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arXiv 2023年

作者： Grosse, Nadine Kohr, Mirela Nistor, Victor Mathematisches Institut Universität Freiburg Freiburg79104 Germany Faculty of Mathematics and Computer Science Babeş-Bolyai University 1 M. Kogǎlniceanu Str. Cluj-Napoca400084 Romania Université de Lorraine Ufr Mim Ile du Saulcy CS 50128 Metz57045 France Inst. Math. Romanian Acad. PO BOX 1-764 Bucharest014700 Romania

A differential operator T satisfies the L2-unique continuation property if every L2-solution of T that vanishes on an open subset vanishes identically. We study the L2-unique continuation property of an operator T acting on a manifold with bounded geometry. In particular, we establish some connections between this property and the regularity properties of T. As an application, we prove that the deformation operator on a manifold with bounded geometry satisfies regularity and L2-unique continuation properties. As another application, we prove that suitable elliptic operators are invertible (Hadamard well-posedness). Our results apply to compact manifolds, which have bounded geometry. © 2023, CC BY.

关键词： Sobolev spaces

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Sobolev spaces and ∇-differential operators on manifolds I: basic properties and weighted spaces

arXiv

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arXiv 2020年

作者： Kohr, Mirela Nistor, Victor Faculty of Mathematics and Computer Science Babeş-Bolyai University 1 M. Kogalniceanu Str. Cluj-Napoca400084 Romania Université de Lorraine UFR MIM CS 50128 Ile du Saulcy METZ57045 France Inst. Math. Romanian Acad. PO BOX 1-764 Bucharest014700 Romania

We study ∇-Sobolev spaces and ∇-differential operators with coefficients in general Hermitian vector bundles on Riemannian manifolds, stressing a coordinate free approach that uses connections (which are typically denoted ∇). These concepts arise naturally from Partial Differential Equations, including some that are formulated on plain Euclidean domains, such as the weighted Sobolev spaces used to study PDEs on singular domains. We prove several basic properties of the ∇-Sobolev spaces and of the ∇-differential operators on general manifolds. For instance, we prove mapping properties for our differential operators and independence of the ∇-Sobolev spaces on the choices of the connection ∇ with respect to totally bounded perturbations. We introduce a Fréchet finiteness condition (FFC) for totally bounded vector fields, which is satisfied, for instance, by open subsets of manifolds with bounded geometry. When (FFC) is satisfied, we provide several equivalent definitions of our ∇-Sobolev spaces and of our ∇-differential operators. We examine in more detail the particular case of domains in the Euclidean space, including the case of weighted Sobolev spaces. We also introduce and study the notion of a ∇-bidifferential operator (a bilinear version of differential operators), obtaining results similar to those obtained for ∇-differential operators. Bilinear differential operators are necessary for a global, geometric discussion of variational problems. We tried to write the paper so that it is accessible to a large audience. Copyright © 2020, The Authors. All rights reserved.

关键词： math.matical operators

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Fredholm conditions on non-compact manifolds: Theory and examples

arXiv

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arXiv 2017年

作者： Carvalho, Catarina Nistor, Victor Qiao, Yu Dep. Matemática Instituto Superior Técnico University of Lisbon Av. Rovisco Pais Lisbon1049-001 Portugal Université de Lorraine UFR MIM Ile du Saulcy CS 50128 57045 METZ Inst. Math. Romanian Acad. PO BOX 1-764 Bucharest014700 Romania School of Mathematics and Information Science Shaanxi Normal University Xi’an710119 China

We give explicit Fredholm conditions for classes of pseudodifferential operators on suitable singular and non-compact spaces. In particular, we include a "user’s guide" to Fredholm conditions on particular classes of manifolds including asymptotically hyperbolic manifolds, asymptotically Euclidean (or conic) manifolds, and manifolds with poly-cylindrical ends. The reader interested in applications should be able read right away the results related to those examples, beginning with Section 5. Our general, theoretical results are that an operator adapted to the geometry is Fredholm if, and only if, it is elliptic and all its limit operators, in a sense to be made precise, are invertible. Central to our theoretical results is the concept of a Fredholm groupoid, which is the class of groupoids for which this characterization of the Fredholm condition is valid. We use the notions of exhaustive and strictly spectral families of representations to obtain a general characterization of Fredholm groupoids. In particular, we introduce the class of the so-called groupoids with Exel’s property as the groupoids for which the regular representations are exhaustive. We show that the class of "stratified submersion groupoids" has Exel’s property, where stratified submersion groupoids are defined by glueing fibered pull-backs of bundles of Lie groups. We prove that a stratified submersion groupoid is Fredholm whenever its isotropy groups are amenable. Many groupoids, and hence many pseudodifferential operators appearing in practice, fit into this framework. This fact is explored to yield Fredholm conditions not only in the above mentioned classes, but also on manifolds that are obtained by desingularization or by blow-up of singular *** Codes 58H05, 46L60, 47L80, 47L90 Copyright © 2017, The Authors. All rights reserved.

