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991.
992.
The subject of this article is solving free vibration problems of isotropic and orthotropic rectangular plates with linearly varying thickness along one direction. For the numerical solution to evaluate the frequencies of plates, the method of discrete singular convolution (DSC) is adopted. Frequency parameters are obtained for different types of boundary conditions, taper and aspect ratios. The effect of the mode number is also analyzed. The results obtained by the present numerical method show an excellent agreement with available published results. 相似文献
993.
In this paper, we extend the auxiliary principle (Cohen in J. Optim. Theory Appl. 49:325–333, 1988) to study a class of Lions-Stampacchia variational inequalities in Hilbert spaces. Our method consists in approximating,
in the subproblems, the nonsmooth convex function by a sequence of piecewise linear and convex functions, as in the bundle
method for nonsmooth optimization. This makes the subproblems more tractable. We show the existence of a solution for this
Lions-Stampacchia variational inequality and explain how to build a new iterative scheme and a new stopping criterion. This
iterative scheme and criterion are different from those commonly used in the special case of nonsmooth optimization. We study
also the convergence of iterative sequences generated by the algorithm.
This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for
the Doctoral Program of Higher Education (20060610005), the National Natural Science Foundation of Sichuan Education Department
of China (07ZB068) and the Open Fund (PLN0703) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest
Petroleum University). 相似文献
994.
In the present paper we introduce a new definition for the Fourier space A (K) of a locally compact Hausdorff hypergroup K and prove that it is a Banach subspace of B (K). This definition coincides with that of Amini and Medghalchi in the case where K is a tensor hypergroup, and also with that of Vrem which is given only for compact hypergroups. We prove that Ap (K)* = PMq (K), where q is the exponent conjugate to p, in particular A (K)* = VN (K). Also we show that for Pontryagin hypergroups, A (K) = L2(K) * L2(K) = F (L1( )), where F stands for the Fourier transform on . Furthermore there is an equivalent norm on A (K) which makes A (K) into a Banach algebra isomorphic with L1( ). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
995.
In this paper, we consider a system of general variational inclusions in q-uniformly smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for the system of general variational inclusions. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature. 相似文献
996.
Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Πm leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Πm for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Πm+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered. 相似文献
997.
In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution,
focusing our attention on the symmetric weakly stable distribution. As in the case of the classical convolution, characterization
of distributions stable in the sense of weak generalized convolution depends on solving some functional equations in the class
of characteristic functions.
This paper was partially written while the second author was a visiting professor of Delft Institute of Applied Mathematics,
Delft University of Technology, Holland. 相似文献
998.
G. I. Shishkin 《Computational Mathematics and Mathematical Physics》2009,49(8):1348-1368
The Dirichlet problem for a singularly perturbed parabolic reaction-diffusion equation with a piecewise continuous initial condition in a rectangular domain is considered. The higher order derivative in the equation is multiplied by a parameter ?2, where ? ∈ (0, 1]. When ? is small, a boundary and an interior layer (with the characteristic width ?) appear, respectively, in a neighborhood of the lateral part of the boundary and in a neighborhood of the characteristic of the reduced equation passing through the discontinuity point of the initial function; for fixed ?, these layers have limited smoothness. Using the method of additive splitting of singularities (induced by the discontinuities of the initial function and its low-order derivatives) and the condensing grid method (piecewise uniform grids that condense in a neighborhood of the boundary layers), a finite difference scheme is constructed that converges ?-uniformly at a rate of O(N ?2ln2 N + n 0 ?1 ), where N + 1 and N 0 + 1 are the numbers of the mesh points in x and t, respectively. Based on the Richardson technique, a scheme that converges ?-uniformly at a rate of O(N ?3 + N 0 ?2 ) is constructed. It is proved that the Richardson technique cannot construct a scheme that converges in ?-uniformly in x with an order greater than three. 相似文献
999.
考虑一阶脉冲泛函微分方程非线性边值问题,利用上下解方法和单调迭代技术得到了耦合解和唯一解存在的充分条件.所得结果改进和推广了文献的相关结果. 相似文献
1000.
OSCILLATION THEOREMS FOR A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS OF EMDEN-FOWLER TYPE
Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature. 相似文献