Bernstein算子对具有奇性函数的加权同时逼近

利用在端点用Lagrange插值代替函数值的方法构造了一种新的Bernstein算子,这种新的算子可以用以逼近端点具有奇性的函数,并给出了它同时逼近的正定理.

奇性波函数及其在原子能量计算中的应用

讨论了波函数在原点的奇异性问题及其与势场的关系，指出在保证径向波函数平方可积，即积分∫｜Ｒｎｌ（ｒ）｜２ｒ２ｄｒ有限的前提下，出现Ｒｎｌ（０）＝∞的奇异性，在物理上是可以接受的。然后，将具有这种奇异性的波函数应用于类氦原子基态能量的计算，并通过对结果的分析指出，采用形如Ｒ１０（ｒ）＝Ｃｒｓ０ｅ－ｚ－β１＋ｓ０ｒ（０＞ｓ０＞－１／２）的奇性径向波函数，相当于将两电子间除屏蔽效应之外的关联作用，等效为中心场－｜γ｜／ｒ２的作用，从而使基态能量的计算结果比ｓ０＝０时的结果有所改进。

修正Bernstein算子的导数及其加权光滑性刻画

Della Vecchia等引进一种修正的Bernstein算子,它可以用来逼近端点具有奇性的函数。文章利用加权光滑模ω2φλ(f,t)w和加权K-泛函K2φλ(f,t2)w,建立了该算子的导数与其目标函数的光滑性之间的等价关系,所得结论对权函数的参数a,b无上界限制,只要求a,b>0。

Bernstein-Stancu算子的加权逼近

文章考虑了Bernstein-Stancu算子对具有奇性函数加Jacobi权的加权逼近问题,建立了加权逼近的正、逆定理.

第二类Fredholm积分方程的快速数值解法

对于具有弱奇性核函数的第二类Fredholm积分方程,将核函数所定义的区域分成大小不同的正方形子区域,利用分层插值多项式逼近核函数,由此得到近似矩阵B实现了积分方程的快速数值解法。在最后,对如何提高方案的数值稳定性作简要讨论并给出要讨论并给出数值结果。

Singularity-free Green's function for EM sources embedded in a stratified medium

We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.

Robust admissibility analysis of uncertain switched singular systems:a switched Lyapunov function approach

The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.

Function S-rough Sets and Their Law Characteristic

Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.

Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation

To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.

A singularity-based eigenfunction decomposition for Kohn-Sham equations

We show that the eigenfunctions of Kohn-Sham equations can be decomposed as ■ = F ψ, where F depends on the Coulomb potential only and is locally Lipschitz, while ψ has better regularity than ■.

Permutation polynomials with low differential uniformity over finite fields of odd characteristic

In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).

A fast integration method for translating-pulsating source Green＇s function in Bessho form

The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.