关于Grünwald型多项式算子的线性组合

研究了Grünwald型多项式算子Hn(f;x,r)对f(x)∈Cj[-1,1],1≤j≤r的逼近阶,在连续状态下给出了点态的逼近阶.     

用投影预变换提高自适应波束形成的稳健性

在快拍数较少和（或）存在系统误差时，自适应波束形成的性能会变差，特别是会引起方向图副瓣电平升高——波束畸变。本文提出的投影变换法利用干扰方向的初略估计，在未精确预知阵列流形的条件下，可以显著改善自适应方向图的副瓣性能，并提高自适应算法的收敛性，计算机仿真结果验证了这一优点。     

Non‐reflecting artificial boundaries for transient scalar wave propagation in a two‐dimensional infinite homogeneous layer

This paper presents an exact non‐reflecting boundary condition for dealing with transient scalar wave propagation problems in a two‐dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x →∞ and another extends toward x→‐ ∞, the non‐reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time‐dependent partial differential equation with only one spatial variable, can be further changed into a linear first‐order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non‐reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non‐reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi‐infinite media. Copyright © 2003 John Wiley & Sons, Ltd.     

Lyapunov equation for infinite-dimensional discrete bilinear systems

Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution.     

Banach空间Fuzzy多值隐拟变分包含

在Banach空间中并在不具紧性的条件下，引入和研究了一类fuzzy多值隐拟变分包含及相应的fuzzy隐预解算子方程，借助预解算子技巧，建立了Banach空间中fuzzy多值隐拟变分包含与预解算子方程的等价性，得到了该类fuzzy多值隐拟变分包含的迭代算法与某些解的存在性定理及解的迭代逼近。     

An integrated automatic test data generation system

The Godzilla automatic test data generator is an integrated collection of tools that implements a relatively new test data generation method—constraint-based testing—that is based on mutation analysis. Constraint-based testing integrates mutation analysis with several other testing techniques, including statement coverage, branch coverage, domain perturbation, and symbolic evaluation. Because Godzilla uses a rule-based approach to generate test data, it is easily extendible to allow new testing techniques to be integrated into the current system. This article describes the system that has been built to implement constraint-based testing. Godzilla's design emphasizes orthogonality and modularity, allowing relatively easy extensions. Godzilla's internal structure and algorithms are described with emphasis on internal structures of the system and the engineering problems that were solved during the implementation.Parts of this research were supported by Contract F30602-85-C-0255 through Rome Air Development Center while the author was a graduate student at the Georgia Institute of Technology.     

Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

筛查基因突变的新技术——循环双脱氧指纹图谱法及其应用

建立了适用于大批量标本基因突变筛查的双脱氧指纹图谱法即ｄｄＦ。该技术民测定ＤＮＡ序列的双脱氧末端终止法及ＳＳＣＰ二者长处于一身，即只作一个双脱氧末端终止反应，然后将反应产物在与ＳＳＣＰ相同的电泳条件下进行聚丙烯酰胺凝胶电泳，这样有突变的样品不会漏检，阳性检出率高达１００％。     

An extended minimax disparity to determine the OWA operator weights

This paper contributes to extend the minimax disparity to determine the ordered weighted averaging (OWA) model based on linear programming. It introduces the minimax disparity approach between any distinct pairs of the weights and uses the duality of linear programming to prove the feasibility of the extended OWA operator weights model. The paper finishes with an open problem.