 主要是各种数学计算软件, 有些是商业软件, 有些是自由软件 商业软件, 主要介绍 : MatLab, Mathematica, Maple, 另有 MuPAD, 现已被 MatLab 收购 自由软件
More informationIntegrated Algebra. Simplified Chinese. Problem Solving
Problem Solving algebraically concept conjecture constraint equivalent formulate generalization graphically multiple representations numerically parameter pattern relative efficiency strategy verbally
More information三类调度问题的复合派遣算法及其在医疗运营管理中的应用
申请上海交通大学博士学位论文 三类调度问题的复合派遣算法及其在医疗运营管理中的应用 博士生 : 苏惠荞 导师 : 万国华教授 专业 : 管理科学与工程 研究方向 : 运作管理 学校代码 : 10248 上海交通大学安泰经济与管理学院 2017 年 6 月 Dissertation Submitted to Shanghai Jiao Tong University for the Degree of
More informationILC Group Annual Report 2018
ILC Group Annual Report 28 D. SHEN 28.2.3 报告摘要 Letter 本报告主要汇总了智能与学习系统中心 (Center of Intelligent and Learning Systems) 在 28 年的研究内容 报告的主要内容包括研究组在本年度的相关数据 会议交流等学术活动 讨论组报告列表 研究生信息表 研究方向概述以及本年度发表论文集 本研究小组的主要研究方向为迭代学习控制
More information西班牙 10.4 米 GTC 望远镜观测时间申请邀请
西班牙 10.4 米 GTC 望远镜观测时间申请邀请 2017B 季度 :2017 年 9 月 1 日 2018 年 2 月 28 日 递交截止日期 :2017 年 4 月 20 日 17:00 ( 北京时间 ) 基于国家天文台和西班牙 GTC 天文台的协议, 国家天文台及其直属单位 ( 云南天文台 南京天文光学技术研究所 新疆天文台和长春人造卫星观测站 ) 将获得有偿使用 10.4 米 GTC 望远镜观测时间的机会
More informationLecture Note on Linear Algebra 16. Eigenvalues and Eigenvectors
Lecture Note on Linear Algebra 16. Eigenvalues and Eigenvectors Wei-Shi Zheng, wszheng@ieee.org, 2011 November 18, 2011 1 What Do You Learn from This Note In this lecture note, we are considering a very
More informationService Bulletin-04 真空电容的外形尺寸
Plasma Control Technologies Service Bulletin-04 真空电容的外形尺寸 在安装或者拆装真空电容时, 由于真空电容的电级片很容易移位, 所以要特别注意避免对电容的损伤, 这对于过去的玻璃电容来说非常明显, 但对于如今的陶瓷电容则不那么明显, 因为它们能够承载更高的机械的 电性能的负载及热负载 尽管从外表看来电容非常结实, 但是应当注意, 由于采用焊接工艺来封装铜和陶瓷,
More informationJules Henri Poincaré
Jules Henri Poincaré Born: 29 April 1854 in Nancy, Lorraine, France Died: 17 July 1912 in Paris, France 法国数学家 物理学家 天文学家 生于一个显赫家族 他具有非凡的心算和数学思维能力 1875 年毕业于巴黎高工, 后来又取得了矿山学院的学位 1879 年任卡昂大学教授, 同年获得巴黎大学的科学博士学位
More information0 0 = 1 0 = 0 1 = = 1 1 = 0 0 = 1
0 0 = 1 0 = 0 1 = 0 1 1 = 1 1 = 0 0 = 1 : = {0, 1} : 3 (,, ) = + (,, ) = + + (, ) = + (,,, ) = ( + )( + ) + ( + )( + ) + = + = = + + = + = ( + ) + = + ( + ) () = () ( + ) = + + = ( + )( + ) + = = + 0
More informationPTAS for Bin-Packing
CS 663: Patter Matchg Algorthms Scrbe: Che Jag /9/00. Itroducto PTAS for B-Packg The B-Packg problem s NP-hard. If we use approxmato algorthms, the B-Packg problem could be solved polyomal tme. For example,
More information上海激光电子伽玛源 (SLEGS) 样机的实验介绍
上海激光电子伽玛源 (SLEGS) 样机的实验介绍 Pan Qiangyan for SLEGS collaborators 一. 引言二. 装置布局三. 实验及其结果四. 结论 一, 引言 为建设 SLEGS 光束线提供参考和研制依据, 中科院上海应用物理研究所于 2005 年成立了以徐望研究员为组长的 SLEGS 小组, 开展 SLEGS 样机的实验工作 ; 在中科院知识创新工程方向性项目 (
More information能源化学工程专业培养方案. Undergraduate Program for Specialty in Energy Chemical Engineering 专业负责人 : 何平分管院长 : 廖其龙院学术委员会主任 : 李玉香
能源化学工程专业培养方案 Undergraduate Program for Specialty in Energy Chemical Engineering 专业负责人 : 何平分管院长 : 廖其龙院学术委员会主任 : 李玉香 Director of Specialty: He Ping Executive Dean: Liao Qilong Academic Committee Director:
More informationEffect of lengthening alkyl spacer on hydroformylation performance of tethered phosphine modified Rh/SiO2 catalyst
