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921.
Recently, the authors introduced some generalizations of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials (see [Q.-M. Luo, H.M. Srivastava, J. Math. Anal. Appl. 308 (2005) 290-302] and [Q.-M. Luo, Taiwanese J. Math. 10 (2006) 917-925]). The main object of this paper is to investigate an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol-Genocchi polynomials of higher order. For these generalized Apostol-Genocchi polynomials, we establish several elementary properties, provide some explicit relationships with the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function. We also deduce their special cases and applications which are shown here to lead to the corresponding results for the Genocchi and Euler polynomials of higher order. By introducing an analogue of the Stirling numbers of the second kind, that is, the so-called λ-Stirling numbers of the second kind, we derive some basic properties and formulas and consider some interesting applications to the family of the Apostol type polynomials. Furthermore, we also correct an error in a previous paper [Q.-M. Luo, H.M. Srivastava, Comput. Math. Appl. 51 (2006) 631-642] and pose two open problems on the subject of our investigation.  相似文献   
922.
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identities for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions.  相似文献   
923.
A new local algorithm for bivariate interpolation of large sets of scattered and track data is presented. The method, which changes partially depending on the kind of data, is based on the partition of the interpolation domain in a suitable number of parallel strips, and, starting from these, on the construction for any data point of a square neighbourhood containing a convenient number of data points. Then, the well-known modified Shepard’s formula for surface interpolation is applied with some effective improvements. The proposed algorithm is very fast, owing to the optimal nearest neighbour searching, and achieves good accuracy. Computational cost and storage requirements are analyzed. Moreover, the efficiency and reliability of the algorithm are shown by several numerical tests, also performed by Renka’s algorithm for a comparison.  相似文献   
924.
In this paper, we first investigate a two-parametric class of smoothing functions which contains the penalized smoothing Fischer-Burmeister function and the penalized smoothing CHKS function as special cases. Then we present a smoothing Newton method for the nonlinear complementarity problem based on the class of smoothing functions. Issues such as line search rule, boundedness of the level set, global and quadratic convergence are studied. In particular, we give a line search rule containing the common used Armijo-type line search rule as a special case. Also without requiring strict complementarity assumption at the P0-NCP solution or the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Preliminary numerical results show the efficiency of the algorithm and provide efficient domains of the two parameters for the complementarity problems.  相似文献   
925.
A normalized univalent function f is called Ma-Minda starlike or convex if zf(z)/f(z)?φ(z) or 1+zf(z)/f(z)?φ(z) where φ is a convex univalent function with φ(0)=1. The class of Ma-Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and close-to-convex functions. Connections with various earlier works are made.  相似文献   
926.
Let B(EF) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UXE) (or HV0(UXE)) and HW(UYF) (or HW0(UYF)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings ? : UY → UX and ψ : UY → B(EF) which generate weighted composition operators between these weighted spaces.  相似文献   
927.
We study the existence of almost periodic (resp., pseudo-almost periodic) mild solutions for fractional differential and integro-differential equations in the case when the forcing term belongs to the class of Stepanov almost (resp., Stepanov-like pseudo-almost) periodic functions.  相似文献   
928.
For each positive integer n?4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n=4 we recover Ingleton's inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also presented.  相似文献   
929.
The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem, and another of integer points. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem.  相似文献   
930.
We derive a number of new results on integrals of products of Airy functions, using various integral transform techniques. As an application, we deduce a compact integral representation, suitable for numerical integration, of the one‐loop photon propagator in a magnetic field in 2 + 1 dimensional scalar quantum electrodynamics. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   
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