Chemical bonding in representative astrophysically relevant neutral,cation, and anion HCnH chains

Most existing studies assign a polyynic and cumulenic character of chemical bonding in carbon-based chains relying on values of the bond lengths. Building on our recent work, in this paper we add further evidence on the limitations of such an analysis and demonstrate the significant insight gained via natural bond analysis. Presently reported results include atomic charges, natural bond order and valence indices obtained from ab initio computations for representative members of the astrophysically relevant neutral and charged HC_2k/2k+1H chain family. They unravel a series of counter-intuitive aspects and/or help naive intuition in properly understanding microscopic processes, e.g., electron removal from or electron attachment to a neutral chain. Demonstrating that the Wiberg indices adequately quantify the chemical bonding structure of the HC_2k/2k+1H chains—while the often heavily advertised Mayer indices do not—represents an important message conveyed by the present study.     

Identifying aspirin polymorphs from combined DFT-based crystal structure prediction and solid-state NMR

A combined experimental and computational approach was used to distinguish between different polymorphs of the pharmaceutical drug aspirin. This method involves the use of ab initio random structure searching (AIRSS), a density functional theory (DFT)-based crystal structure prediction method for the high-accuracy prediction of polymorphic structures, with DFT calculations of nuclear magnetic resonance (NMR) parameters and solid-state NMR experiments at natural abundance. AIRSS was used to predict the crystal structures of form-I and form-II of aspirin. The root-mean-square deviation between experimental and calculated ¹H chemical shifts was used to identify form-I as the polymorph present in the experimental sample, the selection being successful despite the large similarities between the molecular environments in the crystals of the two polymorphs.     

Simultaneous quantification of leukotrienes and hydroxyeicosatetraenoic acids in cell culture medium using liquid chromatography/tandem mass spectrometry

Leukotrienes (LTs) and hydroxyeicosatetraenoic acids (HETEs) are important bioactive lipid mediators that participate in various pathophysiological processes. To advance understanding of the mechanisms that regulate these mediators in physiological and pathological processes, an analytical method using liquid chromatography/tandem mass spectrometry for the simultaneous quantification of LTB₄, LTC₄, LTD₄, LTE₄, 5‐HETE_, 8‐HETE, 12‐HETE and 15‐HETE in cell culture media was developed. A Supel?‐Select HLB solid‐phase extraction cartridge was used for sample preparation. The compounds were separated on a C₁₈ column using gradient elution with acetonitrile–water–formic acid (20:80:0.1, v/v/v) and acetonitrile–formic acid (100:0.1, v/v). The calibration curves of LTB₄, LTD₄, LTE₄ and HETEs were linear in the range of 0.025–10 ng/mL, and the calibration curve of LTC₄ was linear in the range of 0.25–10 ng/mL. Validation assessment showed that the method was highly reliable with good accuracy and precision. The stability of LTs and HETEs was also investigated. Using the developed method, we measured LTs and HETEs in the culture supernatant of the human mast cell line HMC‐1. The present method could facilitate investigations of the mechanisms that regulate the production, release and signaling of LTs and HETEs. Copyright © 2014 John Wiley & Sons, Ltd.     

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

On a stochastic nonlinear equation in one-dimensional viscoelasticity

In this paper we discuss an initial-boundary value problem for a stochastic nonlinear equation arising in one-dimensional viscoelasticity. We propose to use a new direct method to obtain a solution. This method is expected to be applicable to a broad class of nonlinear stochastic partial differential equations.

     

Generic replica symmetric field-theory for short range Ising spin glasses

Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line, along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex rules are presented to help future renormalisation-group calculations. Received 9 October 2001     

Diffusion from sessile droplets through membranes

We analyze diffusion from a periodic array of hemispherical droplets through a membrane. We find that the multiple sources do not interact strongly, even when the droplets are closely spaced, so that the flux through the membrane appears nearly additive.     

仓库容量有限条件下的随机存贮管理问题的评注

给出2005年全国部分高校研究生数学建模竞赛D题的研究背景,对参赛论文作了简要评注,并提供了一种参考解答.     

Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.