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Str.ngly Singular.Convo1ution Op.r.tor. on the Weighted Her.-Typ. Har.y Sp.ces

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Acta Mathematica Sinica,English Ser.es 1998年第1期14卷 67-76页

作者： Li Xiaochun Lu Shanzhen department of mathematics, beijing normal university, beijing 100875, china

Let 01, w2 ∈A1 （Muckenhoup.-class）. In this p.p.r.the author. p.ove that the str.ngly singular.convolution op.r.tor. ar. bounded fr.m the homogeneous weighted Her.-typ. Har.y sp.ces HKqα,p.w1; w2） to the homogen... 详细信息

Let 0p.1q1, w2 ∈A1 （Muckenhoup.-class）. In this p.p.r.the author. p.ove that the str.ngly singular.convolution op.r.tor. ar. bounded fr.m the homogeneous weighted Her.-typ. Har.y sp.ces HKqp.α,p./sup.（w1; w2） to the homogeneous weighted Her. sp.ces Kqp.α,p./sup.（w1;w2）, p.ovided α=n（1--1/q）. Mor.over. the boundedness of these op.r.tor. on the non-homogeneous weighted Her.-typ. Har.y sp.ces HKqp.α,p./sup.（w1, w2） is also investigated.

关键词： Str.ngly singular.convolution op.r.tor Har.y sp.ce

Theor.tical Study on the p.r.lysis Mechanism and Kinetics of 3-Hydr.xy-3-Methyl-2-Butanone

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Chinese Chemical Letter. 1998年第11期9卷 0-0页

作者： Wen Lin FENG Jie Hao chen Yan WANG (department of chemistr., beijing normal university, beijing 100875) beijing normal Univ Dept Chem Beijing 100875 Peoples R China

The mechanism and kinetics for.the decomp.sition of 3-hydr.xy-3-methyl-2-butanone have been studied by using the ab initio r.F/3-21G method. The calculated activation bar.ier.of the r.action is 249.6kJ/mol which is in r.asonable agr.ement with the exp.r.mental data (222.2±3kJ/mol). The calculated r.sults show that the decomp.sition is a concer.ed p.ocess with hydr.gen tr.nsfer.ing and bond br.aking via a five-member.d cyclic tr.nsition state. The ther.al r.te constants of the decomp.sition ar. obtained by calculating micr.canonical p.obability fluxes thr.ugh tr.nsition state1.

关键词： Kinetics mechanism theor.tical study r.te constants

Ab initio studies on the p.r.lysis mechanism of 2-haloacetic acids in the gas p.ase

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Chinese Jour.al of Chemistr. 1995年第1期13卷 10-18页

作者： chen, Li-Tao chen, Guang-Ju FU, Xiao-YuanChemistr. department, beijing normal university, beijing 100875, china Chemistr. department Beijing Normal University Beijing 100875 China SU.EDU

The dehydr.halogenation mechanism of 2-haloacetic acids (XCH2CO2H, X=F, Cl and Br. has been studied theor.tically by HF/3-21G and AM1 methods. The r.sults indicate that these r.actions ar. most p.obably p.oceeded in ter.s of a p.lar.five-member.d cyclic tr.nsition state in the gas p.ase. Their.micr.scop.c p.ocesses ar. beleived to be a step.ise r.action and the r.te-deter.ining step.is the fir.t one. By comp.r.ng the ener.y bar.ier. of differ.nt 2-haloacetic acids, it can be r.alized that 2-fluor.acetic acid is easier.to r.act than 2-chlor.acetic and 2-br.moacetic acids.

关键词： 2-Haloacetic acid p.r.lysis r.action mechanism tr.nsition state.

Boundar. Nevanlinna-p.ck Inter.0}lation for.Mer.mor.0}ic Functions

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Acta Mathematicae Ap.licatae Sinica 2002年第2期18卷 255-262页

作者： Gong-ning chen, Li-xin Jiadepartment of mathematics, beijing normal university, beijing 100875, china Electr.nic and Technology Institute, Zhengzhou 450004, china department of mathematics Beijing Normal University Beijing China Electr.nic and Technology Institute Zhengzhou China

Ver.ions of the multip.e Nevanlinna-p.ck inter.0}lation p.oblem in the class N involving both inter.or.and boundar. data ar. investigated. This leads to solvability cr.ter.a for.the indicated p.oblems and descr.p.ion o... 详细信息

关键词： Nevanlinna-p.ck inter.0}lation gener.lized p.ck matr.x Hankel vector p.wer.moment p.oblem minimally p.sitive Hankel matr.x

△-tame quasi-her.ditar. algebr.s

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Science china mathematics 2007年第2期50卷 240-252页

作者： Yun-ge XU & Ying-bo ZHANG Faculty of mathematics and Comp.ter.Science, Hubei university, Wuhan 430062, china School of mathematics Sciences, beijing normal university, beijing 100875, china Faculty of mathematics and Comp.ter.Science Hubei University Wuhan China School of mathematics Sciences Beijing Normal University Beijing China

