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On Hereditarily Indecomposable Banach Spaces

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Acta Mathematica Sinica,English Series 2006年第3期22卷 751-756页

作者： Li Xin CHENG Huai Jie ZHONG Department of Mathematics Xiamen University The Institute of mathematical Sciences The Chinese University of Hang Kong Department of Mathematics Fujian Normal University

This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily i... 详细信息

关键词： decomposition of spaces hereditarily indecomposable Banach space renormings

Bifurcation and multiplicity of positive solutions for nonhomogeneous fractional Schrödinger equations with critical growth

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Science China Mathematics 2020年第8期63卷 1571-1612页

作者： Xiaoming He Wenming Zou College of Science Minzu University of ChinaBeijing 100081China Department of mathematical Sciences Tsinghua UniversityBeijing 100084China

In this paper we study the nonhomogeneous semilinear fractional Schr?dinger equation with critical growth{(−∆)su + u = u^2∗s−1 + λ(f(x, u) + h(x)), x ∈ R^N ,u ∈ Hs(R^N ), u(x) > 0, x ∈ RN ,where s∈(0,1),N>4 s,andλ>0 is a parameter,2s*=2 N/N-2 s is the fractional critical Sobolev exponent,f and h are some given *** show that there exists 0λ*,a unique solution(λ*,uλ*)ifλ=λ*,which shows that(λ*,uλ*)is a turning point in Hs(RN)for the *** proofs are based on the variational methods and the principle of concentration-compactness.

关键词： fractional Schrödinger equation bifurcation and multiplicity concentration-compactness principle critical Sobolev exponent

The Existence of a Weak Solution of Inhomogeneous Quasilinear Elliptic Equation with Critical Growth Conditions

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Acta Mathematica Sinica,English Series 1995年第2期11卷 146-155页

作者： Li Gongbao Zhou Huansong Wuhan Institute of mathematical Sciences Academia Sinica P. O. Box 71007 Wuhan, 430071 China Wuhan Institute of mathematical Sciences Academia Sinica Wuhan People's Republic of China

In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|m-1eb|u|γat +∞, with γ=N/N-1, m≥1, b>0.

关键词： lim The Existence of a Weak Solution of Inhomogeneous Quasilinear Elliptic Equation with Critical Growth Conditions Math

On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter

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Journal of mathematical Research with Applications 2013年第3期33卷 253-272页

作者： Lavdie RADA Ke CHEN Centre for mathematical Imaging Techniques and Department of mathematical Sciences University of LiverpoolLiverpool L69 7ZL United Kingdom

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl. Math.) on dividing a general surface into piecewise smooth sub-surfaces. A central idea of models based on this work is to minimize the length of feature's boundaries (i.e., H1 Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize L2 Lebesgue measure of the γ-neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method.

关键词： image selective segmentation level set edge detection 2D image segmentation.

Adaptive Tracking Control for Output-Constrained Switched MIMO Pure-Feedback Nonlinear Systems with Input Saturation

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Journal of Systems Science & Complexity 2023年第3期36卷 960-984页

作者： ZHANG Haoyan ZHAO Xudong WANG Huanqing NIU Ben XU Ning College of Control Science and Engineering Bohai UniversityJinzhou 121013China Faculty of Electronic Information and Electrical Engineering Dalian University of TechnologyDalian 116024China College of mathematical Science Bohai UniversityJinzhou 121013China School of Information Science and Engineering Shandong Normal UniversityJinan 250014China College of Information Science and Technology Bohai UniversityJinzhou 121013China

In this paper,an adaptive neural tracking control scheme for a class of uncertain switched multi-input multi-output(MIMO)pure-feedback nonlinear systems is *** considered MIMO pure-feedback nonlinear system contains input and output constraints,completely unknown nonlinear functions and time-varying external *** unknown nonlinear functions representing system uncertainties are identified via radial basis function neural networks(RBFNNs).Then,the Nussbaum function is utilized to deal with the nonlinearity issue caused by the input *** prevent system outputs from violating prescribed constraints,the barrier Lyapunov functions(BLFs)are ***,a switched disturbance observer is designed to make the time-varying external disturbances *** on the backstepping recursive design technique and the Lyapunov stability theory,the developed control method is verified applicable to ensure the boundedness of all signals in the closed-loop system and make the system output track given reference signals ***,a numerical simulation is given to demonstrate the effectiveness of the proposed control method.

关键词： Adaptive control input saturation neural networks output constraints switched MIMO pure-feedback nonlinear systems

Optimal L^(2)Error Estimates for the Interior Penalty DGMethod for Maxwell’s Equations in Cold Plasma

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Communications in Computational Physics 2012年第2期11卷 319-334页

作者： Jichun Li Department of mathematical Sciences University of NevadaLas VegasNevada 89154-4020USA

In this paper,we consider an interior penalty discontinuous Galerkin(DG)method for the time-dependent Maxwell’s equations in cold *** Huang and Li(***.,42(2009),321–340),for both semi and fully discrete DG schemes,we proved error estimates which are optimal in the energy norm,but sub-optimal in the L^(2)-*** by filling this gap,we show that these schemes are optimally convergent in the L^(2)-norm on quasi-uniform tetrahedral meshes if the solution is sufficiently smooth.

关键词： Maxwell’s equations cold plasma discontinuous Galerkin method

Elliptic genera of level N for complete intersections

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Frontiers of Mathematics in China 2021年第4期16卷 1043-1062页

作者： Jianbo WANG Yuyu WANG Zhiwang YU School of Mathematics Tianjin UniversityTianjin 300350China College of mathematical Science Tianjin Normal UniversityTianjin 300387China

We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete *** the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group,we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c_(1)>,=,or<*** particular,the values about the Todd genus,Â-genus,and A_(k)-genus can be derived from the elliptic genera of level N.

关键词： Complete intersection elliptic genera of level N Todd genus A_(k)-genus

Asymptotically efficient parameter estimation for ordinary differential equations

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Science China Mathematics 2017年第11期60卷 2263-2286页

作者： PANG TianXiao YAN PeiSi ZHOU Harrison H. School of mathematical Sciences Zhejiang University Center for Computing and Visualization Brown University Department of Statistics and Data Science Yale University

Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et al.(2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However, little is known about statistical properties of this procedure. In this paper, we provide a theoretical justification of the generalized profiling procedure. Under some regularity conditions, the procedure is shown to be consistent for a broad range of tuning parameters. When the tuning parameters are sufficiently large, the procedure can be further shown to be asymptotically normal and efficient.

关键词：常微分方程参数估计渐近有效正则性条件统计推断传统方法统计特性渐近正态

Skew Pairs of Idempotents in Transformation Semigroups

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1705-1714页

作者： T.S.BLYTH M.H.ALMEIDA SANTOS mathematical Institute University of St Andrews Departamentode Matemática F.C.T.Universidade Nova de Lisboa

An ordered pair （e, f） of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent. We have shown previously that there are four distinct types of skew pairs of idemp... 详细信息

关键词： full transformation semigroups idempotents skew pairs