Chinese Journal of Catalysis 37 (216) 268 272 催化学报 216 年第 37 卷第 2 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Article Effect of lengthening alkyl
More informationILC Group Annual Report 2017
ILC Group Annual Report 2017 D. SHEN 2017.12.31 报告摘要 Letter 本报告主要汇总了迭代学习控制研究组在 2017 年的研究内容 报告的主要内容包括研究组在本年度的相关数据 会议交流等学术活动 讨论组报告列表 研究生信息表 研究方向概述以及本年度发表论文集 本研究小组的主要研究方向为迭代学习控制 围绕这一方向, 研究组在本年度开展了一系列的研究,
More informationJean Baptiste Joseph Fourier
Jean Baptiste Joseph Fourier Born: 21 March 1768 in Auxerre, Bourgogne, France Died: 16 May 1830 in Paris, France 法国数学家 物理学家 生于一个裁缝家庭,9 岁时父母双亡, 由当地一主教收养 曾在地方军校学习, 后成为牧师 1790 年成为巴黎高工的教授 1798 年随拿破仑远征埃及,
More informationTKP students will be guided by the revised school values, PR IDE: ride espect esponsibility ntegrity iscipline mpathy
K i i I 6 i i K I i i Ci k K Pii f j K Pi i k f i i i i i I i j K Pi (KP) i i i 14-- H i ii i i i f 3 Fi Pi( f Fi) Hi B M Pi i f KP i 2001 I f f ff i 3 L i i f i KP i i i i i i i i ii Wi i k i i i i f
More informationEaster Traditions 复活节习俗
Easter Traditions 复活节习俗 1 Easter Traditions 复活节习俗 Why the big rabbit? 为什么有个大兔子? Read the text below and do the activity that follows 阅读下面的短文, 然后完成练习 : It s Easter in the UK and the shops are full of Easter
More informationIncreasing the range of non noble metal single atom catalysts
Chinese Journal of Catalysis 38 (2017) 1489 1497 催化学报 2017 年第 38 卷第 9 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Perspective (Special Issue of
More information王苏宁博士生导师加拿大女王大学科研项目主席 加拿大皇家科学院院士
王苏宁博士生导师加拿大女王大学科研项目主席 加拿大皇家科学院院士 Email : wangsn14@bit.edu.cn suning.wang@chem.queensu.ca http://faculty.chem.queensu.ca/people/faculty/wang /index.htm 欢迎校内外具有相关专业背景的本科生 研究生和博士后加入本课题组! 主要经历 1978-1982 年
More informationLecture 2. Random variables: discrete and continuous
Lecture 2 Random variables: discrete and continuous Random variables: discrete Probability theory is concerned with situations in which the outcomes occur randomly. Generically, such situations are called
More informationLecture Note on Linear Algebra 14. Linear Independence, Bases and Coordinates
Lecture Note on Linear Algebra 14 Linear Independence, Bases and Coordinates Wei-Shi Zheng, wszheng@ieeeorg, 211 November 3, 211 1 What Do You Learn from This Note Do you still remember the unit vectors
More informationConditional expectation and prediction
Conditional expectation and prediction Conditional frequency functions and pdfs have properties of ordinary frequency and density functions. Hence, associated with a conditional distribution is a conditional
More informationHappy Niu Year 牛年快乐 1
Happy Niu Year 牛年快乐 1 Celebrating in Style 庆新年 Happy Niu Year 牛年快乐 Read the text below and do the activity that follows. 阅读下面的短文, 然后完成练习 : 2008 is now finally in the past as millions of Chinese people
More informationChapter 5 Properties of a Random Sample
Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample
More informationXING Sheng-Kai LI Yun ZHAO Xue-Zhuang * CAI Zun-Sheng SHANG Zhen-Feng WANG Gui-Chang *