关键词： Sobolev spaces

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Cooperative service model innovation and pilot application in the prevention and control on diabetic retinopathy with web-movable hand-hold fundus camera in regional health and medicine of digitization

Cooperative service model innovation and pilot application i...

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IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2015

作者： Liang, ZhiWei Jiang, DongXu Lai, XiaoPing Mo, XueLian Liang, QianRong Luo, XiaoYan Zhou, LiWen Yuan, ZhongXun Xu, JianBiao Zhang, XiaoYang Xu, Ning Yuan, Ye An, Jing Zeng, JuanHong Zheng, ShouZeng Li, CanDong Zhou, Yi Dongguan and Guangzhou Univ. of Chinese Med. Coop. Acad. of Math. and Eng. for Chinese Medicine Dongguan Guangdong China Guangzhou University of Chinese Medicine Guangzhou Guangdong China Community Health Service Centers of Machong Town of Dongguan Dongguan Guangdong China Health Information and Statistics Center of Dongguan Dongguan Guangdong China Department of Ophthalmology Guangzhou 8th People's Hospital Guangdong China Company Ltd. of Health Science and Technology Beijing China Fujian University of Chinese Medicine Fuzhou China Computer Center Zhongshan School of Medicine Sun Yat-Sen University Guangzhou Guangdong China

ISBN: (纸本)9781467367981

Objective: systems engineering theory, hand-hold fundus camera(FC) and internet cooperative platform were applied to help community staff, long distance specialists' organizations and teams to cooperate on the screening for diabetic fundus pathological change(or diabetic retinopathy, DR) in regional residents. It aims at promoting the ability to prevent and control (PC) the important non-infectious chronic diseases (NCD) to design a proper value-chain for mutually beneficial mode of interactions among regional health services, and the other corresponding social roles via technological and organizational innovation. Methods: 1. Organizational innovation mode: Based on the Concept of social-huge-system and systems engineering theory, a cross-functional flowchart was applied to hatch a valuable road map of PC of certain single important NCD, i.e. DR, as well as the evaluation on the systematic target efficacy. 2. Technological innovation and its social practice: twenty patients suffered from diabetes with no less than eight years diabetic history were prepared to be recruited from the resident health record in Machong Community Service Center, Dongguan, Guangdong, P.R. China. The health culture for DR was expressed to the residents by specialists' lecture. Besides, their fundus photos were collected via web-movable hand-hold FC assembled with Smartphone for data remote transmission or hand-hold digital FC with self-storage device, and sent to specialists' teams in different places to study. 3. Evaluation on the practice activity: Concerning .the experience of the screening for DR, the satisfaction with the service and quality, the willing to accept the health service & management, and the awareness for DR before and after the health culture for DR, survey forms were collected and analyzed from the spot inquires to the residents at the end of the activity and from the followup visit after one week later than the screening. Results: 1. The essential factors of sustainabl

关键词： Diagnosis

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Uniform shift estimates for transmission problems and optimal rates of convergence for the parametric finite element method

Uniform shift estimates for transmission problems and optima...

引用

5th International Conference on Numerical Analysis and Applications, NAA 2012

作者： Li, Hengguang Nistor, Victor Qiao, Yu Department of Mathematics Wayne State University Detroit MI 48202 United States Department of Mathematics Pennsylvania State University University Park PA 16802 United States Inst. Math. Romanian Acad. PO BOX 1-764 014700 Bucharest Romania College of Mathematics and Information Science Shaanxi Normal University Xi'an Shaanxi 710062 China

ISBN: (纸本)9783642415142

Let Ω ⊂ d, d ≥ 1, be a bounded domain with piecewise smooth boundary ∂Ω and let U be an open subset of a Banach space Y. Motivated by questions in "Uncertainty Quantification," we consider a parametric family P = (Py)y∈U of uniformly strongly elliptic, second order partial differential operators Py on Ω. We allow jump discontinuities in the coefficients. We establish a regularity result for the solution u: Ω x U → of the parametric, elliptic boundary value/transmission problem Py u y = fy, y ∈ U, with mixed Dirichlet-Neumann boundary conditions in the case when the boundary and the interface are smooth and in the general case for d = 2. Our regularity and well-posedness results are formulated in a scale of broken weighted Sobolev spaces Kˆ a+1m+1 (Ω) of Babuška-Kondrat'ev type in Ω, possibly augmented by some locally constant functions. This implies that the parametric, elliptic PDEs (Py)y∈U admit a shift theorem that is uniform in the parameter y ∈ U. In turn, this then leads to hm-quasi-optimal rates of convergence (i. e., algebraic orders of convergence) for the Galerkin approximations of the solution u, where the approximation spaces are defined using the "polynomial chaos expansion" of u with respect to a suitable family of tensorized Lagrange polynomials, following the method developed by Cohen, Devore, and Schwab (2010). © 2013 Springer-Verlag.

