On functions uniquely determined by their asymptotic expansion

We present a maximal class of analytic functions. The elements of this class are uniquely determined by their asymptotic expansions. We also discuss the possibility of recovery of a function from the coefficients of its asymptotic series. In particular, we consider the problem of recovering by using Borel summation. The last published result in this direction was obtained by Alan Sokal in 1980, but his paper well known to physicists (in quantum field theory) seems to have remained unnoticed by mathematicians.     

On a certain boundary value problem arising in shrinking sheet flows

This paper presents an analysis of the boundary value problem resulting from the magnetohydrodynamic (MHD) viscous flow influenced by a shrinking sheet with suction for the cases of two-dimensional (m = 1) and axisymmetric (m = 2) shrinking. The influences of the parameter m as well as the effects of suction parameter s and Hartmann number M² on similar entrainment velocity f(∞) and flow characteristics are studied. To this purpose, the resulting nonlinear ordinary differential equation is solved numerically using the 4th order Runge-Kutta method in combination with a shooting procedure. The obtained results elucidate reliability and efficiency of the technique from which interesting features between the skin friction coefficient f″(0) and the entrainment velocity f(∞) as function of the mass transfer parameter s can also be obtained.     

On the asymptotic expansion of the solution of the plane Stokes problem in a perforated domain

This article deals with the asymptotic behavior as ε → 0 of the solution {u _ɛ, p _ɛ} of the plane Stokes problem in a perforated domain. The limit problem is constructed and estimates for the speed of convergence are obtained. It is shown that the speed of convergence is of order O(ε ^3/2). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 3–20, 2005.     

A stochastic integral arising in discounting continuous cash flows and certain transformed characteristic functions

Transformed characteristic functions are universally recognized as the most powerful tools for investigating distribution functions of complicated stochastic models. The paper is mainly devoted to the establishment of properties and applications of a particular convolution model. More precisely, the paper derives the characteristic function of a convolution model based on a stochastic integral and provides applications of this model in discounting continuous cash flows.     

The asymptotic expansion of certain canonical integrals

Integrals of the form $\text{I(λ) = ∝}{}_{\mathrm{R}}{}^2\text{?(}\text{x}\text{?}\text{)}\text{exp}\text{{iλφ(}\text{x}\text{?}\text{)} d}\text{x}\text{?}$, common in diffraction theory, are usually evaluated asymptotically for large λ using the stationary phase technique. At caustic points the classical technique is not applicable. A computation-oriented algorithm is developed for determining the asymptotic expansion of such integrals with $\text{φ(}\text{x}\text{)}$ a Thom umbilic, the canonical form appropriate at caustic points for most cases of physical interest.     

On the asymptotic joint distributions of certain functions of the eigenvalues of four random matrices

In this paper, the authors obtained asymptotic expressions for the joint distributions of certain functions of the eigenvalues of the Wishart matrix, correlation matrix, MANOVA matrix and canonical correlation matrix when the population roots have multiplicity.     

On a certain class of curves arising in a free boundary problem for stokes flows

The research was supported by the Russian Foundation for Fundamental Research (Grant 93-013-17621).     

On the asymptotic expansion of Bergman kernel

We study the asymptotics of the Bergman kernel and the heat kernel of the ${\mathrm{spin}}^c$ Dirac operator on high tensor powers of a line bundle. To cite this article: X. Dai et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Some new asymptotic expansions of certain partial theta functions

In (Proc. Am. Math. Soc. 139(11):3779–3788, 2011), B.C. Berndt and B. Kim established asymptotic expansions for a class of partial theta functions, generalizing a result by S. Ramanujan. In this paper, we also prove some asymptotic expansions of such functions which are different from the results in (Berndt and Kim in Proc. Am. Math. Soc. 139(11):3779–3788, 2011).     

A complete asymptotic expansion for a sequence of certain sums

In the present note we derive a complete asymptotic expansion for a sequence of certain sums. A special case of our results solves a problem recently proposed in the Research Group in Mathematical Inequalities and Applications (RGMIA) mailing list. Moreover, the result is connected with a certain combinatorial problem.     

The asymptotic behaviour of certain entire functions of order zero

Summary A certain class of entire functionsF(s) of order zero which are asymptotically equal to the sum of just two neighbouring terms of their power series when |s| with |args| < – for any fixed > 0, is investigated. Which two terms one has to take, depends upons. It is shown that these functions have infinitely many negative zeros, and the asymptotic behaviour of the zeros is also determined.     

A complete asymptotic expansion of the jacobi functions with error bounds

In this paper we give a complete asymptotic expansion of the Jacobi functions ^{(, )} (t) as + . The method we employed to get the complete expansion follows that of Olver in treating similar problems. By using a Gronwall-Bellman type inequality for an improper integral in which the integrand is an unbounded function and contains a parameter, we get an error bound of the asymptotic approximation which is different from that of Olver's.     

On the asymptotic behavior of certain infinite-dimensional recurrence sequences

Under certain conditions imposed on an operatorB, we obtain criteria of boundedness of sequencesx _n+1=Ax _n +Bb _n , n>0, for anyx ₀ and bounded {b _n ,n 0} in infinite-dimensional spaces. The results are given in terms of spectral properties of the operatorA.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 133–137, January, 1995.     

On certain nonlinear problems arising in the theory of lubrication

Various nonlinear elliptic boundary value problems motivated by the theory of lubrication are stated and studied. We deal mainly with the aspects of existence and uniqueness of solutions.     

On asymptotic values of meromorphic functions

The following theorem ofLindelöf is known: Iff (z) is meromorphic in |z|<1, and iff (z) admits two distinct asymptotic values at some pointP of |z|=1, thenf (z) assumes infinitely often in any neigh borhood ofP all values of the extended complex plane with at most two possible exceptions.The purpose of this note is to extend Lindelöf's theorem to Riemannian surfaces. Our extension of Lindelöf's theorem includes the fact that the conclusion of Lindelöf's theorem holds, iff (z) is meromorphic in |z|<, and iff (z) admits two distinct asymptotic values atz=.