Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

Torsion theories induced from commutative subalgebras

We begin a study of torsion theories for representations of finitely generated algebras U over a field containing a finitely generated commutative Harish-Chandra subalgebra Gamma. This is an important class of associative algebras, which includes all finite W-algebras of type A over an algebraically closed field of characteristic zero, in particular, the universal enveloping algebra of gl(n) (or sl(n)) for all n. We show that any Gamma-torsion theory defined by the coheight of the prime ideals of Gamma is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec Gamma have the same coheight. Hence, the coheight of these associated prime ideals is an invariant of a given simple U-module. This implies the stratification of the category of U-modules controlled by the coheight of the associated prime ideals of Gamma. Our approach can be viewed as a generalization of the classical paper by Block (1981) [4]; it allows, in particular, to study representations of gl(n) beyond the classical category of weight or generalized weight modules. (C) 2011 Elsevier B.V. All rights reserved.

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.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

Galois orders in skew monoid rings

We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras (C) 2010 Elsevier Inc All rights reserved

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Universal Experimental Measurement System «Sun-Walker» : Automotive measurement system for the evaluation of the solar irradiation distribution for the tests of the solar concentrated systems.

This Thesis project is a part of the research conducted in Solar industry. ABSOLICON Solar Concentrator AB has invented and started production of the prospective solar concentrated system Absolicon X10. The aims of this Thesis project are designing, assembling, calibrating and putting in operation the automatic measurement system intended to evaluate distribution of density of solar radiation in the focal line of the concentrated parabolic reflectors and to measure radiation from the artificial source of light being a calibration-testing tool.On the basis of the requirements of the company’s administration and needs of designing the concentrated reflectors the operation conditions for the Sun-Walker were formulated. As the first step, the complex design of the whole system was made and division on the parts was specified. After the preliminary conducted simulation of the functions and operation conditions of the all parts were formulated.As the next steps, the detailed design of all the parts was made. Most components were ordered from respective companies. Some of the mechanical components were made in the workshop of the company. All parts of the Sun-Walker were assembled and tested. The software part, which controls the Sun-Walker work and conducts measurements of solar irradiation, was created on the LabVIEW basis. To tune and test the software part, the special simulator was designed and assembled.When all parts were assembled in the complete system, the Sun-Walker was tested, calibrated and tuned.

Förlorad i övergången från aritmetik till algebra : Hur gymnasieelever översätter aritmetik till algebra

The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions.

Gymnasieelevers uppfattningar om algebra och problemlösning : En undersökning med utgångspunkt i elevernas kön, slutbetyg i grundskolan och val av gymnasieprogram

Syftet med den här uppsatsen är att undersöka elevers uppfattningar om algebra och problemlösning samt granska hur dessa uppfattningar påverkas beroende på elevernas val av gymnasieprogram, kön och slutbetyg i grundskolan. Syftet är vidare att ta reda på vilka eventuella hinder och svårigheter eleverna själva uppfattar då de använder algebra för att lösa matematiska problem. Som metod för att söka svar på syfte och frågeställningar har valts att genomföra en enkätundersökning med elever som går första året på gymnasiet och som läser antingen naturvetenskapsprogrammet eller bygg- och anläggningsprogrammet. Enkätundersökningen består av två delar, en del som undersöker elevers uppfattningar om matematik i allmänhet och algebra och problemlösning i synnerhet, samt en del som försöker reda ut vilka svårigheter eleverna uppfattar då de ska lösa matematiska problem med algebra. Svaren sammanställs genom en analys av vilka eventuella skillnader och likheter som finns beroende på elevernas val av gymnasieprogram, kön och betyg i grundskolan. Resultatet visar på att elever på naturvetenskapsprogrammet som hade MVG i betyg i grundskolan har en mer positiv inställning till algebra och problemlösning i jämförelse med elever från bygg- och anläggningsprogrammet som fått G i betyg. Vad gäller elevernas kön finns det inte några indikationer på att denna faktor har någon större påverkan på deras uppfattningar. Resultatet kan vara en indikation på att elevernas uppfattningar främst påverkas av deras förståelse för det algebraiska tankesättet. Det eleverna upplever som svårast när de ska lösa problem med hjälp av algebra är att översätta den skrivna texten till en algebraisk framställning. När eleverna löser matematiska problem indikerar även resultatet att de till stor del styrs av sina förväntningar och förutfattade föreställningar om uppgiften. Resultatet ger en indikation om att eleverna behöver arbeta mer med problemlösning i olika former för att genom det kunna träna upp sin resonemangsförmåga och sin förmåga att behärska alla de tre faserna, översättning, omskrivning och tolkning, i den algebraiska cykeln.

