STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Room Temperature Ionic Liquid-Lithium Salt Mixtures: Optical Kerr Effect Dynamical Measurements

The addition of lithium salts to ionic liquids causes an increase in viscosity and a decrease in ionic mobility that hinders their possible application as an alternative solvent in lithium ion batteries. Optically heterodyne-detected optical Kerr effect spectroscopy was used to study the change in dynamics, principally orientational relaxation, caused by the addition of lithium bis(trifluoromethylsulfonyl)imide to the ionic liquid 1-buty1-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Over the time scales studied (1 ps-16 ns) for the pure ionic liquid, two temperature-independent power laws were observed: the intermediate power law (1 ps to similar to 1 ns), followed by the von Schweidler power law. The von Schweidler power law is followed by the final complete exponential relaxation, which is highly sensitive to temperature. The lithium salt concentration, however, was found to affect both power laws, and a discontinuity could be found in the trend observed for the intermediate power law when the concentration (mole fraction) of lithium salt is close to chi(LiTf(2)N) = 0.2. A mode coupling theory (MCT) schematic model was also used to fit the data for both the pure ionic liquid and the different salt concentration mixtures. It was found that dynamics in both types of liquids are described very well by MCT.

Unraveling Dynamical Heterogeneity in the Ionic Liquid 1-Butyl-3-methylimidazolium Chloride

Heterogeneous dynamics within a time range of nanoseconds was investigated by molecular dynamics (MD) simulations of 1 -butyl-3-methylimidazolium chloride ([bmim]Cl). After identifying groups of fast and slow ions, it was shown that the separation between the location of the center of mass and the center of charge of cations, d(CMCC), is a signature of such difference in ionic mobility. The distance d(CMCC) can be used as a signature because it relaxes in the time window of the dynamical heterogeneity. The relationship between the parameter dcmcc and conformations of the side alkyl chain in [bmim] is discussed. Since the relatively slow relaxation of dcmcc is a consequence of coexisting polar and nonpolar domains in the bulk, the MD simulations reveal a subtle interplay between structural and dynamical heterogeneity in ionic liquids.

Landskommunens beslutsfattande kvinnor : Om kvinnors representation i kommunalfullmäktige ochförekomst i fullmäktigeprotokoll i Kalmar länslandskommuner 1939-1951

Syftet med denna uppsats är att undersöka den kvinnliga representationen i Kalmar läns landskommuners kommunalfullmäktige från 1938 till kommunsammanslagningen 1951. Detta innefattar att söka en översikt över i vilken grad kvinnor är representerade i länets kommunalfullmäktigeförsamlingaroch att undersöka hur dessa kvinnliga ledamöter syns i protokollsmaterial i ett par kommuners fullmäktigeprotokoll. Södra Möckelby och Vickleby kommuner med relativt hög andel kvinnliga ledamöter har valts som exempel.Undersökningen av valstatistiken visar en ökning i både antal kvinnor och antal kommunalfullmäktige med kvinnlig representation under perioden. Länet ligger under riksgenomsnittet, men ökningen är ungefär densamma i relativa termer. Närläsningen av protokoll visar att kvinnor främst omnämns vid frånvaro, vid val till olika uppdrag eller vid uppföljning av dessa val. I den kommun som har en längre tradition av relativt hög kvinnlig representation märks kvinnor i fler sammanhang som förutsätter att man tar ett större utrymme på mötena. Dessa tillfällen sammanfaller med en speciell kvinnas aktiva period i fullmäktige och försvinner när den kvinnliga representationen minskar till en ensam kvinna.

La confrontation de la laideur avec la beauté dans lesromans Mercure et Attentat. Une étude sur lareprésentation de la dualité thématique laideur-beautéchez Amélie Nothomb. : "Where there is Quasimodo, there is also Esmeralda." The confrontationbetween ugliness and beauty in the novels Mercure and Attentat. Astudy on the representation of the duality beauty-ugliness in the worksof Amélie Nothomb.

This paper studies one of the recurrent topics of writing found in Amélie Nothomb’snovels: beauty and ugliness. The novels Mercure and Attentat are analyzed in detail,with respect to figures of speech used to describe the extreme physical appearance ofthe protagonists and the role of the duality beauty-ugliness in the advancement of theplot.

Representation and interpretation : textbooks, teachers, and historical culture

This article presents a study of how contemporary Swedish lower secondary school textbooks present the emergence of the Cold War and how 10 active lower secondary school history teachers interpreted a quotation that was ambiguous in relation to the general narrative in the studied Swedish textbooks, seeking to analyse textbooks both from the perspectives of content and reception. Applying a theoretical framework of uses of history, the study finds that the narratives presented in the studied textbooks are what could be called traditional in the sense that they do not acknowledge perspective and representation in history. While the interviewed teachers generally acknowledged that textbook narratives are representations of history and contingent on perspective, few teachers extended this to include how their own views affect their interpretations, suggesting an intermediary appreciation of the contextual contingency of historical narratives.

Representations of culture in EIL : Cultural representation in Swedish EFL textbooks

The English language has become an international language and is globally used as a lingua franca. Therefore, there has been a shift in English-language education toward teaching English as an interna-tional language (EIL). Teaching from the EIL paradigm means that English is seen as an international language used in communication by people from different linguistic and cultural backgrounds. As the approach to English-language education changes from the traditional native-speaker, target country context, so does the role of culture within English-language teaching. The aim of this thesis is to in-vestigate and analyse cultural representations in two Swedish EFL textbooks used in upper-secondary school to see how they correspond with the EIL paradigm. This is done by focusing on the geograph-ical origin of the cultural content as well as looking at what kinds of culture are represented in the textbooks. A content analysis of the textbooks is conducted, using Kachru’s Concentric Circles of English as the model for the analysis of the geographical origin. Horibe’s model of the three different kinds of culture in EIL is the model used for coding the second part of the analysis. The results of the analysis show that culture of target countries and "Culture as social custom" dominate the cultural content of the textbook. Thus, although there are some indications that the EIL paradigm has influ-enced the textbooks, the traditional approach to culture in language teaching still prevails in the ana-lysed textbooks. Because of the relatively small sample included in the thesis, further studies need to be conducted in order to make conclusions regarding the Swedish context as a whole.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.