On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

The effect of sublethal concentration of DimilinR (TH6040) on the larval development of the mud-crab Rhithropanopeus harrisii (Gould)

Sublethal DimilinR (insecticide) concentration significantly decreased the percentage survival of larval R. harrisii . This decrease was marked at low salinities, when it may have become toxic. This was true for both 25 and 30 C. Duration of larval development did not seem to be affected by sublethal DimilinR concentrations even in extremely low or high salinities. High temperature, however, shortened the time of development. No anatomical abnormality was observed. These findings are only tentative as more replicates of the experiments are needed before definite conclusions can be reached. It will be desirable to work with more salinity-temperature combinations to get a complete picture of sublethal effects under different environmental conditions.

Novel equation to determine the hepatic triglyceride concentration in humans by MRI: diagnosis and monitoring of NAFLD in obese patients before and after bariatric surgery

Background: Non-alcoholic fatty liver disease (NAFLD) is caused by abnormal accumulation of lipids within liver cells. Its prevalence is increasing in developed countries in association with obesity, and it represents a risk factor for non-alcoholic steatohepatitis (NASH), cirrhosis and hepatocellular carcinoma. Since NAFLD is usually asymptomatic at diagnosis, new non-invasive approaches are needed to determine the hepatic lipid content in terms of diagnosis, treatment and control of disease progression. Here, we investigated the potential of magnetic resonance imaging (MRI) to quantitate and monitor the hepatic triglyceride concentration in humans. Methods: A prospective study of diagnostic accuracy was conducted among 129 consecutive adult patients (97 obesity and 32 non-obese) to compare multi-echo MRI fat fraction, grade of steatosis estimated by histopathology, and biochemical measurement of hepatic triglyceride concentration (that is, Folch value). Results: MRI fat fraction positively correlates with the grade of steatosis estimated on a 0 to 3 scale by histopathology. However, this correlation value was stronger when MRI fat fraction was linked to the Folch value, resulting in a novel equation to predict the hepatic triglyceride concentration (mg of triglycerides/g of liver tissue = 5.082 + (432.104 * multi-echo MRI fat fraction)). Validation of this formula in 31 additional patients (24 obese and 7 controls) resulted in robust correlation between the measured and estimated Folch values. Multivariate analysis showed that none of the variables investigated improves the Folch prediction capacity of the equation. Obese patients show increased steatosis compared to controls using MRI fat fraction and Folch value. Bariatric surgery improved MRI fat fraction values and the Folch value estimated in obese patients one year after surgery. Conclusions: Multi-echo MRI is an accurate approach to determine the hepatic lipid concentration by using our novel equation, representing an economic non-invasive method to diagnose and monitor steatosis in humans.

Spectroscopic properties of fluorophosphate glass with high Er(3+)supercript stop concentration

Fluorophosphate glass with 4 mol.% ErF3 content was prepared. The different scanning calorimetry was conducted. Raman spectrum, infrared transmission spectrum, absorption spectrum were measured. Fluorescence spectrum and lifetime of emission around 1.53 mu m were measured under 970 nm laser diode excitation. The metaphosphate content in the composition is limited, but the maximum phonon energy of glass amounts to 1290 cm- 1, and is comparatively high. The full width at half maximum is about 56 nm, and is wider than for most of the materials investigated. The measured lifetime of I-4(13/2) -> I-4(15/2) transition, contributed by the high phonon energy, inefficient interaction of Er3+ ions, and low water content, amounts to no less than 7.36 ms though the Er3+ concentration is high. This work might provide useful information for the development of compact optical devices.