SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions

MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40

On a Class of Generalized Elliptic-type Integrals

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized elliptic-type integrals.

New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10

∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.

Practical, Computation Efficient High-Order Neural Network for Rotation and Shift Invariant Pattern Recognition

In this paper, a modification for the high-order neural network (HONN) is presented. Third order networks are considered for achieving translation, rotation and scale invariant pattern recognition. They require however much storage and computation power for the task. The proposed modified HONN takes into account a priori knowledge of the binary patterns that have to be learned, achieving significant gain in computation time and memory requirements. This modification enables the efficient computation of HONNs for image fields of greater that 100 × 100 pixels without any loss of pattern information.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

The Stein-Weiss Type Inequality for Fractional Integrals, Associated with the Laplace-Bessel Differential Operator

2000 Math. Subject Classification: Primary 42B20, 42B25, 42B35

Investigation of a Stolarsky type Inequality for Integrals in Pseudo-Analysis

MSC 2010: 03E72, 26E50, 28E10

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

The gauge invariant currents of the Maxwellian field

We show that a conserved current for the Maxwellian field, which is invariant under the gauge group of that field, is the sum of two currents Ф+T, where Ф corresponds to a Poincare symmetry of the field, and T is a topological form that is conserved under every dynamics.

A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.

Invariant Functions on Neil Parabola in Cn

2000 Mathematics Subject Classification: Primary 32F45.

Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

2000 Mathematics Subject Classification: 53C42, 53C15.