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Polynomial solutions of quasi-homogeneous partial differential equations

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Science china mathematics 2001年第9期44卷 1148-1155页

作者： LUO Xuebo ZHENG Zhujun institute of Applied mathematics, Northwestern Polytechnical university, Xi’an 710072, china institute of mathematics, henan university, kaifeng 475001, china institute of Applied mathematics Northwestem Polytechnical University Xi’an China institute of mathematics Henan University Kaifeng China

By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite

关键词： quasi-homogeneous partial differential operator polynomial solution, dimension of the space of solution method of analytic number theory

Surface-induced interaction of colloidal particles in isotropic liquid crystals

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Communications in Theoretical Physics 2024年第7期76卷 114-122页

作者： Hualing Zhang kaifeng Weng Rui Ma Department of Physics College of Physical Science and TechnologyXiamen UniversityXiamen 361005China Fujian Provincial Key Laboratory for Soft Functional Materials Research Research Institute for Biomimetics and Soft MatterXiamen UniversityXiamen 361005China

In this work,we study the interaction between two colloidal particles in a liquid crystal that is in the isotropic *** interaction is caused by surface-induced polarization of the liquid crystal molecules in the vicinity of the *** find that the interaction is short-ranged in both 2D and 3D *** symmetric homeotropic anchoring conditions,the interaction is *** under anti-symmetric homeotropic anchoring conditions,the interaction is repulsive at short distances but attractive at intermediate *** particle size has a strong impact on the effective interaction force.

关键词： surface-induced interaction colloidal particles liquid crystals

On the Exceptional Set for the Equation n=p+k^2

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Acta Mathematica Sinica,English Series 1995年第2期11卷 156-167页

作者： Wang Tianze Department of mathematics henan university kaifeng, 475001 china Department of mathematics Henan University Kaifeng People's Republic of China

Denote by E（X） the number of integers n≤X which are not a sum of a prime and a square. Set θ=1-0.994428b, where b≤min（0.9365/c3, 0.02578/c4）, c3, c4 being given in Lemma 8. The result E（x） xθ is proved in th... 详细信息

关键词：三尸 On the Exceptional Set for the Equation n

Top 10 Influential Events in carbon neutrality and climate change response for 2023

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Frontiers in Energy 2024年第1期18卷 1-3页

作者： Research institute of Carbon Neutrality of Shanghai Jiao Tong university Research institute of Carbon Neutrality Shanghai Jiao Tong UniversityShanghai 200240China

In 2023, the global community intensified its efforts towards achieving carbon neutrality and addressing climate change, witnessing several impactful events. Research institute of Carbon Neutrality, Shanghai Jiao Tong university compiled the Top 10 Events (in chronological order) in the field of global carbon neutrality and climate change response for 2023, to share with readers these significant moments that document the ongoing ambition and collective efforts of human society.

关键词： neutral collective intensified

A novel homospermidine conjugate inhibits growth and induces apoptosis in human hepatoma cells

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Acta Pharmacologica Sinica 2007年第11期28卷 1827-1834页

作者： Song-qiang XIE~(2,3),Ying-liang WU~2,Peng-fei CHENG~4,Min-wei WANG~2,Guang-chao LIU~5,Yuan-fang MA~5,Jin ZHAO~4,Chao-jie WANG~(4,6)~2 Department of Pharmacology,Shenyang Pharmaceutical university,Shenyang 110016,china ~3 Pharmacy College,henan university,kaifeng 475001,china ~4 institute of Natural Products and Medicinal Chemistry,henan university,kaifeng 475001,china:~5 MedicalCollege,henan university,kaifeng 475001,china Department of Pharmacology Shenyang Pharmaceutical University Shenyang China Pharmacy College Henan University Kaifeng China institute of Natural Products and Medicinal Chemistry Henan University Kaifeng China Medical College Henan University Kaifeng China

