Vacuum Energy Density Fluctuations in Minkowski and Casimir States via Smeared Quantum Fields and Point Separation

We present calculations of the variance of fluctuations and of the mean of the energy momentum tensor of a massless scalar field for the Minkowski and Casimir vacua as a function of an intrinsic scale defined by a smeared field or by point separation. We point out that contrary to prior claims, the ratio of variance to mean-squared being of the order unity is not necessarily a good criterion for measuring the invalidity of semiclassical gravity. For the Casimir topology we obtain expressions for the variance to mean-squared ratio as a function of the intrinsic scale (defined by a smeared field) compared to the extrinsic scale (defined by the separation of the plates, or the periodicity of space). Our results make it possible to identify the spatial extent where negative energy density prevails which could be useful for studying quantum field effects in worm holes and baby universe, and for examining the design feasibility of real-life `time-machines'. For the Minkowski vacuum we find that the ratio of the variance to the mean-squared, calculated from the coincidence limit, is identical to the value of the Casimir case at the same limit for spatial point separation while identical to the value of a hot flat space result with a temporal point-separation. We analyze the origin of divergences in the fluctuations of the energy density and discuss choices in formulating a procedure for their removal, thus raising new questions into the uniqueness and even the very meaning of regularization of the energy momentum tensor for quantum fields in curved or even flat spacetimes when spacetime is viewed as having an extended structure.Comment: 41 pages, 2 figure

Sub-diffusion and population dynamics of water confined in soft environments

We have studied by Molecular Dynamics computer simulations the dynamics of water confined in ionic surfactants phases, ranging from well ordered lamellar structures to micelles at low and high water loading, respectively. We have analysed in depth the main dynamical features in terms of mean squared displacements and intermediate scattering functions, and found clear evidences of sub-diffusive behaviour. We have identified water molecules lying at the charged interface with the hydrophobic confining matrix as the main responsible for this unusual feature, and provided a comprehensive picture for dynamics based on a very precise analysis of life times at the interface. We conclude by providing, for the first time to our knowledge, a unique framework for rationalising the existence of important dynamical heterogeneities in fluids absorbed in soft confining environments

The Linear Combination of Kernels in the Estimation Of Cumulative Distribution Functions

The kernel distribution function estimator method is the most popular nonparametric method to estimate the cumulative distribution function F(x). In this investigation, we propose a new estimator for F(x) based on a linear combination of kernels. The mean integrated squared error, asymptotic mean integrated squared error and the asymptotically optimal bandwidth for the new estimator are derived. Also, based on the plug-in technique in density estimation, we propose a data based method to select the bandwidth for the new estimator. In addition, we evaluate the new estimator using simulations and real life data

Economic and Social Factors that Influence Life Expectancy and Infant Mortality

This paper investigates life expectancy and infant mortality rates in randomly selected countries from around the world. This study takes into consideration many economic and social factors that could potentially have an effect on life expectancy and infant mortality in different countries. Factors are modeled using a least-squared regression model and are determined as significant based on their probability factor. Results show both positive and negative effects depending on the economic and social factor

Negative religious coping styles predict greater depressive symptoms and less life satisfaction

The purpose of this study was to identify negative religious coping methods that have an association with depressive symptoms and life satisfaction among cancer patients. This study was based on Pargament’s (1997) framework of positive and negative religious coping styles that specify how an individual makes use of religion to understand and deal with stressors. The sample included 179 predominantly White, Christian, female patients with stage II through IV cancer. We used a cross-sectional design with self-report measures to examine punishing God reappraisal and spiritual discontent as they relate to depressive symptoms and satisfaction with life. We hypothesized that both negative religious coping styles would predict greater depressive symptoms and less life satisfaction. Controlling for sex, age, education level, and family income level, a standard multiple regression showed that both punishing God reappraisal and spiritual discontent predicted greater levels of depressive symptoms (R-squared = .19, p \u3c .001); however, only punishing God reappraisal predicted less life satisfaction (R- squared = .21, p \u3c .001). These findings suggest that some types of religious coping can have a negative association with well-being among cancer patients. Therapists, nurses, and clergy members who identify patients who use negative religious coping styles may offer additional support to these patients to enhance their well-being