Different from the Taylor polynomials, a new formula for function expansion is proposed where the terms are not polynomials. A new infinite series based on the new formula is also proposed, and the new infinite series can keep some important properties of the original functions. Some forms of remainder are also presented for analysis of convergence. In order to show some internal relationships ...

An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which are uniquely characterized by generalized Lyapunov equations. A numerical method for solving these equations is proposed. It is based on a generalization of ...

In this article, we consider a sequence (Nn)n≥1 of point processes, whose points lie in a subset E of R\{0}, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient conditions for the convergence in distribution of (Nn)n≥1 to an infinitely divisible point process N . As applications, we discuss the exceedance processes and point processes based on r...

We have recently derived infinite-series expressions for performance measures of multiple-input multipleoutput (MIMO) spatial multiplexing with zero-forcing detection (ZF) for Rician–Rayleigh fading, which is relevant in heterogeneous networks. These expressions ensue from a well-known infinite-series expansion around σ = 0 of the confluent hypergeometric function 1F1(·, ·, σ). Theoretically, t...

We consider steady state temperature distribution in a homogeneous rectangular infinite plate the lower part of which is cooled by a fluid flowing at a constant velocity while the upper part satisfies the general mixed boundary conditions. The Wiener-Hopf method has been used to obtain the solution in the infinite series form and some special cases have been discussed.

starting from two-dimensional (2d) equations of motion, discretized formulations for transient behavior of soil-structure interaction problems have been derived. two different dynamic infinite elements taking into account single and two-wave types are presented in transformed space. by coupling the infinite elements with standard finite elements, an ordinary finite element procedure is used for...