Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.

Las transformaciones de la burocracia provincial: capacidades del Estado en la provincia de Córdoba. Transformations of provincial bureaucracy: State´s capacities in the province of Córdoba.

A partir de las políticas de descentralización llevadas adelante en Argentina desde la década de los ochenta, las provincias han adquirido desde entonces una importante serie de nuevas funciones lo cual las ha obligado a ampliar y diversificar sus estructuras burocráticas y administrativas. Lo que este proyecto busca abordar es un análisis de las transformaciones ocurridas durante los últimos veinte años en la organización burocrática del estado provincial en Córdoba. El proyecto pretende indagar dos aspectos de la organización burocrática: por un lado, el diseño organizacional institucional (leyes de Ministerios) y la división del trabajo que ello implica; y por otro lado, los principales procesos administrativos transversales que articulan funcionalmente las diferentes áreas de la burocracia provincial (administración financiera y recursos humanos). A partir de ello nos interesa poner en relación estas transformaciones con los cambios que va experimentando la agenda gubernamental. Suponemos, en este sentido, que los cambios organizacionales responden a cambios en dicha agenda y a la relación de fuerzas políticas que va implícita en la conformación de las mismas. De este modo, nuestra hipótesis plantea que los cambios organizaciones generados por la transformación de las agendas se manifiestan de forma más inmediata en la dimensión del diseño organizacional, mientras que los procesos administrativos transversales experimentan cambios más graduales y no necesariamente vinculados a las transformaciones de la primera dimensión. El objetivo general es analizar las transformaciones de la Administración Pública Provincial (APP) en la provincia de Córdoba, a través de dos dimensiones (el diseño de la organización burocrática y los procesos administrativos transversales), desde el retorno a la democracia (1983) a la actualidad. La investigación será realizada a la luz de posturas epistemológicas y metodológicas que en las ciencias sociales sustentan la triangulación de métodos. Recurriremos tanto a fuentes documentales y estadísticas para reconstruir el proceso de transformación de la APP, como a entrevistas semiestructuradas con actores claves para indagar sobre las dimensiones identificadas en el proyecto. Se encuadra en lo que metodológicamente se denomina "estudio de caso". La investigación permitirá fortalecer el estudio de la administración y las organizaciones públicas, lo que representa una tarea altamente significativa (y necesaria) para el mejoramiento del sector público y las necesidades de la ciudadanía. El impacto esperable es la explicitación y sistematización de las transformaciones del aparato burocrático, que puedan ser observadas, mejoradas y desarrolladas por el conjunto de las carteras ministeriales, y la confección de estrategias y tecnologías de gestión que permitan incrementar las capacidades de la administración pública provincial en la realización de las políticas y la resolución de los problemas sociales.

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.9 (1831)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.3 (1828)

The Philosophical magazine : or Annals of chemistry, mathematics, astronomy, natural history and general science.

2nd ser. : v.4 (1828)

Reine und mit einfachen Molekülen bedeckte (100)-Oberflächen von Natriumfluorid, Natriumchlorid und Rubidiumchlorid : Untersuchungen mittels Beugung langsamer Elektronen (LEED) und Fourier-Transformations-Infrarotspektroskopie (FTIRS)

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2013

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Chemical transformations of neolignans

Neolignans, generated by oxydative dimerization of propenylphenol and/or allylphenol, undergo further modifying steps. These biosynthetic reactions, confirmed in vitro, include Cope, retro-Claisen and Claisen rearrangements. Additionally acid catalysis effects convertions of bicyclo [3.2.1] octanoid neolignans into hydrobenzofuranoid neolignans, or inversely of hydrobenzofuranoid neolignans into bicyclo [3.2.1] octanoid neolignans, of hydrobenzofuranoid neolignans into futoenone type neolignans, of tetrahydrofuran neolignans into aryltetralin neolignans, as well as modifications by Friedel - Crafts reactions and the transformation of aryltetralin neolignans into arylindanones by pinacoline - pinacolone type rearrangement.