共查询到20条相似文献,搜索用时 15 毫秒
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Dennis D. Berkey 《Linear algebra and its applications》1976,14(1):87-94
It is shown that the bounded solutions of the difference equation x(m + 1) = A(m + 1)x(m) arise as fixed points of a contraction mapping when A(m) satisfies a diagonal dominance condition on {0, 1, 2,…}. 相似文献
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Mihály Pituk 《Linear algebra and its applications》2011,434(2):490-500
Let An,n∈N, be a sequence of k×k matrices which converge to a matrix A as n→∞. It is shown that if xn,n∈N, is a sequence of nonnegative nonzero vectors such that
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We establish an analog of the second Bogolyubov theorem for a system of difference equations. 相似文献
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If an ordinary differential equation is discretizised near an asymptotically stable stationary solution with a pair of imaginary eigenvalues by Euler's method with constant step lengthh, small invariant attracting cycles of radiusO(h
1/2) will appear. This Hopf bifurcation theorem is applied to prove the existence of limit cycles in certain difference equations occurring in biomathematics (hypercycle, two loci-two alleles) and is also extended to general Runge—Kutta methods. 相似文献
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Dennis D. Berkey 《Linear algebra and its applications》1975,11(1):27-40
The Gerschgorin circle theorem is used here to give sufficient conditions for the solution space of the difference equation x(m+1) = A (m+1)x(m) to admit a type of exponential dichotomy. The result obtained is then used to establish a result on regions of eigenvalue inclusion for the product of finitely many square matrices. An application to differential equations is also given. 相似文献
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Wee Liang Gan 《manuscripta mathematica》2006,121(1):131-134
We prove a Chevalley restriction theorem and its double analogue for the cyclic quiver. 相似文献
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M. De la Sen 《Applied mathematics and computation》2010,216(1):149-160
A fictitious time-dependent time-varying finite sampling period is defined for each time instant at which the asymptotic expansion of the solution of a continuous-time differential equation is investigated. Such a time-dependent sampling period is defined as the quotient of each time instant and a positive integer which tends to infinity as time tends to infinity. The asymptotic expansion formulas are extendable to the case of stable Lyapunov’s equations and to the use of a constant sampling period with minor modifications in the required mathematical proofs. Additional stability results are also discussed. 相似文献
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Ziyad AlSharawi Saber Elaydi Leela Rakesh 《Journal of Mathematical Analysis and Applications》2006,316(1):128-141
We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties. 相似文献
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A residual existence theorem for linear equations 总被引:1,自引:0,他引:1
Jiri Rohn 《Optimization Letters》2010,4(2):287-292
A residual existence theorem for linear equations is proved: if ${A \in \mathbb{R}^{m\times n}}$ , ${b \in \mathbb{R}^{m}}$ and if X is a finite subset of ${\mathbb{R}^{n}}$ satisfying ${{\rm max}_{x \in X}p^T(Ax-b) \geq 0}$ for each ${p \in \mathbb{R}^{m}}$ , then the system of linear equations Ax = b has a solution in the convex hull of X. An application of this result to unique solvability of the absolute value equation Ax + B|x| = b is given. 相似文献
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The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor-valued function on G satisfying certain restrictions, and let {n} be a sequence of vector-valued functions on G where the L2-norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ?G of G ( = normal to ?G): then {n} has a L2-convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ?G if β is interpreted as electric dielectricity ? or as magnetic permeability μ, respectively. These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations. 相似文献