Heuristics for The Whitehead Minimization Problem

In this paper we discuss several heuristic strategies which allow one to solve the Whitehead's minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most non-minimal elements in a free group can be reduced by a Nielsen automorphism which can be identified by inspecting the structure of the corresponding Whitehead Graph

Structural changes in Russian economy and objectives of investment policy

© 2015, Asian Social Science. All rights reserved. Issues of Russian economy development in the period of economic reforms, tendency of sectorial structure change of national production on different stages of market reformation, reductions of production volumes of advanced technology products in the industries with a high value added are examined in the article. The influence of government policy on the state finances of Russia is considered, the criteria applied for the estimation of reforms realization success are exposed. The analysis of lack of internal credit resources reasons in an economy, forming of national and corporate external debt, and also strengthening of technological dependence of the Russian producers on foreign partners and insufficient stability of the Russian economy in a global competition is conducted

Development of russian economy in conditions of globalization and investment policy

© 2015, Mediterranean Center of Social and Educational Research. All rights reserved. Theoretical issues of Russian economy development in the context of globalization, internal and external factors, forming tendencies of structural changes of national production are considered in the article. The situation on the Russian market of exported goods, and its impact on the financial system of Russia are considered. Conditions for investment business are analyzed, the role of state finance, taxation and monetary policies on the performance of business in Russia are explored. A comparative analysis of investment conditions in Russia and in Western developed countries is made. Possible changes in macroeconomic policies, aimed at improving the conditions for investments in Russia, are determined

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Bacteriophage-encoded depolymerases: their diversity and biotechnological applications

Bacteriophages (phages), natural enemies of bacteria, can encode enzymes able to degrade polymeric substances. These substances can be found in the bacterial cell surface, such as polysaccharides, or are produced by bacteria when they are living in biofilm communities, the most common bacterial lifestyle. Consequently, phages with depolymerase activity have a facilitated access to the host receptors, by degrading the capsular polysaccharides, and are believed to have a better performance against bacterial biofilms, since the degradation of extracellular polymeric substances by depolymerases might facilitate the access of phages to the cells within different biofilm layers. Since the diversity of phage depolymerases is not yet fully explored, this is the first review gathering information about all the depolymerases encoded by fully sequenced phages. Overall, in this study, 160 putative depolymerases, including sialidases, levanases, xylosidases, dextranases, hyaluronidases, peptidases as well as pectate/pectin lyases, were found in 143 phages (43 Myoviridae, 47 Siphoviridae, 37 Podoviridae, and 16 unclassified) infecting 24 genera of bacteria. We further provide information about the main applications of phage depolymerases, which can comprise areas as diverse as medical, chemical, or food-processing industry.DPP acknowledges the financial support from the Portuguese Foundation for Science and Technology (FCT) through the grant SFRH/BD/76440/2011. SS is an FCT investigator (IF/01413/2013). The authors also thank FCT for the Strategic Project of the UID/BIO/04469/2013 unit, FCT and European Union funds (FEDER/COMPETE) for the project RECI/BBB-EBI/0179/2012 (FCOMP-01-0124-FEDER027462)

Development of russian economy in conditions of globalization and investment policy

© 2015, Mediterranean Center of Social and Educational Research. All rights reserved. Theoretical issues of Russian economy development in the context of globalization, internal and external factors, forming tendencies of structural changes of national production are considered in the article. The situation on the Russian market of exported goods, and its impact on the financial system of Russia are considered. Conditions for investment business are analyzed, the role of state finance, taxation and monetary policies on the performance of business in Russia are explored. A comparative analysis of investment conditions in Russia and in Western developed countries is made. Possible changes in macroeconomic policies, aimed at improving the conditions for investments in Russia, are determined

ANSAB newsletter, vol. 1, no. 1, Summer 1992

© 2015, Mediterranean Center of Social and Educational Research. All rights reserved. Theoretical issues of Russian economy development in the context of globalization, internal and external factors, forming tendencies of structural changes of national production are considered in the article. The situation on the Russian market of exported goods, and its impact on the financial system of Russia are considered. Conditions for investment business are analyzed, the role of state finance, taxation and monetary policies on the performance of business in Russia are explored. A comparative analysis of investment conditions in Russia and in Western developed countries is made. Possible changes in macroeconomic policies, aimed at improving the conditions for investments in Russia, are determined

Structural changes in Russian economy and objectives of investment policy

© 2015, Asian Social Science. All rights reserved. Issues of Russian economy development in the period of economic reforms, tendency of sectorial structure change of national production on different stages of market reformation, reductions of production volumes of advanced technology products in the industries with a high value added are examined in the article. The influence of government policy on the state finances of Russia is considered, the criteria applied for the estimation of reforms realization success are exposed. The analysis of lack of internal credit resources reasons in an economy, forming of national and corporate external debt, and also strengthening of technological dependence of the Russian producers on foreign partners and insufficient stability of the Russian economy in a global competition is conducted

Structural changes in Russian economy and objectives of investment policy

© 2015, Asian Social Science. All rights reserved. Issues of Russian economy development in the period of economic reforms, tendency of sectorial structure change of national production on different stages of market reformation, reductions of production volumes of advanced technology products in the industries with a high value added are examined in the article. The influence of government policy on the state finances of Russia is considered, the criteria applied for the estimation of reforms realization success are exposed. The analysis of lack of internal credit resources reasons in an economy, forming of national and corporate external debt, and also strengthening of technological dependence of the Russian producers on foreign partners and insufficient stability of the Russian economy in a global competition is conducted