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.

Bochner-Hecke Theorems for the Weinstein Transform and Application

MSC 2010: 42B10, 44A15

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

Some Distortion Theorems for Starlike Harmonic Functions

MSC 2010: 30C55, 30C45

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces

2000 Mathematics Subject Classification: 47H10, 54E15.

Explicit Solution of Bitsadze-Samarskii Problem

Иван Димовски, Юлиан Цанков - В статията е намерено точно решение на задачата на Бицадзе-Самрски (1) за уравнението на Лаплас, като е използвано операционно смятане основано на некласическа двумернa конволюция. На това точно решение може да се гледа като начин за сумиране на нехармоничния ред по синуси на решението, получен по метода на Фурие.

On a Summability Method Defined by Means of Hermite Polynomials

Георги С. Бойчев - В статията се разглежда метод за сумиране на редове, дефиниран чрез полиномите на Ермит. За този метод на сумиране са дадени някои Тауберови теореми.

Risk Measures for Classical and Perturbed Risk Processes - a Survey

2000 Mathematics Subject Classification: 60B10, 60G17, 60G51, 62P05.

Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.

Functional Transfer Theorems for Maxima of Stationary Processes

2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.

The Limit Theorems for Transportation Networks

2000 Mathematics Subject Classi cation: 60K25 (primary); 60F05, 37A50 (secondary)

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

Target/error overlap in jargonaphasia:the case for a one-source model, lexical and non-lexical summation, and the special status of correct responses

We present three jargonaphasic patients who made phonological errors in naming, repetition and reading. We analyse target/response overlap using statistical models to answer three questions: 1) Is there a single phonological source for errors or two sources, one for target-related errors and a separate source for abstruse errors? 2) Can correct responses be predicted by the same distribution used to predict errors or do they show a completion boost (CB)? 3) Is non-lexical and lexical information summed during reading and repetition? The answers were clear. 1) Abstruse errors did not require a separate distribution created by failure to access word forms. Abstruse and target-related errors were the endpoints of a single overlap distribution. 2) Correct responses required a special factor, e.g., a CB or lexical/phonological feedback, to preserve their integrity. 3) Reading and repetition required separate lexical and non-lexical contributions that were combined at output.