Explicit solutions of two-point boundary value operator problems

This work has been partially supported by a grant from the Conselleria de Cultura, Educació i Ciència de la Generalitat de Valencia     

Evaluation of a rational function

Evaluation of a given rational function can be carried out in various ways, such as by Horner's method, directly through a continued fraction representation, or by a subsequent process that uses three-term recurrences. Four such algorithms are summarized, and their relative performances when they are implemented using a parallel architecture (a four-node transputer system) is investigated.     

Numerical solutions of random mean square Fisher-KPP models with advection

This paper deals with the construction of numerical stable solutions of random mean square Fisher-Kolmogorov-Petrosky-Piskunov (Fisher-KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.     

On the Fourier-Laplace transform of functionals on a space of infinitely differentiable functions on a convex compact

Classes of ultradifferentiable functions are classically defined by imposing growth conditions on the derivatives of the functions. Following this approach we consider a Fréchet-Schwartz space of infinitely differentiable functions on a closure of a bounded convex domain of multidimensional real space with uniform bounds on their partial derivatives. Our aim is to obtain Paley-Wiener-Schwartz type theorem connecting properties of linear continuous functionals on this space with the behaviour of their Fourier-Laplace transforms. Very similar problems were considered by M. Neymark, B.A. Taylor, M. Langenbruch, A.V. Abanin.     

Wideband omnidirectional infrared absorber with a patchwork of plasmonic nanoantennas

In this Letter, we demonstrate experimentally that a patchwork of four metal-insulator-metal patches leads to an unpolarized wideband omnidirectional infrared absorption. Our structure absorbs 70% of the incident light on a 2.5 μm bandwidth at 8.5 μm. It paves the way to the design of wideband efficient plasmonic absorbers in the infrared spectrum.     

Laguerre matrix polynomial series expansion: Theory and computer applications

This paper deals with the expansion of matrix functions in series of Laguerre matrix polynomials of a complex matrix parameter. A new asymptotic expression for positive and large x and n is obtained for this family of matrix polynomials that improves previous existing expressions. This expression is applied to improving the conditions imposed on the matrix function that are to be expanded in a series of non-hermitian Laguerre matrix polynomials, providing a new series expansion theorem that is more general than previous works. An application to solving linear differential systems without matrix exponentials is included.     

Orthogonal matrix polynomials with respect to linear matrix moment functionals: Theory and applications

In this paper orthogonal matrix polynomials with respect to a right matrix moment functional are introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.     

Closed form general solution of nonhomogeneous implicit higher order difference systems

In this paper, a closed form general solution of nonhomogeneous implicit higher order difference systems is given. A condition for the stability of solutions in terms of the data is proposed.     

The semi-analytical method for time-dependent wave problems with uncertainties

This paper provides a constructive procedure for the computation of approximate solutions of random time-dependent hyperbolic mean square partial differential problems. Based on the theoretical representation of the solution as an infinite random improper integral, obtained via the random Fourier transform method, a double approximation process is implemented. Firstly, a random Gauss-Hermite quadrature is applied, and then, the evaluations at the nodes of the integrand are approximated by using a random Störmer numerical method. Numerical results are illustrated with examples.     

Analytic stochastic process solutions of second-order random differential equations

In this work, trigonometric stochastic processes arise as mean square solutions of random differential equations, using a random Fröbenius method. Important operational properties of the trigonometric stochastic processes are established.