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Chinese Annals of Mathematics,Series B 2020年第2期41卷 285-302页

作者： Hongwei XU Li LEI Juanru gu Center of Mathematical Sciences Zhejiang UniversityHangzhou 310027China Department of Applied Mathematics Zhejiang University of TechnologyHangzhou 310023China

Let Mn(n ≥ 4) be an oriented compact submanifold with parallel mean curvature in an(n + p)-dimensional complete simply connected Riemannian manifold Nn+*** there exists a constant δ(n, p) ∈(0, 1) such that if the sectional curvature of N satisfies■ , and if M has a lower bound for Ricci curvature and an upper bound for scalar curvature, then N is isometric to Sn+p. Moreover, M is either a totally umbilic sphere■ , a Clifford hypersurface Sm■ in the totally umbilic sphere ■, or■ . This is a generalization of Ejiri’s rigidity theorem.

关键词： Minimal submanifold Ejiri rigidity theorem Ricci curvature Mean curvature

Antioxidant and Hypoglycemic Ability of Ardisia gigantifolia Stapf Parts

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Medicinal Plant 2024年第1期15卷 88-91页

作者： chaohao gu Shihao LIANG Yuexuan WU Zhiren YAO Jiaojiao LI Kaimei ZHU guilin Medical University Guilin 541000China Second Affiliated Hospital of guilin Medical University Guilin 541000China

[Objectives]To study the antioxidant and hypoglycemic effects of different parts of Ardisia gigantifolia Stapf.[Methods]The hydroxyl radical scavenging activity,DPPH radical scavenging activity and total antioxidant capacity of ABTS of 75%ethanol extract of *** Stapf and the petroleum ether,ethyl acetate,n-butanol,chloroform and aqueous extract were measured with Vc as positive *** the same time,acarbose was used as reference substance to determine the inhibitory effect of each polar site onα-glucosidase.[Results]All parts of *** Stapf had antioxidant activity,among which ethyl acetate had the strongest antioxidant activity,and the scavenging rate of hydroxyl radical and DPPH radical was higher than that of positive *** results showed that petroleum ether,ethyl acetate and chloroform had a good inhibitory effect onα-glucosidase(better than acarbose).[Conclusions]The ethyl acetate part of *** Stapf had the best antioxidant activity and inhibitory effect onα-*** provides a basis for further research and development of *** Stapf.

关键词： Ardisia gigantifolia Stapf Antioxidants Free radicals Hypoglycemic effect

EXPLICIT CONSTRUCTION OFHARMONIC MAPS FROM R^2 TO U(N)

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Chinese Annals of Mathematics,Series B 1995年第2期16卷 139-152页

作者： gu chaohao Hu HESHENG FUDAN UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

ＥＸＰＬＩＣＩＴＣＯＮＳＴＲＵＣＴＩＯＮＯＦＨＡＲＭＯＮＩＣＭＡＰＳＦＲＯＭＲ~２ＴＯＵ（Ｎ）￥ＧｕＣＨＡＯＨＡＯＨｕＨＥＳＨＥＮＧＡｂｓｔｒａｃｔ：Ｄａｒｂｏｕｘｔｒａｎｓｆｏｒｍａｔｉｏｎｍｅｔｈｏｄｉｓｕｓｅｄ... 详细信息

ＥＸＰＬＩＣＩＴＣＯＮＳＴＲＵＣＴＩＯＮＯＦＨＡＲＭＯＮＩＣＭＡＰＳＦＲＯＭＲ~２ＴＯＵ（Ｎ）￥ＧｕＣＨＡＯＨＡＯＨｕＨＥＳＨＥＮＧＡｂｓｔｒａｃｔ：Ｄａｒｂｏｕｘｔｒａｎｓｆｏｒｍａｔｉｏｎｍｅｔｈｏｄｉｓｕｓｅｄｆｏｒｃｏｎｓｔｒｕｃｔｉｎｇｈａ?..

关键词：谐映射显式结构达鲍克斯变换法微分几何

ON THE CLASSIFICATION OF INITIAL DATAFOR NONLINEAR WAVE EQUATIONS

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Chinese Annals of Mathematics,Series B 2002年第2期23卷 205-208页

作者： gu chaohao(C.H.gu) Institute of Mathematics FudanUniversity China.E-mail:guch

The purpose of the present paper is to call for attention to the following question: Which of the initial data (nonsmall) admit global smooth solutions to the Cauchy problem for nonlinear wave equations. A few cases a... 详细信息

关键词：非线性波动方程原始数据双曲型Liouville方程 Cauchy问题光滑解对偶关系

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

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Chinese Annals of Mathematics,Series B 1994年第4期15卷 385-400页

作者： gu chaohao (Institute of Mathematics, Fudan University,Shanghai 200433, China.) FUDAN UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

ＣＯＭＰＬＥＴＥＥＸＴＲＥＭＡＬＳＵＲＦＡＣＥＳＯＦＭＩＸＥＤＴＹＰＥＩＮ３－ＤＩＭＥＮＳＩＯＮＡＬＭＩＮＫＯＷＳＫＩＳＰＡＣＥ￥ＧＵＣＨＡＯＨＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅ... 详细信息

ＣＯＭＰＬＥＴＥＥＸＴＲＥＭＡＬＳＵＲＦＡＣＥＳＯＦＭＩＸＥＤＴＹＰＥＩＮ３－ＤＩＭＥＮＳＩＯＮＡＬＭＩＮＫＯＷＳＫＩＳＰＡＣＥ￥ＧＵＣＨＡＯＨＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２００...

