Propagation of a decentered astigmatic partially coherent beam in a turbulent atmosphere

Propagation properties of a decentered general astigmatic partially coherent beam (i.e., decentered twisted anisotropic Gaussian Schell-model beam) in a turbulent atmosphere are investigated. Analytical formulas for the cross-spectral density and decentered parameter of a decentered astigmatic partially coherent beam propagating in a turbulent atmosphere are derived. Irradiance properties of a decentered astigmatic partially coherent beam in a turbulent atmosphere are studied graphically, and are found to be quite different from its properties in free space.     

Untersuchungen über Zinn(IV)-alkoxide. II. Isolierung und Charakterisierung der Verbindung Sn3O(OiBu)10 · 2i-BuOH. Das erste Beispiel für ein partielles Hydrolyseprodukt eines Zinn(IV)-alkoxids

Investigations into Tin(IV) Alkoxides. II. Isolation and Characterization of the Compound Sn₃O(OⁱBu)₁₀₁₀ · 2i-BuOH. The First Example of a Partially Hydrolized Tin(IV) Alkoxide The partial hydrolysis product Sn₃O(OⁱBu)₁₀ · 2i-BuOH was obtained by slow hydrolysis of the reaction product of tin tetrachloride with sodium isobutoxide. The compound forms colourless, moisture sensitive crystals, which easily release the coordinated solvent molecules in dry air. Its crystal and molecular structure has been determinated by single crystal X-ray diffraction. The compound crystallizes in the triclinic space group P1 with a = 1363.5(7), b = 1462.7(10), c = 1637.7(7) pm, α = 95.40(5)°, β = 96.79(4)°, γ = 102.12(5)° and Z = 2. The crystal structure consists of discrete, trimeric molecules with octahedrally coordinated tin atoms which are connected to each other corresponding to the formulation Sn₃(μ₃-O)(μ₂-OⁱBu)₃(O¹Bu)₇ · (i-BuOH)₂ by three isobutoxide groups bridging two metal atoms and a single threefold bridging oxygen atom     

Adsorption in columns packed with porous adsorbent particles having partially fractal structures

A mathematical model is constructed and solved that could describe the dynamic behavior of the adsorption of a solute of interest in single and stratified columns packed with partially fractal porous adsorbent particles. The results show that a stratified column bed whose length is the same as that of a single column bed, provides larger breakthrough times and a higher dynamic utilization of the adsorptive capacity of the particles than those obtained from the single column bed, and the superior performance of the stratified bed becomes especially more important when the superficial velocity of the flowing fluid stream in the column is increased to accommodate increases in the system throughput. This occurs because the stratified column bed provides larger average external and intraparticle mass transfer and adsorption rates per unit length of packed column. It is also shown that increases in the total number of recursions of the fractal and the ratio of the radii between larger and smaller microspheres that make up the partially fractal particles, increase the intraparticle mass transfer and adsorption rates and lead to larger breakthrough times and dynamic utilization of the adsorptive capacity of the particles. The results of this work indicate that highly efficient adsorption separations could be realized through the use of a stratified column comprised from a practically reasonable number of sections packed with partially fractal porous adsorbent particles having reasonably large (i) total number of recursions of the fractal and (ii) ratio of the radii between larger and smaller microspheres from which the partially fractal particles are made from. It is important to mention here that the physical concepts and modeling approaches presented in this work could be, after a few modifications of the model, applied in studying the dynamic behavior of chemical catalysis and biocatalysis in reactor beds packed with partially fractal porous catalyst particles.     

2-Methylthio-4,5,6,7-tetrahydro-1,2,4-triazolo[1,5-<Emphasis Type="Italic">a</Emphasis>]pyrimidin-5- and -7-Ones

The cyclocondensation of methylcinnamates and arylidene derivatives of Meldrums acid with 3-amino-5-methylthio-1,2,4-triazole in DMF gives 2-methylthio-4,5,6,7-tetrahydro-1,2,4-triazolo[1,5-a]-pyrimidin-5-ones. The reaction involving arylidene derivatives of Meldrums acid or its synthetic equivalents in ethyl acetate with a catalytic amount of pyridine gives a mixture of 2-methylthio-4,5,6,7-tetrahydro-1,2,4-triazolo[1,5-a]pyrimidin-5- and -7-ones.__________Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 246–251, February, 2005.     

Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first–order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution. Research partially supported by Ministerio de Educación y Ciencia and FEDER, Project MTM2004-06652-C03-01, and by Xunta de Galicia and FEDER, Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN     

The Transmission Problem of Viscoelastic Waves

In this paper we consider the transmission problem of viscoelastic waves. That is, we study the wave propagations over materials consisting of elastic and viscoelastic components. We show that for this types of materials the dissipation produced by the viscoelastic part is strong enough to produce exponential decay of the solution, no matter how small is its size. We also show that the linear model is well posed.     

Radar ambiguity function in Lp frame

In modern radar techniques, pulse signal can be replaced by the chirps, which is taken to be signals in Lp space. Wigner's function and ambiguity functions are constructed in an Lp frame and a partial generalization of the uncertainty principle is given by means of the notion of coherent dual.     

Estimation of partially specified spatial panel data models with random-effects

In this article, we study estimation of a partially specified spatial panel data linear regression with random-effects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain sufficient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.     

固定效应部分线性单指标面板模型的惩罚二次推断估计

单指标面板模型已广泛应用于各学科领域的研究中,其估计方法较为丰富,然而鲜有估计方法将个体内的相关性考虑在内.基于此,本文研究了一类个体内存在相关性的固定效应部分线性单指标面板模型,采用惩罚二次推断函数法和LSDV法相结合的方法对模型进行估计,证明了所得估计量的一致性和渐近正态性.Monte Carlo模拟结果显示其具有...     

One case of vortex motion in fluid

This text presents an English translation of the significant paper [6] on vortex dynamics published by the outstanding Russian scientist S. A. Chaplygin, which seems to have almost escaped the attention of later investigators in this field. Although it was published more than a century ago, in our opinion it is still interesting and valuable. __________ Originally published in: Trudy otdeleniya fizicheskikh nauk imperatorskogo Moskovskogo obshchestva lyubitelei estestvoznaniya, antropologii i etnografii (Transactions of the Physical Section of Moscow Society of Friends of Natural Sciences, Anthropology and Ethnography), 1903, Vol. 11, No. 2, pp. 11–14. Translated from Russian by S. Ramodanov; edited by D. Blackmore; commented by V. V. Meleshko (Department of Theoretical and Applied Mechanics, Faculty of Machanics and Mathematics, Kiev National Taras Shevchenko University, 01030 Kiev, Ukraine. E-mail: meleshko@univ.kiev.ua) and G.J.F. van Heijst (Fluid Dynamics Laboratory, Faculty of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands. E-mail: g.j.f.v.heijst@tue.nl).