带模理论的回答集程序设计

基于回答集语义的逻辑程序（ASP）是一种描述性问题求解的典范，目前人们提出了各种ASP的扩张。本文提出带背景理论的回答集程序设计框架，它不仅是正规逻辑程序的一般化，对带聚合函数的ASP而言，也与SPT—PDB的回答集语义一致。经证明，当背景理论是命题逻辑时，该框架与Shen和You提出的方法一致。     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

交换主理想整环上交错矩阵的距离与极大集

讨论了交换主理想整环上交错矩阵的算术距离与距离之间的关系,并用两个矩阵之间的算术距离得到了交换主理想整环上交错矩阵极大集的结构.     

非光滑B- 预不变凸优化问题的解集刻画 (运筹学与控制论)

给出了具有不等式约束的非光滑B-预不变凸优化问题的最优解集的各种刻画。首先,利用Clarke次微分建立了该优化问题最优解的充分必要条件;再讨论了该优化问题在其解集S上的一个性质:最后建立了该优化问题解集的5种等价形式,即S={x∈M〈^ξ,η(z,x)〉=0,^ξ∈cf(x)=(x∈M〈^ξ,η(z,x)〉≥0,^ξ∈cf(x)}={x∈M〈^ξ,η(x,z)〉=〈^ζ,η(z,x)〉,^ξ∈C(z),^ζ∈cf(x)}={x∈M〈^ξ,η(x,z)〉≥〈^ζ,η(z,x)〉,^ξ∈C(z),^ζ∈cf(x)}={x∈M〈^ξ,η(x,z)〉=〈^ζ,η(z,x)〉=0,^ξ∈C(z),^ζ∈cf(x)},并举例验证这5个集合都相等,为S={0}。     

Rough Sets and Three Valued Connectives Extended Abstract

<正>1 Introduction In[5]we investigated the significance of some truth-functional three valued logics of ill-known sets described by pairs of disjoint(or pairs of nested) subsets.In particular,we referred to the case of rough sets showing that if from a mathematical standpoint we obtain sound results,the interpretation with respect to     

Regular saturated graphs and sum-free sets

In a recent paper, Gerbner, Patkós, Tuza and Vizer studied regular F-saturated graphs. One of the essential questions is given F, for which n does a regular n-vertex F-saturated graph exist. They proved that for all sufficiently large n, there is a regular $K_3$-saturated graph with n vertices. We extend this result to both $K_4$ and $K_5$ and prove some partial results for larger complete graphs. Using a variation of sum-free sets from additive combinatorics, we prove that for all $k\ge 2$, there is a regular $C_{2k+1}$-saturated with n vertices for infinitely many n. Studying the sum-free sets that give rise to $C_{2k+1}$-saturated graphs is an interesting problem on its own and we state an open problem in this direction.     

Structural, electronic and optical properties of SrCl2 under hydrostatic stress

The results of first-principles theoretical study of the structural, electronic and optical properties of SrCl₂ in its cubic structure, have been performed using the full-potential linear augmented plane-wave method plus local orbitals (FP-APW+lo) as implemented in the WIEN2k code. In this approach both the local density approximation (LDA) and the generalized gradient approximation (GGA) are used for the exchange-correlation (XC) potential. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. We performed these calculations with and without spin-orbit interactions. Including spin-orbit coupling cause to lifts the triple degeneracy at Γ point and a double degeneracy at X point. Results are given for structural properties. The pressure dependence of elastic constants and band gaps are investigated. The dielectric function, reflectivity spectra and refractive index are calculated up to 30 eV. Also we calculated the pressure and volume dependence of the static optical dielectric constant.     

Gradient control and synchronization of Julia sets

This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial Zn＋1 = zn^2＋ c, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method.     

复系统Julia集的同步

非线性系统中的分形集——Julia集, 在工程技术中有着十分重要的应用,定义了不同系统间的Julia集同步的概念, 并引入一种非线性耦合的方法, 对同一系统不同参数的Julia集进行了有效的同步.并以多项式形式和三角函数形式的Julia集同步为例验证了该方法的有效性.     

基于粗糙集与小波变换的图像融合算法

粗糙集理论是处理不确定性问题的数学方法，本文提出了基于粗糙集与小波变换相结合的图像融合算法。该方法首先将粗糙集理论应用于图像滤波中，对含有椒盐噪声的图像进行粗糙中值滤波，然后对滤波后的图像进行小波融合。实验结果表明，粗糙中值滤波有较强的去噪能力，且较好地保持了图像的细节信息，在此基础上进行小波融合，使得融合结果图像具有良好的效果。