Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Winning controllers and regions in competitive nonlinear dynamic games with two qualitative objectives and uncertain information

The Liapunov technique has been introduced in differential games in a sequence of works over the last decade. We discuss application of this technique to the interface between two competitive semi-games, each with different qualitative objective. The feedback information for controllers is provided from designed, analytically integrable state predictors with reduced dynamics, which considerably shortens the computing time. The case is illustrated on the scenario of target reaching before being intercepted, and intercepting before target is reached.Deceased.     

天然树脂局部结构的径向分布函数研究

本工作用x射线衍射技术分析计算了二种天然树脂的局部结构参数,由测得的衍射强度数据求出了它们的结构因子I(r)和径向分布函数RDF(r),并由此得到了分子链内临近原子和次临近原子平均间距、配位数和短程有序畴。     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

Band bending at the Si(1 1 1)–SiO2 interface induced by low-energy ion bombardment

Experiments employing photoreflectance spectroscopy have uncovered band bending due to electrically active defects at the Si(1 1 1)–SiO₂ interface after sub-keV Ar⁺ ion bombardment. The band bending of about 0.5 eV resembles that for Si(1 0 0)–SiO₂, and both interfaces exhibit two kinetic regimes for the evolution of band bending upon annealing due to defects healing. The healing takes place about an order of magnitude more quickly at the (1 1 1) interface, however, probably because of less fully saturated bonding and higher compressive stress.     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.     

DISTRIBUTION OF THE（0，∞）ACCUMULATIVE LINES OF MEROMORPHIC FUNCTIONS

Suppose that f(z)is a meromorphic function of order λ（0&lt;λ&lt;+∞）and of lower order μ in the plane.Let ρ be a positive number such that μ≤ρ≤λ.(1)If f^(l)(z)(0≤l&lt;+∞）has p(1≤p&lt;+∞）finite nonzero deficient valnes αi(i=1,…，p)with deficiencies δ（αi,f^(l)),then f(z)has a (0,∞）accumulative line of order ≥ρin any angular domain whose vertex is at the origin and whose magnitude is larger than max(π/ρ，2π-4/ρ ∑i=1^p arcsin √δ（αi,f^(l))/2).(2)If f(z) has only p(0&lt;p&lt;+∞）（0,∞）,accumulative lines of order≥ρ：arg z=θk(0≤θ1&lt;θ2&lt;…&lt;θp&lt;2π，θp+1=θ1+2π）,then λ≤π/ω，where ω=min I≤k≤p(θk+1-θk),provided that f^(l)(z)(0≤l&lt;+∞）has a finite nonzero deficient value.     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

TiO2∶Mo体系的光子雪崩上转换

在 978nm激光二极管的激发下 ,Mo掺杂的TiO2 材料表现出很强的宽带上转换发光 ,该发光来源于 [MoO4]2 - 基团的激发态3T1 ,3T2 能级到基态1 A1 能级的电子跃迁 .通过研究发光强度与抽运功率的关系及上转换发光的上升时间曲线 ,发现TiO2 ∶Mo体系的上转换发光中存在着雪崩机制 ,应用转换函数理论分析了光子雪崩的产生条件和主要特征 ,理论结果和实验数据很好地符合