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Alternative Methods of Regular and Singular Perturbation Problems
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作者 Boampong Asare Manohar Sah Ram Krishna Hona 《Applied Mathematics》 2024年第10期687-708,共22页
Making exact approximations to solve equations distinguishes applied mathematicians from pure mathematicians, physicists, and engineers. Perturbation problems, both regular and singular, are pervasive in diverse field... Making exact approximations to solve equations distinguishes applied mathematicians from pure mathematicians, physicists, and engineers. Perturbation problems, both regular and singular, are pervasive in diverse fields of applied mathematics and engineering. This research paper provides a comprehensive overview of algebraic methods for solving perturbation problems, featuring a comparative analysis of their strengths and limitations. Serving as a valuable resource for researchers and practitioners, it offers insights and guidance for tackling perturbation problems in various disciplines, facilitating the advancement of applied mathematics and engineering. 展开更多
关键词 PERTURBATION regular Perturbation singular Perturbation Asymptotic Expansion Matched Asymptotic Strained Coordinates Multiple Scales
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Analytic Regularity for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters
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作者 Irene Sykopetritou Christos Xenophontos 《Communications in Mathematical Research》 CSCD 2024年第2期125-153,共29页
We consider a second order,two-point,singularly perturbed boundary value problem,of reaction-convection-diffusion type with two small parameters,and we obtain analytic regularity results for its solution,under the ass... We consider a second order,two-point,singularly perturbed boundary value problem,of reaction-convection-diffusion type with two small parameters,and we obtain analytic regularity results for its solution,under the assumption of analytic input data.First,we establish classical differentiability bounds that are explicit in the order of differentiation and the singular perturbation parameters.Next,for small values of these parameters we show that the solution can be decomposed into a smooth part,boundary layers at the two endpoints,and a negligible remainder.Derivative estimates are obtained for each component of the solution,which again are explicit in the differentiation order and the singular perturbation parameters. 展开更多
关键词 singularly perturbed problem reaction-convection-diffusion boundary layers analytic regularity.
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REGULARITIES AND SINGULARITIES OF THE ENERGY MINIMIZERS OF THE HEISENBERG GROUP TARGETS 被引量:1
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作者 贾高 《Acta Mathematica Scientia》 SCIE CSCD 2003年第4期447-452,共6页
In this paper, the properties of the maps for the Heisenberg group targets are studied. For u e∈W1,α(Ω, Hm), some Poincare type inequalities are proved. For the energy minimizers, the ∈-regularity theorems and the... In this paper, the properties of the maps for the Heisenberg group targets are studied. For u e∈W1,α(Ω, Hm), some Poincare type inequalities are proved. For the energy minimizers, the ∈-regularity theorems and the singularity theorems are obtained. 展开更多
关键词 Heisenberg group energy minimizer Legendrian map regularity singularity
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Performance Evaluation of Bottom-Standing Submerged Breakwaters in Regular Waves Using the Meshless Singular Boundary Method 被引量:1
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作者 SENOUCI Fawzi CHIOUKH Nadji DRIS Mohammed El-Amine 《Journal of Ocean University of China》 SCIE CAS CSCD 2019年第4期823-833,共11页
In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. ... In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures. 展开更多
关键词 meshless improved singular boundary method regular normal waves rectangular and trapezoidal breakwaters reflection transmission
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Numerical solutions for cracks in an elastic half-plane 被引量:1
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作者 N.R.F.Elfakhakhre N.M.A.Nik Long Z.K.Eshkuvatov 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第1期212-227,I0006,共17页