Universal Design in Higher Education

While colleges and universities increasingly draw upon the concept of Universal Design to create an ideal learning environment, it can be challenging to apply the concept practically in the classroom. This project explores innovative ways to incorporate Universal Design into campus architecture, classroom technology and curriculum development. Further, this brief describes different approaches used by universities to garner faculty interest and offer effective training in Universal Design.

Curso de matematica para economistas, Capitulos I e II: funções, algebra linear e aplicações

Os autores objetivam, com este trabalho preliminar, bem como com aqueles que lhe darão continuidade, na sequência de composição de um livro de matemática para economistas, registrar as suas experiências ao longo dos últimos anos ministrando cadeiras de matemática nos cursos de pós-graduação em economia da Fundação Getúlio Vargas, da UFF (Universidade Federal Fluminense) e da PUC-RJ. Reveste-se de constante repetição em tais cursos a discussão sobre que pontos abordar, bem como com qual grau de profundidade, e em que ordem. É neste sentido que os autores esperam, com a sequência didática que aqui se inicia, trazer alguma contribuição para o assunto.

Igreja Universal do Reino de Deus: análise de um caso de sucesso de estratégia por diferenciação

Is it possible to see elements of an organizational strategy in churches practices, as we can do in public and private organizations? This work intend to show a case study about the Universal Church of the Kingdom of God, and study some factors that can be evidences of a strategic profile. It discusses the success that this church try to show: can it be proved? The conclusion of this study answer these questions.

Gênesis habermasiana e o caso de Catende: pragmática universal e a economia solidária

O presente trabalho se dedica à aproximação entre a pragmática universal, elemento fundamental da racionalidade comunicativa habermasiana, e os conceitos de economia solidária defendidos por Paul Singer. O trabalho, no que diz respeito à complexa teoria de Habermas, se limita à idéia de reconstrução das condições universais de possível compreensão mútua, portanto, não se dedica ao entendimento das relações semânticas nos procedimentos dialógicos, essência da teoria habermasiana. A reflexão teórica utilizou como instrumento empírico, através do estudo de caso não generalizável, o Projeto Harmonia no município de Catende, Zona da Mata pernambucana. Para este fim, foram utilizados dois estudos de campo: entrevistas com questionário semi-estruturado e pesquisa quantitativa com aplicação presencial de questionários. A pesquisa exploratória identificou quatro categorias de trabalhadores que foram analisados distintamente no levantamento de dados. O trabalho se desenvolve em seis capítulos, além da Introdução. O primeiro capítulo faz uma abordagem sumária das raízes da luta pela emancipação. O segundo capítulo trata da teoria habermasiana. O terceiro, descreve a erspectiva da economia solidária como opção ao capitalismo, e não necessariamente como objeto de ruptura paradigmática. O quarto capítulo se dedica à aproximação entre a economia solidária e o pragmatismo universal de Habermas. O quinto capítulo descreve o estudo de caso na Usina Harmonia. Finalmente, o sexto capítulo se dedica às conclusões. O trabalho conclui que há um laço que uni a teoria abermasiana à perspectiva da economia solitária, no que tange ao ambiente que funciona como reconstrução das condições para o entendimento mútuo. A conclusão se baseia no caso de Catende e não tem a pretensão de generalizar para outras experiências solidárias. Conclui-se também que o fato de observar as condições necessárias para o processo intersubjetivo não significa, necessariamente, que estão sendo desenvolvidos os procedimentos que identificam satisfatoriamente, nos termos de Habermas, a aplicação dos atos da fala, e de todas as características semânticas correspondentes.