On the Initial Conditions and Solutions of the Semiclassical Einstein Equations in a Cosmological Scenario

In this paper we shall discuss the backreaction of a massive quantum scalar field on the curvature, the latter treated as a classical field. Furthermore, we shall deal with this problem in the realm of cosmological spacetimes by analyzing the Einstein equations in a semiclassical fashion. More precisely, we shall show that, at least on small intervals of time, solutions for this interacting system exist. This result will be achieved providing an iteration scheme and showing that the series, obtained starting from the massless solution, converges in the appropriate Banach space. The quantum states with good ultraviolet behavior (Hadamard property), used in order to obtain the backreaction, will be completely determined by their form on the initial surface if chosen to be lightlike. Furthermore, on small intervals of time, they do not influence the behavior of the exact solution. On large intervals of time the situation is more complicated but, if the spacetime is expanding, we shall show that the end-point of the evolution does not depend strongly on the quantum state, because, in this limit, the expectation values of the matter fields responsible for the backreaction do not depend on the particular homogeneous Hadamard state at all. Finally, we shall comment on the interpretation of the semiclassical Einstein equations for this kind of problems. Although the fluctuations of the expectation values of pointlike fields diverge, if the spacetime and the quantum state have a large spatial symmetry and if we consider the smeared fields on regions of large spatial volume, they tend to vanish. Assuming this point of view the semiclassical Einstein equations become more reliable.     

Sharp continuity results for the short-time Fourier transform and for localization operators

We completely characterize the boundedness on Wiener amalgam spaces of the short-time Fourier transform (STFT), and on both L ^p and Wiener amalgam spaces of a special class of pseudodifferential operators, called localization operators. Precisely, sufficient conditions for the STFT to be bounded on the Wiener amalgam spaces W(L ^p , L ^q ) are given and their sharpness is shown. Localization operators are treated similarly: using different techniques from those employed in the literature, we relax the known sufficient boundedness conditions for these operators to be bounded on L ^p spaces and prove the optimality of our results. Next, we exhibit sufficient and necessary conditions for such operators to be bounded on Wiener amalgam spaces.     

Hardy–Sobolev Type Inequalities with Sharp Constants in Carnot–Carathéodory Spaces

We prove a generalization with sharp constants of a classical inequality due to Hardy to Carnot groups of arbitrary step, or more general Carnot–Carathéodory spaces associated with a system of vector fields of Hörmander type. Under a suitable additional assumption (see Eq. 1.6 below) we are able to extend such result to the nonlinear case \(p\not= 2\). We also obtain a sharp inequality of Hardy–Sobolev type.     

Magnetic resonance diffusion-weighted imaging: quantitative evaluation of age-related changes in healthy liver parenchyma

The purpose of this study was to verify in healthy liver parenchyma the possible influence of age on DwI-related parameters: apparent diffusion coefficient (ADC), perfusion fraction (PF), diffusion and pseudodiffusion coefficient (D and D^?). Forty healthy adult volunteers (age range 26-86 years), divided into four age groups, were prospectively submitted to a breath-hold magnetic resonance diffusion imaging (MR-DwI) (two b values, 0-300 and 0-1000 s/mm²). A smaller cohort of 16 subjects underwent a free-breath multi-b acquisition (16 b values, 0-750 s/mm²). Quantitative analysis was performed by two observers with manually defined regions of interest, on the most homogeneous portion of the right liver lobe. Individual and group statistical analysis of data was performed: ANOVA to establish differences between groups and Pearson correlation coefficient to investigate the association between DwI parameters and age. The mean, S.D. and 95% limits of agreement of ADC values for each age-defined group are reported. ANOVA showed no significant differences between group means (P always >.05). No significant correlation between subjects' age and DwI parameters was established, both in breath-hold and free-breath acquisitions, on the whole range of adopted b values. Our study conducted on healthy liver parenchyma shows that there are no significant differences in ADC, PF, D and D^? of younger or older subjects.     