The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into... The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into singular integral equations with the distribution dislocation function as unknown. In the formulation, we make used of a modified complex potential. Based on the appropriate quadrature formulas together with a suitable choice of collocation points, the singular integral equations are reduced to a system of linear equations for the unknown coefficients. Numerical examples show that the values of the stress intensity factor are influenced by the distance from the cracks to the boundary of the half-plane and the configuration of the cracks. 展开更多
关键词 ELASTIC half-plane Multiple cracks singular INTEGRAL equation Sine-shaped crack
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REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS
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作者 周焕林 牛忠荣 王秀喜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第10期1208-1214,共7页
A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of ... A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results. 展开更多
关键词 boundary element method (BEM) nearly singular integral regularIZATION potential problem
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Regular-Singular Crossings on Nonlinear Systems with Turning Point
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作者 Zhang Hanlin (Beijing Polytechnic University) Zhang Heping (Beijing Electric Power College) 《Advances in Manufacturing》 SCIE CAS 1998年第3期21-23,共3页
We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, ... We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, f i satisfy 2 f y′ 2 i t =0 =0, we say that F possesses a generalized turning point at t =0. Our goal is to give sufficient conditions for the existence of solution of the problems and to study the asymptotic behavior of the solution when F possesses a generalized turning point at t =0. We mainly discuss regular singular crossings. 展开更多
关键词 turning point regular singular crossing differential inequality
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Determination of stress intensity factors in half-plane containing several moving cracks
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作者 K.MALEKZADEH FARD M.M.MONFARED K.NOROUZIPOUR 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第12期1535-1542,共8页
The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a... The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a single dislocation and without dislocation. An exact solution in a closed form to the stress fields and displacement is ob- tained. The Galilean transformation is used to transform between coordinates connected to the cracks. The stress components are of the Cauchy singular kind at the location of dislocation and the point of application of the the influence of crack length and crack running force. Numerical examples demonstrate velocity on the stress intensity factor. 展开更多
关键词 moving crack stress intensity factor half-plane Cauchy singularity
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RIGHT FOCAL BOUNDARY VALUE PROBLEM WITH SINGULARITY
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作者 田玉 葛渭高 《数学物理学报(A辑)》 CSCD 北大核心 2006年第B12期1064-1076,共13页
This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p + 1,…, n - 1. Here the positive Carathedory f... This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p + 1,…, n - 1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f(t,x0,x1,…,xn-1) are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali's convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article. 展开更多
关键词 高阶微分方程 边值问题 集中收敛定理 规则化
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网络入侵微分方程正则化反演算法仿真
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作者 孔昭毅 李红映 《计算机仿真》 2024年第7期447-450,455,共5页
为了保障网络运行安全,维护网络运行环境,提出基于20-sim软件的网络入侵微分方程反演算法。引入微分方程,在20-sim平台内实现网络入侵模型的构建;通过模型奇点计算,明确网络入侵行为的蔓延程度以及网络入侵行为的扩散趋势。为优化网络... 为了保障网络运行安全,维护网络运行环境,提出基于20-sim软件的网络入侵微分方程反演算法。引入微分方程,在20-sim平台内实现网络入侵模型的构建;通过模型奇点计算,明确网络入侵行为的蔓延程度以及网络入侵行为的扩散趋势。为优化网络入侵模型构建的精准度,引入正则化反演算法,通过对模型构造数据的正则化处理、模型约束目标函数分析,实现反演算法中正则化因子的自适应调节;将正则化反演因子代入反演方程中,实现模型参数向量的推导;根据反演参数推导结果,对网络入侵模型实施纠错与优化。实验结果表明,所提方法能够在较短耗时的前提下,实现网络入侵行为的精准分析,对互联网技术的发展具有重大意义。 展开更多
关键词 微分方程 奇点计算 正则化反演算法
