On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Calceology : an introduction to North Western European archaeological leather footwear (Neolithic period to c. AD 1600)

Calceology is the study of recovered archaeological leather footwear and is comprised of conservation, documentation and identification of leather shoe components and shoe styles. Recovered leather shoes are complex artefacts that present technical, stylistic and personal information about the culture and people that used them. The current method in calceological research for typology and chronology is by comparison with parallel examples, though its use poses problems by an absence of basic definitions and the lack of a taxonomic hierarchy. The research findings of the primary cutting patterns, used for making all leather footwear, are integrated with the named style method and the Goubitz notation, resulting in a combined methodology as a basis for typological organisation for recovered footwear and a chronology for named shoe styles. The history of calceological research is examined in chapter two and is accompanied by a review of methodological problems as seen in the literature. Through the examination of various documentation and research techniques used during the history of calceological studies, the reasons why a standard typology and methodology failed to develop are investigated. The variety and continual invention of a new research method for each publication of a recovered leather assemblage hindered the development of a single standard methodology. Chapter three covers the initial research with the database through which the primary cutting patterns were identified and the named styles were defined. The chronological span of each named style was established through iterative cross-site sedation and named style comparisons. The technical interpretation of the primary cutting patterns' consistent use is due to constraints imposed by the leather and the forms needed to cover the foot. Basic parts of the shoe patterns and the foot are defined, plus terms provided for identifying the key points for pattern making. Chapter four presents the seventeen primary cutting patterns and their sub-types, these are divided into three main groups: six integral soled patterns, four hybrid soled patterns and seven separately soled patterns. Descriptions of the letter codes, pattern layout, construction principle, closing seam placement and list of sub-types are included in the descriptions of each primary cutting pattern. The named shoe styles and their relative chronology are presented in chapter five. Nomenclature for the named styles is based on the find location of the first published example plus the primary cutting pattern code letter. The named styles are presented in chronological order from Prehistory through to the late 16th century. Short descriptions of the named styles are given and illustrated with examples of recovered archaeological leather footwear, reconstructions of archaeological shoes and iconographical sources. Chapter six presents documentation of recovered archaeological leather using the Goubitz notation, an inventory and description of style elements and fastening methods used for defining named shoe styles, technical information about sole/upper constructions and the consequences created by the use of lasts and sewing forms for style identification and fastening placement in relation to the instep point. The chapter concludes with further technical information about the implications for researchers about shoemaking, pattern making and reconstructive archaeology. The conclusion restates the original research question of why a group of primary cutting patterns appear to have been used consistently throughout the European archaeological record. The quantitative and qualitative results from the database show the use of these patterns but it is the properties of the leather that imposes the use of the primary cutting patterns. The combined methodology of primary pattern identification, named style and artefact registration provides a framework for calceological research.

A model of multilingual digital library

This paper addresses the problem of multilingual digital libraries. The motivation for a such a digital library comes from the diversity of languages of the Internet users as well as the diversity of content authors, from e-book authors to writers of courseware. The basic definitions of such a system, the specifications of its functionality and the identification of the items it holds are discussed. The impact of multilinguism in each of the former aspects is presented. A case study of a multilingual digital library - in the Maxwell System in PUC-Rio - is described in the last sections. Its main characteristics are described and the current status of its digital library is shown.

A survey on automatic recommenders in the context of institutional repositories

Peer-reviewed

ISO 9002 -laatujärjestelmän toteutus tukkukaupassa

Työn tavoitteena oli tehdä kohde yritykselle ostoon, kotimaan myyntiin, varastointiin ja toimituksiin ISO 9002 -standardiin pohjautuva laatujärjestelmä, joka voidaan myöhemmin sertifioida. Valmis laatujärjestelmän kuvaus esitetään kirjallisessa muodossa laatukäsikirjan avulla. toisena tavoitteena oli tehdä laatujärjestelmään mittarit, jotka mahdollistava yrityksen laatujärjestelmän toimivuuden seurannan. Kolmantena tavoitteena oli saavuttaa laatujärjestelmän avulla taloudellisia säästöjä yrityksen toiminnassa pitkällä tähtäimellä. Tärkeä osa työtä oli laatia yrityksen laatukäsikirja ISO 9002 -standardin vaatimuksien mukaisesti. Työ jakautuu kahdeksaan suurempaan kokonaisuuteen: laatuun ja palveluihin liittyvien perusajatuksien määrittelyyn, tukkukauppatoiminnan kuvaamiseen, kohdeyrityksen esittelyyn, henkilökuntakyselyn suorittamiseen. laatujärjestelmien käsittelyyn, ISON 9002 -standardin vaatimuksien esittelyyn, kohden yrityksen laatukäsikirjan tarkasteluun ja saavutettujen tulosten tarkastelua ja pohdintaa. Työ tuloksena voidaan todeta, että laatujärjestelmän rakentaminen yritykselle on ollut hyvä ratkaisu. Laatujärjestelmän avulla on voitu saavuttaa säästöjä ja kehitysaskeleita. Investointi parempaan laatuun on kannattanut.

