Remarks on some inequalities of A. M. Fink

Hyperbolic systems of conservation laws augumented with an entropy inequality are studied. It is shown that such systems can be written in a (quasilinear) skew-selfadjoint form. Centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered. Employing the above formulation in bounded regions under the nonsmooth regime as well, a local entropy decay estimate is also concluded. Examples of the shallow-water and the full gasdynamics equations are explicitly treated.     

On the Extended Reversed Meir Inequality

We establish a result which subsumes two versions of the extended reversed Meir inequality.     

Size distribution analysis of polymer latex systems by use of extrema in the angular scattering intensity

The angular position of the extrema of the vertically polarized scattering intensity has previously been utilized for a method of particle size analysis for systems of monodisperse, spherical, isotropic particles which conform to the Rayleigh-Gans-Debye theory. The consequences of a finite polydispersity, which is always present in real systems, was not assessed and the application of the method has resulted in erroneous characterization of some latex systems. This work is concerned with (1) reporting the effects of finite polydispersity on the method of analysis, (2) pointing out previous misuse of the method, and (3) introducing a method of analysis which is based on the position of the extrema but which also considers polydispersity and the exact Mie calculation. This method enables one to characterize a scattering system in terms of a modal diameter and a distribution-width parameter by utilizing prepared diagrams for a particular relative refractive index.     

Iterative methods for solving a poroelastic shell model of Naghdi's type

In this paper, we first formulate a linear quasi‐static poroelastic shell model of Naghdi's type. The model is given in three unknowns: displacement of the middle surface, infinitesimal rotation of the cross section of the shell, and the pressure π. The model has the structure of the quasi‐static Biot's system and can be seen as a system of the shell equation with pressure term as forcing and the parabolic type equation for the pressure with divergence of the filtration velocity as forcing term. On the basis of the ideas of the operator splitting methods, we formulate two sequences of approximate solutions, corresponding to ‘undrained split’ and ‘fixed stress split’ methods. We show that these sequences converge to the solution of the poroelastic shell model. Therefore, the iterations constitute two numerical methods for the model. Moreover, both methods are optimized in a certain sense producing schemes with smallest contraction coefficient and thus faster convergence rates. Also, these convergences imply existence of solutions for the model. Copyright © 2017 John Wiley & Sons, Ltd.     

Indoor radon and lung cancer: a case-control study

Lung-cancer risk to the general population from indoor radon remains controversial, although studies of radon exposure have established that radon decay products have been a cause of lung cancer among miners. For the case group of patients, suffering from lung cancer, and the control group distributions of the number of homes with high indoor levels of radon were compared with the log-normal distribution, the empirical frequency distribution of the control group obeyed the theoretical log-normal distribution. Using the ratio of frequencies of the case group to the control groups, or the relative frequencies, an association between the relative frequencies and indoor radon concentrations was found, and a positive correlation coefficient was obtained, thus enabling the rate of lung cancer to be estimated for certain indoor radon concentrations. The significant difference between the mean radon levels for the case sample and the control led to the conclusion that patients with lung cancer lived in homes with radon concentrations which were significantly higher than those of Osijek's inhabitants for the control sample.     

Evolution Model for Linearized Micropolar Plates by the Fourier Method

In this paper we justify a two-dimensional evolution and eigenvalue model for micropolar plates starting from three-dimensional linearly micropolar elasticity. A small parameter representing the thickness of the plate-like body is introduced in the problem. The asymptotics of the evolution and eigenvalue problems is then developed as this small parameter tends to zero. First the appropriate convergences of the eigenpairs of the three-dimensional problem to the eigenpairs of the two-dimensional eigenvalue problem for micropolar plates is shown. Then these convergences are used in the Fourier method to obtain the convergences of the solution of the three-dimensional evolution problem to the solution of the two-dimensional evolution plate model.      

Effects of Wine Components in Inflammatory Bowel Diseases

With the rising prevalence of Inflammatory bowel disease (IBD) worldwide, and the rising cost of treatment with novel biological drugs, there is an increasing interest in various diets and natural foods as a potential way to control/modulate IBD. As recent data indicates that diet can modify the metabolic responses essential for the resolution of inflammation, and as wine compounds have been shown to provide substantial anti-inflammatory effect, in this review we aimed to discuss the current evidence concerning the impact of biological compounds present in wine on IBD. A number of preclinical studies brought forth strong evidence on the mechanisms by which molecules in wine, such as resveratrol or piceatannol, provide their anti-inflammatory, anti-oxidative, anti-tumor, and microbiota-modulation effects. However, concerning the effects of alcohol, it is still unclear how the amount of ethanol ingested within the framework of moderate wine consumption (1–2 glasses a day) affects patients with IBD, as human studies regarding the effects of wine on patients with IBD are scarce. Nevertheless, available evidence justifies the conductance of large-scale RCT trials on human subjects that will finally elucidate whether wine can offer real benefits to the IBD population.     

A Sharp Multidimensional Bergh Type Inequality

A sharp multidimensional integral inequality for functions satisfying two quasi-mono-tonicity conditions is proved. This result generalizes Bergh's inequality valid for quasi-concave functions.