关键词：外表面混合型 Minkowski空间平均曲率双曲线偏微分方程

Effects of Polysaccharide from Polygala fallax on Apoptosis of B16 Melanoma

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Medicinal Plant 2023年第1期14卷 69-72,75页

作者： chaohao gu Yuanyuan LAN Yang MIAO Zhiren YAO Zhiqiang HUANG Kaimei ZHU Shengjiu gu guilin Medical University Guilin 541101China

[Objectives]The paper was to study the effects of polysaccharide from Polygala fallax on apoptosis of B16 melanoma and its mechanism.[Methods]*** polysaccharide was prepared by water extraction and alcohol precipitation method combined with Sevag *** effects of different concentrations of *** polysaccharide on B16 cell proliferation were detected by MTT *** was detected by Hoechst 33258 staining assay and flow *** expressions of Bcl-2,Bax,Cleaved Caspase-3 mRNA were detected by Real-time PCR *** expressions of Bcl-2,Bax,Caspase-3,Caspase-8,Caspase-9,Cleaved Caspase-3,Cleaved Caspase-9,ERK,p-ERK,JNK,p-JNK proteins were detected by Western Blot assay.[Results]*** polysaccharide inhibited the cell proliferation of B16 melanoma in a concentration-dependent manner(24 h IC 50=0.2133 mg/L;48 h IC 50=0.08489μg/mL).*** polysaccharide up-regulated the expressions of Bax,Cleaved Caspase-3 mRNA and protein,down-regulated the expressions of Bcl-2 mRNA and protein,activated Caspase-3,Caspase-8 and Caspase-9,and decreased the levels of p-ERK/ERK and p-JNK/JNK.[Conclusions]*** polysaccharide can inhibit the cell proliferation of B16 melanoma and induce their apoptosis,probably attributed to the regulation of MAPK,Bcl-2 and Caspase family signaling pathways.

关键词： Polygala fallax polysaccharide Melanoma Apoptosis

CONSTRUCTION OF UNITONS VIA PURELY ALGEBRAIC ALGORITHM

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 1-6页

作者： gu chaohao(C.H.gu) HU HESHENG(H.S.HU)(Institute of Mathematics,Fudan University,Shanghai 200433,China) Institute of Mathematics Fudan University Shanghai 200433 China

***2(oritssimplyconnectedregion)toU(N)***[7].Thereareaseriesofpapers[2,8,9]***[4]theDarbouxtransformationhasbee... 详细信息

***2(oritssimplyconnectedregion)toU(N)***[7].Thereareaseriesofpapers[2,8,9]***[4]theDarbouxtransformationhasbee...

关键词： U(N)单子达布变换重正化代数运算法则

SOME REMARKS ON SINguLAR DARBOUX TRANSFORMATIONS FOR UNITONS

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 263-266页

作者： guGHAOHAO HUHESHENG InstituteofMathematics FudanUniversity.Shanghai200433China. ProjectsupportedbytheSpecialFundsforMajorStateBasicResearchProjectofChina（NonlinearScience） theNationalNaturalScienceFoundationofChinaandtheFoundationoftheCommissionofScienceandTechnologyofShanghai.

Is the paper [2] the authors defined the singular Darboux transformations and established an explicit formula for constructing unitons from a simply connected Riemann surface. M to the group U(N). The formula is obtained as a limit of an infinite consequence of Darboux transformations through some renormalization procedure. In the present paper the authors give a complete proof of the fact that the formula gives a global solution of harmonic maps without singularity.

关键词：奇达布变换显式公式黎曼曲面重正化李群

SOME CONSIDERATIONS ON BASIC RESEARCH

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Bulletin of the Chinese Academy of Sciences 1998年第2期12卷 142-145页

作者： gu chaohao(Fudan University, Shanghai Municipality)

In a 1997 directive, Chinese President Jiang Zemin instructed us: Basic research is very important. The advances of modem civilization have proven that every breakthrough in basic research means an uplift in man’s ability to remould the objective world and gives rise to a tremendous and inestima- ble driving push to S&T innovation, hi-tech industrialization and socio-economic progress. In his keynote report at the CPC’ s 15th National Congress, once again he stressed that "Science and technology are the primary production force and S&T progress is the decisive factor for the economic development." In his report on behalf of the national government at the fifth session of the 8th NPC,

关键词： SOME CONSIDERATIONS ON BASIC RESEARCH BASIC

ON THE BOUNDARY CONDITIONS FOR PARTIAL DIFFERENTIAL EQUATIONS

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Science in China,Ser.A 1980年第8期 939-944页

作者：谷超豪 Fudan University

Let Ω be a bounded and closed region in R~n with a smooth boundary S. It is proved that for any given integers k and m, 0 ≤ k ≤ m, there exists a class of partial differential operators of order m such that the C~m solution to the following boundary value problem exists uniquely. Here P is the differential operator and f, φo, …, φk-1 are arbitrarily sufficient-smooth functions. Especially, when k=0, there exists only one C~m solution to the equation Pu=f.

关键词： ON THE BOUNDARY CONDITIONS FOR PARTIAL DIFFERENTIAL EQUATIONS