Using time and stochastic models for software reliability forecasting and analysis

Tämä työ luo katsauksen ajallisiin ja stokastisiin ohjelmien luotettavuus malleihin sekä tutkii muutamia malleja käytännössä. Työn teoriaosuus sisältää ohjelmien luotettavuuden kuvauksessa ja arvioinnissa käytetyt keskeiset määritelmät ja metriikan sekä varsinaiset mallien kuvaukset. Työssä esitellään kaksi ohjelmien luotettavuusryhmää. Ensimmäinen ryhmä ovat riskiin perustuvat mallit. Toinen ryhmä käsittää virheiden ”kylvöön” ja merkitsevyyteen perustuvat mallit. Työn empiirinen osa sisältää kokeiden kuvaukset ja tulokset. Kokeet suoritettiin käyttämällä kolmea ensimmäiseen ryhmään kuuluvaa mallia: Jelinski-Moranda mallia, ensimmäistä geometrista mallia sekä yksinkertaista eksponenttimallia. Kokeiden tarkoituksena oli tutkia, kuinka syötetyn datan distribuutio vaikuttaa mallien toimivuuteen sekä kuinka herkkiä mallit ovat syötetyn datan määrän muutoksille. Jelinski-Moranda malli osoittautui herkimmäksi distribuutiolle konvergaatio-ongelmien vuoksi, ensimmäinen geometrinen malli herkimmäksi datan määrän muutoksille.

Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Algebraische Zyklen auf abelschen Varietäten der Dimension 4 mit Polarisierung von Typ (1,2,2,2)

Diese Arbeit besch"aftigt sich mit algebraischen Zyklen auf komplexen abelschen Variet"aten der Dimension 4. Ziel der Arbeit ist ein nicht-triviales Element in $Griff^{3,2}(A^4)$ zu konstruieren. Hier bezeichnet $A^4$ die emph{generische} abelsche Variet"at der Dimension 4 mit Polarisierung von Typ $(1,2,2,2)$. Die ersten drei Kapitel sind eine Wiederholung von elementaren Definitionen und Begriffen und daher eine Festlegung der Notation. In diesen erinnern wir an elementare Eigenschaften der von Saito definierten Filtrierungen $F_S$ und $Z$ auf den Chowgruppen (vgl. cite{Sa0} und cite{Sa}). Wir wiederholen auch eine Beziehung zwischen der $F_S$-Filtrierung und der Zerlegung von Beauville der Chowgruppen (vgl. cite{Be2} und cite{DeMu}), welche aus cite{Mu} stammt. Die wichtigsten Begriffe in diesem Teil sind die emph{h"ohere Griffiths' Gruppen} und die emph{infinitesimalen Invarianten h"oherer Ordnung}. Dann besch"aftigen wir uns mit emph{verallgemeinerten Prym-Variet"aten} bez"uglich $(2:1)$ "Uberlagerungen von Kurven. Wir geben ihre Konstruktion und wichtige geometrische Eigenschaften und berechnen den Typ ihrer Polarisierung. Kapitel ref{p-moduli} enth"alt ein Resultat aus cite{BCV} "uber die Dominanz der Abbildung $p(3,2):mathcal R(3,2)longrightarrow mathcal A_4(1,2,2,2)$. Dieses Resultat ist von Relevanz f"ur uns, weil es besagt, dass die generische abelsche Variet"at der Dimension 4 mit Polarisierung von Typ $(1,2,2,2)$ eine verallgemeinerte Prym-Variet"at bez"uglich eine $(2:1)$ "Uberlagerung einer Kurve vom Geschlecht $7$ "uber eine Kurve vom Geschlecht $3$ ist. Der zweite Teil der Dissertation ist die eigentliche Arbeit und ist auf folgende Weise strukturiert: Kapitel ref{Deg} enth"alt die Konstruktion der Degeneration von $A^4$. Das bedeutet, dass wir in diesem Kapitel eine Familie $Xlongrightarrow S$ von verallgemeinerten Prym-Variet"aten konstruieren, sodass die klassifizierende Abbildung $Slongrightarrow mathcal A_4(1,2,2,2)$ dominant ist. Desweiteren wird ein relativer Zykel $Y/S$ auf $X/S$ konstruiert zusammen mit einer Untervariet"at $Tsubset S$, sodass wir eine explizite Beschreibung der Einbettung $Yvert _Thookrightarrow Xvert _T$ angeben k"onnen. Das letzte und wichtigste Kapitel enth"ahlt Folgendes: Wir beweisen dass, die emph{ infinitesimale Invariante zweiter Ordnung} $delta _2(alpha)$ von $alpha$ nicht trivial ist. Hier bezeichnet $alpha$ die Komponente von $Y$ in $Ch^3_{(2)}(X/S)$ unter der Beauville-Zerlegung. Damit und mit Hilfe der Ergebnissen aus Kapitel ref{Cohm} k"onnen wir zeigen, dass [ 0neq [alpha ] in Griff ^{3,2}(X/S) . ] Wir k"onnen diese Aussage verfeinern und zeigen (vgl. Theorem ref{a4}) begin{theorem}label{maintheorem} F"ur $sin S$ generisch gilt [ 0neq [alpha _s ]in Griff ^{3,2}(A^4) , ] wobei $A^4$ die generische abelsche Variet"at der Dimension $4$ mit Polarisierung vom Typ $(1,2,2,2)$ ist. end{theorem}

