Solving the factorization problem with P systems

P systems have been used many times to face with computationally difficult problems, such as NP-complete decision problems and NP-hard optimization problems. In this paper we focus our attention on another computationally intractable problem: factorization. In particular, we first propose a simple method to encode binary numbers using multisets. Then, we describe three families of P systems: the first two allow to add and to multiply two binary encoded numbers, respectively, and the third solves the factorization problem.     

多复变函数的一些边值问题

本文主要研究二元复变解析函数与一阶椭圆型复方程组在双圆柱区域上的某些边值问题,包括Dirichlet问题与Riemann-Hilbert问题。文中给出了这些问题适定的变态提法,先证明了相应变态问题解的存在性与唯一性,然后导出原边值问题可解的充要条件。这里,我们使用的方法与别人不同,对于一阶椭圆型复方程组,我们所加的条件较弱,没有看到国内外有其他人获得这样完整的结果。在本文的后一部分,我们还讨论了二元解析函数与一阶椭圆型复方程组在双圆环柱区域上的Dirichlet问题与Riemann—Hilbert问题,给出了这些边值问题可解的充要条件。使用本文中的方法,还可讨论多个复变函数相应边值问题的可解性。     

Binary Particle Swarm Optimization Based Hyper-Heuristic for Solving the Set-Union Knapsack Problem

The set-union knapsack problem(SUKP) is proved to be a strongly NP-hard problem, and it is an extension of the classic NP-hard problem: the 0-1 knapsack problem(KP). Solving the SUKP through exact approaches is computationally expensive. Therefore, several swarm intelligent algorithms have been proposed in order to solve the SUKP. Hyper-heuristics have received notable attention by researchers in recent years, and they are successfully applied to solve the combinatorial optimization problems. In this article, we propose a binary particle swarm optimization(BPSO) based hyper-heuristic for solving the SUKP, in which the BPSO is employed as a search methodology. The proposed approach has been evaluated on three sets of SUKP instances. The results are compared with 6 approaches: BABC, EMS, gPSO, DHJaya, b WSA, and HBPSO/TS, and demonstrate that the proposed approach for the SUKP outperforms other approaches.     

一类二阶两个自变数两个未知函数的抛物形方程组的第一问题

本文讨论了给定边值条件下二阶两个自变数两个未知函数的抛物型方程组的第一问题的求解方法。并给出了解的表达式。     

P systems with array objects and array rewriting rules

Array P systems were introduced by Paun Gh. which is linking the two areas of membrane computing and picture grammars. Puzzle grammars were introduced by us for generating connected picture arrays in the two-dimensional plane, motivated by the problem of tiling the plane. On the other hand, incorporating into arrays the developmental type of generation used in the well-known biologically motivated L systems, Siromoney and Siromoney proposed a very general rectangular array generating model, called extended controlled tabled L array system (ECTLAS). In this paper we introduce two variations of the array P system, called BPG array P system and parallel array P system. The former has in the regions array objects and basic puzzle grammar rules (BPG), which are a specific kind of puzzle grammar rules. In the latter, the regions have rectangular array objects and tables of context-free rules. We examine these two types of P systems for their array generative power.     

P systems with array objects and array rewriting rules

Array P systems were introduced by Paun Gh. which is linking the two areas of membrane computing and picture grammars. Puzzle grammars were introduced by us for generating connected picture arrays in the two-dimensional plane, motivated by the problem of tiling the plane. On the other hand, incorporating into arrays the developmental type of generation used in the well-known biologically motivated L systems, Siromoney and Siromoney proposed a very general rectangular array generating model, called extended controlled tabled L array system (ECTLAS). In this paper we introduce two variations of the array P system, called BPG array P system and parallel array P system. The former has in the regions array objects and basic puzzle grammar rules (BPG), which are a specific kind of puzzle grammar rules. In the latter, the regions have rectangular array objects and tables of context-free rules. We examine these two types of P systems for their array generative power.     

Arithmetic computation using self-assembly of DNA tiles: subtraction and division

Recently,experiments have demonstrated that simple binary arithmetic and logical operations can be computed by the process of selfassembly of DNA tiles.In this paper,we show how the tile assembly process can be used for subtraction and division.In order to achieve this aim,four systems,including the comparator system,the duplicator system,the subtraction system,and the division system,are proposed to compute the difference and quotient of two input numbers using the tile assembly model.This work indicates that these systems can be carried out in polynomial time with optimal O(1)distinct tile types in parallel and at very low cost.Furthermore,we provide a scheme to factor the product of two prime numbers,and it is a breakthrough in basic biological operations using a molecular computer by self-assembly.     