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On von Neumann Regularity of Commutators
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作者 Nam Kyun Kim Tai Keun Kwak +2 位作者 Yang Lee Sung Ju Ryu Nanqing Ding 《Algebra Colloquium》 SCIE CSCD 2024年第2期181-198,共18页
We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R... We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[X]=W(R)[X]■Z(R[X]),where J(A),N^(*)(A),W(A),Z(A)are the Jacobson radical,upper nilradical,Wedderburn radical,and center of a given ring A,respectively,and A[X]denotes the polynomial ring with a set X of commuting indeterminates over A;we also prove that R is semiprime if and only if the right(left)singular ideal of R is zero.We provide methods to construct C-regular rings which are neither commutative nor von Neumann regular,from any given ring.Moreover,for a C-regular ring R,the following are proved to be equivalent:(i)R is Abelian;(ii)every prime factor ring of R is a duo domain;(ii)R is quasi-duo;and(iv)R/W(R)is reduced. 展开更多
关键词 C-regular ring COMMUTATOR regular ring commutative ring RADICAL singular ideal
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Optimal regularity of positive solutions of the Hénon-Hardy equation and related equations
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作者 Zongming Guo Fangshu Wan 《Science China Mathematics》 SCIE CSCD 2024年第10期2283-2302,共20页
We present a new method to determine the optimal regularity of positive solutions u∈C^(4)(Ω\{0})∩C^(0)(Ω) of the Hénon-Hardy equation,i.e.,Δ^(2)u=|x|^(α)u^(p)inΩ,(0,1) where Ω■RN(N≥4) is a bounded smoot... We present a new method to determine the optimal regularity of positive solutions u∈C^(4)(Ω\{0})∩C^(0)(Ω) of the Hénon-Hardy equation,i.e.,Δ^(2)u=|x|^(α)u^(p)inΩ,(0,1) where Ω■RN(N≥4) is a bounded smooth domain with 0∈Ω,α>-4,and p∈R.It is clear that 0 is an isolated singular point of solutions of(0.1) and the optimal regularity of u in Ω relies on the parameter α.It is also important to see that the regularity of u at x=0 determines the regularity of u in Ω.We first establish asymptotic expansions up to arbitrary orders at x=0 of prescribed positive solutions u ∈C^(4)(Ω{0}) ∩ C^(0)(Ω)of(0.1).Then we show that the regularity at x=0 of each positive solution u of(0.1) can be determined by some terms in asymptotic expansions of the related positive radial solution of the equation(0.1) with Ω=B,where B is the unit ball of R^(N).The main idea works for more general equations with singular weights. 展开更多
关键词 H´enon-Hardy equation positive solutions optimal regularity singular point asymptotic expansions
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求解一类平行四边形域上热传导反问题的无网格方法
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作者 刘源 张永富 《长春师范大学学报》 2024年第8期24-34,共11页
基于基本解和径向基函数相结合的方法,对采用不同径向基作为近似解的基底,用平行四边形域反演一类热传导反问题的初值和热源项进行研究.因插值构造的方程系数矩阵是病态的,即系数矩阵的条件数较大,本文基于GCV准则的奇异值分解正则化方... 基于基本解和径向基函数相结合的方法,对采用不同径向基作为近似解的基底,用平行四边形域反演一类热传导反问题的初值和热源项进行研究.因插值构造的方程系数矩阵是病态的,即系数矩阵的条件数较大,本文基于GCV准则的奇异值分解正则化方法求解线性方程组,选取不同噪声级,通过数值算例显示所给方法是稳定有效的. 展开更多
关键词 热传导反问题 基本解方法 径向基函数 奇异值分解正则化方法 GCV准则
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奇异值分解下在线鲁棒正则化随机网络
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作者 于洋 邓瑞 +1 位作者 余刚 庞新富 《控制理论与应用》 EI CAS CSCD 北大核心 2024年第3期407-415,共9页
在线鲁棒随机权神经网络(OR-RVFLN)具有较好的逼近性、较快的收敛速度、较高的鲁棒性能以及较小的存储空间.但是,OR-RVFLN算法计算过程中会产生矩阵的不适定问题,使得隐含层输出矩阵的精度较低.针对这个问题,本文提出了奇异值分解下在... 在线鲁棒随机权神经网络(OR-RVFLN)具有较好的逼近性、较快的收敛速度、较高的鲁棒性能以及较小的存储空间.但是,OR-RVFLN算法计算过程中会产生矩阵的不适定问题,使得隐含层输出矩阵的精度较低.针对这个问题,本文提出了奇异值分解下在线鲁棒正则化随机网络(SVD-OR-RRVFLN).该算法在OR-RVFLN算法的基础上,将正则化项引入到权值的估计中,并且对隐含层输出矩阵进行奇异值分解;同时采用核密度估计(KDE)法,对整个SVD-OR-RRVFLN网络的权值矩阵进行更新,并分析了所提算法的必要性和收敛性.最后,将所提的方法应用于Benchmark数据集和磨矿粒度的指标预测中,实验结果证实了该算法不仅可以有效地提高模型的预测精度和鲁棒性能,而且具有更快的训练速度. 展开更多
关键词 随机权神经网络 正则化 奇异值分解 磨矿过程 磨矿粒度
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联合改进稀疏正则化ECT图像重建算法
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作者 马敏 孙妮 《计量学报》 CSCD 北大核心 2024年第8期1132-1138,共7页
针对电容层析成像技术逆问题求解过程中的病态性和不适定问题,提出了联合改进稀疏正则化图像重建算法。首先利用自适应截断奇异值算法对灵敏度矩阵进行优化预处理,以消除矩阵中的冗余信息;其次,基于优化后的灵敏度矩阵联合改进的L1-αL... 针对电容层析成像技术逆问题求解过程中的病态性和不适定问题,提出了联合改进稀疏正则化图像重建算法。首先利用自适应截断奇异值算法对灵敏度矩阵进行优化预处理,以消除矩阵中的冗余信息;其次,基于优化后的灵敏度矩阵联合改进的L1-αL2稀疏正则化,构建凸函数项,增强解的稀疏性和稳定性;最后通过快速迭代阈值收缩算法进行求解,加速迭代收敛速度。改进算法在重建图像中相关系数平均达0.8813,图像误差平均降至0.2111,成像速度保持在0.10 s以内。仿真与实验结果表明,改进算法改善了逆问题的病态性和不适定性,提高了图像重建精度,同时具有较强的鲁棒性和实时性。 展开更多
