Nonlinear Bihari Type Integral Inequalities with Maxima

Some new nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable are solved. The considered inequalities are generalizations of the classical nonlinear integral inequality of Bihari. The importance of these integral inequalities is defined by their wide applications in qualitative investigations of differential equations with "maxima" and it is illustrated by some direct applications.

Noninear Integral Inequalities Involving Maxima

Снежана Христова, Кремена Стефанова, Лозанка Тренкова - В статията се изучават някои интегрални неравенства, които съдържат макси-мума на неизвестната функция на една променлива. Разглежданите неравенства са обобщения на класическото неравенство на Бихари. Значимостта на тези интегрални неравенства се дълже на широкото им приложение при качественото изследванене на различни свойства на решенията на диференциални уравнения с “максимум” и е илюстрирано с някои директни приложения.

Integral Inequalities and Applications to Partial Differential Equations with “Maxima”

Кремена В. Стефанова - В тази статия са разрешени някои нелинейни интегрални неравенства, които включват максимума на неизвестната функция на две променливи. Разгледаните неравенства представляват обобщения на класическото неравенство на Гронуол-Белман. Значението на тези интегрални неравенства се определя от широките им приложения в качествените изследвания на частните диференциални уравнения с “максимуми” и е илюстрирано чрез някои директни приложения.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Programa Mais Educação : um instrumento para uma política educativa integral no Brasil

Tese de mestrado, Ciências da Educação (Área de especialidade em Administração Educacional), Universidade de Lisboa, Instituto de Educação, 2015

Landau and Kolmogoroff type polynomial inequalities

Let 0integral(-infinity)(infinity) f(2)(x) exp(-x(2)) dx. For various positive values of A and B we establish Kolmogoroff type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

On Integral Means for Fractional Calculus Operators of Multivalent Functions

2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80

An Application of Convolution Integral

MSC 2010: 30C45

Increasing socio-economic inequalities in drug-induced deaths in Australia : 1981-2002

Introduction and Aims: Since the 1990s illicit drug use death rates in Australia have increased markedly. There is a notable gap in knowledge about changing socio-economic inequalities in drug use death rates. Some limited Australian and overseas data point to higher rates of drug death in the lowest socio-economic groups, but the paucity of available studies and their sometimes conflicting findings need to be addressed. Design and Methods: This paper uses data obtained from the Australian Bureau of Statistics (ABS) to examine changes in age-standardised drug-induced mortality rates for Australian males over the period 1981 – 2002. Socio-economic status was categorised as manual or non-manual work status. Results: With the rapid increase in drug-induced mortality rates in the 1990s, there was a parallel increase in socio-economic inequalities in drug-induced deaths. The decline in drug death rates from 2000 onwards was associated with a decline in socio-economic inequalities. By 2002, manual workers had drug death rates well over twice the rate of non-manual workers. Discussion: Three factors are identified which contribute to these socio-economic inequalities in mortality. First, there has been an age shift in deaths evident only for manual workers. Secondly, there has been an increase in availability until 1999 and a relative decline in the cost of the drug, which most often leads to drug death (heroin). Thirdly, there has been a shift to amphetamine use which may lead to significant levels of morbidity, but few deaths. [Najman JM, Toloo G, Williams GM. Increasing socio-economic inequalities in drug-induced deaths in Australia: 1981–2002.

Social inequalities and parent involvement in children’s education in the early years of school

Strengthening cooperation between schools and parents is critical to improving learning outcomes for children. The chapter focuses on parental engagement in their children’s education in the early years of school. It considers issues of social and cultural capital as important to whether, or not, parents are involved in their children’s schooling. Analyses of data from a national representative sample of children and their families who participate in Growing up in Australia: The Longitudinal Study of Australian Children are presented. Results indicated that higher family socio-economic position was associated with higher levels of parental involvement and higher expectations about children’s future level of education.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.