The bound quiver of a split extension

In this paper, we give a sufficient (which is also necessary under a compatibility hypothesis) condition on a set of arrows in the quiver of an algebra A so that A is a split extension of A/M, where M is the ideal of A generated by the classes of these arrows. We also compare the notion of split extension with that of semiconvex extension of algebras.

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.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

An easy algebra for beginners; being a simple, plain presentation of the essentials of elementary algebra, and also adapted to the use of those who can take only a brief course in this study.

"Answers": p. 143-157.

An algebra upon the inductive method of instruction /

Spine title: Harney's algebra.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

The impact of an online mathematics education project (MATACTIVA) on higher education students

The Online Mathematics Education Project (MatActiva) is an exciting new initiative which aims to support and enhance mathematics education. The project is led by the Institute of Accounting and Administration of Porto (ISCAP), part of the Polytechnic Institute of Porto (IPP). It provides innovative resources and carefully constructed materials around themes such as Elementary Mathematics, Calculus, Algebra, Statistics and Financial Mathematics to help support and inspire students and teachers of mathematics. The goal is to increase mathematical understanding, confidence and enjoyment, enrich the mathematical experience of each person, and promote creative and imaginative approaches to mathematics. Furthermore the project can be used to deliver engaging and effective mathematics instruction through the flipped classroom model. This paper also presents the findings of a large survey, whose propose was to study the student’s reaction to the project.

A graded subring of an inverse limit of polynomial rings

We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.

A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Computer-aided tool for the teaching of relational algebra in data base courses

This article describes the design and implementation of computer-aided tool called Relational Algebra Translator (RAT) in data base courses, for the teaching of relational algebra. There was a problem when introducing the relational algebra topic in the course EIF 211 Design and Implementation of Databases, which belongs to the career of Engineering in Information Systems of the National University of Costa Rica, because students attending this course were lacking profound mathematical knowledge, which led to a learning problem, being this an important subject to understand what the data bases search and request do RAT comes along to enhance the teaching-learning process.It introduces the architectural and design principles required for its implementation, such as: the language symbol table, the gramatical rules and the basic algorithms that RAT uses to translate from relational algebra to SQL language. This tool has been used for one periods and has demonstrated to be effective in the learning-teaching process.  This urged investigators to publish it in the web site: www.slinfo.una.ac.cr in order for this tool to be used in other university courses.

Malignant Transformation Of An Odontogenic Cyst In A Period Of 10 Years.

Primary intraosseous carcinoma of the jaws (PIOSCC) might arise from odontogenic epithelium, more commonly from a previous odontogenic cyst. The aim of this case is to illustrate that the clinician should consider that an apparent benign dentigerous cyst can suffer malignant transformation and that all material removed from a patient must be evaluated histologically. A 44-year-old man presented in a routine periapical X-ray an impacted lower left third molar with radiolucency over its crown. Ten years later, the patient complained of pain in the same region and the tooth was extracted. After one month, the patient still complained of pain and suffered a fracture of the mandible. A biopsy was performed and carcinoma was diagnosed. The patient was treated surgically with adjuvant radio- and chemotherapy and after 8 years, he is well without signs of recurrences. This report describes a central mandibular carcinoma probably developed from a previous dentigerous cyst.

[the Sociology Of Health In Brazil - The Creation Of An Identity].

This article analyzes the historical, social and cognitive dimensions of the sociology of medicine in the construction of its identity, from Wolf Lepenies' perspective. It is understood that the construction of an identity does not end with the first historical manifestations, but is consolidated when it is institutionalized and structured as a field of knowledge by creating its own forms of cognitive expression. The text is divided into three parts: in the first the precursors are presented, highlighting the role played by some travelers, naturalists and folklore scholars, followed by social physicians-scientists and the first social scientists (1940-1969). In the second part, aspects of the consolidation of the social sciences in health are presented at two significant moments, namely the 1970s and 1980s. In the third part, the issues raised by the field are addressed in general terms. It is considered that once the main structural stages are in place there is still a need for the formation of new generations of social scientists in health. It is also essential to disseminate scientific production and to ensure that the relations are studied in depth and institutionalized with the sociological matrices on the one hand and with the field of health on the other.