The Computational Analysis of Bulgarian Dialect Pronunciation

The paper presents a computational analysis of Bulgarian dialect variation, concentrating on pronunciation differences. It describes the phonetic data set compiled during the project* ‘Measuring Linguistic Unity and Diversity in Europe’ that consists of the pronunciations of 157 words collected at 197 sites from all over Bulgaria. We also present the results of analyzing this data set using various quantitative methods and compare them to the traditional scholarship on Bulgarian dialects. The results have shown that various dialectometrical techniques clearly identify east-west division of the country along the ‘jat’ border, as well as the third group of varieties in the Rodopi area. The rest of the groups specified in the traditional atlases either were not confirmed or were confirmed with a low confidence.

An Observation about Variations of the Diffie-Hellman Assumption

We generalize the Strong Boneh-Boyen (SBB) signature scheme to sign vectors; we call this scheme GSBB. We show that if a particular (but most natural) average case reduction from SBB to GSBB exists, then the Strong Diffie-Hellman (SDH) and the Computational Diffie-Hellman (CDH) have the same worst-case complexity.

Computing with the Square Root of NOT

To the two classical reversible 1-bit logic gates, i.e. the identity gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square root of NOT. This leads to a new kind of calculus, situated between classical reversible computing and quantum computing.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Development and Implementation of NURBS Models of Quadratic Curves and Surfaces

This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using the NURBS models presented here, specialized software modules (plug-ins) have been developed for a 3D graphic system. An analysis of their implementation and the primitives they create has been performed.