A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables

This paper deals with a generalized form of nonlinear retarded Gronwall-Bellman type integral inequality in which the maximum of the unknown function of two variables is involved. This form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. Requiring neither monotonicity nor separability of given functions, we apply a technique of monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results

user's guide to viscosity solutions of second order partial differential equations

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.Comment: 67 page

Обчислювальна математика та програмування (Інженерні розрахунки в середовищі Mathcad)

The teaching and practical guide is devoted to study how to make the engineering calculations using the Mathcad software. The different examples of engineering tasks with the varied complexity are provided with step-by-step explanation with corresponding illustrations. The obtained results are provided. Each subject includes the explained case studies and the tasks for work in class and individually. The teaching and practical guide is aimed for the students studying in chemical engineering, which want to use Mathcad for engineering calculations.Навчально-методичний посібник присвячений вивченню середовища Mathcad та практичному застосуванню цього програмного забезпечення для інженерних розрахунків. Наведено велику кількість прикладів вирішення розрахункових завдань різної складності. До прикладів надаються пояснення. Усі приклади забезпечені результатами виконання. По кожній темі представлені практичні завдання для виконання лабораторних робіт. Призначено для студентів хімічних спеціальностей, які бажають застосовувати середовище Mathcad для інженерних розрахунків