Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

On stability of solutions to systems of convex inequalities

"Vegeu el resum a l'inici del document del fitxer adjunt."

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Quantitative analysis of image factors in a cultural heritage tourist destination

The tourism consumer’s purchase decision process is, to a great extent, conditioned by the image the tourist has of the different destinations that make up his or her choice set. In a highly competitive international tourist market, those responsible for destinations’ promotion and development policies seek differentiation strategies so that they may position the destinations in the most suitable market segments for their product in order to improve their attractiveness to visitors and increase or consolidate the economic benefits that tourism activity generates in their territory. To this end, the main objective we set ourselves in this paper is the empirical analysis of the factors that determine the image formation of Tarragona city as a cultural heritage destination. Without a doubt, UNESCO’s declaration of Tarragona’s artistic and monumental legacies as World Heritage site in the year 2000 meant important international recognition of the quality of the cultural and patrimonial elements offered by the city to the visitors who choose it as a tourist destination. It also represents a strategic opportunity to boost the city’s promotion of tourism and its consolidation as a unique destination given its cultural and patrimonial characteristics. Our work is based on the use of structured and unstructured techniques to identify the factors that determine Tarragona’s tourist destination image and that have a decisive influence on visitors’ process of choice of destination. In addition to being able to ascertain Tarragona’s global tourist image, we consider that the heterogeneity of its visitors requires a more detailed study that enables us to segment visitor typology. We consider that the information provided by these results may prove of great interest to those responsible for local tourism policy, both when designing products and when promoting the destination.

Hereditary completeness for systems of exponentials and reproducing kernels

Vegeu el resum a l'inici del document del fitxer adjunt.

New insights on the crystalline forms in binary systems of n-alkanes: Characterization of the solid ordered phases in the phase diagram tricosane + pentacosane

X-ray diffraction analyses of the pure components n-tricosane and n-pentacosane and of their binary mixed samples have enabled us to characterize the crystalline phases observed at low temperature. On the contrary to what was announced in literature on the structural behavior of mixed samples in odd-odd binary systems with D n = 2, the three domains are not all orthorhombic. This work has enabled us to show that two of the domains are, in fact, monoclinic, (Aa, Z = 4) and the other one is orthorhombic (Pca21, Z = 4). The conclusions drawn in this work can be easily transposed to other binary systems of n-alkanes.

Interaccion among systems of finite size in predictive relativistic mechanics I. General framework

We derive a Hamiltonian formulation for the three-dimensional formalism of predictive relativistic mechanics. This Hamiltonian structure is used to derive a set of dynamical equations describing the interaction among systems in perturbation theory.

Interaccion among systems of finite size in predictive relativistic mechanics -II. Electromagnetic and gravitational interactions

We explicitly construct a closed system of differential equations describing the electromagnetic and gravitational interactions among bodies to first order in the coupling constants, retaining terms up to order c-2. The Breit and Barker and O'Connell Hamiltonians are recovered by means of a coordinate transformation. The method used throws light on the meaning of these coordinates.

Interactions among systems of finite size en predictive relativistic mechanics III. Short-range interaction and second-order terms

We compute up to and including all the c-2 terms in the dynamical equations for extended bodies interacting through electromagnetic, gravitational, or short-range fields. We show that these equations can be reduced to those of point particles with intrinsic angular momentum assuming spherical symmetry.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

Kumar's algorithm for solving Toeplitz systems of equations over finite fields

Adaptació de l'algorisme de Kumar per resoldre sistemes d'equacions amb matrius de Toeplitz sobre els reals a cossos finits en un temps 0 (n log n).

Design and optimization of selfnanoemulsifying drug delivery systems for enhanced dissolution of gemfibrozil

Self-nanoemulsifying drug delivery systems of gemfibrozil were developed under Quality by Design approach for improvement of dissolution and oral absorption. Preliminary screening was performed to select proper components combination. BoxBehnken experimental design was employed as statistical tool to optimize the formulation variables, X1 (Cremophor® EL), X2 (Capmul® MCM-C8), and X3 (lemon essential oil). Systems were assessed for visual characteristics (emulsification efficacy), turbidity, droplet size, polydispersity index and drug release. Different pH media were also assayed for optimization. Following optimization, the values of formulation components (X1, X2, and X3) were 32.43%, 29.73% and 21.62%, respectively (16.22% of gemfibrozil). Transmission electron microscopy demonstrated spherical droplet morphology. SNEEDS release study was compared to commercial tablets. Optimized SNEDDS formulation of gemfibrozil showed a significant increase in dissolution rate compared to conventional tablets. Both formulations followed Weibull mathematical model release with a significant difference in td parameter in favor of the SNEDDS. Equally amodelistic parameters were calculated being the dissolution efficiency significantly higher for SNEDDS, confirming that the developed SNEDDS formulation was superior to commercial formulation with respect to in vitro dissolution profile. This paper provides an overview of the SNEDDS of the gemfibrozil as a promising alternative to improve oral absorption.

Phase mask selection in wavefront coding systems: an adaptive approach

A method for optimizing the strength of a parametric phase mask for a wavefront coding imaging system is presented. The method is based on an optimization process that minimizes a proposed merit function. The goal is to achieve modulation transfer function invariance while quantitatively maintaining nal image delity. A parametric lter that copes with the noise present in the captured images is used to obtain the nal images, and this lter is optimized. The whole process results in optimum phase mask strength and optimal parameters for the restoration lter. The results for a particular optical system are presented and tested experimentally in the labo- ratory. The experimental results show good agreement with the simulations, indicating that the procedure is useful.

Calculation of the variance in surveys of the economic climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated. As in any survey conducted on a sample the question of the measurement of the sample error of the results has to be addressed, since the error influences both the reliability of the results and the calculation of the sample size adequate for a desired confidence interval. The results presented here are based on data from the Survey of the Business Climate (Encuesta de Clima Empresarial) developed through the collaboration of the Statistical Institute of Catalonia (Institut d’Estadística de Catalunya) with the Chambers of Commerce (Cámaras de Comercio) of Sabadell and Terrassa.