广义二阶流体涡流速度的衰减和温度扩散

将分数阶微积分运算引入到二阶流体的本构关系中,建立了带分数阶导数的广义二阶流体模型．研究了广义二阶流体涡流速度的衰减和温度扩散,利用分数阶导数的Laplace变换和广义Mittag-Leffler函数,得到了涡流速度场和温度场的精确解,分析了分数阶指数对涡流速度的衰减和温度扩散的影响．     

二维三温热传导方程组的分数步隐式差分格式

本文给出一个解二维三温热传导方程组的分数步隐式有限差分格式，利用离散变分形式及能量方法，给出差分格式的最优阶离散H^1范数先验误差及稳定性估计。     

一种对称损失函数下正态总体刻度参数的估计

本文研究正态分布中刻度参数在损失函数L(σ，δ)=[(σ-δ)^2]/σδ下的最小风险同变估计及Bayes估计，并讨论(cT(x) d)^1/2形式估计的可容许性与不可容许性，我们发现在这种损失下σ的极大似然估计是不可容许的．     

Concerning seven and eight mutually orthogonal Latin squares

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 419. © 2003 Wiley Periodicals, Inc.     

偶数阶中立型差分方程多正解的存在性

利用不动点指数理论,得到了高阶非自治非线性中立型差分方程多正解的存在性准则,推广了有关文献中的相关结论.     

Nonaxisymmetric thermal stress state of laminated rotational bodies of orthotropic materials under nonisothermic loading

A procedure for numerical investigation of nonaxisymmetric temperature fields and the elastic stress-strain state of laminated rotational bodies of cylindrically and rectilinearly orthotropic materials under nonisothermal loading is proposed. The deformation of orthotropic materials is described by the equations of anisotropic elasticity theory. The equations of state are written in the form of Hookes law for homogeneous materials, with additional terms which take into account the thermal deformation, changes in the mechanical properties of materials in the circumferential direction, and their dependence on temperature. A semianalytic finite-element method in combination with the method of successive approximations is used. An algorithm for numerical solution of the corresponding nonlinear boundary problem is elaborated, which is realized as a package of applied FORTRAN programs. Some numerical results are presented.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 731–752, November–December, 2004.     

Moderate Deviations for the overlap parameter in the Hopfield model

We derive moderate deviation principles for the overlap parameter in the Hopfield model of spin glasses and neural networks. If the inverse temperature is different from the critical inverse temperature _c=1 and the number of patterns M(N) satisfies M(N)/N 0, the overlap parameter multiplied by N, 1/2 < < 1, obeys a moderate deviation principle with speed N^1–2 and a quadratic rate function (i.e. the Gaussian limit for = 1/2 remains visible on the moderate deviation scale). At the critical temperature we need to multiply the overlap parameter by N, 1/4 < < 1. If then M(N) satisfies (M(N)⁶ log N M(N)²N⁴ log N)/N 0, the rescaled overlap parameter obeys a moderate deviation principle with speed N^1–4 and a rate function that is basically a fourth power. The random term occurring in the Central Limit theorem for the overlap at _c = 1 is no longer present on a moderate deviation scale. If the scaling is even closer to N^1/4, e.g. if we multiply the overlap parameter by N^1/4 log log N the moderate deviation principle breaks down. The case of variable temperature converging to one is also considered. If _N converges to _c fast enough, i.e. faster than the non-Gaussian rate function persists, whereas for _N converging to one slower than the moderate deviations principle is given by the Gaussian rate. At the borderline the moderate deviation rate function is the one at criticality plus an additional Gaussian term.Research supported by the Volkswagen-Stiftung (RiP-program at Oberwolfach, Germany).Mathematics Subject Classification (2000): 60F10 (primary), 60K35, 82B44, 82D30 (secondary)     

Least Squares Convex-Concave Data Smoothing

We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n ²) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.     

New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

In this paper, for a prime power q, new cyclic difference sets with Singer para- meters ((q ⁿ –1/q–1), (q ^n–1–1/q–1), (q ^n–2–1/q–1)) are constructed by using q-ary sequences (d-homogeneous functions) of period q ⁿ –1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When q is a power of 3, new cyclic difference sets with Singer parameters ((q ⁿ –1/q–1), (q ^n–1–1/q–1), (q ^n–2–1/q–1)) are constructed from the ternary sequences of period q ⁿ –1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen.     

On Error Bounds for Approximation Schemes for Non-Convex Degenerate Elliptic Equations

In this paper we provide estimates of the rates of convergence of monotone approximation schemes for non-convex equations in one space-dimension. The equations under consideration are the degenerate elliptic Isaacs equations with x-depending coefficients, and the results applies in particular to certain finite difference methods and control schemes based on the dynamic programming principle. Recently, Krylov, Barles, and Jakobsen obtained similar estimates for convex Hamilton–Jacobi–Bellman equations in arbitrary space-dimensions. Our results are only valid in one space-dimension, but they are the first results of this type for non-convex second-order equations.