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关于偶数阶中立型微分方程的线性化振动的一个注记 总被引:2,自引:0,他引:2
就偶数阶中立型时滞微分方程的所有有界解的振动性而言,研究了偶数阶非 线性中立型时滞微分方程[x(t)-p(t)x(t-τ)]-q(t)h(x(t-σ))=0和与它相应的 线性方程[x(t)-p_0x(t-τ)]-q-0x(t-τ)=0在振动性上的等价性.所得结果改进 了 Ladas G,和 Qian C.的一个结果. 相似文献
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具有交互神经传递时滞的神经网络的稳定性 总被引:15,自引:0,他引:15
本文研究了具有交互神经传递时滞的神经网络模型x′i(t)=-bixi(t)+∑nj=1ωijfj(xj(t-τj))+pi(t>0;i=1,2,…,n)平衡点的全局渐近稳定性,并获得了若干充分条件· 相似文献
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本文给出了二阶中立型微分方程x(t)+x(t-τ)+bx(t)+b1x(t-τ)+cx(t)+c1x(t-τ)=0零解稳定的代数判据. 相似文献
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一类中立型微分方程的比较定理及应用 总被引:1,自引:0,他引:1
考虑中立型微分方程[x(t)-x(t-τ)](n)+Q(t)x(t-σ)=0,tt0,其中n1为奇数,τ∈(0,∞),σ∈R+=[0,∞),Q∈C([t0,∞),R+).本文获得了此方程存在最终正解以及所有解振动的新的比较定理.并据此获得了所有解振动的“sharp″条件以及存在最终正解的一般性结果,改进了文[4]的主要结果. 相似文献
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1IntroductionInthispaperweconsiderthefolowingequationswithperiodiccoeficientsx=A(t)x2+B(t)x+C(t),(1.1)x=-A(t)x2+B(t)x+C(t),(1... 相似文献
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脉冲中立型时滞微分方程解的振动性 总被引:18,自引:0,他引:18
本文讨论一阶脉冲中立型时滞微分方程[y(t)+Py(t-σ)]′+Q(t)y(t-σ)=0,t0,t≠tk,k=1,2,…,y(t+k)-y(t-k)=bky(tk),k=1,2,…,{(E)这里τ,σ,P均为常数,τ>0,σ>0,Q(t)∈C([0,∞),R+),bk>-1,k=1,2,….分三种情况,P-1;-1<P<0;P>0给出了方程(E)所有解振动的充分条件. 相似文献
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具连续变量的线性时滞差分方程的振动性 总被引:4,自引:0,他引:4
本文研究如下具有连续变量的线性时滞差分方程y(t)-y(t-τ)+∑mj=1pj(t)y(t-σj)=0,t≥0,其中pj(t)∈c(R^+,R^+),0〈τ〈σ1≤σ2≤…≤m,j=1,2,…,m,获得了该方程的每个解都振动的若干充分条件,改进了现有文献中的结果。 相似文献
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Theorem1 Letm∈Nandm1,P(x)beanarbitraryorderpartialdifferentialopera-tor.Thenf(x,t),φj(x)∈J.(WhereJstandforthesetofanalyticfunctioninthispaper)t+P(x)mu=f(x,t)jutjt=0=φj(x) x∈Rn,t∈R1j=0,1,2,…,m-1.u(x,t)=∫t0(t-τ)m-1(m-1)!e-(t-τ)P(x)f(x,τ)dτ+e-… 相似文献
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One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows 相似文献
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ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals. 相似文献
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Pankaj Mathur 《分析论及其应用》2006,22(2)
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x). 相似文献
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It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
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《高校应用数学学报(英文版)》2014,29(4)
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with 相似文献
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《数学研究及应用》2014,(6)
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics. 相似文献
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A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6]. 相似文献