Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

The famous irreducibility criteria of Schönemann–Eisenstein and Dumas rely on information on the divisibility of the coefficients of a polynomial by a single prime number. In this paper, we will use some results and ideas of Dumas to provide several irreducibility criteria of Schönemann–Eisenstein–Dumas-type for polynomials with integer coefficients, criteria that are given by some divisibility conditions for their coefficients with respect to arbitrarily many prime numbers. A special attention will be paid to those irreducibility criteria that require information on the divisibility of the coefficients by two distinct prime numbers.     

FRACTIONAL 2D-STOCHASTIC CURRENTS

Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.     

Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators

We obtain continuous-time and discrete-time Lyapunov operator inequalities for the exponential stability of strongly continuous, one-parameter semigroups acting on Banach spaces. Thus we extend the classic result of Datko (1970) [2] from Hilbert spaces to Banach spaces.     

Asymptotic Theory for Fractional Regression Models via Malliavin Calculus

We study the asymptotic behavior as n→∞ of the sequence

Simultaneous PET–MRI in oncology: a solution looking for a problem?

With the recent development of integrated positron emission tomography–magnetic resonance imaging (PET–MRI) scanners, new possibilities for quantitative molecular imaging of cancer are realized. However, the practical advantages and potential clinical benefits of the ability to record PET and MRI data simultaneously must be balanced against the substantial costs and other requirements of such devices. In this review, we highlight several of the key areas where integrated PET–MRI measurements, obtained simultaneously, are anticipated to have a significant impact on clinical and/or research studies. These areas include the use of MR-based motion corrections and/or a priori anatomical information for improved reconstruction of PET data, improved arterial input function characterization for PET kinetic modeling, the use of dual-modality contrast agents, and patient comfort and practical convenience. For widespread acceptance, a compelling case could be made if the combination of quantitative MRI and specific PET biomarkers significantly improves our ability to assess tumor status and response to therapy, and some likely candidates are now emerging. We consider the relative advantages and disadvantages afforded by PET–MRI and summarize current opinions and evidence as to the likely value of PET–MRI in the management of cancer.     

Stein’s method for invariant measures of diffusions via Malliavin calculus

Given a random variable F$F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and any probability measure with a density function which is continuous, bounded, strictly positive on an interval in the real line and admits finite variance. The bounds are given in terms of the Malliavin derivative of F$F$. Our approach is based on the theory of Itô diffusions and the stochastic calculus of variations. Several examples are considered in order to illustrate our general results.     

Relativistic Bosons in Time-Harmonic Electric Fields

In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field and a static magnetic induction, both directed along the normal to the sample’s plane. The Klein–Gordon equation describing the relativistic bosons leads to a Mathieu’s type equation for the temporal part of the wave functions. It follows that, for the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic stationary amplitude behavior.     

On the bifurcations of the Lamé solutions in plane-strain elasticity

We consider the in-plane bifurcations experienced by the Lamé solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the Shapiro–Lopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.     

Dependence of adenine isolation efficiency on the chain length evidenced using paramagnetic particles and voltammetry measurements

The main aim of this work was to study the dependence of oligoadenine isolation efficiency on the chain length by using paramagnetic particles covered by homo-deoxythymidines ((dT)25) with subsequent detection by adsorptive transfer technique coupled with square wave voltammetry. For this purpose, the oligonucleotides of the length A5, A10, A15, A20, A25, A30, A35, A40 and poly(A) in various concentrations were chosen. We determined that the isolation efficiency defined as “isolated oligonucleotide concentration”/“given oligonucleotide concentration” was about 55% on average. Sequence A25 demonstrated the best binding onto microparticles surface.     

The effect of silicon substrate on thickness of SiO2 thin film analysed by spectral reflectometry and interferometry

Techniques of spectral reflectometry and interferometry are used for measuring small changes in thickness of SiO₂ thin film grown by thermal oxidation on different silicon substrates. A slightly dispersive Michelson interferometer with one of its mirrors replaced by a thin-film structure is used to measure the reflectance and interferometric phase of the thin-film structure at the same time. The experimental data are used to determine precisely the thickness of the SiO₂ thin film on silicon wafers of two crystallographic orientations and different dopant concentrations. We confirmed very good agreement between the experimental data and theory and revealed that the thin-film thickness, which varies with the type of silicon substrate, depends linearly on the wavelength at which minimum in the spectral reflectance occurs. Similar behaviour was revealed for the interferometric phase.