Variation of physicochemical properties in the aggregates of structual isomers

The regions of variation of density, enthalpy of formation, and detonation velocity of all of the formally possible structual isomers were determined for several molecular formulas of C,H,N,O-containing explosives. The histograms of the distribution of the structual isomers over these parameters were constructed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 859–862, May, 1995.The authors are grateful to Mrs. I. D. Solodukhina for the design of the graphical material.The work was carried out with the financial support of the Russian Foundation for Basic Research (Project No. 94-03-09323).     

On the rate of change of the sharp constant in the Sobolev–Poincaré inequality

The rate of change of the sharp constant in the Sobolev–Poincaré or Friedrichs inequality is estimated for a Euclidean domain that moves outward. The key ingredients are a Hadamard variation formula and an inequality that reverses the usual Hölder inequality.     

The Calculus of Moving Surfaces and Laplace Eigenvalues on an Ellipse with Low Eccentricity

Our goal is to demonstrate the utility of the calculus of moving surfaces (CMS) in boundary variation problems. We discuss the relative advantages of the CMS compared to the alternative approach of interior variations. We illustrate the technique by calculating the two leading terms of a power series for the Laplace eigenvalues on an ellipse with semi-axes 1 + a and 1 + b, where a and b are small. We compare the CMS estimates with those obtained by the conventional finite element method with Richardson extrapolation. The comparison confirms the cubic rate of convergence for the CMS estimates.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Investigation of molar concentration effect on structural,optical, electrical,and photovoltaic properties of spray‐coated Cu2O thin films

High quality copper oxide thin films were prepared by nebulizer spray pyrolysis technique using different concentrations of copper precursor solution. Concentration‐dependent structural, morphological, optical, and electrical properties of the prepared films are discussed. X‐ray diffraction studies done for the samples confirmed that the deposited films are in Cu₂O phase with polycrystalline cubic structure. Atomic force microscopy analysis revealed that all the films are composed of nano sheet shaped grains covering the substrate surface. Optical studies done on the samples showed band gap values 2.42, 2.31, and 2.02 eV for the solution concentration 0.01, 0.05, and 0.1 M, respectively. Photoluminescence spectral analysis showed the emission band at 620 nm confirming the formation of cuprous oxide. Electrical analysis of the films showed p‐type conductivity with a low resistivity 2.19 × 10² Ω.cm and high carrier concentration 16.76 × 10 ¹⁵ cm⁻³ for the molar concentration 0.1 M. In this work, Cu₂O/ZnO heterojunctions were also prepared, and solar cell properties were studied; they were found to show increased open circuit voltage and short circuit current for higher copper concentration.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

针对连续变化法测定络合物稳定常数实验中可能出现的设计缺陷的讨论

连续变化法测定络合物组成和稳定常数是大学化学中的经典学生实验。但针对1：2和1：3的络合反应，实验教科书的设计中可能出现数据点过少也就是溶液配制过少的问题。如果按照要求配制溶液，由于没有完全反应的混合溶液，而其他混合溶液给出的数据又都呈良好的线性，就缺少了用来估算曲线的数据点，结果是，将没有足够的数据对稳定常数进行估算。对这种可能出现的数据点过少的实验设计的原因、结果和解决方法进行了探讨。     

Ultra high performance liquid chromatography-quadrupole-time of flight analysis for the identification and the determination of resveratrol and its metabolites in mouse plasma

Resveratrol is a polyphenol that has numerous interesting biological properties, but, per os, it is quickly metabolized. Some of its metabolites are more concentrated than resveratrol, may have greater biological activities, and may act as a kind of store for resveratrol. Thus, to understand the biological impact of resveratrol on a physiological system, it is crucial to simultaneously analyze resveratrol and its metabolites in plasma. This study presents an analytical method based on UHPLC-Q-TOF mass spectrometry for the quantification of resveratrol and of its most common hydrophilic metabolites. The use of ¹³C- and D-labeled standards specific to each molecule led to a linear calibration curve on a larger concentration range than described previously. The use of high resolution mass spectrometry in the full scan mode enabled simultaneous identification and quantification of some hydrophilic metabolites not previously described in mice. In addition, UHPLC separation, allowing run times lower than 10 min, can be used in studies that requiring analysis of many samples.