Behaviour and applications of elastic waves in structures and metamaterials

The present thesis focuses on elastic waves behaviour in ordinary structures as well as in acousto-elastic metamaterials via numerical and experimental applications. After a brief introduction on the behaviour of elastic guided waves in the framework of non-destructive evaluation (NDE) and structural health monitoring (SHM) and on the study of elastic waves propagation in acousto-elastic metamaterials, dispersion curves for thin-walled beams and arbitrary cross-section waveguides are extracted via Semi-Analytical Finite Element (SAFE) methods. Thus, a novel strategy tackling signal dispersion to locate defects in irregular waveguides is proposed and numerically validated. Finally, a time-reversal and laser-vibrometry based procedure for impact location is numerically and experimentally tested. In the second part, an introduction and a brief review of the basic definitions necessary to describe acousto-elastic metamaterials is provided. A numerical approach to extract dispersion properties in such structures is highlighted. Afterwards, solid-solid and solid-fluid phononic systems are discussed via numerical applications. In particular, band structures and transmission power spectra are predicted for 1P-2D, 2P-2D and 2P-3D phononic systems. In addition, attenuation bands in the ultrasonic as well as in the sonic frequency regimes are experimentally investigated. In the experimental validation, PZTs in a pitch-catch configuration and laser vibrometric measurements are performed on a PVC phononic plate in the ultrasonic frequency range and sound insulation index is computed for a 2P-3D phononic barrier in the sonic frequency range. In both cases the numerical-experimental results comparison confirms the existence of the numerical predicted band-gaps. Finally, the feasibility of an innovative passive isolation strategy based on giant elastic metamaterials is numerically proved to be practical for civil structures. In particular, attenuation of seismic waves is demonstrated via finite elements analyses. Further, a parametric study shows that depending on the soil properties, such an earthquake-proof barrier could lead to significant reduction of the superstructure displacement.

Cyclic automorphic graph decompositions

Chapter 1 introduces the tools and mechanics necessary for this report. Basic definitions and topics of graph theory which pertain to the report and discussion of automorphic decompositions will be covered in brief detail. An automorphic decomposition D of a graph H by a graph G is a G-decomposition of H such that the intersection of graph (D) @H. H is called the automorhpic host, and G is the automorphic divisor. We seek to find classes of graphs that are automorphic divisors, specifically ones generated cyclically. Chapter 2 discusses the previous work done mainly by Beeler. It also discusses and gives in more detail examples of automorphic decompositions of graphs. Chapter 2 also discusses labelings and their direct relation to cyclic automorphic decompositions. We show basic classes of graphs, such as cycles, that are known to have certain labelings, and show that they also are automorphic divisors. In Chapter 3, we are concerned with 2-regular graphs, in particular rCm, r copies of the m-cycle. We seek to show that rCm has a ρ-labeling, and thus is an automorphic divisor for all r and m. we discuss methods including Skolem type difference sets to create cycle systems and their correlation to automorphic decompositions. In the Appendix, we give classes of graphs known to be graceful and our java code to generate ρ-labelings on rCm.

