On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials

Mathematics Subject Classification: Primary 42B20, 42B25, 42B35

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Importance and Benefits of OPEN SCIENCE for Ubiquitous Sharing, Dissemination and Impact

While openness is well applied to software development and exploitation (open sources), and successfully applied to new business models (open innovation), fundamental and applied research seems to lag behind. Even after decades of advocacy, in 2011 only 50% of the public-funded research was freely available and accessible (Archambault et al., 2013). The current research workflows, stemming from a pre-internet age, result in loss of opportunity not only for the researchers themselves (cf. extensive literature on topic at Open Access citation project, http://opcit.eprints.org/), but also slows down innovation and application of research results (Houghton & Swan, 2011). Recent studies continue to suggest that lack of awareness among researchers, rather than lack of e-infrastructure and methodology, is a key reason for this loss of opportunity (Graziotin 2014). The session will focus on why Open Science is ideally suited to achieving tenure-relevant researcher impact in a “Publish or Perish” reality. Open Science encapsulates tools and approaches for each step along the research cycle: from Open Notebook Science to Open Data, Open Access, all setting up researchers for capitalising on social media in order to promote and discuss, and establish unexpected collaborations. Incorporating these new approaches into a updated personal research workflow is of strategic beneficial for young researchers, and will prepare them for expected long term funder trends towards greater openness and demand for greater return on investment (ROI) for public funds.

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.

Direct and Converse Theorems for Generalized Bernstein-Type Operators

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

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.

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

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

MSC 2010: 03E72, 26E50, 28E10

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.