共查询到18条相似文献,搜索用时 765 毫秒
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设Y_i=x'iβ+ei,1≤i≤n为线性模型,βn=(βn1,…,βnp)'为β=(β1,…,βp)'的最小二乘估计,以u_n记(sum from i=1 to n(xix'i))的(1,1)元,vn=un-1.证明了在Eei=O且{ei}满足Gauss-Markov条件时,vi→∞及sum from i=2 to ∞(vi-2(vi-vi-1)log~2i<∞)为βn1强相合的充分条件,且对任何εn→0,vi→∞及sum from i=2 to ∞(εivi-2(vi-vi-1)log2i<∞)已不再充分.提出了βn1强相合的一个充要条件,它把βn1强相合归结为正交随机变量级数的收敛问题. 相似文献
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该文研究一类非线性高阶波动方程utt-a1Uxx+a_2ux4+a3ux4tt=φ(ux )x+f(u,ux,uxxuxxx,ux4)的初边值问题.证明整体古典解的存在唯一性并给出古典解爆破的充分条件. 相似文献
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广义 Petersen 图 P(n, m) 是这样的一个图:它的顶点集是{ui, vi | i=0,1, … , n-1}, 边集是 {uiui+1, vivi+m, uivi | i=0,1, …, n-1}, 这里 m, n 是正整数、加法是在模n 下且 m<|n/2| . 这篇文章证明了P(2m+1, m)(m≥ 2) 的 Euler 亏格是1, 并且 P(2m+2, m)(m≥ 5) 的 Euler 亏格是2. 相似文献
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对x = (x1, x2,···, xn) ∈ (0,1)n 和 r ∈ {1, 2,···, n} 定义对称函数
Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1∑j=1r(1+xi3/1- xi3)1/r,
其中i1, i2, ···, ir 是整数. 该文证明了Fn(x, r) 是(0,1)n 上的Schur凸、Schur乘性凸和Schur调和凸函数. 作为应用,利用控制理论建立了若干不等式. 相似文献
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研究具有高阶非线性项的广义KdV方程 ut + a (1 + bun)un ux + uxxx = 0, 这里n ≥1, a, b是实数且a ≠ 0. 用动力系统的定性理论和分支方法, 讨论了该方程的孤立波解的解析表达式和孤立波的分支, 并给出了孤立波的分支图, 解决了孤立波的存在性及其个数等问题. 相似文献
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When sample size is a sequence of r.v., the parametric estimates in linear models are interesting both theoretically and practically. For linear models Yi=xiβ+ei,i=1,2,…where {ei} are p-dimensional i .i .d.r.v′.s with Ee1=0. Var e1=σ2,0<σ2<∞. we consider estimate σ2(vn) of error variance σ2 and least squares estimate β(vn) of regression coefficient β, here {vn} is a sequence of r.v. with positve integers larger than P. In this paper some properties of estimates are discussed . Those are unbiasedness, consistency and normality . For σ2(vn), we also obtain some orders for convergence to normal distribution. 相似文献
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对二阶非线性椭圆型方程∑ i,j=1n Di[Aij(x)Djy]+∑i=1n bi(x)Diy+q(x)f(y)=e(x)建立了若干新的振动准则, 所得结果仅依赖于方程在外区域Ω С Rn的一个子区域序列的信息而有别于已知的大多数结论. 相似文献
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Liang Hanying Zhang Dongxia Lu Baoxian Dept.of Appl.Math. Tongji Univ. Shanghai China. 《高校应用数学学报(英文版)》2004,19(3):302-310
§1 IntroductionConsider the following heteroscedastic regression model:Yi =g(xi) +σiei, 1≤i≤n,(1.1)whereσ2i=f(ui) ,(xi,ui) are nonrandom design points,0≤x0 ≤x1 ≤...≤xn=1and0≤u0≤u1 ≤...≤un=1,Yi are the response variables,ei are random errors,and f(·) andg(·) are unknown functions defined on closed interval[0 ,1] .It is well known thatregression model has many applications in practical problems,sothe model (1.1) and its special cases have been studied extensively. For instance,… 相似文献
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The problem of determining the pair w:={F(x, t);f(t)} of sourceterms in the hyperbolic equation utt = (k(x)ux)x + F(x, t) andin the Neumann boundary condition k(0)ux(0, t) = f(t) from themeasured data µ(x):=u(x, T) and/or (x):=ut(x, t) at thefinal time t = T is formulated. It is proved that both componentsof the Fréchet gradient of the cost functionals J1(w)= ||u(x, t;w) – µ(x)||02 and J2(w) = ||ut(x, T;w)– (x)||02 can be found via the solutions of correspondingadjoint hyperbolic problems. Lipschitz continuity of the gradientis derived. Unicity of the solution and ill-conditionednessof the inverse problem are analysed. The obtained results permitone to construct a monotone iteration process, as well as toprove the existence of a quasi-solution. 相似文献
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Consider the following infinite dimensional stochastic evolutionequation over some Hilbert space H with norm |·|:
It is proved that under certain mild assumptions, the strongsolution Xt(x0)VHV*, t 0, is mean square exponentially stableif and only if there exists a Lyapunov functional (·,·):HxR+R1 which satisfies the following conditions: (i)c1|x|2k1eµ1t(x,t)c2|x|2+k2+k2eµ2t; (ii) L(x,t)c3(x,t)+k3eµ3t, xV, t0; where L is the infinitesimal generator of the Markov processXt and ci, ki, µi, i = 1, 2, 3, are positive constants.As a by-product, the characterization of exponential ultimateboundedness of the strong solution is established as the nulldecay rates (that is, µi = 0) are considered. 相似文献
