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.

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).

Marine and transitional Middle/Upper Eocenen units of the Southeastern Pyrenean Foreland Basin (NE Spain)

The stratigraphic basis of this work has allowed the use of larger foraminifers in the biostratigraphic characterisation of the new Shallow Benthic Zones (SBZ). This part of the volume presents a description of the sedimentary cycles formed by the transgressive-regressive systems of the Lutetian and Bartonian in the southeastern sector of the Ebro Foreland Basin. Concerning the Lutetian deposits studied in the Amer-Vic and Empordà areas, four sedimentary cycles have been characterised. The first and second are found within the Tavertet/Girona Limestone Formation (Reguant, 1967; Pallí, 1972), while the third and fourth cycles cover the Coll de Malla Marl Formation (Clavell et al., 1970), the Bracons Formation (Gich, 1969, 1972), the Banyoles Marl Formation (Almela and Ríos, 1943), and the Bellmunt Formation (Gich, 1969, 1972). In the Bartonian deposits studied in the Igualada area, two transgressive-regressive sedimentary cycles have been characterised in the Collbàs Formation (Ferrer, 1971), the Igualada Formation (Ferrer, 1971), and the Tossa Formation (Ferrer, 1971). The Shallow Benthic Zones (SBZs) recognised within the Lutetian are the following: SBZ 13, from the Early Lutetian, in the transgressive system of the first cycle; SBZ 14, from the Middle Lutetian, in the second cycle and the lower part of the transgressive system of the third cycle; SBZ 15, from the Middle Lutetian, in the remaining parts of the third system; SBZ 16, from the Late Lutetian, throughout the fourth cycle. The association of larger foraminifers in the first and second cycles of the Bartonian in the Igualada area has been used as the basis for the definition of SBZs 17 and 18 recognised in the Bartonian of the western Tethys.

Marine and transitional Middle/Upper Eocenen units of the Southeastern Pyrenean Foreland Basin (NE Spain)

The stratigraphic basis of this work has allowed the use of larger foraminifers in the biostratigraphic characterisation of the new Shallow Benthic Zones (SBZ). This part of the volume presents a description of the sedimentary cycles formed by the transgressive-regressive systems of the Lutetian and Bartonian in the southeastern sector of the Ebro Foreland Basin. Concerning the Lutetian deposits studied in the Amer-Vic and Empordà areas, four sedimentary cycles have been characterised. The first and second are found within the Tavertet/Girona Limestone Formation (Reguant, 1967; Pallí, 1972), while the third and fourth cycles cover the Coll de Malla Marl Formation (Clavell et al., 1970), the Bracons Formation (Gich, 1969, 1972), the Banyoles Marl Formation (Almela and Ríos, 1943), and the Bellmunt Formation (Gich, 1969, 1972). In the Bartonian deposits studied in the Igualada area, two transgressive-regressive sedimentary cycles have been characterised in the Collbàs Formation (Ferrer, 1971), the Igualada Formation (Ferrer, 1971), and the Tossa Formation (Ferrer, 1971). The Shallow Benthic Zones (SBZs) recognised within the Lutetian are the following: SBZ 13, from the Early Lutetian, in the transgressive system of the first cycle; SBZ 14, from the Middle Lutetian, in the second cycle and the lower part of the transgressive system of the third cycle; SBZ 15, from the Middle Lutetian, in the remaining parts of the third system; SBZ 16, from the Late Lutetian, throughout the fourth cycle. The association of larger foraminifers in the first and second cycles of the Bartonian in the Igualada area has been used as the basis for the definition of SBZs 17 and 18 recognised in the Bartonian of the western Tethys.

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.

Trans-equatorial migration and mixing in the wintering areas of a pelagic seabird

Despite increasing interest in long-distance migration, the wintering areas, migration corridors, and population mix in winter quarters of most pelagic marine predators are unknown. Here, we present the first study tracking migration movements of shearwaters through the non-breeding period. We used geolocators (global location sensing [GLS] units based on ambient light levels) to track 22 Cory's shearwaters (Calonectris diomedea) breeding in three different areas. Most birds wintered in one or more of three relatively small areas, all clearly associated with major coastal upwelling systems of the tropical and south Atlantic. Trans-equatorial movements were dominated by prevailing trade winds and westerlies, while calm, oligotrophic areas were avoided. Breeding populations clearly differed in their preference amongst the three major wintering areas, but showed substantial mixing. This illustrates the exceptional value of GLS, not only for determining and describing the influence of oceanographic features on migration patterns, but also for assessing population mix in winter quarters. This knowledge is essential to understanding the impacts of population-level threats, such as longlining, offshore windfarms, and oil spills on multiple breeding sites, and will be critical in devising conservation policies that guarantee the sustainable exploitation of the oceans.