共查询到18条相似文献,搜索用时 15 毫秒
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DAXINGDE LUSHJE 《高校应用数学学报(英文版)》1996,11(1):77-84
Abstract. In this paper we show how to construct a scaling function and an orthonormal wavelet basis from a multiresolution approximation using an operator theoretic method. 相似文献
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A maximum principle is proved for the weak solutions of the telegraph equation in space dimension three utt−Δxu+cut+λu=f(t,x), when c>0, λ∈(0,c2/4] and (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semilinear equation utt−Δxu+cut=F(t,x,u). Also, they can be employed in the study of almost periodic solutions of the forced sine-Gordon equation. A counterexample for the maximum principle in dimension four is given. 相似文献
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《复变函数与椭圆型方程》2012,57(2):161-164
We prove a gap theorem and the “Fatou change-of-sign theorem” [Fatou, P., 1906, Sèries trigonométriques e séries de Taylor. Acta Mathematica, 39, 335–400] for expansions in common Schauder basis of holomorphic functions. 相似文献
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Suppose M and N are two r × r and s × s dilation matrices,respectively.Let ΓM and ΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-TZr/Zr and N-TZs/Zs,respe... 相似文献
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Let {X
n
,n ≥ 1} be a sequence of i.i.d. random variables. Let M
n
and m
n
denote the first and the second largest maxima. Assume that there are normalizing sequences a
n
> 0, b
n
and a nondegenerate limit distribution G, such that . Assume also that {d
k
,k ≥ 1} are positive weights obeying some mild conditions. Then for x > y we have
when G(y) > 0 (and to zero when G(y) = 0).
相似文献
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In this short note, we establish an existence and uniqueness theorem about a positive bounded solution for a nonlinear infinite delay integral equation, which arises in some epidemic problems. As one can see, our main result can deal with some cases, to which many previous results cannot be applied. In addition, we show that our main result can also be applied to a Lasota–Wazewska model. 相似文献
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Gaussian radial basis functions (RBFs) have been very useful in computer graphics and for numerical solutions of partial differential equations where these RBFs are defined, on a grid with uniform spacing h, as translates of the “master” function (x;α,h)≡exp(-[α2/h2]x2) where α is a user-choosable constant. Unfortunately, computing the coefficients of (x-jh;α,h) requires solving a linear system with a dense matrix. It would be much more efficient to rearrange the basis functions into the equivalent “Lagrangian” or “cardinal” basis because the interpolation matrix in the new basis is the identity matrix; the cardinal basis Cj(x;α,h) is defined by the set of linear combinations of the Gaussians such that Cj(kh)=1 when k=j and Cj(kh)=0 for all integers . We show that the cardinal functions for the uniform grid are Cj(x;h,α)=C(x/h-j;α) where C(X;α)≈(α2/π)sin(πX)/sinh(α2X). The relative error is only about 4exp(-2π2/α2) as demonstrated by the explicit second order approximation. It has long been known that the error in a series of Gaussian RBFs does not converge to zero for fixed α as h→0, but only to an “error saturation” proportional to exp(-π2/α2). Because the error in our approximation to the master cardinal function C(X;α) is the square of the error saturation, there is no penalty for using our new approximations to obtain matrix-free interpolating RBF approximations to an arbitrary function f(x). The master cardinal function on a uniform grid in d dimensions is just the direct product of the one-dimensional cardinal functions. Thus in two dimensions . We show that the matrix-free interpolation can be extended to non-uniform grids by a smooth change of coordinates. 相似文献
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Yong Zhang Xiao-Yun Yang Zhi-Shan Dong 《Journal of Mathematical Analysis and Applications》2009,355(2):708-41
Let be a strictly stationary positively or negatively associated sequence of positive random variables with EX1=μ>0, and VarX1=σ2<∞. Denote , and γ=σ/μ the coefficient of variation. Under suitable conditions, we show that
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A highly regarded method to obtain an orthonormal basis,Z, for the null space of a matrixA
T is theQR decomposition ofA, whereQ is the product of Householder matrices. In several optimization contextsA(x) varies continuously withx and it is desirable thatZ(x) vary continuously also. In this note we demonstrate that thestandard implementation of theQR decomposition doesnot yield an orthonormal basisZ(x) whose elements vary continuously withx. We suggest three possible remedies.
Work supported in part by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of
the U.S. Department of Energy under Contract W-31-109-Eng-38. 相似文献
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Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree 总被引:3,自引:0,他引:3
In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree. 相似文献
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S. Chandra Sekhara Rao Sunil Kumar 《Journal of Computational and Applied Mathematics》2011,235(11):3342-3354
We consider a system of M(≥2) singularly perturbed equations of reaction-diffusion type coupled through the reaction term. A high order Schwarz domain decomposition method is developed to solve the system numerically. The method splits the original domain into three overlapping subdomains. On two boundary layer subdomains we use a compact fourth order difference scheme on a uniform mesh while on the interior subdomain we use a hybrid scheme on a uniform mesh. We prove that the method is almost fourth order ε-uniformly convergent. Furthermore, we prove that when ε is small, one iteration is sufficient to get almost fourth order ε-uniform convergence. Numerical experiments are performed to support the theoretical results. 相似文献
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An almost sure central limit theorem for self-normalized products of sums of i.i.d. random variables
Let X,X1,X2,… be a sequence of independent and identically distributed positive random variables with EX=μ>0. In this paper we show that the almost sure central limit theorem for self-normalized products of sums holds only under the assumptions that X belongs to the domain of attraction of the normal law. 相似文献
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We give an alternative and much simpler proof of the uniqueness of unconditional basis (up to equivalence and permutation) in the quasi-Banach spaces ℓp(c0) for 0<p<1 and its complemented subspaces with unconditional basis. The new approach uses the fact that the Banach envelope of these spaces is not sufficiently Euclidean with the lattice structure induced by its unconditional basis. 相似文献
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W. Wefelmeyer 《Annals of the Institute of Statistical Mathematics》1994,46(2):309-315
Consider a stationary first-order autoregressive process, with i.i.d. residuals following an unknown mean zero distribution. The customary estimator for the expectation of a bounded function under the residual distribution is the empirical estimator based on the estimated residuals. We show that this estimator is not efficient, and construct a simple efficient estimator. It is adaptive with respect to the autoregression parameter. 相似文献
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V. V. Rimatskiĭ 《Siberian Mathematical Journal》2009,50(4):692-699
We study bases for the admissible inference rules in a broad class of modal logics. We construct an explicit basis for all admissible rules in the logics S4.1, Grz, and their extensions whose number is at least countable. The resulting basis consists of an infinite sequence of rules in a concise and simple form. In the case of a logic of finite width a basis for all admissible rules consists of a finite sequence of rules. 相似文献