On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects

For a topological vector space (X, τ ), we consider the family LCT (X, τ ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ . We prove that for an infinite-dimensional reflexive Banach space (X, τ ), the cardinality of LCT (X, τ ) is at least c.

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

Modificación de las propiedades de matrices cementantes mediante la adición de nanopartículas de sílice

En la presente investigación, se evaluó el efecto de adicionar nanopartículas de sílice a dos matrices cementes buscando establecer su influencia en las propiedades finales de dichos materiales. Para llevar a cabo esta evaluación, se adicionaron las nanopartículas en dosificaciones desde 0.30% - 5.0% en peso, con la finalidad de determinar la dosificación a la cual se obtienen los mejores resultados. Una de las conclusiones obtenidas de la presente investigación señala que al utilizar este tipo de materiales, el mayor reto a superar, es la correcta dispersión de las nanopartículas en las matrices cementantes, ya que de no asegurar dicha dispersión y debido a la alta energía superficial que poseen las nanopartículas, se presenta una tendencia natural a aglomerarse conformando así materiales de tamaños muy superiores a los que presentan en su estado original, perdiendo así la ventaja de su uso. Para prevenir este efecto y como resultado de la primera etapa de esta investigación, se propuso un método de mezclado en el cual se utilizó como dispersante un aditivo superplastificante (en adelante llamado SP) de base policarboxilato de calcio en dosificaciones de 0.5% en peso que se adicionó a ambas matrices cementantes. Los resultados obtenidos sugieren que algunas propiedades tales como la resistencia mecánica a la compresión, la resistencia a la flexión y sobre todo, la resistencia al ataque químico por sulfatos, se ven mejoradas mediante la adición de nanopartículas de sílice. Dicha mejoría se observó tanto en la matriz de cemento Portland como en la matriz de cemento sulfoaluminoso. Los resultados finales de la investigación mostraron que la resistencia mecánica a la compresión para un cemento Portland ordinario se mejoró hasta en un 40% a edad de 24 h cuando se adicionaron las nanopartículas en porcentaje de 0.50% en peso, sin embargo, los resultados al resto de las edades no presentaron mejoría. Para la matriz de cemento sulfoaluminoso (en adelante CSA), los mejores resultados se obtuvieron también con la dosificación de 0.50% en peso con relación al cemento, sin embargo, la mejoría no fue de la misma magnitud a la obtenida con la matriz de cemento Portland. Por otro lado, la resistencia al ataque químico por sulfatos presentó una mejoría de hasta un 80% para la matriz de cemento sulfoaluminoso cuando se adicionaron las nanopartículas de sílice. Este resultado sugiere que la matriz con nanopartículas presenta una mayor densificación propiciando por ende, un menor grado de porosidad.

Approaches to Provisioning Network Topology of Virtual Machines in Cloud Systems

The current infrastructure as a service (IaaS) cloud systems, allow users to load their own virtual machines. However, most of these systems do not provide users with an automatic mechanism to load a network topology of virtual machines. In order to specify and implement the network topology, we use software switches and routers as network elements. Before running a group of virtual machines, the user needs to set up the system once to specify a network topology of virtual machines. Then, given the user’s request for running a specific topology, our system loads the appropriate virtual machines (VMs) and also runs separated VMs as software switches and routers. Furthermore, we have developed a manager that handles physical hardware failure situations. This system has been designed in order to allow users to use the system without knowing all the internal technical details.

Solution to reduce nonlinearity in LTE RoF system for an efficient das topology:a brief review

In this paper, a review on radio-over-fiber (RoF) technology is conducted to support the exploding growth of mobile broadband. An RoF system will provide a platform for distributed antenna system (DAS) as a fronthaul of long term evolution (LTE) technology. A higher splitting ratio from a macrocell is required to support large DAS topology, hence higher optical launch power (OLP) is the right approach. However, high OLP generates undesired nonlinearities, namely the stimulated Brillouin scattering (SBS). Three different aspects of solving the SBS process are covered in this paper, where the solutions ultimately provided an additional 4 dB link budget.

