Analysis of Experiments on Determining the Turbulent Mixing Constant on the Basis of Two-Dimensional Calculations

Based on numerical calculations, the experiments on mixing at the interface of gases are analyzed. Single-mode and random disturbances of the interface and superposition of random disturbances onto long-wave perturbations are considered. Possible reasons for the higher value of the mixing constant obtained in the experiments are discussed.     

关于修正的Baskakov算子的Stechin-Marchaud型不等式

利用K-泛函研究了修正的Baskakov型算子的Stechin-Marchaud型不等式,由此不等式,我们得到了关于ω2φλ的逆结果.     

Molecular weight dependence of diblock copolymer segregation at a polymer/polymer interface

Utilizing forward recoil spectrometry (FRES), we have determined the segregation isotherm which describes the interfacial excess z_i^* of diblock copolymers of poly (d₈-styrene-b-2-vinylpyridine) (dPS-PVP) at the interface between the homopolymers PS and PVP as a function of ?_∞, the volume fraction of diblock copolymer remaining in the host homopolymer. All the samples were analyzed after annealing at temperatures and times sufficient to achieve equilibrium segregation. The effect of the degree of polymerization of both the diblock copolymers and the host homopolymers on the segregation isotherm is investigated. When the degree of polymerization of the homopolymer is much larger than that of the diblock copolymer, the normalized interfacial excess (z_i^*/R_g), where R_g is the radius of gyration of an isolated block copolymer chain, is a universal function of that portion of the block copolymer chemical potential due to chain stretching. The existence of such a universal function is predicted by theory and its form is in good agreement with self-consistent mean field calculations. Using these results, one can predict important aspects of the block copolymer segregation (e.g., the saturation interfacial excess) without recourse to the time-consuming numerical calculations. © 1994 John Wiley & Sons, Inc.     

关于Fejer点上的一种复有理型插值的一致逼近阶

设D是一个Jordan,Г为其边界，并设Г满足Aльпер条件。本文得到了一种基于Fejer点的有理型插值算子对于f(z)∈C（Г）的一致逼近阶。     

The Möbius distribution on the disc

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.     

等厚双层涂层材料受集中力作用的平面问题理论解

界面应力的正确评价是分析薄膜涂层材料力学特性的难题之一。利用镜像点法和Dirichlet等值性原理，本文推导了等厚双层薄膜涂层材料受表面集中力作用的平面问题理论解。该显式理论解是以固定在各镜像点上的局部坐标系下的Goursat应力函数的形式给出的。对应于高阶镜像点的应力函数，可通过递推的方法，从对应于低阶镜像点的应力函数求得，而且也易于计算机编程。随着镜像点阶数的增大，它与界面的距离也越来越大，因而相对应的应力函数对界面应力的影响越来越小。最后的算例表明，只需考虑前面有限个镜像点，便可获得足够精度的解。该理论解可作为格林函数，以求解复杂问题的理论解，也可用作边界元法的基本解，提高数值计算的精度和效率。     

Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.     

The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

New characterizations of Hajlasz-Sobolev spaces on metric spaces

This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given.