1000 物理化学学报 (Wuli Huaxue Xuebao) Acta Phys. Chim. Sin. 2011, 27 (5), 1000-1004 May [Communication] www.whxb.pku.edu.cn Möbius 环并苯的分子对称性 * 邢生凯李云赵学庄 ( 南开大学化学学院, 天津 300071) * 蔡遵生尚贞锋王贵昌 摘要 : 一般来说, 点群理论认为 Möbius
More informationWorkshop on Numerical Partial Differential Equations and Scientific Computing
Workshop on Numerical Partial Differential Equations and Scientific Computing On the occasion of Prof. Houde Han's 80th Birthday Department of Mathematical Sciences Tsinghua University May 27-28, 2017
More informationType and Propositions
Fall 2018 Type and Propositions Yu Zhang Course web site: http://staff.ustc.edu.cn/~yuzhang/tpl Yu Zhang: Types and Propositions 1 Outline Curry-Howard Isomorphism - Constructive Logic - Classical Logic
More information國立中正大學八十一學年度應用數學研究所 碩士班研究生招生考試試題
國立中正大學八十一學年度應用數學研究所 碩士班研究生招生考試試題 基礎數學 I.(2%) Test for convergence or divergence of the following infinite series cos( π (a) ) sin( π n (b) ) n n=1 n n=1 n 1 1 (c) (p > 1) (d) n=2 n(log n) p n,m=1 n 2 +
More informationASSESSING THE QUALITY OF OPEN ACCESS JOURNALS
ASSESSING THE QUALITY OF OPEN ACCESS JOURNALS 审核开放获取期刊的质量 S E M I N A R A T C H I N A O P E N A C C E S S W E E K O C T O B E R 1 9, 2 0 1 6, B E I J I N G T O M @ D O A J. O R G E D I T O R - I N - C
More informationInternational Workshop on Advances in Numerical Analysis and Scientific Computation
International Workshop on Advances in umerical Analysis and Scientific Computation Shanghai ormal University, Shanghai, China June 30-July 3, 2018 Contents Themes and Objectives...3 Sponsors...3 Organizing
More information+δ -δ. v vcm. v d + 2 VO1 I1 VO2. V in1. V in2. Vgs1 Vgs2 I O R SINK V SS V DD. Sheet 1 of 9. MOS Long Tail Pair (Diffferential Amplifier)
of 9 MS ong ail air (Diffferential Amplifier) he basic differential amplifier schematic is shown in Figure. A voltage applied to in will cause a current to flow through R, but as vcm is a virtual ground
More informationHalloween 万圣节. Do you believe in ghosts? 你相信有鬼吗? Read the text below and do the activity that follows. 阅读下面的短文, 然后完成练习 :
Halloween 万圣节 1 Halloween 万圣节 Do you believe in ghosts? 你相信有鬼吗? Read the text below and do the activity that follows. 阅读下面的短文, 然后完成练习 : Though many people think it is an American festival, Halloween is
More informationSichuan Earthquake 四川地震
Sichuan Earthquake 四川地震 1 Sichuan Earthquake 四川地震 China Mourns Victims of the Sichuan Earthquake 中国为震灾遇难者哀悼 Read the text below and do the activity that follows. 阅读下面的短文, 然后完成练习 : Flags are flying at half-mast
More informationAlgorithms and Complexity
Algorithms and Complexity 2.1 ALGORITHMS( 演算法 ) Def: An algorithm is a finite set of precise instructions for performing a computation or for solving a problem The word algorithm algorithm comes from the
More informationRigorous back analysis of shear strength parameters of landslide slip
Trans. Nonferrous Met. Soc. China 23(2013) 1459 1464 Rigorous back analysis of shear strength parameters of landslide slip Ke ZHANG 1, Ping CAO 1, Rui BAO 1,2 1. School of Resources and Safety Engineering,
More informationA new approach to inducing Ti 3+ in anatase TiO2 for efficient photocatalytic hydrogen production
