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91.
Hassan Khosravian‐Arab Mehdi Dehghan M. R. Eslahchi 《Mathematical Methods in the Applied Sciences》2017,40(18):6389-6410
This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders. 相似文献
92.
M. Ferreira M. M. Rodrigues N. Vieira 《Mathematical Methods in the Applied Sciences》2017,40(18):7033-7050
In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems. 相似文献
93.
94.
Hongmei Liu Wenshu Zhou Shuyan Ding 《Journal of Difference Equations and Applications》2017,23(7):1204-1218
By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers. 相似文献
95.
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples. 相似文献
96.
Paolo Boggiatto Carmen Fernández Antonio Galbis 《Applied and Computational Harmonic Analysis》2017,42(1):65-87
Inspired by results of Kim and Ron, given a Gabor frame in , we determine a non-countable generalized frame for the non-separable space of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences. 相似文献
97.
Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) . This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space . The quality of the spectral approximation and the choice of the parameter c when approximating a function in by its truncated PSWFs series expansion, are the main issues. By considering a function as the restriction to of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples. 相似文献
98.
99.
100.
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first characterize some functions having linear translators, based on which several families of permutations are then derived. Extending the results of [9], we give in several cases the compositional inverse of these permutations. The connection with complete permutations is also utilized to provide further infinite classes of permutations. Moreover, we propose new tools to study permutations of the form and a few infinite classes of permutations of this form are proposed. 相似文献