Inverse Problem for Fractional Diffusion Equation

MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements

Asymptotic formulas for generalized elliptic-type integrals

AbstractEpstein-Hubbell [1] elliptic-type integrals occur in radiation field problems. The object of the present paper is to consider a unified form of different elliptic-type integrals, defined and developed recently by several authors. We obtain asymptotic formulas for the generalized elliptic-type integrals

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form

Transmutations for Strings

We investigate the existence and representation of transmutations, also known as transformation operators, for strings. Using measure theory and functional analytic methods we prove their existence and study their representation. We show that in general they are not close to unity since their representation does not involve a Volterra operator but rather the eigenvalue parameter. We also obtain conditions under which the transmutation is either a bounded or a compact operator. Explicit examples show that they cannot be reduced to Volterra type operators.

Curie Temperature of Diluted Magnetic Semiconductors: the Influence of the Antiferromagnetic Exchange Interaction

The coherent potential approximation and mean field approximation are used to calculate the free energy of the coupled carrier – localized spin system in III-V diluted magnetic semiconductors. Thus the magnetic transition temperature Tc can be determined and its dependence on important model parameters. We show that the strong antiferromagnetic superexchange interaction between nearest neighbour sites considerably reduces the Curie temperature

Two Band Model for Diluted Magnetic Semiconductors: Study of the Ferromagnetic Transition Temperature

The ferromagnetic transition temperature (Tc) of a two band model for diluted magnetic semiconductors (DMS) is calculated by using the coherent potential approximation (CPA). It is shown that Tc is strongly parameter dependent on density of the carriers, magnetic coupling constants, and the hopping terms. The maximal Tc of the two band model is found when both impurity bands fully overlap and this value is approximately twice larger than the highest Tc obtained in the single band model

Temperature dependent magnetization of the two band model for diluted magnetic semiconductors

The temperature dependent magnetization of a two band model for diluted magnetic semiconductors as a function of magnetic coupling constant, hopping parameters and carrier densities is calculated by using the coherent potential approximation.  It is shown that the degree of overlapping of the impurity bands  and carrier density are crucial parameters determining the magnetization behavior of the system

H

An H-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining the H-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given