Chinese Journal of Catalysis 39 (2018) 510 516 催化学报 2018 年第 39 卷第 3 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Article (Special Issue of Photocatalysis
More informationTHE INVERSE DERIVATIVE
Phsics Disquisition THE INVERSE DERIVATIVE The new algorithm of the derivative GuagSan Yu ( Harbin Macro Dnamics Institute. 1566, P. R. China ) E-mail:1951669731@qq.com ( 15.1.1 16.1.6 ) Abstract: The
More informationNon-uniform Turán-type problems
Joural of Combatoral Theory, Seres A 111 2005 106 110 wwwelsevercomlocatecta No-uform Turá-type problems DhruvMubay 1, Y Zhao 2 Departmet of Mathematcs, Statstcs, ad Computer Scece, Uversty of Illos at
More informationGalileo Galilei ( ) Title page of Galileo's Dialogue concerning the two chief world systems, published in Florence in February 1632.
Special Relativity Galileo Galilei (1564-1642) Title page of Galileo's Dialogue concerning the two chief world systems, published in Florence in February 1632. 2 Galilean Transformation z z!!! r ' = r
More informationMicrobiology. Zhao Liping 赵立平 Chen Feng. School of Life Science and Technology, Shanghai Jiao Tong University
1896 1920 1987 2006 Microbiology By Zhao Liping 赵立平 Chen Feng 陈峰 School of Life Science and Technology, Shanghai Jiao Tong University http://micro.sjtu.edu.cn 1896 1920 1987 2006 Preface : Introduction
More informationEnhancement of the activity and durability in CO oxidation over silica supported Au nanoparticle catalyst via CeOx modification
Chinese Journal of Catalysis 39 (2018) 1608 1614 催化学报 2018 年第 39 卷第 10 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Article Enhancement of the activity
More informationUNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postpoed exam: ECON430 Statstcs Date of exam: Jauary 0, 0 Tme for exam: 09:00 a.m. :00 oo The problem set covers 5 pages Resources allowed: All wrtte ad prted
More informationSynthesis of PdS Au nanorods with asymmetric tips with improved H2 production efficiency in water splitting and increased photostability
Chinese Journal of Catalysis 39 (2018) 407 412 催化学报 2018 年第 39 卷第 3 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Communication (Special Issue of
More informationBasic& ClinicalMedicine March2017 Vol.37 No.3 : (2017) 研究论文,-./ )89:;/Ⅱ,,,,,,!,"#$,%&' ("# <= 9>? B,"# 400
2017 3 37 3 Basic& ClinicalMedicine March2017 Vol.37 No.3 :1001 6325(2017)03 0341 05 研究论文,-./01 2343567)89:;/Ⅱ,,,,,,!,"#$,%&' ("# ? =@=A B,"# 400016)!": # CD,E -./ 2343567)89 89:;/Ⅱ(Ang Ⅱ) F $% GHIJ-./KL,E
More information第五届控制科学与工程前沿论坛 高志强. Center for Advanced Control Technologies
第五届控制科学与工程前沿论坛 自抗扰控制技术的理念 方法与应用 纪念韩京清先生逝世五周年 高志强 二零一三年四月十九日 Center for Advanced Control Technologies http://cact.csuohio.edu 概要 引言自抗扰控制的渊源自抗扰控制的应用自抗扰控制的论证抗扰技术研究小结 引言 君子务本, 本立而道生 韩京清 :1937-2008 六十年代 : 最优控制,
More informationInvestigating Cellular Automata
Researcher: Taylor Dupuy Advsor: Aaro Wootto Semester: Fall 4 Ivestgatg Cellular Automata A Overvew of Cellular Automata: Cellular Automata are smple computer programs that geerate rows of black ad whte
More informationOptical diffraction from a liquid crystal phase grating
