Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

Mathematics Subject Classification: 26A33, 93B51, 93C95

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Weak Ergodicity of Mt /Mt /N /N + R Queue

2000 Mathematics Subject Classification: 60J27, 60K25.

Anomalous Singularities for Hyperbolic Equations with Degeneracy of Infinite Order

2002 Mathematics Subject Classification: 35L80

Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

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.

Virtual Reconstruction of the Ancient Russian Fortress Koporye

One of the major strategic tasks in Russia’s northwest of the past centuries was the defense of the country’s territories from enemy incursions coming from the West. In order to solve this task, a robust shield in the form of a system of fortresses was created between the 13th and 15th centuries. The system included such fortresses as Koporye, Yam, Korela, Oreshek, and others. In our age, these monuments have become an essential part of Russia’s historic and cultural heritage and an important element of the tourism cluster “The Silver Ring of Russia.” The Centre of Design and Multimedia at St. Petersburg National Research University of Information Technologies, Mechanics and Optics, jointly with the Department of History and the Faculty of Arts at St. Petersburg State University, working under a three-year grant from the Russian Foundation for Humanities Research (#12-01-12041), is implementing a multimedia information system “Ancient Fortresses of Russia’s Northwest”. Historically accurate virtual reconstruction of several fortresses as they existed during certain historic periods, done in such a way as to allow the future creation of virtual tours of these sites, has become the focus of this project’s research. In the present paper, we describe the main phases and results of virtual reconstruction of the best-preserved fortress, Koporye.