A Cut-Invariant Law of Large Numbers for Random Heaps

We consider the framework of Bernoulli measures for heap monoids. We introduce in this framework the notion of asynchronous stopping time, which generalizes the notion of stopping time for classical probabilistic processes. A strong Bernoulli property is proved. A notion of cut-invariance is formulated for convergent ergodic means. Then, a version of the strong law of large numbers is proved for heap monoids with Bernoulli measures. We study a sub-additive version of the law of large numbers in this framework.     

Functional Differential Equations With Delay and Random Effects

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results.     

Rapid identification of environmental bacterial strains by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

In recent years, various mass spectrometry procedures have been developed for bacterial identification. The accuracy and speed with which data can be obtained by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) could make this a powerful tool for environmental monitoring. However, minor variations in the sample preparation can influence the mass spectra significantly. Therefore, the first objectives of this study were the adjustment and the optimization of experimental parameters allowing a rapid identification of whole bacterial cells without laborious sample preparation. The tested experimental parameters were matrix, extraction solvent, salt content, deposition method, culture medium and incubation time. This standardized protocol was applied to identify reference and environmental bacterial strains of Escherichia coli, Salmonella and Acinetobacter. The environmental bacterial strains were isolated from sewage sludge using an original microextraction procedure based on repeated sonications and enzymatic treatments. The bacterial identification was realized by the observation of the respective genus-, species- and strain-specific biomarkers. This bacterial taxonomy could be completed within one hour, with minimal sample preparation, provided that sufficient bacteria had been collected prior to MALDI-TOF analysis.     

Control of the oscillator strength of the exciton in a single InGaN-GaN quantum dot

We report direct evidence for the control of the oscillator strength of the exciton state in a single quantum dot by the application of a vertical electric field. This is achieved through the study of the radiative lifetime of a single InGaN-GaN quantum dot in a p-i-n diode structure. Our results are in good quantitative agreement with theoretical predictions from an atomistic tight-binding model. Furthermore, the increase of the overlap between the electron and hole wave functions due to the applied field is shown experimentally to increase the attractive Coulomb interaction leading to a change in the sign of the biexcitonic binding energy.     

Frequency self deconvolution in the quantitative analysis of near infrared spectra

In this paper a new model based on frequency self deconvolution (FSD) is proposed for the quantitative analysis of a near infrared (NIR) spectrum. The model couples FSD and partial least square regression (PLS). The grid search optimization method is used to select the optimal values of the full width at half height (FWHH) and the truncation point of the apodization function. The proposed FSD-PLS provides a significant improvement in the prediction ability of the PLS model. Furthermore, a modification of the new FSD-PLS method is introduced to enable the removal of the baseline variations from the NIR spectra. The proposed models were validated using absorbance spectra of mixtures composed from glucose, urea and triacetin in a phosphate buffer solution where the concentrations of the components are selected to be within their physiological range in blood. The whole experiments were carried out in a non-controlled environment to show that the model can suppress effectively most of the experimental variations. The results show that the standard error of prediction (SEP) decreases from 35.58 mg dL(-1) using 8 factors for the PLS model to 15.53 mg dL(-1) by using 12 factors for the modified FSD-PLS model. The proposed models are also shown to yield a slightly improved performance than a newly developed second derivative-PLS model without incurring the shortcoming associated with the derivative approach in not providing interpretable results and in degrading the SNR of the spectra at a faster rate.     

Quasistatic frictional thermo‐piezoelectric contact problem

We consider here a mathematical model describing the bilateral frictional contact between a thermo‐piezoelectric body and a thermally conductive foundation. We model the behavior of the material with a linear thermo‐electro‐elastic constitutive law. The process is assumed to be quasistatic and the contact is modeled with a nonlocal version of Coulomb's dry friction law, in which the frictional heat generated in the process, is taken into account. We drive a variational formulation of the problem and establish the existence of its weak solution.     

The characteristic class and ramification of an ℓ-adic étale sheaf

We introduce the characteristic class of an ℓ-adic étale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz–Verdier trace formula, its trace computes the Euler–Poincaré characteristic of the sheaf. We compare the characteristic class to two other invariants arising from ramification theory. One is the Swan class of Kato-Saito [17] and the other is the 0-cycle class defined by Kato for rank 1 sheaves in [16]. Dedicated to Luc Illusie, with admiration     

Stability of Viscoelastic Wave Equation with Structural $\delta$-Evolution in $\mathbb{R}^{n}$

The aim of this paper is to study the Cauchy problem for the viscoelastic wave equation for structural $\delta$-evolution models. By using the energy method in the Fourier spaces, we obtain the decay estimates of the solution to considered problem.     

A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.