Vu Kim Tuan

Simulated annealing for discrete optimization with estimation

We extend the basic convergence results for the Simulated Annealing (SA) algorithm to a stochastic optimization problem where the objective function is stochastic and can be evaluated only through Monte Carlo simulation (hence, disturbed with random error). This extension is important when either the objective function cannot be evaluated exactly or such an evaluation is computationally expensive. We present a modified SA algorithm and show that under suitable conditions on the random error, the modified SA algorithm converges in probability to a global optimizer. Computational results and comparisons with other approaches are given to demonstrate the performance of the proposed modified SA algorithm.

Solution of a fractional differintegral equation

We aim to extend the use of the Riemann-Liouville definition of fractional calculas to solve a differintegral equation of Volterras type of the form , with positive Re(μ) and Re(ν), α∊C. and g(x) being a given function. The solution is expressed in terms of the Mittag-Leffler functions and the approach used in the paper allows us to extend the range of the parameters μ and ν to a wider range than in Al-Saqabi [7].

Asymptotic formulas for generalized elliptic-type integrals

Abstract Epstein-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.

Generalized elliptic-type integrals and asymptotic formulas

A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.

Spectrum of signals

Finite-energy high frequency signals, band-pass frequency signals, and band-stop frequency signals are characterized.

Integral Transforms Related to a Generalized Convolution

AbstractIntegral transformations of the formn from Lp(ℝ+) into Lq(ℝ+); (1 ≤ p ≤ 2, p−1+ q−1 = 1) are studied. Necessary and sufficient conditions on k to ensure that the transformation is unitary on L2(ℝ+) are obtained, and a formula for the inverse transformation is derived in this case.

New type Paley-Wiener theorems for the modified multidimensional Mellin transform

New type Paley-Wiener theorems for the modified multidimensional Mellin and inverse Mellin transforms are established. The supports of functions are described in terms of their modified Mellin (or inverse Mellin) transform without passing to the complexification.

Unified probability density function involving a confluent hypergeometric function of two variables

In this paper first we define a new gamma-type function by means of an integral involving the confluent hypergeometric function of two variables @F1(a,b,c;w,z). The gamma-type function is expressed in explicit form, using generalized hypergeometric series. Associated incomplete functions are defined, some special cases are noted and some relations for the new gamma-type function are given. A generalized probability density is considered, using the gamma-type function. This density represents a unified form for several gamma-type and inverse gaussian densities. A new probability density function with Gauss hypergeometric function is obtained. A number of known probability density functions follow as special cases. Some statistical functions, associated with the new density are obtained. Some figures are drawn for the probability density, to show the effect of the parameters involved. Results given recently by Al-Zamel, Ali et al. and others can be recovered from the formulas established here.

On the supports of functions

Different configurations of supports of functions on R k including bounded, unbounded, convex, and nonconvex domains are described through certain properties of their images under a linear operator T without passing to the complexification.

Asymptotics of singular values of volterra integral operators

The singular values sn(K) of the Volterra integral operator in L2(0,1) are proved to have the asymptotics when and h(x,t) is a smooth enough function with respect to the variable x and square integrate. The asymptotics of the singular values of the fractional integral operator (the case [math004]) is given more precisely by