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991.
Nguyen Minh Tuan Nguyen Thi Thu Huyen 《Journal of Mathematical Analysis and Applications》2010,369(2):712-718
This paper presents the necessary and sufficient conditions for the solvability of two integral equations of convolution type; the first equation generalizes from integral equations with the Gaussian kernel, and the second one contains the Toeplitz plus Hankel kernels. Furthermore, the paper shows that the normed rings on L1(Rd) are constructed by using the obtained convolutions, and an arbitrary Hermite function and appropriate linear combination of those functions are the weight-function of four generalized convolutions associating F and . The open question about Hermitian weight-function of generalized convolution is posed at the end of the paper. 相似文献
992.
Radu Balan 《Journal of Mathematical Analysis and Applications》2010,370(2):339-349
We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener's Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts. 相似文献
993.
Bernard K. Bonzi 《Journal of Mathematical Analysis and Applications》2010,370(2):392-405
We study the boundary value problem in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN (N?3) and is a p(x)-Laplace type operator with p(.):Ω→[1,+∞) a measurable function and b a continuous and nondecreasing function from R→R. We prove the existence and uniqueness of an entropy solution for L1-data f. 相似文献
994.
Based on He’s Exp-function method, a series of new exact solutions of the generalized Burger-Huxley equation have been obtained. It is shown that the Exp-function method is straightforward and concise, and its applications are promising. 相似文献
995.
The recursive method for computing the generalized LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007) [16] and [17]. The corresponding algorithm for the sequential determination of the generalized LM-inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized LM-inverse and the algorithm for the computation of the weighted Moore-Penrose inverse developed by Wang and Chen (1986) in [23] are equivalent algorithms. Both of the algorithms are implemented in the present paper using the package MATHEMATICA. Several rational test matrices and randomly generated constant matrices are tested and the CPU time is compared and discussed. 相似文献
996.
We study the long-time behavior of the finite difference solution to the generalized Kuramoto-Sivashinsky equation in two space dimensions with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system and the upper semicontinuity d(Ah,τ,A)→0. Finally, we obtain the long-time stability and convergence of the difference scheme. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems. 相似文献
997.
We generalize the classical Lyapunov, Opial and Beesack inequalities for one-dimensional differential equations to nonstandard growth p(t)-Laplacian. 相似文献
998.
The paper is concerned with robust stability for generalized neural networks (GNNs) with both interval time-varying delay and time-varying distributed delay. Through partitioning the time-delay, choosing one augmented Lyapunov-Krasovskii functional, employing free-weighting matrix method and convex combination, the sufficient conditions are obtained to guarantee the robust stability of the concerned systems. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked. Finally, three numerical examples are given to demonstrate the effectiveness and reduced conservatism of the obtained results. 相似文献
999.
In the present paper, a collocation finite element approach based on cubic splines is presented for the numerical solution of a generalized wave equation subject to non-local conservation condition. The efficiency, accuracy and stability of the method are assessed by applying it to a number of test problems. The results are compared with the existing closed-form solutions; the scheme demonstrates that the numerical outcomes are reliable and quite accurate when contrasted with the analytical solutions and an existing numerical method. 相似文献
1000.
Erik Sweet 《Applied mathematics and computation》2010,217(8):4147-4166
A class of trigonometric and hyperbolic type solutions to the generalized Drinfel’d-Sokolov (GDS) equations