On a Two-Dimensional Search Problem

In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist infinitely many loose squares.

A Two Layered Model for Evolving Web Resources

In this paper the key features of a two-layered model for describing the semantic of dynamical web resources are introduced. In the current Semantic Web proposal [Berners-Lee et al., 2001] web resources are classified into static ontologies which describes the semantic network of their inter-relationships [Kalianpur, 2001][Handschuh & Staab, 2002] and complex constraints described by logical quantified formula [Boley et al., 2001][McGuinnes & van Harmelen, 2004][McGuinnes et al., 2004], the basic idea is that software agents can use techniques of automatic reasoning in order to relate resources and to support sophisticated web application. On the other hand, web resources are also characterized by their dynamical aspects, which are not adequately addressed by current web models. Resources on the web are dynamical since, in the minimal case, they can appear or disappear from the web and their content is upgraded. In addition, resources can traverse different states, which characterized the resource life-cycle, each resource state corresponding to different possible uses of the resource. Finally most resources are timed, i.e. they information they provide make sense only if contextualised with respect to time, and their validity and accuracy is greatly bounded by time. Temporal projection and deduction based on dynamical and time constraints of the resources can be made and exploited by software agents [Hendler, 2001] in order to make previsions about the availability and the state of a resource, for deciding when consulting the resource itself or in order to deliberately induce a resource state change for reaching some agent goal, such as in the automated planning framework [Fikes & Nilsson, 1971][Bacchus & Kabanza,1998].

Information Modelling of Two-Dimensional Optical Parameters Measurement

A method for measurement and visualization of the complex transmission coefficient of 2-D micro- objects is proposed. The method is based on calculation of the transmission coefficient from the diffraction pattern and the illumination aperture function for monochromatic light. A phase-stepping method was used for diffracted light phase determination.

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

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.