JOURNAL OF APPLIED PHYSICS VOLUME 91, NUMBER 6 15 MARCH 2002 Optical diffraction from a liquid crystal phase grating C. V. Brown, a) Em. E. Kriezis, and S. J. Elston Department of Engineering Science,
More information2NA. MAYFLOWER SECONDARY SCHOOL 2018 SEMESTER ONE EXAMINATION Format Topics Comments. Exam Duration. Number. Conducted during lesson time
Art NA T2 W3-W6 Project Work 1) Investigation and Interpretation of Theme 2) Control of Technical Processes 3) Reflection Conducted during lesson time Bahasa Melayu Express Stream SBB 1 2h Bahagian A E-mel
More informationGeorg Friedrich Bernhard Riemann
Georg Friedrich Bernhard Riemann Born: 17 Sept 1826 in Breselenz, Hanover (now Germany) Died: 20 July 1866 in Selasca, Italy 德国数学 1846 年进入哥廷根大学神学院学习,1847-1849 年在柏林大学学习, 1849 年回到哥廷根大学任教,1851 年获博士学位,1854
More information= lim(x + 1) lim x 1 x 1 (x 2 + 1) 2 (for the latter let y = x2 + 1) lim
1061 微乙 01-05 班期中考解答和評分標準 1. (10%) (x + 1)( (a) 求 x+1 9). x 1 x 1 tan (π(x )) (b) 求. x (x ) x (a) (5 points) Method without L Hospital rule: (x + 1)( x+1 9) = (x + 1) x+1 x 1 x 1 x 1 x 1 (x + 1) (for the
More information电子科技大学研究生专项奖学金申请表 学生类别
电子科技大学研究生专项奖学金申请表 姓名罗金南学号 2016112 20108 学生类别 博士 硕士 年级 2016 政治面貌团员导师姓名 田文 洪 专业 软件工程 中国银行帐户 ( 即发助研助学金的帐户 ) 6216633100000328889 申请奖学金类别世强奖学金 ( 特等 ) 个人 总结 本人在读博士研究生期间思想政治上坚定拥护党和国家的路线方针政策, 具有正确的政治方向 ; 学习科研上勤奋刻苦,
More informationThe internal structure of natural numbers, one method for the definition of large prime numbers, and a factorization test
Fal verso The teral structure of atural umbers oe method for the defto of large prme umbers ad a factorzato test Emmaul Maousos APM Isttute for the Advacemet of Physcs ad Mathematcs 3 Poulou str. 53 Athes
More informationIdeal multigrades with trigonometric coefficients
Ideal multgrades wth trgoometrc coeffcets Zarathustra Brady December 13, 010 1 The problem A (, k) multgrade s defed as a par of dstct sets of tegers such that (a 1,..., a ; b 1,..., b ) a j = =1 for all
More informationPacking of graphs with small product of sizes
Joural of Combatoral Theory, Seres B 98 (008) 4 45 www.elsever.com/locate/jctb Note Packg of graphs wth small product of szes Alexadr V. Kostochka a,b,,gexyu c, a Departmet of Mathematcs, Uversty of Illos,
More informationPROJECTION PROBLEM FOR REGULAR POLYGONS
Joural of Mathematcal Sceces: Advaces ad Applcatos Volume, Number, 008, Pages 95-50 PROJECTION PROBLEM FOR REGULAR POLYGONS College of Scece Bejg Forestry Uversty Bejg 0008 P. R. Cha e-mal: sl@bjfu.edu.c
More informationSpecial Instructions / Useful Data
JAM 6 Set of all real umbers P A..d. B, p Posso Specal Istructos / Useful Data x,, :,,, x x Probablty of a evet A Idepedetly ad detcally dstrbuted Bomal dstrbuto wth parameters ad p Posso dstrbuto wth
More informationCLASS E amplifiers [1] are advantageous networks for
484 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 3, MARCH 2007 Design of Class E Amplifier With Nonlinear and Linear Shunt Capacitances for Any Duty Cycle Arturo Mediano, Senior Member,
More informationChapter 22 Lecture. Essential University Physics Richard Wolfson 2 nd Edition. Electric Potential 電位 Pearson Education, Inc.
