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MORSE CONCAVITY FOR CLOSED GEODESICS

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Acta Mathematica Scientia 2009年第3期29卷 731-750页

作者：段华桂龙以明 School of mathematics Chern Institute of mathematics key lab of pure mathematics and combinatorics of ministry of education Nankai UniversityTianjin 300071 China

In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.

关键词： closed geodesic concavity sypletic matrix Morse index

Deterministic relation between thermalphonon dressings and a non-Hermitian multi-Fano interferences router in iondoped microcrystals

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Chip 2024年第1期3卷 24-34页

作者： Huanrong Fan Faizan Raza Anas Mujahid Peng Li Yafen Wang Haitian Tang Muhammad Usman Bo Li Changbiao Li Yanpeng Zhang key laboratory for Physical Electronics and Devices of the ministry of education&Shaanxi key lab of Information Photonic Technique Xi’an Jiaotong UniversityXi’an 710049China Center for Regenerative and Reconstructive Medicine Med-X InstituteThe First Affiliated Hospital of Xi’an Jiaotong UniversityXi’an 710061China State key lab of Modern Optical Instrumentation Centre for Optical and Electromagnetic ResearchCollege of Optical Science and EngineeringInternational Research Center for Advanced PhotonicsZhejiang UniversityHangzhou 310058China

The multi-Fano interference,which is obtained through the simultaneous acquisition of bright and dark states in different phase transitions of Eu3+:BiPO4(7:1,6:1,1:1,and 0.5:1)and Eu3+:NaYF4(1:1/4)crystals,were reported in this *** spontaneous four-wave mixing and multidressed fluorescence(multiorder)were adopted to optimize the strong photon–phonon nested dressing effect,which results in more obvious multi-Fano ***,the multi-Fano is produced through interference in continuous and multibound ***,five multi-Fano dips are originated from the nested five dressings(one photon and four phonons)under symmetrical splitting of 7F1 energy *** is found that the pure H-phase(0.5:1)sample exhibits the strongest photon–phonon dressed effect(five Fano dips).Further,high-order non-Hermitian exceptional points in multi-Fano interference were investigated by adjusting the ratio of Rabi frequency to dephase rate through nested photon and phonon *** experimental results are validated by theoretical simulations,which may be applied to designing optoelectronic devices such as non-Hermitian multi-Fano interferences(multichannel)router.

关键词： Multi-Fano interferences Thermal-phonon dressings Non-Hermitian Router

Differentiable structure of ω-subsets of symplectic groups

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Science China mathematics 2001年第5期44卷 545-554页

作者：龙以明朱朝锋 Nankai Institute of mathematics Nankai University Tianjin China key laboratory of pure mathematics and combinatorics Ministry of Education Tianjin China

In this paper, we study the differentiable structure of the ω-subset of Sp(2n), which is formed by all matrices in Sp(2n) possessing ω as an eigenvalue, for ω on the unit circle in the complex plane. Based on this ... 详细信息

关键词： symplectic group ω-subset stratification differentiable structure transversal structure.

Stochastic Cahn-Hilliard equations driven by Poisson random measures

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Science China mathematics 2014年第12期57卷 2563-2576页

作者： JIANG YiMing SHI KeHua WANG SuXin School of Mathematical Sciences and the key laboratory of pure mathematics and combinatorics Ministry of Education Nankai University

We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov functio... 详细信息

关键词： Cahn-Hilliard equations Poisson random measures Lyapunov function invariant measure

Stable recovery of signals from frame coefficients with erasures at unknown locations

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Science China mathematics 2018年第1期61卷 151-172页

作者： Deguang Han Fusheng Lv Wenchang Sun Department of mathematics University of Central Florida School of Mathematical Sciences and the key laboratory of pure mathematics and combinatorics Ministry of Education Nankai University

In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.

关键词： frames erasures signal recovery almost robust frames totally robust frames

Experimental Study on Mixed-Mode(Ⅰ–Ⅱ)Fracture Toughness of Freshwater Ice

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Acta Mechanica Solida Sinica 2024年第2期37卷 252-264页

作者： Yaozhong Xu Mao Zhou Xian Yi Wen Hua Jiuzhou Huang Wenyu Zhang Shiming Dong key laboratory of Deep Underground Science and Engineering Ministry of EducationCollege of Architecture and EnvironmentSichuan UniversityChengdu610065China Failure Mechanics and Engineering Disaster Prevention key laboratory of Sichuan Province Sichuan UniversityChengdu610065China China Aerodynamics Research and Development Center/Low Speed Aerodynamics Research Institute Mianyang621000China College of Mechanical and Electrical Engineering Xichang UniversityXichang615000China

In recent years,the issue of aircraft icing has gained widespread *** breaking and detachment of dynamic ice can pose a threat to flight ***,the shedding and fracture mechanisms of dynamic ice are unclear and cannot meet the engineering needs of ice-shedding hazard ***,studying the fracture toughness of ice bodies has extremely important practical *** address this issue,this article uses a centrally cracked Brazilian disk(CCBD)specimen to measure the pure modeⅠtoughness and pure modeⅡfracture toughness of freshwater ice at different loading *** mixed-mode(Ⅰ–Ⅱ)fracture characteristics of ice are discussed,and the experimental results are compared and analyzed with the theoretical values of the generalized maximum tangential stress(GMTS)criterion considering the influence of *** results indicated that as the loading rate increases,the pure modeⅠtoughness and pure modeⅡfracture toughness of freshwater ice decrease,and the fracture toughness of freshwater ice is more sensitive to the loading rate.Ⅰn terms of fracture criteria,the theoretical value of the ratio of pure modeⅡfracture toughness to pure modeⅠfracture toughness based on the GMTS criterion is in good agreement with the experimental value,while the theoretical value based on the maximum tangential stress(MTS)criterion deviates significantly from the experimental value,indicating that the GMTS criterion considering the influence of T-stress can better predict the experimental results.

