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一维Mar.ov过程的Nash不等式

数学学报（中文版） 2004年第6期47卷 1231-1236页

作者：毛永华北京师范大学数学系北京100875

本文得到了生灭过程和一维扩散过程满足Nash不等式的判别准则,并证明了对此二类过程,非常返性蕴含相应半群如下收敛速度||p.t)||1→∞≤Ct-1.同时也给出一般马氏链满足Nash不等式的充分条件.

关键词： Nash不等式 Har.y不等式生灭过程扩散

Hollow Multishelled Str.ctur.: Synthesis Chemistr. and Ap.lication

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Chemical r.sear.h in Chinese Univer.ities 2024年第3期40卷 346-393页

作者： mao Dan WANG Chao LI Wei ZHOU Liang LIU Jian ZHENG Zjian ZHAO yong CAO An-min WANG Shutao huaNG Jiaxing HUO Fengwei CHEN Hongyu MAI Liqiang YU r.nbo WANG Lianzhou LU Yunfeng YU Chengzhong YANG Qihua YANG Zhenzhong ZENG hua Chun ZHAO Hujun TANG Zhiyong ZHAO Dongyuan WANG Dan State Key Labor.tor. of Biochemical Engineer.ng Institute of Process EngineeringChineseAcademy of SciencesBeijing 100190P.R.China Key Labor.tor. of Biop.ar.aceutical p.ep.r.tion and Deliver. Chinese Academy of SciencesBejing 100190P.R.China School of Fashion and Textiles The Hong Kong Polytechnic UniversityHong Kong SARP.R.China department of Chemistr. Fudan UniversityShanghai 200433P.R.China State Key Labor.tor. of Advanced Technology for.Mater.als Synthesis and {4.ocessing Wuhan University of TechnologyWuhan 430070P.R.China State Key Labor.tor. of Catalysis Dalian Institute of Chemical PhysicsChinese Academy of SciencesDalian 116023P.R.China School of Chemistr. Beihang UniversityBejing 100191P.R.China CAS Key Labor.tor. of Molecular.Nanostr.ctur. and Nanotechnology and beijing National Labor.tor. for.Molecular.Sciences Institute of ChemistryChinese Academy of SciencesBeijing 100190P.R.China CAS Key Labor.tor. of Bio-insp.r.d Mater.als and Inter.acial Science Technical Institute of Physics and ChemistryChinese Academy of SciencesBeijing 100190P.R.China School of Engineer.ng Westlake UniversityHangzhou 310024P.R.China School of Flexible Electr.nics(Futur. Technologies) Nanjing Tech UniversityNanjing 211816P.R.China School of Science Westlake UniversityHangzhou 310024P.R.China School of Mater.als Science and Engineer.ng Wuhan University of TechnologyWuhan 430070P.R.China School of Metallur.ical and Ecological Engineer.ng University of Science and Technology BeijingBeijing 100083P.R.China School of Chemical Engineer.ng and Austr.lian Institute for.Bioengineer.ng and Nanotechnology The University of QueenslandBrisbaneQueensland 4072Australia College of Life Science and Technology Bejing University of Chemical TechnologyBejing 100029P.R.China School of Chemistr. and Molecular.Engineer.ng East China Normal UniversityShanghai 200241P.R.China College of Life Sciences Zhejiang Normal UniversityJinhua 321004P.R.China department of Chemical Engineer.ng Tsinghua UniversityBeijing 100

Hollow multishelled str.ctur.(HoMS),a p.omising and comp.ex multifunctional str.ctur.l system,featur.s at least two shells that ar. sep.r.ted by inter.al *** unique str.ctur. endows it with numer.us advantages including low density,high loading cap.city,lar.e sp.cific sur.ace ar.a,facilitated mass tr.nsp.r.,and multip.e sp.tial confinement *** the p.st twenty year.,benefiting fr.m the booming develop.ent of synthesis methods,var.ous HoMS mater.als have been p.ep.r.d and show p.omising ap.lications in diver.e ar.as.

关键词： Hollow multishelled str.ctur. Synthesis chemistr. Ener.y stor.ge Catalysis Electr.magnetic wave absor.0}ion Dr.g deliver. Sensor

On Sup.r.ontr.ctivity for.Mar.ov Semigr.up.

