Anelastic Approximation as a Singular Limit of the Compressible Navier–Stokes System

Considering compressible Navier–Stokes system in a slab geometry in the regime when both Mach and Froude numbers vanish at the same rate, we study the behavior of corresponding weak solutions, that are known to exist globally-in-time (for large data). We establish their convergence to a solution of the so-called anelastic approximation when the limit flow is stratified, i.e., the limit density depends effectively on the vertical coordinate.     

Study of blood collection and sample preparation for analysis of vitamin D and its metabolites by liquid chromatography–tandem mass spectrometry

The analysis of vitamin D status, with special emphasis on 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D, is gaining interest in clinical studies due to the classical and non-classical effects attributed to this prohormone. In this research, the influence of the two steps preceding determination (viz. sample collection and preparation) on the quantitative analysis of vitamin D and its more important metabolites has been studied. Two preparation approaches, deproteination and solid-phase extraction (SPE), have been evaluated in terms of sensitivity to delimit their application, thus establishing that detection of 1,25-dihydroxyvitamin D cannot be addressed by protein precipitation. Concerning sample collection, serum and plasma reported high accuracy (above 83.3%) for vitamin D and metabolites, while precision, expressed as relative standard deviation, was below 12.9% for all analytes in both samples. Statistical analysis revealed that serum and plasma provided similar physiological levels for vitamin D₃, 24,25-dihydroxyvitamin D₃ and 25-hydroxyvitamin D₃, while significantly different levels were obtained for 1,25-dihydroxyvitamin D₃, always higher in plasma than in serum. Sample collection and treatment have proved to be significant in the analysis of vitamin D and its relevant metabolites.     

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Summary of ISO/TC 201 standard: ISO 19668—Surface chemical analysis—X‐ray photoelectron spectroscopy—Estimating and reporting detection limits for elements in homogeneous materials

This International Standard specifies a procedure by which elemental detection limits in X‐ray photoelectron spectroscopy (XPS) can be estimated from data for a particular sample in common analytical situations and reported. This document is applicable to homogeneous materials and is not applicable if the depth distribution of elements is inhomogeneous within the information depth of the technique.     

Simplicial Homotopical Algebra and Satellites

We study here a notion of simplicial satellites, as a first step towards a characterisation of simplicial derived functors, a problem unsolved since the latter were introduced.The problem comes from the fact that, in contrast with the abelian case, simplicial derived functors do not produce by themselves an exact sequence. Our solution consists in extending them to commutative k-cubes, for all k, forming thus an exact system of functors universal within the connected ones; or, in other words, a system of simplicial satellites. The tool we develop here for this extension is the homotopy kernel of a commutative k-dimensional cubic diagram, generalising the homotopy kernel of a map; its 2-dimensional version has already been proved essential in other homotopical topics.     

Determination of the elemental contents in stream sediments collected from Cheongju city by instrumental neutron activation analysis

Sediment samples were collected from seven locations of the MeeHo stream in Cheongju city, strained out by a sieve, dried by an oven and pulverized by an agate mortar. Instrumental neutron activation analysis (INAA) was applied for the determination of the elemental contents in the sediment samples by using the NAA #1 and #2 irradiation holes of the HANARO research reactor and HPGe gamma-ray spectrometers. Twenty-five elements were determined by a relative method with NIST SRM 2711-Montan Soil and the ranges of the elemental contents for the seven locations were identified. The contamination levels for elements such as As, Ba, Cr, Mn, Fe and Zn were compared with the guidelines of USEPA. The detection limits and combined uncertainties for the hazardous elements such as As, Ba, Cr, Mn, Sb, V and Zn were estimated under the given analytical conditions.     

Universal connections in Fréchet principal bundles

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector space, we endow the bundle J ¹ P of 1-jets of the sections of a Fréchet principal bundle P with a connection form by means of which we may “reproduce” every connection of P.      

Radiative Transport in a Periodic Structure

We derive radiative transport equations for solutions of a Schrödinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, and the scattering part by the random fluctuations.     

Loss of Invisibility in Metamaterials under Thermal Fluctuation Induced Radiation

Metamaterials have been extensively investigated for the development of invisibility cloaks; however, the role of nonequilibrium thermal fluctuations in the operation of metamaterial‐based cloaking remains an unexplored avenue. Here, an analytical study on nonequilibrium thermal fluctuations induced charges and currents in metamaterials which generate electromagnetic modes is presented. It is argued that thermally induced charges in metamaterials cannot remain shielded from incoming electromagnetic radiation and excitation of such charges, by incoming electromagnetic waves, can enhance specific modes, whose radiation limits the invisibility effects associated with metamaterial‐based cloaking. The analysis leads to the conclusion that thermodynamic equilibrium is an essential condition of the invisibility of metamaterial‐based cloaking.     

Universality limits for random matrices and de Branges spaces of entire functions

We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case. In particular, under mild conditions on a measure with compact support, we show that each possible universality limit is the reproducing kernel of a de Branges space of entire functions that equals a classical Paley-Wiener space. We also show that any such reproducing kernel, suitably dilated, may arise as a universality limit for sequences of measures on [−1,1].