Integrals involving Euler-Bernoulli flexure and Saint-Venant torsion eigenfunctions

Tables of the integral ∝₀^LX_i(x)θ_j(x) dx where X_i(x) and θ_j(x) are Euler-Bernoulli and Saint-Venant eigenfunctions respectively are presented for 1?i, j?5 for beams with combinations of clamped, pinned and free ends. These integrals arise in application of the Rayleigh-Ritz and Ritz-Galerkin methods to free vibration and dynamic stability problems involving coupled torsion and bending.     

An Objective Prior from a Scoring Rule

In this paper, we introduce a novel objective prior distribution levering on the connections between information, divergence and scoring rules. In particular, we do so from the starting point of convex functions representing information in density functions. This provides a natural route to proper local scoring rules using Bregman divergence. Specifically, we determine the prior which solves setting the score function to be a constant. Although in itself this provides motivation for an objective prior, the prior also minimizes a corresponding information criterion.     

High spatial and angular resolution diffusion-weighted imaging reveals forniceal damage related to memory impairment

Introduction

Diffusion tensor imaging (DTI) measures in patients with multiple sclerosis (MS), particularly those measures associated with a specific white matter pathway, have consistently shown correlations with function. This study sought to investigate correlations between DTI measures in the fornix and common cognitive deficits in MS patients, including episodic memory, working memory and attention.

Materials and Methods

Patients with MS and group age- and sex-matched controls underwent high-resolution diffusion scanning (1-mm isotropic voxels) and cognitive testing. Manually drawn forniceal regions of interest were applied to individual maps of tensor-derived measures, and mean values of transverse diffusivity (TD), mean diffusivity (MD), longitudinal diffusivity (LD) and fractional anisotropy (FA) were calculated.

Results

In 40 patients with MS [mean age±S.D.= 42.55±9.1 years; Expanded Disability Status Scale (EDSS)=2.0±1.2; Multiple Sclerosis Functional Composite (MSFC) score=0.38±0.46] and 20 healthy controls (mean age±S.D.= 41.35±9.7 years; EDSS=0.0±0; MSFC score=0.74±0.24), we found that FA, MD and TD values in the fornix were significantly different between groups (P< .03), and patient performance on the Brief Visuospatial Memory Test-Revised (BVMT-R) was correlated with DTI measures (P< .03).

Discussion

These results are consistent with findings of axonal degeneration in MS and support the use of DTI as an indicator of disease progression.     

Fluorinated Eu‐Doped SnO2 Nanostructures with Simultaneous Phase and Shape Control and Improved Photoluminescence

Fluorinated Eu‐doped SnO₂ nanostructures with tunable morphology (shuttle‐like and ring‐like) are prepared by a hydrothermal method, using NaF as the morphology controlling agent. X‐ray diffraction, field‐emission scanning electron microscopy, high‐resolution transmission electron microscopy, X‐ray photoelectron spectroscopy, and energy dispersive spectroscopy are used to characterize their phase, shape, lattice structure, composition, and element distribution. The data suggest that Eu³⁺ ions are uniformly embedded into SnO₂ nanocrystallites either through substitution of Sn⁴⁺ ions or through formation of Eu‐F bonds, allowing for high‐level Eu³⁺ doping. Photoluminescence features such as transition intensity ratios and Stark splitting indicate diverse localization of Eu³⁺ ions in the SnO₂ nanoparticles, either in the crystalline lattice or in the grain boundaries. Due to formation of Eu‐F and Sn‐F bonds, the fluorinated surface of SnO₂ nanocrystallites efficiently inhibits the hydroxyl quenching effect, which accounts for their improved photoluminescence intensity.     

High P–T Brillouin scattering study of H2O melting to 26 GPa

The properties of solid and liquid phases of H₂O at high pressure and temperature remain an active area of research. In this study, Brillouin spectroscopy has been used to determine the temperature dependence of sound velocities in H₂O as a function of pressure up to 26 GPa through the phase field of ice VII and into the liquid to a maximum temperature of 1200 K. The Brillouin shift of the quasi-longitudinal acoustic mode moves to lower frequencies upon melting at each pressure. As a test of the method, measurements of the melting of Ar by Brillouin scattering at several pressures show a similar behavior for the acoustic mode, and measured melting points are consistent with previous results. The results of H₂O melting are consistent with previously reported melting curves below 20 GPa. The data at higher pressure indicate that ice melts at a higher temperature than a number of previous studies have indicated.     

High pressure X-ray diffraction experiments on NpS and PUS up to 60 GPa

Abstract

Neptunium and plutonium monosulfides were studied under high pressure up to ～60 GPa using a diamond anvil cell in an energy dispersive X-ray diffraction facility. The compounds, of cubic rock salt structure type at ambient pressure, do not show any crystallographic phase transition in the domain of investigation. From the pressure-volume relationship, we determined bulk moduli of 92 and 120 GPa with pressure derivatives of 4.6 and 4.1 for NpS and PUS respectively.     

Melting,freezing and other peculiarities in small systems

The theory of solid-liquid phase changes in small systems implies that such systems may—but need not—exhibit sharp but unequal freezing and melting temperatures. The origin of this conclusion is reviewed and its implications for the theory of first-order phase transitions in bulk matter are discussed. The logical separation is made of the two temperatures as limits of stable existence, each of its own ‘phase’; and the convergence, with increasing size of cluster, of the observable coexistence to a sharp transition temperature is discussed. The equilibrium ratios of concentrations for such a coexistence are discontinuous functions of temperature at the limits of stability. The possibility of observing coexisting forms in equilibrium depends on there being a time scale separability, who validity lies outside the realm of thermodynamics. It is conjectured that spinodals are the loci of the same kind of locally stable states responsible for coexisting solid and liquid forms of clusters, and that the limits of spinodals are the points of discontinuity in the equilibrium concentration ratios, the chemical ‘equilibrium constants’.     

Partial order complementation graphs

Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos _n consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos _n . In particular, we show:

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.