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Acta Mathematica Sinica,English Ser.es 2007年第5期23卷 905-914页

作者： yong hua mao School of Mathematical Science Beijing Normal University Beijing 100875 P. R. China

In this p.p.r. we study the sup.r.ontr.ctivity for.Maxkov semigr.up. and obtain some sufficient and necessar. conditions; esp.cially exp.icit for.ulae ar. obtained for.bir.h-death p.ocess and diffusion on the line. Sufficient conditions and necessar. conditions in ter.s of isop.r.metr.c inequalities ar. also p.esented. Mor.over. we p.ove that the sup.r.ontr.ctivity is equivalent to the comp.ct embedding of Sobolev sp.ce into an Or.icz sp.ce.

关键词： Mar.ov semigr.up logar.thmic Sobolev inequality sup.r.ontr.ctivity comp.ct embedding

L^p.p.incar. Inequality for.Gener.l Symmetr.c For.s

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Acta Mathematica Sinica,English Ser.es 2009年第12期25卷 2055-2064页

作者： yong hua mao School of Mathematical Science LMCS Ministing of Education Beijing Normal University Beijing 100875 P. R. China

Lp.p.incar. inequalities for.gener.l symmetr.c for.s ar. established by new Cheeger.s isop.r.metr.c constants. Lp.sup.r.p.incar. inequalities ar. intr.duced to descr.be the equivalent conditions for.the Lp.comp.ct embedding, and the cr.ter.a via the new Cheeger.s constants for.those inequalities ar. p.esented. Finally, the concentr.tion or.the volume gr.wth of measur.s for.these inequalities ar. studied.

关键词： Lp.p.incar. inequality symmetr.c for. isop.r.metr.c constant comp.ct embedding concentr.tion

Constr.ction of Gener.lized Diffusion p.ocesses: the r.solvent Ap.r.ach

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Acta Mathematica Sinica,English Ser.es 2020年第6期36卷 691-710页

作者： Ying LI yong hua mao School of mathematics.and Comp.tational Science Xiangtan UniversityXiangtan 411105P.R.China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China

In this p.p.r.we define the gener.lized diffusion op.r.tor.L=d/dMd/dS for.two suitable measur.s on the line,which includes the gener.tor. of the bir.h-death p.ocesses,the one-dimensional diffusion and the gap.diffusio... 详细信息

关键词： Gener.lized diffusion op.r.tor bir.h-death p.ocesses diffusion gap.diffusion r.solvent gener.lized diffusion p.ocesses

New p.anetar. nebulae in the outskir.s of the Andr.meda Galaxy discover.d with the Guoshoujing Telescop. (LAMOST)

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r.sear.h in Astr.nomy and Astr.{4.ysics 2010年第7期10卷 599-611页

作者： Hai-Bo Yuan Xiao-Wei Liu Zhi-Ying Huo Hui-hua Zhang yong-Heng Zhao Jian-Jun Chen Zhong-r.i Bai Hao-Tong Zhang hua-Wei Zhang r.ben Gar.ia-Benito mao-Sheng Xiang Hong-Liang Yan Juan-Juan r.n Shi-Wei Sun yong Zhang Ye-p.ng Li Qi-Shuai Lu You Wang Ji-Jun Ni Hai Wang department of Astr.nomy Peking University Beijing 100871 China Kavli Institute for.Astr.nomy and Astr.p.ysics Peking University Beijing 100871 China National Astr.nomical Obser.ator.es Chinese Academy of Sciences Beijing 100012 China department of Astr.nomy Beijing Normal University Beijing 100875 China Nanjing Institute of Astr.nomical Op.ics ＆ Technology Chinese Academy of Sciences Nanjing 210042 China

p.anetar. nebulae （p.e） ar. good tr.cer. of the stellar.p.p.lations, chemical comp.sition and dynamics of their.host galaxies. This p.p.r.r.p.r.s the discover. of new p.e in the outskir.s of the Andr.meda Galaxy （M31） with the Guoshoujing Telescop. （GSJT, for.er.y named the Lar.e Sky Ar.a Multi-Object Fiber.Sp.ctr.scop.c Telescop.-LAMOST） dur.ng its ear.y commissioning p.ase. In total, 36 candidates selected fr.m SDSS p.otometr. ar. confir.ed in ter.s of their.p. natur., including 17 new discover.es and another.19 p.eviously known emission line objects. Their.p.sitions, sp.ctr., r.dial velocities and m5007 magnitudes ar. p.esented. We discuss the p.tential for.detecting mor. p.e in M 31 with GSJT＇s multi-object sp.ctr.scop. and the r.lated ap.lications in studies of the dynamics and chemistr. of M 31 and its assemblage histor..

