Approximations and Mittag-Leffler conditions the applications

A classic result by Bass says that the class of all projective modules is covering if and only if it is closed under direct limits. Enochs extended the if-part by showing that every class of modules C, which is precovering and closed under direct limits, is covering, and asked whether the converse is true. We employ the tools developed in [18] and give a positive answer when C = A, or C is the class of all locally A^≤ω-free modules, where A is any class of modules fitting in a cotorsion pair (A, B) such that B is closed under direct limits. This setting includes all cotorsion pairs and classes of locally free modules arising in (infinite-dimensional) tilting theory. We also consider two particular applications: to pure-semisimple rings, and Artin algebras of infinite representation type.     

Strict Mittag-Leffler conditions and locally split morphisms

In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.     

Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions

In terms of the two-parameter Mittag-Leffler function with specified parameters, this paper introduces the Mittag-Leffler vector random field through its finite-dimensional characteristic functions, which is essentially an elliptically contoured one and reduces to a Gaussian one when the two parameters of the Mittag-Leffler function equal 1. Having second-order moments, a Mittag-Leffler vector random field is characterized by its mean function and its covariance matrix function, just like a Gaussian one. In particular, we construct direct and cross covariances of Mittag-Leffler type for such vector random fields.     

On Mittag-Leffler functions and related distributions

The distribution F () = 1 – E (–), 0 < 1; 0 , where E (x) is the Mittag-Leffler function is studied here with respect to its Laplace transform. Its infinite divisibility and geometric infinite divisibility are proved, along with many other properties. Its relation with stable distribution is established. The Mittag-Leffler process is defined and some of its properties are deduced.     

Strict Mittag-Leffler Conditions and Gorenstein Modules

In this paper, firstly, we characterize some rings by strict Mittag-Leffler conditions. Then, we investigate when Gorenstein projective modules are Gorenstein flat by employing tilting modules and cotorsion pairs. Finally, we study the direct limits of Gorenstein projective modules.     

Certain geometric properties of the Mittag-Leffler functions

In the present investigation, the Mittag-Leffler functions with their normalization are considered. Several sufficient conditions are obtained so that the Mittag-Leffler functions have certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Partial sums of Mittag-Leffler functions are also studied. The results obtained are new and their usefulness is depicted by deducing several interesting corollaries and examples.     

Operational Methods and Truncated Exponential-Based Mittag-Leffler Polynomials

This article deals with the introduction of truncated exponential-based Mittag-Leffler polynomials and derivation of their properties. The operational correspondence between these polynomials and Mittag-Leffler polynomials is established. An integral representation for these polynomials is also derived.     

Integral representation of the four-parametric generalized Mittag-Leffler function

In this paper, we give a new integral representation of the four-parametric generalized Mittag-Leffler function introduced and studied by Djrbashian (Dzherbashian). The representation, obtained in this paper, contains an iterated integral, wherein the internal integral is a Cauchy-type integral, and the external one is a simple improper integral along the so-called Hankel path. The representation also contains the values of the special Wright functions.     

A note on property of the Mittag-Leffler function

Recently the authors have found in some publications that the following property (0.1) of Mittag-Leffler function is taken for granted and used to derive other properties.

(0.1)     

Approximations of solutions to neutral functional differential equations with nonlocal history conditions

This work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a Hilbert space. The approximation of solution to a class of such problems is studied. Moreover, the convergence of Faedo-Galerkin approximation of solution is shown. For illustration, an example is worked out.     

On a generalization of Mittag-Leffler function and its properties

Let s and z be complex variables, Γ(s) the Gamma function, and for any complex ν the generalized Pochhammer symbol. The principal aim of the paper is to investigate the function

     

Integral Equations Involving Generalized Mittag-Leffler Function

Ukrainian Mathematical Journal - We deal with the solution of the integral equation with generalized Mittag-Leffler function $$ {E}_{alpha, beta}^{upgamma, mathrm{q}}(z) $$ specifying the...