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Linear.op.r.tor. p.eser.ing the gener.lized decomp.sable numer.cal r.nge

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Chinese Science Bulletin 1997年第1期42卷 22-26页

作者： LEI Tiangangdepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

LET G be a subgr.up.of the symmetr.c gr.up.Sm. Denote by CG the set of all functions f: G→C. A function f∈CG is said to be p.sitive semi-definite （p. s. d. ） if ther. exists c∈CG such that for.all τ∈G. In p.r.icular. the ir.educible comp.ex char.cter. of G ar. p. s. d. Let Cn×m denote the set of all n×m comp.ex matr.ces. For.f∈CG, the

关键词： decomp.sable numer.cal r.nge linear op.r.tor p.sitive semi-definite function gener.lized matr.x function.

A Besov Estimate for.Multilinear.Singular.Integr.ls

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Acta Mathematica Sinica,English Ser.es 2000年第4期16卷 613-626页

作者： Wengu chen department of mathematics, Cap.tal normal university. beijing 100037. p. r. china department of mathematics Capital Normal University Beijing 100037 P. R. China

The main p.r.0}se of this p.p.r.is to p.ove a good λ inequality for.a multilinear.singular.integr.l in r.n.

关键词： Multilinear.op.r.tor Besov sp.ce Good λ inequality

The Besov Sp.ce B_1^(0.1) on Domains

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Acta Mathematica Sinica,English Ser.es 2001年第2期17卷 181-196页

作者： Yi Qing GUI Shan Zhen LU Da Chun YANG department of mathematics. beijing normal university. beijing 100875. p. r. china department of mathematics Beijing Normal University Beijing 100875 P. R. China

Let Ω be a bounded Lip.chitz domain. Define B1,r..1（Ω）={f∈L1（Ω）: ther. is an F∈ B10.1（r.） such that F|Ω=f| and B1,z0.1（Ω）={f∈B10.1（r.）: f=0 on r.\}. In this p.p.r. the author. establish the atomic de... 详细信息

Let Ω be a bounded Lip.chitz domain. Define B1,r./sub>p.0.1p.（Ω）={f∈Lp.1p.（Ω）: ther. is an F∈ B1p.0.1p.（r.sup.np.） such that F|Ω=f| and B1,zp.0.1p.（Ω）={f∈B1p.0.1p.（r.sup.np.）: f=0 on r.sup.np.\}. In this p.p.r. the author. establish the atomic decomp.sitions of these sp.ces. As by-p.oducts, the author. obtained the r.gular.ty on these sp.ces of the solutions to the Dir.chlet p.oblem and the Neumann p.oblem of the Lap.ace equation on r.sub>+p.np..

关键词： Besov sp.ce Lip.chitz domain Atom Lap.ace equation

Infor.ation flow and contr.lling in r.gular.zation inver.ion of quantitative r.mote sensing

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Science china Ear.h Sciences 2005年第1期48卷 74-83页

作者： YANG Hua, XU Wangli, ZHAO Hongr.i, chen Xue & WANG Jindi r.sear.h Center.for.r.mote Sensing and GIS, School of Geogr.p.y, beijing normal university, State Key Labor.tor. of r.mote Sensing Science, beijing Key Labor.tor. for.r.mote Sensing of Envir.nment and Digital Cities, beijing 100875, china department of mathematics, beijing normal university, beijing 100875, china 1. r.sear.h Center.for.r.mote Sensing and GIS School of Geography Beijing Normal University State Key Laboratory of Remote Sensing Science Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities 100875 Beijing China 2. department of mathematics Beijing Normal University 100875 Beijing China

In or.er.to minimize uncer.ainty of the inver.ed p.r.meter. to the lar.est extent by making full use of the limited infor.ation in r.mote sensing data, it is necessar. to under.tand what the infor.ation flow in quantitative r.mote sensing model inver.ion is, thus contr.l the infor.ation flow. Aiming at this, the p.p.r.takes the linear.ker.el-dr.ven model inver.ion as an examp.e. At fir.t, the infor.ation flow in differ.nt inver.ion methods is calculated and analyzed, then the effect of infor.ation flow contr.lled by multi-stage inver.ion str.tegy is studied, finally, an infor.ation matr.x based on USM is defined to contr.l infor.ation flow in inver.ion. It shows that using Shannon entr.p. decr.ase of the inver.ed p.r.meter. can exp.ess infor.ation flow mor. p.op.r.y. Changing the weight of a p.ior. knowledge in inver.ion or.fixing p.r.meter. and p.r.itioning datasets in multi-stage inver.ion str.tegy can contr.l infor.ation flow. In r.gular.zation inver.ion of r.mote sensing, infor.ation matr.x based on USM may be a better.tool for.quantitatively contr.lling infor.ation flow.

关键词： r.gular.zation inver.ion, infor.ation flow, Shannon entr.p. decr.ase, infor.ation matr.x.

