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Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems 被引量:1
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作者 Zhaoqiang Ge 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第12期1956-1963,共8页
Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used... Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation. 展开更多
关键词 Descriptor infinite dimensional systems distribut-ional solution exact controllability exact observability
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The Loeb Space of Denumerable Infinite Dimensional Probability Product Measure Spaces 被引量:2
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作者 陈东立 《Northeastern Mathematical Journal》 CSCD 2003年第3期249-253,共5页
Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We... Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning. 展开更多
关键词 denumerable infinite dimensional product measure space Loeb measure space internal set external set
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On the ascent of infinite dimensional Hamiltonian operators
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作者 吴德玉 陈阿拉坦仓 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第8期421-425,共5页
In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 ×... In this paper, the ascent of 2 × 2 infinite dimensional Hamiltonian operators and a class of 4 × 4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2 × 2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4 × 4 infinite dimensional Hamiltonian operators that arises in study of elasticity is2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions. 展开更多
关键词 root vector COMPLETENESS infinite dimensional Hamiltonian operator ASCENT
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Two Dimensional Indecomposable Modules over Infinite Dimensional Hereditary Path Algebras
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作者 Hou Ru-chen Wang Guo-hui +1 位作者 Cheng Zhi Du Xian-kun 《Communications in Mathematical Research》 CSCD 2015年第2期171-179,共9页
Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
关键词 infinite dimensional hereditary path algebra path algebra quiver rep-resentation indecomposable module
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Establishment of infinite dimensional Hamiltonian system of multilayer quasi-geostrophic flow & study on its linear stability
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作者 黄思训 王宇 项杰 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第11期300-309,共10页
A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic... A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms. 展开更多
关键词 infinite dimensional Hamiltonian system multilayer quasi-geostrophic flow linear stability
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The Characteristic in Infinite Dimension Space
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作者 Qing Li 《Advances in Pure Mathematics》 2021年第7期645-651,共7页
In modern mathematics, geometric and algebraic properties of space can be applied by calculus in which the concept of gradually increasings of dimensions is existence (such as zero-dimension, one-dimension, two-dimens... In modern mathematics, geometric and algebraic properties of space can be applied by calculus in which the concept of gradually increasings of dimensions is existence (such as zero-dimension, one-dimension, two-dimension, and three-dimension, etc). However, this is not fact because some new concepts have been put forward in this paper where there is only a concept of infinitely great that is one quantitative continuum implied by the change of direction. The accurate description of this one quantitative continuum is that its parts are connected each other as a unity at the infinite distance (infinitely great) relative to any orientation (all orientations) of our existence. It is unity in which its random parts are these infinitely great quantities and thus we call this unity as infinite quantities of infinite dimensions. 展开更多
关键词 infinite dimension The Change of Direction One Quantitative Continuum
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Sobolev embeddings in infinite dimensions
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作者 Haimeng Luo Xu Zhang Shiliang Zhao 《Science China Mathematics》 SCIE CSCD 2023年第10期2157-2178,共22页
In this paper,we study Sobolev spaces in infinite dimensions and the corresponding embedding theorems.Our underlying spaces areℓ^(r)for r ∈[1,∞),equipped with corresponding probability measures.For the weighted Sobo... In this paper,we study Sobolev spaces in infinite dimensions and the corresponding embedding theorems.Our underlying spaces areℓ^(r)for r ∈[1,∞),equipped with corresponding probability measures.For the weighted Sobolev space W_(b)^(1,p)(ℓ^(r),γa)with a weight a∈ℓ^(r)of the Gaussian measureγa and a gradient weight b∈l^(∞),we characterize the relation between the weights(a and b)and the continuous(resp.compact)log-Sobolev embedding for p∈[1,∞)(resp.p∈(1,∞)).Several counterexamples are also constructed,which are of independent interest. 展开更多
关键词 Sobolev embedding infinite dimensions Sobolev space Orlicz space
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Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator 被引量:22
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作者 Alatancang WU DeYu 《Science China Mathematics》 SCIE 2009年第1期173-180,共8页
The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the sufficient conditions of the completeness in the sense of Cauchy principal value of the eigenfunc... The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the sufficient conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional Hamiltonian operators are given. In the end, concrete examples are constructed to justify the effectiveness of the criterion. 展开更多
关键词 infinite dimensional Hamiltonian operator k-compact operator EIGENVALUE eigenfunction system Cauchy principal value COMPLETENESS 47A75
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Structure of the spectrum of infinite dimensional Hamiltonian operators 被引量:26
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作者 Alatancang 《Science China Mathematics》 SCIE 2008年第5期915-924,共10页
This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all... This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover,it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis;and a complete characterization of the residual spectrum in terms of the point spectrum is then given.As applications of these structure results,we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty. 展开更多
关键词 non-self-adjoint operator infinite dimensional Hamiltonian operator structure of spectrum 47A10 47B99
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Completeness of Eigenfunction Systems for Off-Diagonal Infinite-Dimensional Hamiltonian Operators 被引量:15
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作者 侯国林 阿拉坦仓 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第2期237-241,共5页
For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi... For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations. 展开更多
关键词 Hamiltonian system infinite dimensional Hamiltonian operator COMPLETENESS Cauchy principalvalue magnetoelectroelastic solid
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ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS 被引量:3
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作者 Yuhong LI 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2008年第3期416-426,共11页
Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the followin... Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the following equations {dz(t)=A(t,z(t))dt+σ(t,z(t))dW(t),z(0)=z0∈X,are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre (1989) and Mao (1992). 展开更多
关键词 Almost surely asymptotic bounds infinite dimension M-type 2 Banach space Ornstein-Uhlenbeck Processes
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Some infinite dimensional representations of reductive groups with Frobenius maps 被引量:3
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作者 XI NanHua 《Science China Mathematics》 SCIE 2014年第6期1109-1120,共12页
In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex represe... In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps. 展开更多
关键词 infinite dimensional representation reductive group induced module
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Local Continuity Modulus for Wiener and Infinite Dimensional OU Processes 被引量:3
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作者 Lu Chuanrong Shen Siwei Wang Xiuyun Department of Mathematics Hangzhou University Hangzhou, 310028 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第2期219-224,共6页
In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W(s)|/(2s log log(1/s))<sup>1/2</sup>=1 a.s. This result was given by Csrg... In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W(s)|/(2s log log(1/s))<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz (1981), but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes. 展开更多
关键词 In OU Local Continuity Modulus for Wiener and infinite dimensional OU Processes
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Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators 被引量:2
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作者 WANG Hua Alatancang HUANG dun die 《Journal of Mathematical Research and Exposition》 CSCD 2009年第5期907-912,共6页
In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP(A) and σ1/... In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP(A) and σ1/P(-A^*) with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results. 展开更多
关键词 non-self-adjoint operator infinite dimensional Hamiltonian operator point spectrum symmetry.