Aim:To elucidate the mechanism responsible for the antiproliferative effects of anovel homospermidine conjugate,anthracenylmethyl homospermidine(ANTMHspd),in the human hepatoma BEL-7402 cell ***:The viabilityof the cells was assessed by MTT assay and the trypan blue dye exclusion *** changes were observed by fluorescence microscopy with Hoechst33258 *** cycle distribution,apoptosis,and mitochondrial membranepotential were measured by flow *** expression was detected byWestern blot ***:ANTMHspd strongly decreased BEL-7402 cellproliferation in a dose-and time-dependent *** 33258 staining andthe flow cytometry assay showed that ANTMHspd induced cell apoptosis andcell cycle ***,ANTMHspd could induce mitochondrialmembrane potential loss and cytochrome c release and enhance cleaved caspase-3,cleaved caspase-9,and Bax protein expression without caspase-8 *** could also decrease the expression of Bcl-2 and cytochrome c *** addition,the specific inhibitors of caspase-9 and caspase-3almost abolished the ANTMHspd-induced caspase-9 and caspase-3 activation,***:ANTMHspd could induce BEL-7402 cell apoptosis viathe mitochondrial/caspase-dependent pathway and the Bcl-2 family was involvedin the control of apoptosis.

关键词： polyamine apoptosis cell cycle mitochondrial membrane potential caspase Bcl-2

P-twisted affine Lie algebra and its realizations by twisted vertex operators

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Science china mathematics 2005年第Z1期48卷 295-305页

作者： LU Keping, CHU Yanjun, ZHENG Zhujun & DONG Wenfeng institute of mathematics, henan university, kaifeng 475001, china USTC Shanghai institute for Advanced Studies, university of Science and Technology of china, Shanghai 201315, china institute of mathematics Henan University Kaifeng China USTC Shanghai institute for Advanced Studies University of Science and Technology of China Shanghai China

In this paper, we define a P-twisted affine Lie algebra, and construct its realizations by twisted vertex operators.

关键词： P-twisted affine Lie algebra, twisted vertex operator, extended P-twisted afline algebra.

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

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Science china mathematics 2006年第10期49卷 1392-1404页

作者： XU Yichao,CHEN Minru & MA Songya Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, china College of mathematics and Information Sciences, henan university, kaifeng 475001, china Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China College of mathematics and Information Sciences Henan University Kaifeng China

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso (D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN,F)) and Iso (D(VN, F))(0), where G(0) is the unit connected component of the Lie group G.

关键词： holomorphic automorphism group, homogeneous Siegel domain, normal Siegel domain, complex homogeneous bounded domain.

Existence of inner functions on classical domain

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Chinese Science Bulletin 1997年第1期42卷 84-85页

作者： LIU Taishun and ZHANG Wenjun1 Department of mathematics, university of Science and Technology of china, Hefei 230026, china 2. Department of mathematics henan university, kaifeng 475001, china

IN function of one complex variable, the inner function on the unit disc plays an important role in the theory of H^p functions. In the mid-1960s, W. Rudin and A. Vitushkin independently raised the question of whether there exist nonconstant inner functions on the unit ball B_n. Then quickly amassed considerable evidence indicated that such functions would be so pathological that they could not exist. Lately Rudin posed the conjecture on the nonexistence

关键词： In Existence of inner functions on classical domain

Pointwise estimates for the maximal multilinear singular integral operators

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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 Applied mathematics, university of Information Engineering, P. O. Box 1001 -747, Zhengzhou 450002, china College of Mathematical and Information Sciences, henan university, kaifeng 475001, china Department of mathematics, Beijing Normal university, Beijing 100875, china Department of Applied mathematics University of Information Engineering Zhengzhou 450002 China College of Mathematical and Information Sciences Henan University Kaifeng 475001 China Department of mathematics Beijing Normal University Beijing 100875 China

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) est... 详细信息

关键词： multilinear singular integral,maximal operator,BMO (Rn),BLO (Rn).