关键词 多相流测量 电容层析技术 自适应截断奇异值 稀疏正则化 图像重建
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Sufficient and Necessary Condition of Admissibility for Fractional-order Singular System 被引量:14
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作者 YU Yao JIAO Zhuang SUN Chang-Yin 《自动化学报》 EI CSCD 北大核心 2013年第12期2160-2164,共5页
这份报纸与顺序为部分顺序的单个系统集中于考虑条件吗?(0, 1 ) 。整齐的定义,没有推动并且考虑被给第一,然后,为部分顺序的单个系统的考虑的一个足够、必要的条件被建立。一个数字例子被包括说明建议条件。
关键词 奇异系统 分数阶 充要条件 可容许 充分必要条件
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THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS 被引量:1
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作者 钟同德 陈吕萍 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期679-690,共12页
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^(1) smooth boundary on a Stein manifold. As an a... Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation. 展开更多
关键词 Stein manifold singular integral with Bochner-Martinelli kernel permutation formula regularization problem
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VIBRATING VELOCITY RECONSTRUC-TION USING IBEM AND TIKHONOV REGULARIZATION
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作者 Xu ZhangmingShen RongyingHua HongxingState Key Laboratory of Vibration,Shock and Noise,Shanghai Jiaotong University,Shanghai 200030, China 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2003年第1期75-78,共4页
The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate so... The inverse problem to determine the vibrating velocity from known exteriorfield measurement pressure, involves the solution of a discrete ill-posed problem. To facilitate thecomputation of a meaningful approximate solution possible, the indirect boundary element method(IBEM) code for investigating vibration velocity reconstruction and Tikhonov regularization methodby means of singular value decomposition (SVD) are used. The amount of regularization is determinedby a regularization parameter. Its optimal value is given by the L-curve approach. Numerical resultsindicate the reconstructed normal surface velocity is a good approximation to the real source. 展开更多
关键词 Vibrating velocity reconstruction Tikhonov regularization singular valuedecomposition Indirect boundary method
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The Products of Regularly Solvable Operators with Their Spectra in Direct Sum Spaces
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作者 Sobhy El-Sayed Ibrahim 《Advances in Pure Mathematics》 2013年第4期415-429,共15页
In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on... In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on each of the separate intervals with the cases of one and two singular end-points and when all solutions of the equation and its adjoint are in (the limit circle case) that all well-posed extensions of the minimal operator have resolvents which are HilbertSchmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression studied in [1-10] and those of general quasi-differential expressions in [11-19]. 展开更多
关键词 Product of Quasi-Differential EXPRESSIONS regular and singular ENDPOINTS regularly SOLVABLE OPERATORS Essential Spectra Hilbert-Schmidt Integral OPERATORS
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Singular Stabilization and H_∞ Control of Nonlinear Systems with Ordinary Homogeneous Properties
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作者 FANG Jian-yin MU Xiao-wu 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第3期280-288,共9页
In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogen... In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogeneous. Secondly, by vitue of Hamilton-Jacobi-Isaacs equations or inequalities, we solve regular H∞ of nonlinear systems with homogeneous properties. To overcome the H∞ problem of singular nonlinear system, we try to transform inputs of the singular nonlinear system into two parts: regular part input and singular part input. Following the previous results, we solve the singular nonlinear system H∞ control, we give the Lyapunov function and the state feedback controller of the singular nonlinear systems with homogeneous properties. 展开更多
关键词 STABILIZATION H∞ control homogeneous system singular system regular system feedback state control
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