Chapter 22 Lecture Essential University Physics Richard Wolfson 2 nd Edition Electric Potential 電位 Slide 22-1 In this lecture you ll learn 簡介 The concept of electric potential difference 電位差 Including
More informationAn IntRoduction to grey methods by using R
An IntRoduction to grey methods by using R Tan Xi Department of Statistics, NUFE Nov 6, 2009 2009-2-5 Contents: A brief introduction to Grey Methods An analysis of Degree of Grey Incidence Grey GM(, )
More informationIntroduction to local (nonparametric) density estimation. methods
Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest
More informationExercises for Square-Congruence Modulo n ver 11
Exercses for Square-Cogruece Modulo ver Let ad ab,.. Mark True or False. a. 3S 30 b. 3S 90 c. 3S 3 d. 3S 4 e. 4S f. 5S g. 0S 55 h. 8S 57. 9S 58 j. S 76 k. 6S 304 l. 47S 5347. Fd the equvalece classes duced
More informationQ-analogue of a Linear Transformation Preserving Log-concavity
Iteratoal Joural of Algebra, Vol. 1, 2007, o. 2, 87-94 Q-aalogue of a Lear Trasformato Preservg Log-cocavty Daozhog Luo Departmet of Mathematcs, Huaqao Uversty Quazhou, Fua 362021, P. R. Cha ldzblue@163.com
More informationBrainwashed Tom Burrell Pdf Download >>> DOWNLOAD
Brainwashed Tom Burrell Pdf Download >>> DOWNLOAD 1 / 5 2 / 5 ,...TomBurr... WPanorama's...download...includes...both...the...image...viewer...program...and...a...scr eensaverbrainwashed:.challenging.the.myth.of.black.inferiority.tom.burrell.2017-11...
More informationDesign, Development and Application of Northeast Asia Resources and Environment Scientific Expedition Data Platform
September, 2011 J. Resour. Ecol. 2011 2(3) 266-271 DOI:10.3969/j.issn.1674-764x.2011.03.010 www.jorae.cn Journal of Resources and Ecology Vol.2 No.3 NE Asia Design, Development and Application of Northeast
More informationMICROSTRIP directional couplers have been commonly
756 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO., DECEMBER 008 The Complete Design of Microstrip Directional Couplers Using the Synthesis Technique Abdullah Eroglu, Member, IEEE,
More informationLINEAR REGRESSION ANALYSIS
LINEAR REGRESSION ANALYSIS MODULE V Lecture - Correctg Model Iadequaces Through Trasformato ad Weghtg Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur Aalytcal methods for
More information目錄 Contents. Copyright 2008, FengShui BaZi Centre < 2
目錄 Contents 1. 子平八字命理学简介 Introduction of [Zi Ping Ba Zi] Destiny, Fate & Luck Analysis 1.1 日历种类 Type of Calendar 1.2 年, 月, 日, 时, 的关系 The Relationships between Year, Month, Day & Hour 1.3 命运的原理 The Principle
More informationMATH 247/Winter Notes on the adjoint and on normal operators.
MATH 47/Wter 00 Notes o the adjot ad o ormal operators I these otes, V s a fte dmesoal er product space over, wth gve er * product uv, T, S, T, are lear operators o V U, W are subspaces of V Whe we say
More informationDesignation: D
Designation: D556 0 An American National Standard Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies Using Waveguide
More informationChapter 1 Linear Regression with One Predictor Variable
Chapter 1 Linear Regression with One Predictor Variable 許湘伶 Applied Linear Regression Models (Kutner, Nachtsheim, Neter, Li) hsuhl (NUK) LR Chap 1 1 / 41 Regression analysis is a statistical methodology
More informationA highly efficient flower-like cobalt catalyst for electroreduction of carbon dioxide
Chinese Journal of Catalysis 39 (2018) 914 919 催化学报 2018 年第 39 卷第 5 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Article A highly efficient flower-like
More informationFunctions of Random Variables
Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,
More information