Compactness in Groups of Group-Valued Mappings

We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Frechet-Smulian and Ascoli-Arzela compactness criteria found in the literature

Regular measures of noncompactness and Ascoli-Arzela type compactness criteria in spaces of vector-valued functions

In this paper we estimate the Kuratowski and the Hausdorff measures of noncompactness of bounded subsets of spaces of vector-valued bounded functions and of vector-valued bounded differentiable functions. To this end, we use a quantitative characteristic modeled on a new equicontinuity-type concept and classical quantitative characteristics related to pointwise relative compactness. We obtain new regular measures of noncompactness in the spaces taken into consideration. The established inequalities reduce to precise formulas in some classes of subsets. We derive Ascoli-Arzela type compactness criteria

Rearrangement and Convergence in Spaces of Measurable Functions

We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to the set of rearrangements

Massless Interacting Scalar Fields in de Sitter space

We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrt\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\sqrt\lambda$ and in $1/N$.Comment: 8 pages. Summarized version of JHEP 09 (2016) 117 [arXiv:1606.03481]. Published in the Proceedings of the 19th International Seminar on High Energy Physics (QUARKS-2016

O(N)O(N) model in Euclidean de Sitter space: beyond the leading infrared approximation

We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant $\sqrt\lambda$ and in 1/N. We explicitly perform the calculation up to the next-to-next-to-leading order in $\sqrt\lambda$ and up to next-to-leading order in 1/N. The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.Comment: 31 pages, 5 figures. Minor changes. Published versio

Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions

We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $\lambda\phi^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.Comment: 32 pages, 4 figure

The Effects of Diethyldithiocarbamate (DDC) on the Astrocytic Cytoskeleton

The dithiocarbamates are a group of compounds that are used extensively in industry, agriculture and medicine. Exposure to these compounds has caused deleterious effects to both the central and peripheral nervous systems. Cultured rat hippocampal astroglia treated with 35 μg/ml diethyldithiocarbamate (DDC) in media were studied for alterations to the cytoskeleton. Examination by both immunohistochemistry and scanning electron microscopy revealed disruption of the cytoskeletal elements. This occurred in a progressive time-dependent manner. Electrophoretic patterns demonstrated two cytoskeletal protein alterations. The microtubular protein, β-tubulin, appeared to have an altered mobility while the major intermediate filament protein, glial fibrillary acidic protein (GF AP), was decreased. The cytoskeleton appears to be an important cellular target for injury by DDC exposure. This study has demonstrated that DDC induces alterations in the architecture of the cytoskeleton of astroglia and suggests that these changes involve microtubular and intermediate filament proteins

Effect of Particle Size and Starch Gelatinization on the Mechanical and Metallurgical Performance of Jarosite Plus Blast Furnace Sludge Self-Reducing Briquettes

Jarosite and blast furnace sludge (BFS) are two of the main wastes from hydrometallurgical zinc production and iron production by blast furnace, respectively. Jarosite is a hazardous material that can, however, be reused in the steel industry after the recovering of the iron contained within it through carbothermal reduction in which BFS is exploited as a reducing agent. Yet, both wastes have a powdery nature that makes it necessary to agglomerate them for industrial use. On the other hand, despite the advantages of producing a self-reducing product, the particle size of the starting powders and the level of gelatinization of the binder could play a crucial role on the mechanical and metallurgical performance and, consequently, on the industrial applicability of the briquettes. Accordingly, two powder particle sizes (very fine sand vs. coarse silt) and three degree of corn starch binder retrogradation (10%, 30% and non-gelatinized starch) were used to produce briquettes, and their influence was studied by experimental and statistical investigation. The results showed that gelatinization plays the main role on the mechanical properties of briquettes, while particle size affects both density and reduction behavior; in particular, although all the mixtures were able to recover iron at 950 °C the most optimal mixture were obtained by using a granulometry of 63–125 μm for jarosite and less than 63 μm for BFS, while the local maximum of mechanical performance was obtained for a 30% starch retrogradation level