Retrenching the Purse: Finite Exception Logs, and Validating the Small

The Mondex Electronic Purse is an outstanding example of industrial scale formal refinement, and was the first verification to achieve ITSEC level E6 certification. A formal abstract model and a formal concrete model were developed, and a formal refinement was hand-proved between them. Nevertheless, certain requirements issues were set beyond the scope of the formal development, or handled in an unnatural manner. The retrenchment Tower Pattern is used to address one such issue in detail: the finiteness of the purse log (which records unsuccessful transactions). A retrenchment is constructed from the lowest level model of the purse system to a model in which logs are finite, and is then lifted to create two refinement developments of the purse, working at different levels of detail, and connected via retrenchments, forming the tower. The tower development is appropriately validated, vindicating the design used

Cultural barriers in the moulding of prosocial attitudes among participants in economic life in Poland

Celem artykułu jest wskazanie na elementy szeroko pojętej kultury, które stanowić mogą różnego rodzaju utrudnienia i bariery w skutecznym kształtowaniu postaw prospołecznych wśród uczestników życia gospodarczego w Polsce. Autor wychodzi z założenia, że satysfakcjonujące kształcenie odpowiednich postaw obywatelskich – zarówno obecnych, jak i przyszłych studentów, kadr pracowniczych i menedżerskich, a nawet konsumentów i klientów – nie może być oderwane od kontekstu kulturowego. Innymi słowy, jeśli podejmowane działania edukacyjne przynieść mają pożądany rezultat, nie mogą abstrahować od dominujących w danym społeczeństwie wartości, norm, postaw czy wzorów zachowań. Należy przy tym zdawać sobie sprawę, że dokonywanie zmian w sferze kultury jest dość ograniczone i zawsze rozciągnięte w czasie. Artykuł podejmuje próbę wskazania na najbardziej charakterystyczne cechy polskiej mentalności, ugruntowane zwłaszcza w ostatnich dekadach, które stanowią uciążliwą spuściznę komunizmu. To wówczas wykształciły się antyspołeczne postawy egoizmu, prywaty, wyuczonej bierności, braku motywacji i inicjatywy. Autor referatu podkreśla, że zarówno jako społeczeństwo, jak i poszczególni jego członkowie nie do końca potrafiliśmy zerwać z tą spuścizną. Wydaje się zatem, że współczesne działania edukacyjne nie przyniosą w pełni zadowalających efektów póki nie pozbędziemy się tego zbędnego balastu.The aim of the article is to point to those elements of broadly understood culture that may constitute various obstacles and barriers to the effective development of prosocial attitudes among participants of Polish economic life. The author assumes that the satisfactory education of appropriate civic attitudes – among present and future students, staff and managers, and even consumers and customers – cannot be detached from the cultural context. In other words, if the educational activities are to produce the desired result, they cannot abstain from the v alues, norms, attitudes or behavioural patterns prevailing in a given society. It is important to realise that changes in the sphere of culture are quite limited, and always stretched out in time. The paper attempts to point to the most characteristic features of Polish mentality, grounded in particular in the last decades, that constitute a burdensome legacy of communism. It was then that the antisocial attitudes of selfishness, self-interest, learned passivity, and a lack of motivation or initiative emerged. The author of the paper emphasises that both as a society and its individual members, we have been unable to break free of this legacy. It seems therefore that modern educational activities will not produce satisfactory results until we get rid of this redundant ballast

Charge stripes due to electron correlations in the two-dimensional spinless Falicov-Kimball model

We calculate the restricted phase diagram for the Falicov-Kimball model on a two-dimensional square lattice. We consider the limit where the conduction electron density is equal to the localized electron density, which is the limit related to the S_z=0 states of the Hubbard model. After considering over 20,000 different candidate phases (with a unit cell of 16 sites or less) and their thermodynamic mixtures, we find only about 100 stable phases in the ground-state phase diagram. We analyze these phases to describe where stripe phases occur and relate these discoveries to the physics behind stripe formation in the Hubbard model.Comment: (34 pages, 9 figures, submitted to Journal of Statistical Physics to celebrate Elliott Lieb's 70th birthday