Influence of the counterion on the synthesis of ZnO mesocrystals under solvothermal conditions

Polymers and coordinating solvents have been shown to serve as templating agents to assist the precipitation of ZnO nanoparticles and address their morphology. In this work we show for the first time that a difference in the coordination strength between the polymer (poly‐N‐vinylpyrrolidone (PVP)) and the two Zn^II precursor salts (nitrate and acetate) is able to promote or suppress the formation of mesocrystalline structures and even more importantly to tune their three‐dimensional organization. On the basis of FTIR and ¹³C NMR spectroscopic studies, we propose that not only the polymer (PVP) but also the solvent (DMF) play a key role as directing agents.     

Tin Dioxide Sensing Layer Grown on Tubular Nanostructures by a Non‐Aqueous Atomic Layer Deposition Process

A new atomic layer deposition (ALD) process for nanocrystalline tin dioxide films is developed and applied for the coating of nanostructured materials. This approach, which is adapted from non‐hydrolytic sol‐gel chemistry, permits the deposition of SnO₂ at temperatures as low as 75 °C. It allows the coating of the inner and outer surface of multiwalled carbon nanotubes with a highly conformal film of controllable thickness. The ALD‐coated tubes are investigated as active components in gas‐sensor devices. Due to the formation of a p‐n heterojunction between the highly conductive support and the SnO₂ thin film an enhancement of the gas sensing response is observed.     

Porous Single Crystals of Calcite from Colloidal Crystal Templates: ACC Is Not Required for Nanoscale Templating

This article investigates the formation of nanostructured single crystals of calcite using direct, ion‐by‐ion precipitation methods and shows that single crystals with complex morphologies and curved surfaces can readily be formed using this technique. Calcite crystals with inverse opal and direct opal structures are prepared using templates of colloidal crystals and polystyrene reverse opals, respectively, and excellent replication of the template structures are achieved, including the formation of 200‐nm spheres of calcite in the direct opal structure. These highly porous crystals also display extremely regular, crystalline gross morphologies. The methodology is extremely versatile and challenges the preconception that nanostructured crystals cannot be prepared by simple diffusion of reagents into the template due to blocking of the channels. The results are also discussed in light of alternative templating methods using amorphous calcium carbonate (ACC) as a precursor phase and provide insight into the role of ACC in biological calcification processes.     

COMPLEXITY,MULTIRESOLUTION, NON-STATIONARITY AND ENTROPIC SCALING: TEEN BIRTH THERMODYNAMICS

This paper presents a statistical methodology for analyzing a complex phenomenon in which deterministic and scaling components are superimposed. Our approach is based on the wavelet multiresolution analysis combined with the scaling analysis of the entropy of a time series. The wavelet multiresolution analysis decomposes the signal in a scale-by-scale manner. The scale-by-scale decomposition generates smooth and detail curves that are evaluated and studied. A wavelet-based smoothing filtering is used to estimate the daily birth rate and conception rate during the year. The scaling analysis is based on the Diffusion Entropy Analysis (DEA). The joint use of the DEA and the wavelet multiresolution analysis allows: 1) the separation of the deterministic and, therefore, non-scaling component from the scaling component of the signal; 2) the determination of the stochastic information characterizing the teen birth phenomenon at each time scale. The daily data cover the number of births phenomenon at each time scale. The daily data cover the number of births to teens in Texas during the period 1964-1999.     

Investigating low-frequency dielectric properties of a composite using the distribution of relaxation times technique

The distribution of relaxation times approach, a less frequently employed dielectric data analysis technique, is utilized to better understand the relaxation characteristics of composites consisting of metal-coated, hollow glass spheres dispersed in a paraffin wax matrix. The dielectric properties of the composite samples are measured by means of impedance spectroscopy in the frequency range 0.1?mHz to 10?MHz. The application of a mixture law is not appropriate for the analysis of the frequency-dependent properties of the considered system on this broad frequency range. However, utilization of the distribution of relaxation times procedure to study the dielectric behaviour shows clear trends in the mixtures’ relaxation spectra. Relaxation processes of the paraffin wax and those specific to the composites are found from the extracted distribution of relaxation times spectra. The influence of the filler concentration, q, on the dielectric properties is examined; a relaxation with a narrow distribution at intermediate frequencies becomes broad with the addition of the filler. This relaxation, in the form of the low-frequency-dispersions (also known as constant phase angle) phenomenon, dominates the dielectric properties of the composites with high bead concentration, q>0.15. The variation in dielectric properties of individual samples whose bead concentrations q are nominally the same is discussed in terms of possible microstructural variations.