关键词： galaxies individual (M 31) -- p.anetar. nebulae gener.l

New backgr.und quasar. in the vicinity of the Andr.meda Galaxy discover.d with the Guoshoujing Telesco{4. (LAMOST)

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r.sear.h in Astr.nomy and Astr.{4.ysics 2010年第7期10卷 612-620页

作者： Zhi-Ying Huo Xiao-Wei Liu Hai-Bo Yuan Hui-hua Zhang yong-Heng Zhao Jian-Jun Chen Zhong-r.i Bai Hao-Tong Zhang hua-Wei Zhang r.ben Gar.ia-Benito mao-Sheng Xiang Hong-Liang Yan Juan-Juan r.n Shi-Wei Sun yong Zhang Ye-p.ng Li Qi-Shuai Lu You Wang Ji-Jun Ni Hai Wang department of Astr.nomy Peking University Beijing 100871 China Kavli Institute for.Astr.nomy and Astr.p.ysics Peking University Beijing 100871 China National Astr.nomical Obser.ator.es Chinese Academy of Sciences Beijing 100012 China department of Astr.nomy Beijing Normal University Beijing 100875 China Nanjing Institute of Astr.nomical Op.ics ＆ Technology Chinese Academy of Sciences Nanjing 210042 China

We p.esent p.eliminar. analyses of sp.ctr. of quasar.candidates in two Guoshoujing Telescop. （GSJT, for.er.y named the Lar.e Sky Ar.a Multi-Object Fiber.Sp.ctr.scop.c Telescop. - LAMOST） test fields near.M 31 wher. one is close to the op.ical center.of the disk and the other.is towar.s the nor.heaster. outskir.s of the halo, obtained dur.ng the ear.y stage of the GSJT commissioning in the last season of 2009. Both fields contain backgr.und low-r.dshift quasar.candidates selected fr.m the SDSS p.otometr.. In total, 14.new quasar. with r.dshifts up.to 2 and i magnitudes between 16.7 and 19.2, ar. discover.d, including 7 within the 2.5° centr.l r.gion of M 31. We br.efly discuss the p.tential ap.lications of these newly discover.d br.ght quasar..

关键词： galaxies individual (M31) -- quasar. gener.l -- quasar. emission lines

The Bir.h–death p.ocesses with r.gular.Boundar.: Stationar.ty and Quasi-stationar.ty

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Acta Mathematica Sinica,English Ser.es 2022年第5期38卷 890-906页

作者： Wu Jun GAO yong hua mao Chi ZHANG College of Big Data and Inter.et Shenzhen Technology UniversityShenzhen 518118P.R.China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China College of Mathematical Sciences Ocean University of ChinaQingdao 266100P.R.China

For.the bir.h–death Q-matr.x with r.gular.boundar.,its minimal p.ocess and its maximal p.ocess ar. closely *** this p.p.r.we obtain the unifor. decay r.te and the quasi-stationar. distr.bution for.the minimal *** via the constr.ction theor.,we mainly der.ve the eigentime identity and the distr.bution of the fastest str.ng stationar. time(FSST)for.the maximal p.ocess.

关键词： Bir.h-death p.ocess r.gular.boundar. eigenvalue hitting time str.ng stationar. time quasi-stationar. distr.bution

Var.ational p.incip.es for.Asymp.otic Var.ance of Gener.l Mar.ov p.ocesses

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Acta Mathematica Sinica,English Ser.es 2023年第1期39卷 107-118页

作者： Lu Jing huaNG yong hua mao Tao WANG School of mathematics.and Statistics Fujian Normal UniversityFuzhou 350007P.R.China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875P.R.China

A var.ational for.ula for.the asymp.otic var.ance of gener.l Mar.ov p.ocesses is *** ap.lication,we get an up.er.bound of the mean exit time of r.ver.ible Mar.ov p.ocesses,and some comp.r.son theor.ms between the r.ve... 详细信息

关键词： Mar.ov p.ocess asymp.otic var.ance var.ational for.ula the mean exit time comp.r.son theor.m semi-Dir.chlet for.