Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Production-frame Model of Representation of Data Domain

One of the most important problems of e-learning system is studied in given paper. This problem is building of data domain model. Data domain model is based on usage of correct organizing knowledge base. In this paper production-frame model is offered, which allows structuring data domain and building flexible and understandable inference system, residing in production system.

A Domain-Independent Otology-based Approach to Representation of Courseware Knowledge

This paper proposes an ontology-based approach to representation of courseware knowledge in different domains. The focus is on a three-level semantic graph, modeling respectively the course as a whole, its structure, and domain contents itself. The authors plan to use this representation for flexibie e- learning and generation of different study plans for the learners.

Representation of Neural Networks by Dynamical Systems

Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

Ontology-Based Model of Representation of Knowledge about Language Mappings

The paper presents a short review of some systems for program transformations performed on the basis of the internal intermediate representations of these programs. Many systems try to support several languages of representation of the source texts of programs and solve the task of their translation into the internal representation. This task is still a challenge as it is effort-consuming. To reduce the effort, different systems of translator construction, ready compilers with ready grammars of outside designers are used. Though this approach saves the effort, it has its drawbacks and constraints. The paper presents the general idea of using the mapping approach to solve the task within the framework of program transformations and overcome the disadvantages of the existing systems. The paper demonstrates a fragment of the ontology model of high-level languages mappings onto the single representation and gives the example of how the description of (a fragment) a particular mapping is represented in accordance with the ontology model.

Method for Analytical Representation of the Maximum Inaccuracies of Indirectly Measurable Variable

Let us have an indirectly measurable variable which is a function of directly measurable variables. In this survey we present the introduced by us method for analytical representation of its maximum absolute and relative inaccuracy as functions, respectively, of the maximum absolute and of the relative inaccuracies of the directly measurable variables. Our new approach consists of assuming for fixed variables the statistical mean values of the absolute values of the coefficients of influence, respectively, of the absolute and relative inaccuracies of the directly measurable variables in order to determine the analytical form of the maximum absolute and relative inaccuracies of an indirectly measurable variable. Moreover, we give a method for determining the numerical values of the maximum absolute and relative inaccuracies. We define a sample plane of the ideal perfectly accurate experiment and using it we give a universal numerical characteristic – a dimensionless scale for determining the quality (accuracy) of the experiment.

AstroWeb – A Graphical Representation of an Astronomical WFPDB Database Using a Web-Based Open Source Geographical Information System

ACM Computing Classification System (1998): H.5.2, H.2.8, J.2, H.5.3.

A Representation of Binary Matrices

Христина Костадинова, Красимир Йорджев - В статията се обсъжда представянето на произволна бинарна матрица с помощта на последователност от цели неотрицателни числа. Разгледани са някои предимства и недостатъци на това представяне като алтернатива на стандартното, общоприето представяне чрез двумерен масив. Показано е, че представянето на бинарните матрици с помощта на наредени n-торки от естествени числа води до по-бързи алгоритми и до съществена икономия на оперативна памет. Използуван е апарата на обектно-ориентираното програмиране със синтаксиса и семантиката на езика C++.

Digital Representation of Knitting Patterns in Traditional Costumes

The paper presents the application of a CAD system for digital representation of traditional knitting. The CAD system is oriented to hand knitting. As a software application the system is developed by using C# programming language and .NET platform. The paper focuses on the applied side of the software and its usage as a means of representing and storing ethnographic exhibits.

Branching Particle Representation of a Class of Semilinear Equations

2000 Mathematics Subject Classification: 60J80, 60J85

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12