On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

Some Inequalities of the Uniform Ergodicity and Strong Stability of Homogeneous Markov Chains

2000 Mathematics Subject Classification: 60J45, 60K25

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.

Hardware-based and Software-based Security in Digital Rights Management Solutions

The main requirements to DRM platforms implementing effective user experience and strong security measures to prevent unauthorized use of content are discussed. Comparison of hardware-based and software- based platforms is made showing the general inherent advantages of hardware DRM solutions. Analysis and evaluation of the main flaws of hardware platforms are conducted, pointing out the possibilities to overcome them. The overview of the existing concepts for practical realization of hardware DRM protection reveals their advantages and disadvantages and the increasing demand for creation of multi-core architecture, which could assure an effective DRM protection without decreasing the user’s freedom and importing risks for end system security.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.

e-Learning, e-Practising and e-Tutoring: an Integrated Approach

In this paper is described a didactic methodology combining current e-learning methods and the support of Intelligent Agents technologies. The aim is to favor the synthesis among theoretical approach and based practical approach using the so-called Intelligent Agent, software that exploits the Artificial Intelligence and that operates as tutor, facilitating the consumers in the training operations. The paper illustrates how such new Intelligent Agent algorithm (IA) is used in the training of employees working in the transportation sector, thanks to the experience gained with the PARMENIDE project - Promoting Advanced Resources and Methodologies for New Teaching and Learning Solutions in Digital Education.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.