关键词： Freshwater ice Fracture criteria Centrally cracked Brazilian disk(CCBD) Mixed-mode(Ⅰ-Ⅱ) Loading rate

Geometric characterizations for variational minimizing solutions of charged 3-body problems

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Frontiers of mathematics in China 2016年第2期11卷 309-321页

作者： Wentian KUANG Yiming LONG Chern Institute of mathematics Nankai University Tianjin 300071 China key laboratory of pure mathematics and combinatorics of the ministry of education Nankai University Tianjin 300071 China

We study the charged 3-body problem with the potential function being （-a）-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the τ/2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.

关键词： Charged 3-body problem variational minimizer geometric characterization

Research Progress in the Fabrication of Covalent Organic Framework Membranes for Chemical Separations

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Chinese Journal of Polymer Science 2024年第2期42卷 141-158,I0005页

作者： Cui-Ting Ding Jin-Qiu Yuan Meng-Ying Xie Qing-Yuan Liu Zeng-Guang Yao Shi-Yu Zhang Run-Nan Zhang Hong Wu Zhong-Yi Jiang key laboratory for Green Chemical Technology of ministry of education School of Chemical Engineering and TechnologyTianjin UniversityTianjin300072China Zhejiang Institute of Tianjin University NingboZhejiang315201China Haihe laboratory of Sustainable Chemical Transformations Tianjin300192China Tianjin key laboratory of Membrane Science and Desalination Technology Tianjin UniversityTianjin300072China Joint School of National University of Singapore and Tianjin University International Campus of Tianjin UniversityBinhai New CityFuzhou350207China

Membrane technology has become one of the most promising separation technologies for its energy saving, high separation efficiency, environmental friendliness, and economic feasibility. Covalent organic frameworks(COFs) with intrinsically high porosity, controllable pore size, uniform pore size distribution and long-range ordered channel structure, have emerged as next-generation materials to fabricate advanced separation membranes. This feature article summarizes some latest studies in the development of pure COF membranes in our lab, including their fabrication and applications in chemical separations. Finally, current challenges facing high-performance COF separation membranes are discussed.

关键词： Covalent organic frameworks Covalent organic framework membranes Water treatment Organic solvent nanofiltration Gas separation

Excess Activity Tuned by Distorted Tetrahedron in CoMoO_(4) for Oxygen Evolution

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Energy & Environmental Materials 2024年第1期7卷 247-252页

作者： Hengbo Xiao Kai Chi Hongxia Yin Xiangji Zhou Pengxiang Lei Peizhi Liu Jiakun Fang Xiuhong Li Songliu Yuan Zhen Zhang Yaqiong Su Junjie Guo Lihua Qian School of Physics Huazhong University of Science and TechnologyWuhan 430074China key laboratory of Material Chemistry for Energy Conversion and Storage School of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan 430074China School of Chemistry and Chemical Engineering Hubei University of TechnologyWuhan 430068China key laboratory of Interface Science and Engineering in Advanced Materials Ministry of EducationTaiyuan University of TechnologyTaiyuan 030024China State key lab of Advanced Electromagnetic Engineering and Technology School of Electrical and Electronic EngineeringHuazhong University of Science and TechnologyWuhan 430074China School of Mechanical Engineering Hubei University of TechnologyWuhan 430068China Department of Stomatology Union HospitalTongji Medical CollegeHuazhong University of Science and TechnologyWuhan 430074China School of Chemistry Xi'an Jiaotong UniversityXi'an 710049China

Oxygen vacancies enable modulating surface reconstruction of transition metal oxides containing metal-oxygen polyhedrons into metallic oxyhydroxide for oxygen evolution reaction(OER),while revealing reconstructing mechanism is stuck by the requirement to precisely control exact sites of these ***,oxygen vacancies are localized only within MoO_(4)tetrahedrons rather than CoO_(6)octahedrons in CoMoO_(4)catalyst,guaranteeing coherent reconstruction of CoO_(6)octahedrons into pure CoOOH with tunable activities for ***,distorted tetrahedron accelerates the dissolution of Mo atoms into alkaline electrolyte,triggering spontaneous transition of partial CoMoO_(4)into Co(OH)_(2).CoO_(6)octahedrons in both CoMoO_(4)and Co(OH)_(2)can transform pure CoOOH completely at lower potential,resulting in excess intrinsic activity whose summit is identified by overpotential at 10 mA cm^(-2)with 22.9%reduction and Tafel slope with 65.3%***-defined manipulation over the distorted polyhedrons offers one versatile knob to precisely modulate electronic structure of oxide catalysts with outstanding OER performance.

关键词： metal-oxygen polyhedron oxygen evolution reaction oxygen vacancy Raman spectroscopy