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Difference Approximation of Stochastic Elastic Equation Driven by Infinite Dimensional Noise 被引量:1
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作者 Yinghan Zhang Xiaoyuan Yang Ruisheng Qi 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2016年第1期123-146,共24页
An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant ... An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant random processes and the integral formula of the stochastic elastic equation is approximated by a truncated series.Error analysis of the numerical method yields estimate of convergence rate.The rate of convergence is demonstrated with numerical experiments. 展开更多
关键词 Stochastic partial differential equations difference scheme stochastic elastic equation infinite dimensional noise rate of convergence
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Symmetry of the Point Spectrum of Infinite Dimensional Hamiltonian Operators and Its Applications 被引量:1
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作者 Hua WANG Alatancang Jun-jie HUANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2012年第1期149-156,共8页
This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp(H)... This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp(H) = σp (A) U σp1 (-A*). Using the characteristic of the set σp1(-A*), we divide the point spectrum σp (d) of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1(-A*) and one part of σp(A) are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp(H) is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations. 展开更多
关键词 infinite dimensional Hamiltonian operator point spectrum SYMMETRY thin plate on elasticfoundation plane elasticity problem harmonic equation
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Approximate solutions to infinite dimensional LQ problems over infinite time horizon
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作者 PAN Liping, ZHANG Xu & CHEN Qihong School of Mathematical Sciences, Fudan University, Shanghai 200433, China School of Mathematics, Sichuan University, Chengdu 610064, China Department of Applied Mathematics, Shanghai University of Finance & Economics, Shanghai 200433, China 《Science China Mathematics》 SCIE 2006年第7期865-876,共12页
This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solut... This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense. 展开更多
关键词 approximate solution LQ problem infinite dimensional infinite time hori-
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OUTPUT REGULATION PROBLEM FOR A CLASS OF SISO INFINITE DIMENSIONAL SYSTEMS VIA A FINITE DIMENSIONAL DYNAMIC CONTROL
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作者 WANG Xinghu JI Haibo SHENG Jie 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第6期1172-1191,共20页
This paper deals with the output regulation problem for a class of SISO infinite dimensional systems with an uncertain exosystem.For these systems,a concept of relative degree is firstly introduced and used to constru... This paper deals with the output regulation problem for a class of SISO infinite dimensional systems with an uncertain exosystem.For these systems,a concept of relative degree is firstly introduced and used to construct a transformation which leads to the canonical form of output feedback systems.Then,based on this canonical form,by means of an internal model and a recursive adaptive control,the authors obtain an adaptive regulator which solves the problem.It should be pointed out that the proposed regulator is finite dimensional while it is usually infinite dimensional in existing literatures. 展开更多
关键词 infinite dimensional systems output feedback form output regulation problem.
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AN INFINITE DIMENSIONAL ANALOGUE OF THE ALBEVERIO-RCKNER'S THEOREM ON FUKUSHIMA'S CONJECTURE
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作者 宋士奇 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1993年第2期115-124,共10页
Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where ... Let X be the solution of the SDE:dX_t=σ(X_t)dB_t+b(X_t)dt,with σ and b ∈C_B~∞(R) such that σ≥λ>0 for some constant λ,and B a real Brownian motion.Let μ be the law of X on E=C([0,1],R)and k ∈E~*-{0},where E~* is the topological dual space of E.Consider the classical form:where u and v are smooth functions on E.We prove that,if is closable for any k in a dense subset of E~* and if the smooth functions are contained in the domain of the generator of the closure of ε_k,σ must be a constant function. 展开更多
关键词 CKNER’S THEOREM ON FUKUSHIMA’S CONJECTURE AN infinite dimensionAL ANALOGUE OF THE ALBEVERIO-R SDE
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INFINITE DIMENSIONAL MALLIAVIN CALCULUS AND ITS APPLICATION
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作者 周先银 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1992年第2期97-114,共18页
In this paper we study the infinite dimensional Malliavin calculus, and apply it to determingwhen the solution of an infinite dimensional stochastic differential equation has the property thatits finite dimensional di... In this paper we study the infinite dimensional Malliavin calculus, and apply it to determingwhen the solution of an infinite dimensional stochastic differential equation has the property thatits finite dimensional distributions possess smooth density. 展开更多
关键词 SDE infinite dimensionAL MALLIAVIN CALCULUS AND ITS APPLICATION
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