Répartitio n simulta née de S( n) et $$ S( n+1)$$ S( n+1) da ns les progressio ns arithmétiques

If \(q\ge 2\) is an integer, we denote by \(S_q(n)\) the sum of the digits in base q of the positive integer n and by \(v_q(n)\) its q-adic valuation. The goal of this work is to study exponential sums of the form \(\displaystyle \sum \nolimits _{n\le x}\exp \big (2i\pi \big (\frac{l}{m} S_q(n)+\frac{k}{m'}S_q(n+1)+\theta n\big )\big )\) in order to prove some statistical properties of integers n for which \(S_q(n)\) and \(S_q(n+1)\) belong to given arithmetic progressions. This extends the results obtained by Gelfond in 1968 and those obtained by Mauduit–Sárközy in 1996.     

Effect of organic modifier and temperature on the resolution of betamethasone and dexamethasone using a porous graphitic carbon column: application to their identification and confirmation in human urine by LC-ESI-MS/MS

The effects of temperature, organic modifier and the type of acid on the retention factor, the resolution and peak shape of betamethasone and dexamethasone are described. The study is performed using narrow bore porous graphitic carbon (PGC) columns online with diode-array detector (DAD) and ESI MS/MS. The results show that temperature affects the retention behaviour of the two compounds and ACN yields the best separation while no effect is obtained by changing the type of organic acid. The developed method is applied for the confirmation of dexamethasone and betamethasone in human urine.     

q-Oscillator Algebra And d-Orthogonal Polynomials

In this paper we express the matrix coefficients of the Fock representation of a q-oscillator algebra in terms of the d-orthogonal Al-Salam Carlitz polynomials. Also, we derive a generating functions, recurrence relations and q-difference equations for these d-orthogonal polynomials.     

Synchronized analysis of an unsteady laminar flow downstream of a circular cylinder centred between two parallel walls using PIV and mass transfer probes

Experiments are carried out in the wake of a cylinder of d _c  = 10 mm diameter placed symmetrically between two parallel walls with a blockage ratio r = 1/3 and a Reynolds number varying between 75 ≤ Re ≤ 277. Particle image velocimetry is exerted to obtain the instantaneous velocity components in the cylinder wake. A snapshot proper orthogonal decomposition (POD) is also applied to these PIV results in order to extract the dominant modes through the implementation of an inhomogeneous filtering of these different snapshots, apart from an interpolation to estimate the wall shear rate at the lower wall downstream the cylinder. Mass transfer circular probes are placed at the lower wall downstream this obstacle so as to further determine the time evolution of the wall shear rate, by bringing the inverse method to bear on the convective-diffusion equation. Comparisons between the two synchronized techniques demonstrate that electrochemical method can give more accurate information about the coherent structures present in the flow and about the interaction of the von Kármán vortices with the walls of the tunnel as well. The comparison between the two measurement techniques in the flow regions concerns the spatiotemporal evolutions of the wall shear rate obtained from PIV measurements and the wall shear rate using mass transfer probes. Discrepancy between the PIV measurements and the electrochemical ones near the wall, where the secondary vortices P ₁′ are generated at wall, are caused by a PIV bias and a limitations of the singular mass transfer probes.     

Experimental and theoretical study of AC electrical conduction mechanisms of semicrystalline parylene C thin films

The electrical conduction mechanisms of semicrystalline thermoplastic parylene C (-H(2)C-C(6)H(3)Cl-CH(2)-)(n) thin films were studied in large temperature and frequency regions. The alternative current (AC) electrical conduction in parylene C is governed by two processes which can be ascribed to a hopping transport mechanism: correlated barrier hopping (CBH) model at low [77-155 K] and high [473-533 K] temperature and the small polaron tunneling mechanism (SPTM) from 193 to 413 K within the framework of the universal law of dielectric response. The conduction mechanism is explained with the help of Elliot's theory, and the Elliot's parameters are determined. From frequency- and temperature-conductivity characteristics, the activation energy is found to be 1.27 eV for direct current (DC) conduction interpreted in terms of ionic conduction mechanism. The power law dependence of AC conductivity is interpreted in terms of electron hopping with a density N(E(F)) (~10(18) eV cm(-3)) over a 0.023-0.03 eV high barrier across a distance of 1.46-1.54 ?.     

Orthogonally Additive Homogenous Polynomials on Vector Lattices

We study orthogonally additive homogeneous polynomials on a uniformly complete vector lattice taking values either in a separated bornological vector space or in a separated topological vector space. This study is based on the notions of orthosymmetric multilinear maps and vector lattice powers.     

The q-cosine Fourier transform and the q-heat equation

The aim of this work is to establish in great detail The q-Fourier analysis related to the q-cosine. The wise reader will note that the considered q-cosine coincides with the one given by T.H.?Koornwinder and S.F.?Swarttouw. Through the q-cosine product formula, we define and analyze the properties of the q-even translation and the q-convolution. Adopting the Titchmarsh approach, we study the q-cosine Fourier transform and its inverse formula. The second theme of this paper is an application of the q-Fourier analysis developed earlier. We extend the heat representation theory inaugurated by P.C.?Rosenbloom and D.V.?Widder to the q-analogue. We construct the q-solution source, the q-heat polynomials and solve the q-analytic Cauchy problem.     

Coupling Electrochemical Adsorption and Long‐range Electron Transfer: Label‐free DNA Mismatch Detection with Ultramicroelectrode (UME)

A new electrochemical hybridization transduction pathway, obtained by coupling electrochemical adsorption and long‐range electron transfer through double‐stranded DNA, was investigated using ultramicroelectrode (UME). The results show that long‐range electron transfer does not occurs exclusively throws well‐packed and organized self‐assembled DNA monolayers. This approach is used to investigate long‐range electron transfer properties of both single‐ and double‐ stranded short synthetic DNA and DNA plasmids. Single mismatch electrochemical detection protocol of non‐labelled short synthetic DNA, without heating or probe labelling, in a 10 minutes protocol, was in fine performed.     

Monitoring Conformational Changes in an Enzyme Conversion Inhibitor Using Pure Shift Exchange NMR Spectroscopy

We report the acquisition of 2D NMR EXSY spectra with ultrahigh resolution, which allows for probing the slow conformational exchange process in a pharmaceutical compound. The resolution enhancement is achieved by implementing interferogram based PSYCHE homonuclear decoupling to generate a pure shift proton spectrum along the direct domain of the resulting data. The performance of this pure shift EXSY pulse sequence is compared to the standard experiment recorded under identical conditions. It is found that although being less sensitive and requiring a longer acquisition time, the quality of pure shift spectra allows for extracting exchange rates values that are coherent with the ones determined by standard approach, on a temperature range that demonstrates the robustness of the chosen homonuclear decoupling method. The resolution enhancement provided by the simplification of proton line shape allows for probing a higher number of proton sites whose analysis would have been biased using a standard method. These results open the way to a thorough and accurate study of chemical exchange processes based on a multi-site analysis of 2D pure shift EXSY spectra