An efficient numerical method for the resolution of the Kirchhoff‐Love dynamic plate equation

We solve numerically the Kirchhoff‐Love dynamic plate equation for an anisotropic heterogeneous material using a spectral method. A mixed velocity‐moment formulation is proposed for the space approximation allowing the use of classical Lagrange finite elements. The benefit of using high order elements is shown through a numerical dispersion analysis. The system resulting from this spatial discretization is solved analytically. Hence this method is particularly efficient for long duration experiments. This time evolution method is compared with explicit and implicit finite differences schemes in terms of accuracy and computation time. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Design of phase plates for shaping partially coherent beams by simulated annealing

Taking the Gaussian Schell-model beam as a typical example of partially coherent beams, this paper applies the simulated annealing （SA） algorithm to the design of phase plates for shaping partially coherent beams. A flow diagram is presented to illustrate the procedure of phase optimization by the SA algorithm. Numerical examples demonstrate the advantages of the SA algorithm in shaping partially coherent beams. An uniform flat-topped beam profile with maximum reconstruction error RE 〈 1.74% is achieved. A further extension of the approach is discussed.     

Commutativity of the Arens product in lattice ordered algebras

Let be an Abelian Archimedean lattice ordered algebra. The order bidual furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the up-down-up approximation of positive elements in the order continuous order bidual by elements in the canonical image of in Components of positive elements in are characterized and the result is applied to the Arens product of -and almost -algebras.     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

Continual approximations of displacements in thick layered plates upon decomposition of thermomechanical loads into bilateral symmetric and antisymmetric components

Continual models of deformation of thick layered plates, where the general order of resolving equations does not depend on the number of layers, are constructed with account of the specific character of the unflexural and flexural deformation caused by the symmetric and antisymmetric components of bilateral loads and temperature. Account of the load decomposition during the process of refining a certain reasonable initial solution, consisting in the analytical iterative integration, makes it possible to obtain rather precise continual approximations of stresses and displacements over the transverse coordinate and thus to revise the known continual models.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 743–756, November–December, 1999.     

微通道板表面发雾的AES分析

应用俄歇电子能谱对微通道板表面发雾区域进行分析。分析结果表明,发雾区碳含量比正常区高三倍。由此可推测出,发雾是由碳污染引起的,而这种碳污染很可能是残留于微通道板上的某些有机物在烧氢时碳化所致。     

Position of starting spot in TLC: Influence on average plate height

Summary The influence of the distance between the solvent entry and the starting zone positions, Z₀, on the average plate height was studied. This factor was found to be of major importance and could be optimized. The Guiochon and Siouffi model greatly underestimates the plate height for low values of Z₀.     

一种位相板衍射图样的图像处理新方法

本文介绍了在半导体激光光纤和位相板相结合的准直情况下，利用ＣＣＤ探测器测量大尺寸形位误差的原理，并针对位相板衍射图像的特点，提出了一种处理此类衍射图样的图像处理新方法——投影法。同在时间上采用的多次平均的方法相比较，投影法相当于采用了空间上的平均，消除了ＣＣＤ表面保护玻璃形成的干涉条纹的影响，对空气扰动也起到了很好的抑制作用。并且使二维图像处理变为一维计算，大大提高了计算速度     

An exactly soluble case of the triangular ising model in a magnetic field

An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.     

On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E ^*(t)=E(t)-2πΔ^*(t/2π) with , then we obtain