La capacitat analı́tica en problemes d’aproximació racional

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Albert Mas Blesa[en] This paper studies the relationship, depending on the compact set $K \subset \mathbb{C}$, between the family of continuous functions on $K, \mathcal{C}(K)$, the family of continuous functions on $K$ and analytics on $\overset{\circ}{K}, \mathcal{A}(K)$, the family of uniformly approximable functions on $K$ by rational functions with poles out on $K, \mathcal{R}(K)$, and the family of uniformly approximable functions on $K$ by polynomials, $\mathcal{P}(K)$. We will see that it is easy to characterise $K$ in order to achive $\mathcal{P}(K)=\mathcal{R}(K)$ or $\mathcal{A}(K)=\mathcal{C}(K)$, but it is more complicated to do the same in order to achieve $\mathcal{R}(K)=\mathcal{A}(K)$. In order to see all the possible relationships, we present some new concepts like the Hausdorff measure, content and dimension, the analytic capacity and the continuous analytic capacity. The main part of this essay is focused on the Vitushkin Theorem, which allows us to characterise the compacts $K$, such as $\mathcal{R}(K)=\mathcal{A}(K)$. we present a demostration scheme and the results obtained from it. In addition, we will also state the Inner Boundary Conjecture that provides us with the sufficient condition on $K$ to ensure that $\mathcal{R}(K)=\mathcal{A}(K)$

Local rigidity for actions of Kazhdan groups on non commutative LpL_p-spaces

Given a discrete group $\Gamma$, a finite factor $\mathcal N$ and a real number $p\in [1, +\infty)$ with $p\neq 2,$ we are concerned with the rigidity of actions of $\Gamma$ by linear isometries on the $L_p$-spaces $L_p(\mathcal N)$ associated to $\mathcal N$. More precisely, we show that, when $\Gamma$ and $\mathcal N$ have both Property (T) and under some natural ergodicity condition, such an action $\pi$ is locally rigid in the group $G$ of linear isometries of $L_p(\mathcal N)$, that is, every sufficiently small perturbation of $\pi$ is conjugate to $\pi$ under $G$. As a consequence, when $\Gamma$ is an ICC Kazhdan group, the action of $\Gamma$ on its von Neumann algebra ${\mathcal N}(\Gamma)$, given by conjugation, is locally rigid in the isometry group of $L_p({\mathcal N}(\Gamma)).$Comment: 20 page

El desarrollo moral en la infancia

El presente Trabajo Fin de Grado tiene como objeto dar una visión general acerca del desarrollo moral en la infancia y de todos los conceptos que éste incluye. Para ello, se ha realizado un marco teórico que nos permita entender qué es el desarrollo moral y qué conlleva. En la segunda parte del trabajo se ha realizado una investigación que nos ha permitido corroborar o replicar los datos obtenidos por el autor más importante en cuánto al desarrollo moral, Jean Piaget. Para ello, se han realizado varias entrevistas que nos han permitido contrastar nuestros resultados con los resultados de la investigación de dicho autor.Grado en Educación Infanti

Mathematics Is Physics

In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.Comment: 15 pages, LaTeX. Second prize winner in 2015 FQXi Essay Contest (see http://fqxi.org/community/forum/topic/2364

Dynamic aspects of retrenchments through temporal logic

Refinement is used as a way to verify an implementation with respect to a specification. States of related systems are linked through a so called gluing invariant which remains always true during the synchronous execution of both systems. Refinement is a sufficient condition for this property. Retrenchment is a generalization of refinement which relax the constraints between both systems. This paper proposes a temporal logic counterpart for some specific forms of retrenchment

Quantum Stability of (2+1)-Spacetimes with Non-Trivial Topology

Quantum fields are investigated in the (2+1)-open-universes with non-trivial topologies by the method of images. The universes are locally de Sitter spacetime and anti-de Sitter spacetime. In the present article we study spacetimes whose spatial topologies are a torus with a cusp and a sphere with three cusps as a step toward the more general case. A quantum energy momentum tensor is obtained by the point stripping method. Though the cusps are no singularities, the latter cusps cause the divergence of the quantum field. This suggests that only the latter cusps are quantum mechanically unstable. Of course at the singularity of the background spacetime the quantum field diverges. Also the possibility of the divergence of topological effect by a negative spatial curvature is discussed. Since the volume of the negatively curved space is larger than that of the flat space, one see so many images of a single source by the non-trivial topology. It is confirmed that this divergence does not appear in our models of topologies. The results will be applicable to the case of three dimensional multi black hole\cite{BR}.Comment: 17 pages, revtex, 3 uuencoded figures containe