Diversity and Stability in Food Webs : Impacts of Non-Equilibrium Dynamics, Topology and Variation

With progressive climate change, the preservation of biodiversity is becoming increasingly important. Only if the gene pool is large enough and requirements of species are diverse, there will be species that can adapt to the changing circumstances. To maintain biodiversity, we must understand the consequences of the various strategies. Mathematical models of population dynamics could provide prognoses. However, a model that would reproduce and explain the mechanisms behind the diversity of species that we observe experimentally and in nature is still needed. A combination of theoretical models with detailed experiments is needed to test biological processes in models and compare predictions with outcomes in reality. In this thesis, several food webs are modeled and analyzed. Among others, models are formulated of laboratory experiments performed in the Zoological Institute of the University of Cologne. Numerical data of the simulations is in good agreement with the real experimental results. Via numerical simulations it can be demonstrated that few assumptions are necessary to reproduce in a model the sustained oscillations of the population size that experiments show. However, analysis indicates that species "thrown together by chance" are not very likely to survive together over long periods. Even larger food nets do not show significantly different outcomes and prove how extraordinary and complicated natural diversity is. In order to produce such a coexistence of randomly selected species—as the experiment does—models require additional information about biological processes or restrictions on the assumptions. Another explanation for the observed coexistence is a slow extinction that takes longer than the observation time. Simulated species survive a comparable period of time before they die out eventually. Interestingly, it can be stated that the same models allow the survival of several species in equilibrium and thus do not follow the so-called competitive exclusion principle. This state of equilibrium is more fragile, however, to changes in nutrient supply than the oscillating coexistence. Overall, the studies show, that having a diverse system means that population numbers are probably oscillating, and on the other hand oscillating population numbers stabilize a food web both against demographic noise as well as against changes of the habitat. Model predictions can certainly not be converted at their face value into policies for real ecosystems. But the stabilizing character of fluctuations should be considered in the regulations of animal populations.

Evaluación de la exposición laboral a sílice en empresas de diferentes sectores económicos en Colombia

Introducción: La sílice es un elemento de fácil aprovechamiento y por sus características fisicoquímicas ha sido ampliamente empleado en la industria como objetivo, materia prima o subproducto que genera silicosis en los trabajadores que han estado expuestos a polvo de sílice a través de los años y es una enfermedad que progresa incluso cuando la exposición cesa. La silicosis es conocida como una enfermedad de alta e histórica incidencia y prevalencia a nivel mundial, por lo que es necesario evaluar la exposición laboral a sílice (fracción respirable) en empresas pertenecientes a diferentes sectores económicos que están afiliadas una ARL en Colombia, para contribuir con información diagnóstica actualizada en diferentes regiones y en variadas actividades económicas. Objetivos: Evaluar la exposición laboral a sílice y el nivel de riesgo en empresas afiliadas a una ARL de acuerdo con su ubicación geográfica, actividad económica, área de trabajo, cargo y relacionar las medidas de control empleadas en cada empresa. Materiales y métodos: Se llevó a cabo un estudio de corte transversal sobre 239 mediciones de higiene industrial de 159 empresas de diferentes actividades través de la asociación de variables ocupacionales con las características de la exposición a sílice. Las variables cuantitativas fueron calculadas empleando medidas de tendencia central como media y mediana y medidas de dispersión como rango y desviación estándar con sus correspondientes coeficientes de variación. El nivel máximo permisible o TLV establecido de acuerdo con los parámetros señalados por la Conferencia Americana de Higienistas Industriales Gubernamentales (ACGIH en inglés) y empleado en este estudio para sílice cristalina, fue de 0,025 mg/m3. Resultados: Las actividades económicas que reportaron las mayores concentraciones corregidas a condiciones estándar de polvo de sílice fueron: la minería y actividades Extractivas con 6,340 mg/m3, el mantenimiento industrial, montajes electromecánicos y civiles con 1,312 mg/m3, la maquinaria, metalmecánica, electrodomésticos y equipos con 0,096 mg/m3 y la construcción con 0,702 mg/m3; Discusión: Se realizó un análisis segmentado en dos grupos A y B de acuerdo con el tiempo de medición, se encontró que para el índice de riesgo en ambos grupos indican una sobre-exposición de los trabajadores a niveles críticos, razón por la cual es necesario generar una estrategia de intervención que permita disminuir a tiempo las concentraciones de sílice en las áreas de trabajo y así reducir la exposición de los trabajadores.

Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles SrM of a Riemannian manifold (M,g) of dim ≥ 3, assuming different variable radius functions r and weighted Sasaki metrics induced by the conformal class of g. New examples are shown of manifolds with constant positive or with constant negative scalar curvature which are not Einstein. Recalling results on the associated almost complex structure I^G and symplectic structure ω^G on the manifold TM , generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds TM and SrM.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.