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In this paper we present adaptive procedures for the numericalstudy of positive solutions of the following problem: ut = uxx (x, t) (0, 1) x [0, T), ux(0, t) = 0 t [0, T), ux(1, t) = up(1, t) t [0, T), u(x, 0) = u0(x) x (0, 1), with p > 1. We describe two methods. The first one refinesthe mesh in the region where the solution becomes bigger ina precise way that allows us to recover the blow-up rate andthe blow-up set of the continuous problem. The second one combinesthe ideas used in the first one with moving mesh methods andmoves the last points when necessary. This scheme also recoversthe blow-up rate and set. Finally, we present numerical experimentsto illustrate the behaviour of both methods. 相似文献
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Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition 总被引:2,自引:0,他引:2
de Pablo Arturo; Quiros Fernando; Rossi Julio D. 《IMA Journal of Applied Mathematics》2002,67(1):69-98
We study non-negative solutions of the porous medium equationwith a source and a nonlinear flux boundary condition, ut =(um)xx + up in (0, ), x (0, T); (um)x (0, t) = uq (0,t) for t (0, T); u (x, 0) = u0 (x) in (0, ), where m > 1,p, q > 0 are parameters. For every fixed m we prove thatthere are two critical curves in the (p, q-plane: (i) the criticalexistence curve, separating the region where every solutionis global from the region where there exist blowing-up solutions,and (ii) the Fujita curve, separating a region of parametersin which all solutions blow up from a region where both globalin time solutions and blowing-up solutions exist. In the caseof blow up we find the blow-up rates, the blow-up sets and theblow-up profiles, showing that there is a phenomenon of asymptoticsimplification. If 2q < p + m the asymptotics are governedby the source term. On the other hand, if 2q > p + m theevolution close to blow up is ruled by the boundary flux. If2q = p + m both terms are of the same order. 相似文献
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In order to present the results of this note, we begin withsome definitions. Consider a differential system [formula] where IR is an open interval, and f(t, x), (t, x)IxRn, is acontinuous vector function with continuous first derivativesfr/xs, r, s=1, 2, ..., n. Let Dxf(t, x), (t, x)IxRn, denote the Jacobi matrix of f(t,x), with respect to the variables x1, ..., xn. Let x(t, t0,x0), tI(t0, x0) denote the maximal solution of the system (1)through the point (t0, x0)IxRn. For two vectors x, yRn, we use the notations x>y and x>>yaccording to the following definitions: [formula] An nxn matrix A=(ars) is called reducible if n2 and there existsa partition [formula] (p1, q1, p+q=n) such that [formula] The matrix A is called irreducible if n=1, or if n2 and A isnot reducible. The system (1) is called strongly monotone if for any t0I, x1,x2Rn [formula] holds for all t>t0 as long as both solutions x(t, t0, xi),i=1, 2, are defined. The system is called cooperative if forall (t, x)IxRn the off-diagonal elements of the nxn matrix Dxf(t,x) are nonnegative. 1991 Mathematics Subject Classification34A30, 34C99. 相似文献
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A new methodology for the stability analysis of pairwise triangularizable and related switching systems 总被引:2,自引:0,他引:2
We consider the asymptotic stability of the time-varying dynamicsystem : = A(t)x, A(t) Rn x n, A(t) A= {A1, ..., Am}, where Ai is Hurwitz and where a set of non-singularmatrices Ti j exist such that any pair of matrices {Ti j AiTi j1, Ti j Aj Ti j1}, i, j {1, ..., m}, areupper triangular. Switching systems of this form are referredto as pairwise triangularizable switching systems. It can beestablished that (a) pairwise triangularizability is not sufficientto guarantee the existence of a common quadratic Lyapunov functionfor the linear time-invariant dynamic systems Ai : = Ai x; (b) additional conditions can be specified which guaranteeasymptotic stability of the switching system . In this paperwe also show that pairwise triangularizability is not even sufficientto guarantee asymptotic stability of the switching system .We also show that the method of proof of stability in (b), whichdoes not assume the existence of a common quadratic Lyapunovfunction, can be used to prove the asymptotic stability of moregeneral switching systems (systems that are not pairwise triangularizable).Finally, we show that our results can be used as the basis forthe design of practical control systems; namely, for the designof an automobile speed switched controller with guaranteed stabilityproperties. 相似文献