Szego-Type Limit Theorems for Generalized Discrete Convolution Operators

We study the asymptotic behavior of the averaged f-trace of a truncated generalized multidimensional discrete convolution operator as the truncation domain expands. By definition, the averaged f-trace of a finite-dimensional operator A is equal to , where n is the dimension of the space in which the operator A acts, the set of numbers γ_k, k = 1,..., n, is the complete collection of eigenvalues of the operator A, counting multiplicity; a generalized discrete convolution is an operator from the closure of the algebra generated by discrete convolution operators and by operators of multiplication by functions admitting a continuous continuation onto the sphere at infinity.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 265–277.Original Russian Text Copyright © 2005 by I. B. Simonenko.     

Painlev property of the modified C-KdV equation and its exact solutions

In this paper,the Painlev’e properties of the modified C-KdV equation are verified by using the W-K algorithm.Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the nonstandard truncated expansion method with the help of Maple software,respectively.     

The proof of Tchakaloff's Theorem

We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of degree for Borel measures with moments up to order . The result improves known results for non-compact support, since we do not need conditions on st moments. In fact, we reduce the classical assertion of Tchakaloff's Theorem to a well-known statement going back to F. Riesz.

     

Development of a competitive ELISA for the quantification of F5 conjugate in HER2-targeted STEALTH immunoliposome doxorubicin in plasma samples

HER2 (human epidermal growth factor receptor 2, erbB2, or neu) is overexpressed by a large number of tumor types and has been identified as an important target for cancer therapy. F5 is a single-chain human antibody fragment that recognizes HER2 receptor and is covalently conjugated to PEGylated lipid to form F5 conjugate (F5CG) in the product HER2 targeted STEALTH immunoliposome doxorubicin. Here we described the method development of a competitive enzyme-linked immunosorbent assay (ELISA) for the determination of total concentration of F5 conjugate in plasma samples. The method involved the biotinylation of F5CG, detergent treatment of plasma sample to solubilize F5CG into monomeric form, and competitive ELISA for solubilized F5CG competitively binding to anti-F5CG antibody with biotinylated F5CG for the determination of total F5CG in plasma. The detection range of this method was from 0.2 ng/mL to 125 ng/mL for F5CG in plasma. The lower limit of quantification (LLOQ) was 0.2 ng/mL. This method was established and used for the measurement of F5CG concentration to provide information about F5CG circulation after the administration of immunoliposome in preclinical studies.      

An adaptive truncation criterion,for linesearch-based truncated Newton methods in large scale nonconvex optimization

Starting from the paper by Nash and Sofer (1990), we propose a heuristic adaptive truncation criterion for the inner iterations within linesearch-based truncated Newton methods. Our aim is to possibly avoid “over-solving” of the Newton equation, based on a comparison between the predicted reduction of the objective function and the actual reduction obtained. A numerical experience on unconstrained optimization problems highlights a satisfactory effectiveness and robustness of the adaptive criterion proposed, when a residual-based truncation criterion is selected.     

Wave diffraction from the Biconical Section in the semi-infinite conical region

The electromagnetic problem by the finite bicone, which is formed with the perfectly conducting semi-infinite cone and the finite cone with truncated vertex, is studied. Bicone is excited axial-symmetrically by the ring magnetic source. The diffracted field is represented through the series of the transversal magnetic (TM) modes; the lower mode among them is called the transversal electromagnetic wave (TEM). On the basis of this representation and using the mode matching technique, we derive the series equations to determine the unknown complex modes magnitudes. In view of the electric field singularities at the conical edges, these equations are represented in the form of the limiting transition from the finite sums to the series. We derive the rule of this transition, as well as the procedure for reducing them to the infinite system of linear algebraic equations (ISLAE) of the first kind. We study asymptotic properties of the matrix elements and find that the main part of their static limit and their behavior for large indexes form the matrix operator of the convolution type; the corresponding inverted operator in the analytical form is obtained. Both these operators, which we call the regularization operators, are used for the transition from the ISLAE of the first kind to the ISLAE of the second kind. The ISLAE thus obtained allow for the solution of any geometrical parameters and frequency with the given accuracy. The asymptotic properties of their solutions are analyzed, and the numerical examinations of the far field patterns are provided.     

删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

卤化银乳剂微晶体的结构与性能研究 Ⅶ.切角立方体乳剂微晶体的核壳复合结构

本工作应用双注仪制备了一系列不同碘含量的切角立方体核壳乳剂,用紫外光度法测定了它们的光吸收,用介电损耗法和微波光导法分别测定了它们的离子电导及光电导。结果表明,乳剂微晶体的光吸收和离子电导率都随着碘含量的增加而增加,光电导也随碘含量增加而增大,光电子衰减遵循二级反应动力学过程。碘的引入以及立方体切角使立方体乳剂微晶体的感光性能成倍地增长。