Algorithms for Evaluation of the Wright Function for the Real Arguments��� Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

On q-Laplace Transforms of the q-Bessel Functions

Mathematics Subject Classification: 33D15, 44A10, 44A20

Fractional Integration and Fractional Differentiation of the M-Series

Mathematics Subject Classification: 26A33, 33C60, 44A15

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If �� < �� and �� is a countable ordinal, then the Banach space B�� (X) of all bounded real-valued functions of Baire class �� on X is a proper subspace of the Banach space B�� (X). In this paper it is shown that: 1. B�� (X) has a representation as C(b�� X), where b�� X is a compactification of the space P X ��� the underlying set of X in the Baire topology generated by the G�� -sets in X. 2. If 1 ��� �� < �� ��� ��, where �� is the first uncountable ordinal number, then B�� (X) is uncomplemented as a closed subspace of B�� (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space ��� by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade���s and Dashiell���s methods.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

On the Mellin Transforms of Dirac���S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Mathematics Subject Classification: 44A05, 46F12, 28A78

Generalization of the Modified Bessel Function and Its Generating Function

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

AMS Subj. Classi���cation: MSC2010: 11F72, 11M36, 58J37

The Operators A�� = ��A + -��A for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.