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The isometric extension of “into” mappings on unit spheres of AL-spaces

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Science china mathematics 2008年第10期51卷 1904-1918页

作者： DING GuangGui School of mathematics Science, chern institute of mathematics and LPMC, nankai university, tianjin 300071, china School of mathematics Science Chern Institute of Mathematics and LPMC Nankai University Tianjin China

In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.

关键词： isometric extension (atomic) AL-space

On the anomaly formula for the Cappell-Miller holomorphic torsion

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Science china mathematics 2010年第12期53卷 3225-3241页

作者： LIU Bo & YU JianQing chern institute of mathematics & LPMC, nankai university, tianjin 300071, china chern institute of mathematics & LPMC Nankai University Tianjin China

We present an explicit expression of the anomaly formula for the Cappell-Miller holomorphic torsion for Khler manifolds.

关键词： Cappell-Miller holomorphic torsion anomaly formula heat kernel

The Degree of Symmetry of Certain Compact Smooth Manifolds II

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Chinese Annals of mathematics,Series B 2007年第2期28卷 195-204页

作者： Bin XU Department of mathematics, university of Science and Technology of china, Hefei 230026, china chern institute of mathematics, nankai university, tianjin 300071, china Department of mathematics, Johns Hopkins university, Baltimore, MD 21218, USA. Department of mathematics University of Science and Technology of China Hefei China chern institute of mathematics Nankai University Tianjin China Department of mathematics Johns Hopkins University Baltimore USA

We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.

关键词：紧光滑流形对称度纤维丛调和映射刚性理论配边

COBORDISM AND ROKHLIN CONGRUENCES

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Acta Mathematica Scientia 2009年第3期29卷 609-612页

作者：张伟平 chern institute of mathematics & LPMC Nankai UniversityTianjin 300071 China

In this paper, we give a cobordism proof of the higher dimensional Rokhlin congruences established in [8].

关键词： cobordism Rokhlin congruence

A Cheeger-Mller Theorem for Symmetric Bilinear Torsions

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Chinese Annals of mathematics,Series B 2008年第4期29卷 385-424页

作者： Guangxiang SU Weiping ZHANG chern institute of mathematics and LPMC Nankai University Tianjin 300071 China.

作者为 Burghelea 和 Haller 为带非退化的对称的双线性的形式的扁平的向量捆介绍的复杂珍视的分析扭转建立一条 Cheeger-M ü l ler 类型定理。作为后果，他们证明 Burghelea 大厅在完整的概论推测，它给分析解释(平方) Turaev 扭转。

关键词：解析挠率对称双线性 Cheeger-Müller理论 Bismut-Zhang理论

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

中国政治经济学年度发展报告（2023）（下）

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政治经济学评论 2024年第3期 90+207-208页

作者： Center for Studies of Contemporary Political Economy,Research institute for 21st-Century Marxism,nankai university·university of Chinese Academy of Social Science Center for Teaching and Research on Capital,Renmin university of china National institute of Socialist Political Economy with Chinese Characteristics,Renmin university of china 南开大学·中国社会科学院大学21世纪马克思主义研究院当代政治经济学研究中心中国人民大学《资本论》教学与研究中心中国人民大学全国中国特色社会主义政治经济学研究中心

编者按2023年，高质量发展扎实推进，新质生产力加快形成，我国经济总体回升向好，圆满实现发展主要预期目标。为针对性地破解经济恢复发展中的难题，聚焦推进中国式现代化进程中的重点、难点问题，中国政治经济学界开展系统深入研究，...

编者按2023年，高质量发展扎实推进，新质生产力加快形成，我国经济总体回升向好，圆满实现发展主要预期目标。为针对性地破解经济恢复发展中的难题，聚焦推进中国式现代化进程中的重点、难点问题，中国政治经济学界开展系统深入研究，取得系列代表性成果。为准确刻画学界研究进展和轨迹，推动中国经济学理论体系的构建和完善，本刊精选议题如期奉上《中国政治经济学年度发展报告（2023）》。自2010年起，本刊连续十四年发布《中国政治经济学年度发展报告》，“年度发展报告”专栏已成为本刊标志性特色栏目。2023年报告聚焦12个专题，分为（上）（下）两篇，其中专题1—6于报告（上）篇刊登，专题7—12由报告（下）篇刊登。2023年报告（下）选题如下：

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Blast waveform tailoring using controlled venting in blast simulators and shock tubes

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Defence Technology（防务技术） 2024年第7期37卷 14-26页

作者： Edward chern Jinn Gan Alex Remennikov David Ritzel Faculty of Engineering and Information Sciences University of WollongongWollongongNSW2522Australia Dyn-FX Consulting Ltd 19 Laird Ave NorthAmherstburgONN9V 2T5Canada

A critical challenge of any blast simulation facility is in producing the widest possible pressure-impulse range for matching against equivalent high-explosive *** tubes and blast simulators are often constrained with the lack of effective ways to control blast wave profiles and as a result have a limited performance *** wave shaping techniques employed in some facilities are reviewed but often necessitate extensive geometric modifications,inadvertently cause flow anomalies,and/or are only applicable under very specific *** paper investigates controlled venting as an expedient way for waveforms to be tuned without requiring extensive modifications to the driver or existing geometry and could be widely applied by existing and future blast simulation and shock tube *** use of controlled venting is demonstrated experimentally using the Advanced Blast Simulator(shock tube)at the Australian National Facility of Physical Blast Simulation and via numerical flow simulations with Computational Fluid *** venting is determined as an effective method for mitigating the impact of re-reflected waves within the blast *** control method also allows for the adjustment of parameters such as tuning the peak overpressure,the positive phase duration,and modifying the magnitude of the negative phase and the secondary shock of the blast *** paper is concluded with an illustration of the potential expanded performance range of the Australian blast simulation facility when controlled venting for blast waveform tailoring as presented in this paper is applied.

关键词： Advanced blast simulator Shock wave propagation Far-field explosion Blast loads Blast waves Computational fluid dynamics

η-INVARIANT AND chern-SIMONS CURRENT

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Chinese Annals of mathematics,Series B 2005年第1期26卷 45-56页

作者： ZHANGWEIPING nankaiinstituteofmathematics NankaiUniversityTianjin300071China

The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the aualytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles,and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.

关键词： η-不变式直接象 k指数定理迪拉克算子有界黎曼流形