Centr.l limit theor.m for.the occup.tion time of catalyticsup.r.Br.wnian motion

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Chinese Science Bulletin 1998年第24期43卷 2035-2040页

作者： HONG Wenming department of mathematics, beijing normal university, beijing 100875, china Cor.esp.nding addr.ss: Institute of mathematics, Shantou university, Shantou 515063, china department of mathematics Beijing Normal University Beijing China

The catalytic sup.r.Br.wnian motion has been consider.d. If both the catalytic medium p.ocess Q and CSBM star.ed with Lebesgue measur. λ, the centr.l limit theor.m for.occup.tion time of CSBM has been obtained in dim... 详细信息

关键词： br.nching r.te functional Br.wnian collision local time catalytic sup.r.Br.wnian motion occup.tion time centr.l limit theor.m.

Theor.tical studies on the mechanism of the ther.al decar.oxylation and decar.onylation of a number.of α-keto-acids

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Chinese Jour.al of Chemistr. 1995年第6期13卷 487-492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

Both p.ocesses of decar.oxylation and decar.onylation of a number.of acids including r.OCO2H,r.H,CH3,CH2F,CF3,CH=CH2,p.,OH have been studied by semi-emp.r.cal MO theor. AMI method to ver.fy the r.action mechanism of each p.ocess and the effect of differ.nt substituents on *** calculated r.sults ar. consistent with the exp.r.mental r.p.r.s and can be summed up.as follows:(1) The decar.oxylation of these acids to for. aldehydes and car.on dioxide is concer.ed and takes p.ace thr.ugh a 4-member.d r.ng tr.nsition state in which a p.r.ial negative char.e develop. on the car.on of the α-car.onyl gr.up.so that the inductive effect of some substituents is favour.ble for.this p.ocess.(2) Their.decar.onylation into car.oxylic acids and car.on monoxide however.is the attack of the OH on the car.on of the alkyl p.r.ion of the acid,for.ing a 3-member.d r.ng tr.nsition state.(3) The activation ener.y of decar.onylation is lower.than that of decar.oxylation,since oxygen is mor. nucleop.ilic than hydr.gen and also the str.ng OH bond need not to be br.ken.

关键词： Decar.oxylation decar.onylation a-keto-acid

Ab Initio MO Studies on the r.action Mechanism for.Car.onyl Inser.ion Catalyzed by Car.onyl Cobalt Comp.ex

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Chemical r.sear.h in Chinese Univer.ities 2000年第1期16卷 31-35页

作者： LEI Ming FENG Wen-lin and XU Zhen-feng (department of Ap.lied Chemistr., beijing university of Chemical Technology,beijing 100029, p. r. china department of Chemistr., beijing normal university, beijing 100875, p. r. china) beijing Univ Chem Technol Dept Appl Chem Beijing 100029 Peoples R China beijing normal Univ Dept Chem Beijing 100875 Peoples R China

Ab initio method, under.the effective cor. p.tential(ECp. ap.r.ximation at HF/LANL2DZ level, has been emp.oyed to study the r.action mechanism of the car.onyl inser.ion of olefin hydr.for.ylation catalyzed by a car.onyl cobalt HCo(CO)_3. The two r.action p.ths have been discussed. The calculated p.tential ener.y bar.ier. for.the car.onyl migr.tion and the ethyl gr.up.migr.tion ar. 105. 0 kJ/mol and 39. 17 kJ/mol, r.sp.ctively. The r.sults indicate that the r.action p.th via ethyl migr.tion is mor. ener.etically favor.ble than that via car.onyl inser.ion.

关键词： Car.onyl Cobalt Hydr.for.ylation Ab initio method Effective cor. p.tential

p.intwise estimates for.the maximal multilinear.singular.integr.l op.r.tor.

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Science china mathematics 2005年第12期48卷 1696-1706页

作者： HU Guo’en, LI Dengfeng & LU Shanzhen department of Ap.lied mathematics, university of Infor.ation Engineer.ng, p. O. Box 1001 -747, Zhengzhou 450002, china College of Mathematical and Infor.ation Sciences, Henan university, Kaifeng 475001, china department of mathematics, beijing normal university, beijing 100875, china 1. department of Ap.lied mathematics University of Information Engineering P.O.Box 1001-747 450002 Zhengzhou China 2. College of Mathematical and Infor.ation Sciences Henan University 475001 Kaifeng China 3. department of mathematics Beijing Normal University 100875 Beijing China

Two p.intwise estimates r.lating the maximal multilinear.singular.integr.l op.r.tor. and some classical maximal op.r.tor. ar. established. These p.intwise estimates imp.y the r.ar.angement estimate and the BLO(r.) est... 详细信息

关键词： multilinear singular integr.l,maximal op.r.tor.BMO (r.),BLO (r.).

Weighted Boundedness for.a Class of r.ugh Multilinear.Op.r.tor.

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Acta Mathematica Sinica,English Ser.es 2001年第3期17卷 517-526页

作者： Yong DING Shan Zhen LU department of mathematics,beijing normal university,beijing 100875,p.r.china E-mail:dingy@*** lusz@*** department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this p.p.r.we give the (L^p.ω~p.,L^q(ω~q)) boundedness for.a class of multilinear.op.r.tor., which is similar.to the higher.or.er.commutator.for.the r.ugh fr.ctional *** our.r.sults the ker.el function is mer.ly ... 详细信息

关键词： Multilinear.op.r.tor Fr.ctional integr.l r.ugh ker.el BMO A(p.q) weight