Convergent Flows of Molten Polymers Modeled by Generalized Second-Grade Fluids of Power-Law Type

The molding processes of polymer melts involve geometrically complex dies. Such dies are usually tapered or streamlined to achieve a maximum output rate under conditions of laminar flow. The model of a generalized second-grade fluid of power-law type is used and the results obtained are illustrated by examples of convergent flows in conical and wedge-shaped dies.     

Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

Slutsky定理在样本分位数的极限分布证明上的应用

为了更好地理解和应用样本分位数的极限分布,利用Slutsky定理,推导了样本分位数的极限分布.     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

On the Statistics of Partial Quotients of Finite Continued Fractions

We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics.     

Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.

     

Interpolatory integration rules and orthogonal polynomials with varying weights

We investigate which types of asymptotic distributions can be generated by the knots of convergent sequences of interpolatory integration rules. It will turn out that the class of all possible distributions can be described exactly, and it will be shown that the zeros of polynomials that are orthogonal with respect to varying weight functions are good candidates for knots of integration rules with a prescribed asymptotic distribution.Research supported by the Deutsche Forschungsgemeinschaft (AZ: Sta 299/4-2).     

A concise route to the right wing of ciguatoxin

A concise route to the HIJKLM-ring fragment 10 of ciguatoxin (CTX) and 51-hydroxyCTX3C was developed in which oxiranyl anion addition and intramolecular carbonyl olefination were utilized as key transformations. The present procedure requires only 23 steps from the I-ring 5, while 35 steps were employed in a previous synthesis of the corresponding right wing 11 of CTX3C. The high efficiency of the present synthesis ensures a supply of 10 for total synthesis and biomedical applications.     

Structural and Chemical Analysis of Materials with High Spatial Resolution

 An understanding of the correlation between microstructures and properties of materials require the characterization of the material on many different length scales. Often the properties depend primarily on the atomistics of defects, such as dislocations and interfaces. The different techniques of transmission electron microscopy allow the characterization of the structure and of the chemical composition of materials with high spatial resolution to the atomic level: high resolution transmission electron microscopy allows the determination of the position of the columns of atoms (ions) with high accuracy. The accuracy which can be achieved in these measurements depends not only on the instrumentation but also on the quality of the transmitted specimen and on the scattering power of the atoms (ions) present in the analyzed column. The chemical composition can be revealed from investigations by analytical microscopy which includes energy dispersive X-ray spectroscopy, mainly quantitatively applied for heavy elements, and electron energy-loss spectroscopy. Furthermore, the energy-loss near-edge structure of EELS data results in information on the local band structure of unoccupied states of the excited atoms and, therefore, on bonding. A quantitative evaluation of convergent beam electron diffraction results in information on the electron charge density distribution of the bulk (defect-free) material. The different techniques are described and applied to different problems in materials science. It will be shown that nearly atomic resolution can be achieved in high resolution electron microscopy and in analytical electron microscopy. Recent developments in electron microscopy instrumentation will result in atomic resolution in the foreseeable future.     

Convergent synthesis of the A-F ring segment of yessotoxin and adriatoxin

A convergent synthesis of the A-F ring segment of yessotoxin and adriatoxin was achieved via the intramolecular allylation of an α-chloroacetoxy ether and subsequent ring-closing metathesis.