经典单色短峰水波理论的三阶完备解

针对经典的有限水深三阶单色短峰波,考虑环境均匀流效应,赋予一新的解析解,从而与原经典解析解构成完备的解析解.这就在第二阶解、第三阶解结构上显示出多种相互作用机制.     

直喷式柴油机燃烧系统均匀优化设计的多维仿真研究

以直喷式柴油机的动力性和经济性为优化目标,对柴油机燃烧系统进行了基于均匀设计的多维仿真研究。通过回归分析的方法,综合考虑了柴油机的进气系统、喷油系统和燃烧室形状等参数,得到了燃烧系统参数的最优组合。结果表明:均匀设计法能以较少的仿真计算次数得到优化结果;通过回归分析和回归方程的分析得出,涡流比、油束夹角,以及涡流比和油束夹角的交互作用对柴油机的动力性和经济性影响最大;均匀设计的优化结果准确可靠,因此均匀设计法可以用于柴油机的多维仿真研究;涡流比和油束夹角的交互作用对油气混合有较大的影响。     

具有时滞食物链系统周期解的存在性和全局渐近稳定性

本文考虑时滞三种群食物链系统,给出周期解存在和全局渐近的充分条件。     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].     

优化端点条件的平面二次均匀B样条插值曲线

在利用反求法构造B样条插值曲线时,往往需要选取端点条件。 因此,可对端点条件进行优化选取,使得构造的B样条插值曲线满足特定要求。提出了一种利用曲线内能极小选取平面二次均匀B样条插值曲线端点条件的算法。首先给出了二次均匀B样条插值曲线分控制顶点与首个控制顶点（即端点条件）的递推关系式;然后给出了利用曲线内能极小优化选取首个控制顶点的算法,证明了利用该算法构造的C¹连续二次均匀B样条插值曲线为保形插值,并通过数值算例证明了算法的有效性;最后,为便于实际应用,基于MATLAB平台设计了算法所对应的图形用户界面,用户通过简单的操作即可获得光顺的C¹连续二次均匀B样条保形插值曲线。     

多通道表面放电光泵浦源触发特性研究

介绍了多通道表面放电光泵浦源的设计,理论分析了触发电压幅值及上升时间、绝缘基板厚度等参数对所设计光泵浦源触发特性的影响。分析表明：在触发电压作用下,通道两电极处电场出现强烈畸变,而通道中间电场基本为零。采用高速相机拍摄泵浦源的放电图像以及电流线圈测量各通道的放电电流这两种方法实验研究了泵浦源的同步性及放电均匀性。当氮氩混合气体总气压为0.1 MPa (氮氩体积比为3∶7),充电电压20 kV,触发电压30 kV,前沿约10 ns时,成功实现了10通道均匀放电,抖动约20 ns。实验结果表明：在保证放电装置绝缘良好的情况下,若充电电压和触发电压越高,触发电压上升时间越短,触发电极至通道的有效距离越短,则多通道放电的抖动就越小,放电均匀性越好。     

On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

Lip_J-扩张域和一致域(英文)

本文证明了如下两个结果:(1)域D(?)R~n是一致域当且仅当D是Lip_J-扩张域;(2)Jordan域D(?)R~2是拟圆当且仅当对在D上满足|f′(z)|≤d(z,(?)D)~(-1)的任意的解析函数f恒有f∈Lip_J(D),其中J(x_1,x_2)=1/2 log(1+|x_1-x_2|/d(x_1,(?)D))(1+|x_1-x_2|/d(x_2,(?)D)),x_1,x_2∈D.     

The Spearman footrule and a Markov chain property

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.