Biaxial ordering of terminal diene groups in lipid membranes: an infrared linear dichroism study

The molecular order within the hydrophobic core of membranes of the diene lipid di-tetradecadienoylphosphatidylcholine was studied by means of infrared spectroscopy on multibilayer assemblies which orient macroscopically on the surface of an attenuated total reflection crystal. The relative humidity and temperature were used as variable parameters to demonstrate that there were profound differences in the melting transition of lipids possessing predominantly cis and trans diene groups. The cis isomer undergoes the phase transition at a vapor pressure which is increased by 0.15 GPa when compared with that of the trans isomer. The methylene wagging band progression gives no indication of differences between the acyl chain conformation of the cis and trans forms in the gel state. The frequencies of a number of absorption bands of the diene groups reveal that these moieties are predominantly in the s-trans conformation to accommodate a favorable packing within the bilayer. The linear dichroism of selected in-plane and out-of-plane vibrations of the diene groups gives indications of the biaxial ordering of these moieties. We present the basic equations for the quantitative analysis of IR dichroism data of lamellar structures in terms of transverse and longitudinal molecular order parameters. It turns out that the planes of the rigid diene groups orient preferentially in a perpendicular direction with respect to the bilayer surface and parallel to each other forming in this way a layer of well-aligned diene groups in the bilayer center. This finding is confirmed by the results of X-ray measurements. We suggest that the partial interdigitation of the diene groups of the sn-1 acyl chains promotes the formation of the inverse H_II phase and/or enables the formation of covalent bonds between both the monolayers upon polymerization of diene lipids.     

最高阶元素个数为40的非可解群的分类

设$\varphi$为群${\rm Aut}(N)$的同态,记$H_\varphi\times N$为群$N$借助于群$H$的半直积.设$G$为有限不可解群,本文证明: 若$G$中最高阶元素个数为40, 则$G$同构于下列群之一:(1)~$Z_{4\varphi}\times A_5$,\,${\rm ker}\varphi=Z_2$; (2)~$D_{8\varphi}\times A_5,\,{\rm ker}\varphi=Z_2\times Z_2$; (3)~$G/N=S_5$, $N=Z(G)=Z_2$; (4)~$G/N=S_5$, $N=Z_2\times Z_2,\,N\cap Z(G)=Z_2$.     

A concise route to the C2-symmetric tricyclic skeleton of ryanodine

Ryanodine is a potent calcium channel modulator. In this Letter, we report the 10-step synthesis of the highly substituted tricyclic ring system of ryanodine. Diels-Alder reaction via dearomatization of 2,5-dimethylbenzene-1,4-diol and subsequent SmI₂-mediated reductive coupling of eight-membered 1,5-diketone efficiently introduced the four consecutive fully substituted carbons of the tricyclo[3.3.2.0^2,6]decane system.     

A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O(h⁴+τ⁵). It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.     

Optimal expansion of subspaces for eigenvector approximations

We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.     

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

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求解随机微分方程的二级Milstein方法(英文)

In this paper we discuss two-stage Miistein methods for solving Ito stochastic differential equations （SDEs）. Six fully explicit methods （TSM 1 -- TSM 6） are given in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of Ito SDEs.     

The uniform convergence and precise asymptotics of generalized stochastic order statistics

Let X(i,n,m,k), i=1,…,n, be generalized order statistics based on F. For fixed r∈N, and a suitable counting process N(t), t>0, we mainly discuss the precise asymptotic of the generalized stochastic order statistics X(N(n)−r+1,N(n),m,k). It not only makes the results of Yan, Wang and Cheng [J.G. Yan, Y.B. Wang, F.Y. Cheng, Precise asymptotics for order statistics of a non-random sample and a random sample, J. Systems Sci. Math. Sci. 26 (2) (2006) 237-244] as the special case of our result, and presents many groups of weighted functions and boundary functions, but also permits a unified approach to several models of ordered random variables.     

On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order

In the paper we study the existence of solutions of a nonlinear quadratic Volterra integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive.