Symplectic spreads, planar functions and mutually unbiased bases

In this paper we give explicit descriptions of complete sets of mutually unbiased bases (MUBs) and orthogonal decompositions of special Lie algebras $sl_n(\mathbb{C})$ obtained from commutative and symplectic semifields, and from some other non-semifield symplectic spreads. Relations between various constructions are also studied. We show that the automorphism group of a complete set of MUBs is isomorphic to the automorphism group of the corresponding orthogonal decomposition of the Lie algebra $sl_n(\mathbb{C})$. In the case of symplectic spreads this automorphism group is determined by the automorphism group of the spread. By using the new notion of pseudo-planar functions over fields of characteristic two we give new explicit constructions of complete sets of MUBs.Comment: 20 page

Zero forcing sets and controllability of dynamical systems defined on graphs

In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present paper together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases

Currency Substitution: A Case of Kazakhstan (2000:1-2007:12)

This paper aims to investigate the demand for money in Kazakhstan. This study covers the period starting from 2000:01, when capital liberalization program was launched and National Bank approved managed float regime (National Bank employed adjustable exchange rate regime before exchange rate crisis in Kazakhstan in 1999) to 2007:12 as recent available data for investigation variables. In order to achieve the goal we set demand for money function is estimated using cointegration methodology aimed for variables integrated of order one. The results show important key factors for controlling money demand could be applied by National Bank of Kazakhstan. Besides, there was reversal of currency in Kazakhstan over the period under the investigation.http://deepblue.lib.umich.edu/bitstream/2027.42/64401/1/wp946.pd

CURRENCY SUBSTITUTION: A CASE OF KAZAKHSTAN (2000:1-2007:12)

This paper aims to investigate the demand for money in Kazakhstan. This study covers the period starting from 2000:01, when capital liberalization program was launched and National Bank approved managed float regime (National Bank employed adjustable exchange rate regime before exchange rate crisis in Kazakhstan in 1999) to 2007:12 as recent available data for investigation variables. In order to achieve the goal we set demand for money function is estimated using cointegration methodology aimed for variables integrated of order one. The results show important key factors for controlling money demand could be applied by National Bank of Kazakhstan. Besides, there was reversal of currency in Kazakhstan over the period under the investigation.Demand for money, currency substitution, dollarization, Kazakhstan

Contrastive Studies on Proverbs

AbstractFolk proverbs and sayings are an integral part of the spiritual treasures of the culture and language of the people, the age-old wisdom and skills used by them - an important part of the culture of human language. In fact, the main purpose of the article is interpretations of English and Kazakh folk proverbs, which can artistically embody various aspects of life, social experience, outlook, the originality of artistic attitudes and tastes, mental and ethical and aesthetic values. Also in this article are considered several methods and descriptive techniques such as analysis, synthesis, analogy, and observation. Additionally, the author tried to identify in his research whether British and Kazakh proverbs with similar content, but due to different historical conditions express similar thoughts in different ways, thus reflecting the different social structures and lifestyles of their respective peoples, and often are only roughly equivalent. While interpreting English and Kazakh proverbs the author divided them into four categories. This paper focuses on the learning of: pedagogic practices that operate from an approach that emphasizes learners’ strengths, rather than deficits, and critically interrogates learners’ experiences as a resource for learning which were the most successful in enabling this translation. Moreover, this article deals with the analysis of methodical and methodological value of using proverbs in English classes (that is to classify English proverbs in relation to the Kazakh equivalents, to consider the difficulties of translation from English proverbs into Kazakh language, and to conduct a comparative description of translation of English proverbs in Kazakh)

Numerical solution of highly oscillatory differential equations by Magnus Series Method

Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2006Includes bibliographical references (leaves: 50-51)Text in English; Abstract: Turkish and Englishix, 62 leavesIn this study, the differential equation known as Lie-type equation where the solutions of the equation stay in the Lie-Group is considered. The solution of this equation can be represented as an infinite series whose terms consist of integrals and commutators, based on the Magnus Series. This expansion is used as a numerical geometrical integrator called Magnus Series Method, to solve this type of equations. This method which is also one of the Lie-Group methods, has slower error accumulation and more efficient computation results during the long time interval than classical numerical methods such as Runge-Kutta, since it preserves the qualitative features of the exact solutions. Several examples are considered including linear and nonlinear oscillatory problems to illustrate the efficiency of the method