Optimum Trajectory of Dynamic Input-Output Balance Model for Open Economy

When export and import is connected with output of basic production, and criterion functional represents a final state of economy, the generalization of classical qualitative results of the main-line theory on a case of dynamic input-output balance optimization model for open economy is given.

Application of the Multivariate Prediction Method to Time Series

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

Monitoring of deployment process of shape memory polymers for morphing structures with embedded fibre Bragg grating sensors

This article demonstrates the use of embedded fibre Bragg gratings as vector bending sensor to monitor two-dimensional shape deformation of a shape memory polymer plate. The shape memory polymer plate was made by using thermal-responsive epoxy-based shape memory polymer materials, and the two fibre Bragg grating sensors were orthogonally embedded, one on the top and the other on the bottom layer of the plate, in order to measure the strain distribution in both longitudinal and transverse directions separately and also with temperature reference. When the shape memory polymer plate was bent at different angles, the Bragg wavelengths of the embedded fibre Bragg gratings showed a red-shift of 50 pm/°caused by the bent-induced tensile strain on the plate surface. The finite element method was used to analyse the stress distribution for the whole shape recovery process. The strain transfer rate between the shape memory polymer and optical fibre was also calculated from the finite element method and determined by experimental results, which was around 0.25. During the experiment, the embedded fibre Bragg gratings showed very high temperature sensitivity due to the high thermal expansion coefficient of the shape memory polymer, which was around 108.24 pm/°C below the glass transition temperature (Tg) and 47.29 pm/°C above Tg. Therefore, the orthogonal arrangement of the two fibre Bragg grating sensors could provide a temperature compensation function, as one of the fibre Bragg gratings only measures the temperature while the other is subjected to the directional deformation. © The Author(s) 2013.

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.

Influence of processing and clay type on nanostructure and stability of polypropylene-clay nanocomposites

Melt processing is a critical step in the manufacture of polymer articles and is even more critical when dealing with inhomogeneous polymer-clay nanocomposites systems. The chemical composition, and in particular the clay type and its organic modification, also plays a major contribution in determining the final properties and in particular the thermal and long-term oxidative stability of the resulting polymer nanocomposites. Proper selection and tuning of the process variable should, in principle, lead to improved characteristics of the fabricated product. With multiphase systems containing inorganic nanoclays, however, this is not straightforward and it is often the case that the process conditions are chosen initially to improve one or more desired properties at the expense of others. This study assesses the influence of organo-modified clays and the processing parameters (extrusion temperature and screw speed) on the rheological and morphological characteristics of polymer nanocomposites as well as on their melt and thermo-oxidative stability. Nanocomposites (PPNCs) based on PP, maleated PP and organically modified clays were prepared in different co-rotating twin-screw extruders ranging from laboratory scale to semi-industrial scale. Results show that the amount of surfactant present in similar organo-modified clays affects differently the thermo-oxidative stability of the extruded PPNCs and that changes in processing conditions affect the clay morphology too. By choosing an appropriate set of tuned process variables for the extrusion process it would be feasible to selectively fabricate polymer-clay nanocomposites, with the desired mechanical and thermo-oxidative characteristics. © 2013 Elsevier Ltd. All rights reserved.

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.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

Noninear Integral Inequalities Involving Maxima

Снежана Христова, Кремена Стефанова, Лозанка Тренкова - В статията се изучават някои интегрални неравенства, които съдържат макси-мума на неизвестната функция на една променлива. Разглежданите неравенства са обобщения на класическото неравенство на Бихари. Значимостта на тези интегрални неравенства се дълже на широкото им приложение при качественото изследванене на различни свойства на решенията на диференциални уравнения с “максимум” и е илюстрирано с някои директни приложения.

Principles of Extremum and Application to some Problems of Analysis

AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.

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.

Design of nonlinear regenerative transmission systems with high capacity

We present the design of nonlinear regenerative communication channels that have capacity above the classical Shannon capacity of the linear additive white Gaussian noise channel. The upper bound for regeneration efficiency is found and the asymptotic behavior of the capacity in the saturation regime is derived. © 2013 IEEE.