Blogs: On the Cutting Edge of the Next-generation Web

This article analyses a number of social and cultural aspects of the blog phenomenon with the methodological aid of a complexity model, the New Techno-social Environment (hereinafter also referred to by its Spanish acronym, NET, or Nuevo Entorno Tecnosocial) together with the socio-technical approach of the two blogologist authors. Both authors are researchers interested in the new reality of the Digital Universal Network (DUN). After a review of some basic definitions, the article moves on to highlight some key characteristics of an emerging blog culture and relates them to the properties of the NET. Then, after a brief practical parenthesis for people entering the blogosphere for the first time, we present some reflections on blogs as an evolution of virtual communities and on the changes experienced by the inhabitants of the infocity emerging from within the NET. The article concludes with a somewhat disturbing question; whether among these changes there might not be a gradual transformation of the structure and form of human intelligence.

Rational conchoid and offset constructions: algorithms and implementation

This paper is framed within the problem of analyzing the rationality of the components of two classical geometric constructions, namely the offset and the conchoid to an algebraic plane curve and, in the affirmative case, the actual computation of parametrizations. We recall some of the basic definitions and main properties on offsets (see [13]), and conchoids (see [15]) as well as the algorithms for parametrizing their rational components (see [1] and [16], respectively). Moreover, we implement the basic ideas creating two packages in the computer algebra system Maple to analyze the rationality of conchoids and offset curves, as well as the corresponding help pages. In addition, we present a brief atlas where the offset and conchoids of several algebraic plane curves are obtained, their rationality analyzed, and parametrizations are provided using the created packages.

Diseño del curso para operador "Coeficientes inherentes de reactividad" a plataforma e-Learning

Las centrales nucleares necesitan de personal altamente especializado y formado. Es por ello por lo que el sector de la formación especializada en centrales nucleares necesita incorporar los últimos avances en métodos formativos. Existe una gran cantidad de cursos de formación presenciales y es necesario transformar dichos cursos para utilizarlos con las nuevas tecnologías de la información. Para ello se necesitan equipos multidisciplinares, en los que se incluyen ingenieros, que deben identificar los objetivos formativos, competencias, contenidos y el control de calidad del propio curso. En este proyecto se utilizan técnicas de ingeniería del conocimiento como eje metodológico para transformar un curso de formación presencial en formación on-line a través de tecnologías de la información. En la actualidad, las nuevas tecnologías de la información y comunicación están en constante evolución. De esta forma se han sumergido en el mundo transformando la visión que teníamos de éste para dar lugar a nuevas oportunidades. Es por ello que este proyecto busca la unión entre el e-learning y el mundo empresarial. El objetivo es el diseño, en plataforma e-learning, de un curso técnico que instruya a operadores de sala de control de una central nuclear. El trabajo realizado en este proyecto ha sido, además de transformar un curso presencial en on-line, en obtener una metodología para que otros cursos se puedan transformar. Para conseguir este cometido, debemos preocuparnos tanto por el contenido de los cursos como por su gestión. Por este motivo, el proyecto comienza con definiciones básicas de terminología propia de e-learning. Continúa con la generación de una metodología que aplique la gestión de conocimiento para transformar cualquier curso presencial a esta plataforma. Definida la metodología, se aplicará para el diseño del curso específico de Coeficientes Inherentes de Reactividad. Finaliza con un estudio económico que dé viabilidad al proyecto y con la creación de un modelo económico que estime el precio para cualquier curso futuro. Abstract Nuclear power plants need highly specialized and trained personnel. Thus, nuclear power plant Specialized Training Sector requires the incorporation of the latest advances in training methods. A large array of face-to-face training courses exist and it has become necessary to transform said courses in order to apply them with the new information systems available. For this, multidisciplinary equipment is needed where the engineering workforce must identify educational objectives, competences and abilities, contents and quality control of the different courses. In this project, knowledge engineering techniques are employed as the methodological axis in order to transform a face-to-face training course into on-line training through the use of new information technologies. Nowadays, new information and communication technologies are in constant evolution. They have introduced themselves into our world, transforming our previous vision of them, leading to new opportunities. For this reason, the present Project seeks to unite the use of e-learning and the Business and Corporate world. The main objective is the design, in an e-learning platform, of a technical course that will train nuclear power plant control-room operators. The work carried out in this Project has been, in addition to the transformation of a face-to-face course into an online one, the obtainment of a methodology to employ in the future transformation of other courses. In order to achieve this mission, our interest must focus on the content as well as on the management of the various courses. Hence, the Project starts with basic definitions of e-learning terminology. Next, a methodology that applies knowledge management for the transformation of any face-to-face course into e-learning has been generated. Once this methodology is defined, it has been applied for the design process of the Inherent Coefficients of Reactivity course. Finally, an economic study has been developed in order to determine the viability of the Project and an economic model has been created to estimate the price of any given course