Recognizing Decomposition of a Partial Boolean Function

A hard combinatorial problem is investigated which has useful application in design of discrete devices: the two-block decomposition of a partial Boolean function. The key task is regarded: finding such a weak partition on the set of arguments, at which the considered function can be decomposed. Solving that task is essentially speeded up by the way of preliminary discovering traces of the sought-for partition. Efficient combinatorial operations are used by that, based on parallel execution of operations above adjacent units in the Boolean space.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

∗ Partially supported by INTAS grant 97-1644

Partial Quasi-Bilateral Generating Function Involving some Special Functions

A group-theoretic method of obtaining more general class of generating functions from a given class of partial quasi-bilateral generating functions involving Hermite, Laguerre and Gegenbaur polynomials are discussed.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Implementation of a Heuristic Method of Decomposition of Partial Boolean Functions

An original heuristic algorithm of sequential two-block decomposition of partial Boolean functions is researched. The key combinatorial task is considered: finding of suitable partition on the set of arguments, i. e. such one, on which the function is separable. The search for suitable partition is essentially accelerated by preliminary detection of its traces. Within the framework of the experimental system the efficiency of the algorithm is evaluated, the boundaries of its practical application are determined.

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

Theoretical Hyperbolic Model of a Partial Agonism: Explicit Formulas for Affinity, Efficacy and Amplification

The quantitative analysis of receptor-mediated effect is based on experimental concentration-response data in which the independent variable, the concentration of a receptor ligand, is linked with a dependent variable, the biological response. The steps between the drug–receptor interaction and the subsequent biological effect are to some extent unknown. The shape of the fitting curve of the experimental data may give some in-sights into the nature of the concentration–receptor–response (C-R-R) mechanism. It can be evaluated by non-linear regression analysis of the experimental data points of the independent and dependent variables, which could be considered as a history of the interaction between the drug and receptors. However, this information is not enough to evaluate such important parameters of the mechanism as the dissociation constant (affinity) and efficacy. There are two ways to provide more detailed information about the C-R-R mechanism: (i) an experimental way for obtaining data with new or

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

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.

Classification of the Maximal Subsemigroups of the Semigroup of all Partial Order-Preserving Transformations

Илинка А. Димитрова, Цветелина Н. Младенова - Моноида P Tn от всички частични преобразования върху едно n-елементно множество относно операцията композиция на преобразования е изучаван в различни аспекти от редица автори. Едно частично преобразование α се нарича запазващо наредбата, ако от x ≤ y следва, че xα ≤ yα за всяко x, y от дефиниционното множество на α. Обект на разглеждане в настоящата работа е моноида P On състоящ се от всички частични запазващи наредбата преобразования. Очевидно P On е под-моноид на P Tn. Направена е пълна класификация на максималните подполугрупи на моноида P On. Доказано е, че съществуват пет различни вида максимални подполугрупи на разглеждания моноид. Броят на всички максимални подполугрупи на POn е точно 2^n + 2n − 2.