On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Exploring social representations of adapting to climate change using topic modeling and Bayesian networks

When something unfamiliar emerges or when something familiar does something unexpected people need to make sense of what is emerging or going on in order to act. Social representations theory suggests how individuals and society make sense of the unfamiliar and hence how the resultant social representations (SRs) cognitively, emotionally, and actively orient people and enable communication. SRs are social constructions that emerge through individual and collective engagement with media and with everyday conversations among people. Recent developments in text analysis techniques, and in particular topic modeling, provide a potentially powerful analytical method to examine the structure and content of SRs using large samples of narrative or text. In this paper I describe the methods and results of applying topic modeling to 660 micronarratives collected from Australian academics / researchers, government employees, and members of the public in 2010-2011. The narrative fragments focused on adaptation to climate change (CC) and hence provide an example of Australian society making sense of an emerging and conflict ridden phenomena. The results of the topic modeling reflect elements of SRs of adaptation to CC that are consistent with findings in the literature as well as being reasonably robust predictors of classes of action in response to CC. Bayesian Network (BN) modeling was used to identify relationships among the topics (SR elements) and in particular to identify relationships among topics, sentiment, and action. Finally the resulting model and topic modeling results are used to highlight differences in the salience of SR elements among social groups. The approach of linking topic modeling and BN modeling offers a new and encouraging approach to analysis for ongoing research on SRs.

Social representations of nursing students about hospital assistance and primary health care

Objective: To analyze how social representations of hospital and community care are structured in two groups of nursing students – 1st and 4th years. Method: Qualitative research oriented by the Theory of Social Representations. We used a questionnaire with Free Association of Words. Data were analyzed in the Software IRaMuTeQ 0.6 alpha 3. Results: We applied the method of Descending Hierarchical Classifi cation and obtained four classes. Class 4 has the largest social representation (30.41%) within the corpus. The two organizational axes are nurse and disease/patient in the central core. On the periphery are the care and help related to the nurse and the treatment and prevention associated with the disease. Conclusion: Social representations focus on disease/patient and on the role of nurses in the treatment, prevention, and care. Health promotion and the social determinants of health are absent from the social representations of students.

The other of myself: representations of portuguese teachers about intercultural education related concepts

Having into consideration that we live in a multicultural society, it is important to analyse how far people view and accept each other. Therefore, one should reflect upon concepts such as: representations and stereotypes, because they are interpersonal constructs which are (re)built during the interaction of different sociocultural groups. In this study, we focus our attention on the representations a sociocultural group – Portuguese teachers - has of intercultural education and the role of teachers and educators in the promotion of an intercultural approach at school. We believe that teachers have the responsibility to: find out the representations students have of the Other; reconfigure stereotyped representations; and create representations which favor dialogue and relationship with the Other flourish. Following a sociolinguistic approach (Müller, 1998; Vasseur, 2001; Vasseur & Hudelot, 1998), which is related to the construction and diffusion of representations in discourse, we analyse the discourse of teachers during a workshop called ‘The Other and Myself’, in which they build and discuss about a didactic mask that portrays their own vision of both themselves and their ideas of intercultural education.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.