Application of the Multivariate Prediction Method to Time Series

* This work was financially supported by RFBR-04-01-00858.

Multidimensional Heterogeneous Variable Prediction Based on Experts’ Statements

* The work was supported by the RFBR under Grant N07-01-00331a.

About Learning Discrete Mathematics at Bulgarian School

The present work is dedicated to the learning discrete mathematics at Bulgarian school. A review of syllabuses and standards has been made. A project of learning discrete mathematics elements from first to twelve class is proposed.

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.

A Basis for Z-Graded Identities of Matrices over Infinite Fields

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50

Dickson Polynomials that are Permutations

2000 Mathematics Subject Classification: 11T06, 13P10.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Model Mining and Efficient Verification of Software Product Lines

Software product line modeling aims at capturing a set of software products in an economic yet meaningful way. We introduce a class of variability models that capture the sharing between the software artifacts forming the products of a software product line (SPL) in a hierarchical fashion, in terms of commonalities and orthogonalities. Such models are useful when analyzing and verifying all products of an SPL, since they provide a scheme for divide-and-conquer-style decomposition of the analysis or verification problem at hand. We define an abstract class of SPLs for which variability models can be constructed that are optimal w.r.t. the chosen representation of sharing. We show how the constructed models can be fed into a previously developed algorithmic technique for compositional verification of control-flow temporal safety properties, so that the properties to be verified are iteratively decomposed into simpler ones over orthogonal parts of the SPL, and are not re-verified over the shared parts. We provide tool support for our technique, and evaluate our tool on a small but realistic SPL of cash desks.

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

Extention of Apolarity and Grace Theorem

MSC 2010: 30C10

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35