Let (K, M,H) be an up.er.tr.angular.bimodule p.oblem. Br.istle and Hille showed that the op.osite algebr. A of the endomor.0}ism algebr. of a p.ojective gener.tor.p.of the matr.ces categor. of (K., M, H) is quasi-her.ditar., and ther. is an equivalence between the categor. of△-good modules of A and Mat(K, M). In this note, based on the tame theor.m for.bimodule p.oblems, we show that if the algebr. A associated with an up.er.tr.angular.bimodule p.oblem is of△-tame r.p.esentation typ., then the categor. F(△) has the homogeneous p.op.r.y, i.e. almost all modules in F(△) ar. isomor.0}ic to their.Auslander.r.iten tr.nslations. Mor.over. if (K, M,H)is an up.er.tr.angular.bip.r.ite bimodule p.oblem, then A is of△-tame r.p.esentation typ. if and only if F(△) is homogeneous.

关键词： bimodule p.oblem quasi-her.ditar. algebr. △-tameness homogeneity.

Asymmetr.c p.otocatalyzed Addition of Cyclic Ammes to the Chir.l 5-(l)-Menthyloxy-2(5H)-fur.none

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Chinese Chemical Letter. 1999年第11期10卷 889-892页

作者： Zhao Yang WANG Tian Ying JIAN Qing Hua chen(department of Chemistr.,beijing normal university, beijing 100875) department of Chemistr. Beijing Normal University Beijing 100875 China

The benzop.enone-initiated p.otoaddition of N-methyl ammes 2 to the chir.l synthon1 p.oceeds in a r.giosp.citlc and highlyr.ster.ocontr.lled thshion to give the C-C p.otoadductscontaining a ne\viy ster.ogenic center.3a-3c. The enantiomer.cally p.r. N-C p.otoadducts, aminobutenolides 5a-5c have been obtained fr.m the enantioselective p.otoaddition of secondar. cyclicammes 4 with the chir.l synthon 1 under.the same conditions.

关键词： Asymmetr.c p.otocatalysed conjugate addition enantiomer.cally p.r. C-Cp.otoadducts. secondar. cyclic amine enantiomer.cally p.r. N-C p.otoaducts.

A Novel Synthesis of Isoxazole Der.vatives

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Chinese Chemical Letter. 1998年第9期9卷 801-802页

作者： Jun Feng WANG Bao Shan DU Qing Hua chen (department of Chemistr., beijing normal university, beijing 100875) beijing normal Univ Dept Chem Beijing 100875 Peoples R China

The new synthetic method of isoxazole der.vatives was succesfully achieved. The exp.r.mental r.sults demonstr.te that ther.al decomp.sition r.actions of nitr.ne could take p.ace with yields of 41 similar.to 81%, to gi... 详细信息

关键词： nitr.ne isoxazole

Continuity of Higher.Or.er.Commutator. on Cer.ain Har.y Sp.ces

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Acta Mathematica Sinica,English Ser.es 2002年第2期18卷 391-404页

作者： DING Yong LU Shan Zhen department of mathematics,beijing normal university,beijing 100875.p.r.china E-mail:dingy@*** lusz@***ZHANG p. department of mathematics.Zhejiang university(at Xixi Camp.s).Hangzhou 310028,p.r.china,E-mail:zhp.j@263,net department of mathematics Beijing Normal University Beijing P.R. China department of mathematics Zhejiang University (at Xixi Campus) Hangzhou P.R. China

In this *** author. study the continuity p.op.r.ies of higher.or.er.commutator. gener.ted by the homogeneous fr.ctional integr.l and BMO functions on cer.ain Har.y sp.ces,weak Har.y sp.ces and Her.-typ. Har.y sp.ces.

关键词： Fr.ctional integr.l Homogeneous ker.el L^r.Dini condition Har.y sp.ce Her.-typ. Har.y sp.ce

Char.cter.zation for.commutator. of n-dimensional fr.ctional Har.y op.r.tor.

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Science china mathematics 2007年第10期50卷 1418-1426页

作者： Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1+) Hong-bin WANG~3 ~1 School of Mathematical Sciences,beijing normal university,beijing 100875,china ~2 department of mathematics,Linyi normal university,Linyi 276005,china ~3 department of mathematics,china university of Mining and Technology (beijing),beijing 100083,china 1. School of Mathematical Sciences Beijing Normal University Beijing 100875 China 2. department of mathematics Linyi Normal University Linyi 276005 China 3. department of mathematics China University of Mining and Technology (Beijing) Beijing 100083 China

In this p.p.r.it was p.oved that the commutator.H_(β,b)gener.ted by an n-dimensional fr.ctional Har.y op.r.tor.and a locally integr.ble function b is bounded fr.m L^(p.)(r.n)to L^(p.)(r.n)if and only if b is a CMO(r.n)function,wher. 1/p.-1/p.=β/n,1p.r.cter.zation of H_(β,b)on the homogenous Her. sp.ce K_q^(α,p.(r.n)was obtained.

关键词： n-dimensional fr.ctional Har.y op.r.tor. commutator. C(M)O function, homogeneous Her. sp.ce