关键词： Banach spaces

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Theory and Applications of Complex Networks: Advances and Challenges

Theory and Applications of Complex Networks: Advances and Ch...

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IEEE International Symposium on Circuits and systems

作者： Jinhu Lu Guanrong Chen Maciej J. Ogorzalek Ljiljana Trajkovic Acad. Math. Syst. Sci. Chinese Acad. Sci. Beijing P. R. China Sch. Electr. Comput. Eng. RMIT University Australia Dept. Electronic Engineering City University of Hong Kong Kowloon Hong Kong SAR P. R. China Dept. Information Technologies Jagiellonian University Krakow Poland School of Engineering Science Simon Fraser University Vancouver Canada

ISBN: (纸本)9781467357609

Over the last decade, complex networks have emerged to be a promising research field in the area of circuits and systems. This mini-review paper introduces the special session that deals with theory and applications of complex networks and provides brief review of their advances and challenges. The paper further promotes some important research topics in the field with emphasis on the multidisciplinary research interests.

关键词： last decade area field

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Convergence properties of preconditioned hermitian and skew-hermitian splitting methods for non-hermitian positive semidefinite matrices

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math.matics of Computation 2007年第257期76卷 287-298页

作者： Bai, Zhong-Zhi Golub, Gene H. Li, Chi-Kwong Department of Mathematics Fudan University Shanghai 200433 China State Key Laboratory of Scientific Acad. of Math. and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 P.O. BOX 2719 China Scientific Computing and Computational Mathematics Program Department of Computer Science Stanford University Stanford CA 94305-9025 United States Department of Mathematics College of William and Mary Williamsburg VA 23187-8795 P.O. Box 8795 United States

For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditiorrs for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. © 2006 American math.matical Society.

关键词： Convergence Hermitian and skew-Hermitian splitting Non-Hermitian matrix Positive semidefinite matrix Splitting iteration method

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Meta-synthesis approach to complex system modeling

Meta-synthesis approach to complex system modeling

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作者： Gu, Jifa Tang, Xijin Institute of Systems Science Acad. of Math. and Systems Sciences Chinese Academy of Sciences 55 Zhongguancun Donglu Beijing 100080 China

Meta-synthesis method is proposed to tackle with open complex giant system problems which cannot be effectively solved by traditional reductionism methods by a Chinese system scientist Qian, Xuesen (Tsien HsueShen) around the early 1990s. The method emphasizes the synthesis of collected information and knowledge of various kinds of experts, and combining quantitative methods with qualitative knowledge. Since then, continuous endeavors have been taken to put those ideas into practice. In this paper, firstly we review meta-synthesis approach and other research relevant to complex system modeling briefly. Then we discuss two main issues, model integration and opinion synthesis, which are often confronted when applying meta-synthesis approach, together with an exhibit of the development of an embryonic meta-synthetic support prototype. Such a demonstration shows how to model complex problems, such as macro-economic problems in Hall for Workshop on Meta-Synthetic Engineering with versatile resources in information collection, model integration and opinion synthesis. Finally, some future work is indicated. © 2004 Elsevier B.V. All rights reserved.

关键词： Large scale systems

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Testing Normality for Linear AR(p) Models

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Communications in Statistics - Theory and Methods 2005年第4期33卷 891-908页

作者： Ip, Wai-Cheung Wong, Hueng Chen, Min Department of Applied Mathematics Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Acad. of Math. and System Science Chinese Academy of Sciences Beijing China

This paper proposes a nonparametric mixed test for normality of linear autoregressive time series. The test is based on the best one-step forecast in mean square with time reverse. The test statistic is the mixture of a goodness of fit statistic and Cramer-Von Mises statistic. Some asymptotic properties are developed for the *** results have shown that the test is easy to use and has good powers. Three examples of applying the test to real data are also included.

关键词： Statistical tests

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An elliptic problem with critical exponent and positive hardy potential

Abstract and Applied Analysis

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Abstract and Applied Analysis 2004年第2期2004卷 91-98页

作者： Chen, Shaowei Li, Shujie Institute of Mathematics Acad. of Math. and System Sciences Chinese Academy of Sciences Beijing 100080 China

We give the existence result and the vanishing order of the solution in 0 for the following equation: -δu(x) + (μ/|x|2)u(x) = λu(x) + u2*-1(x), where x ∈ B1, μ > 0, and the potential μ/|x|2 - λ is positive i... 详细信息

We give the existence result and the vanishing order of the solution in 0 for the following equation: -δu(x) + (μ/|x|²)u(x) = λu(x) + u^2*-1(x), where x ∈ B₁, μ > 0, and the potential μ/|x|² - λ is positive in B ₁.

关键词： 35J20 35J25

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