两类图的边控制集划分

通过分类归纳的方法,对图的边控制集划分问题进行了探讨,研究了两类特殊图的边控制集划分问题,获得了一些相关结论:得到了扇形图F_n的集边控制数和全集边控制数,并确定了乘积图P_2×P_n的全集边控制数.     

耗散Schrdinger-Poisson方程组解的渐近性

考虑耗散Schr dinger Poisson方程组的Cauchy问题 ,对吸引力情形 ,证明了该问题整体强解的存在唯一性和解的渐近性。     

基于CUDA并行平台实现核膜系统求解可满足性问题的研究

膜系统能以空间换时间的方式在多项式时间内求解NP难问题,作为膜系统中的一个新类型,核膜系统不仅包含了不同类型膜系统的特征,而且能提供一种统一性的描述．因此基于核膜系统构建系统模型,并以此求解一个典型的NP难问题：可满足性问题．为了加速对核膜系统的仿真过程,程序将在CUDA并行方式下仿真实现,通过与传统的串行方式比较,使用CUDA能减少95％的仿真时间,这也表明使用CUDA并行方式非常适合仿真核膜系统．     

模式集成代数

在全局模式多数据库系统中模式集成是一个非常重要的问题·为解决面向对象多数据库系统的模式集成,提出了一套集成代数,主要包括５类集成操作:合并操作类,相交操作类,聚合操作类,概括操作类和特化操作类·它们对其他类型的多数据库系统的模式集成也具有一定的普遍意义·     

一类非严格双曲型可化约组Cauchy问题的整体经典解

讨论了线性退化情形下的非严格双曲型可化约组Ｃａｕｃｈｙ问题经典解的整体存在性，给出了保证其经典解整体存在的充分及必要条件．     

关于求解全局优化的途径:从局部到全局(英文)

在实际应用中常常要求求解全局优化问题, 而用有效的求解全局优化问题是非常困难的.填充函数方法和打洞函数方法是两种全局优化的函数变换方法,有关文献的计算说明这些方法是有效的.本文将给出这两种全局优化方法最近的发展.首先分析原先由葛仁溥提出的填充函数和Levy与Montalvo提出的打洞函数方法的缺点.其次给出在箱子集或者全空间上无约束或者不等式约束的全局优化问题的单参数的新填充函数和变形打洞函数的定义,并构造出相应的填充函数和变形打洞函数.此外亦讨论整数全局优化问题的填充函数和变形打洞函数方法.最近还讨论了全空间上等式约束全局优化问题.最后给出综述,指出非线性规划的一个主要发展方向:混合整数非线性规划,给出用填充函数和变形打洞函数的求解途径.     

Parameterized Algorithmics for Computational Social Choice：Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science,and Social Science on the one side, and Mathematics and Computer Science（including Artificial Intelligence and Multiagent Systems） on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. This work is dedicated to Jianer Chen, one of the strongest problem solvers in the history of parameterized algorithmics,on the occasion of his 60 th birthday.     

个性化推荐算法研究

随着全球信息总量的爆炸式增长,信息超载问题无法避免且日趋严重化．个性化推荐系统是当前解决信息过载问题的有效技术．该文首先阐述了推荐系统概念定义及其三大组成模块,其次深入分析了个性化推荐算法,详细讨论了当前主流的四大类推荐算法:基于内容的推荐算法、协同过滤推荐算法、基于知识的推荐算法和混合的推荐算法,从多角度对各算法的优缺点进行对比,然后阐述了常用评价方法、评测指标及对测试标准进行分类,并且介绍了常用数据集,最后展望个性化推荐未来研究热点．     

非线性离散系统最优控制--逐次逼近方法

研究了非线性离散系统最优控制问题,提出一种逐次逼近方法;首先将系统的最优控制问题转化为非线性两点边值问题族,然后通过构造线性两点边值问题族,将非线性两点边值问题转化为非奇次线性两点边值问题族;得到的最优控制律由精确控制项和非线性补偿项两部分组成,精确控制项可以通过求解R iccati方程求出其精确解,非线性补偿项由逐次逼近法求解一族线性伴随向量方程的解序列求得;仿真结果证明了逐次逼近方法的有效性。     

一类时间可逆系统的逆积分因子

由于含有系统的许多有用信息,逆积分因子被认为是解决常微分方程定性理论中两大公开问题:中心焦点问题、希尔伯特第十六问题的统一工具.而且逆积分因子与常微分方程的李对称性和Darboux可积性有密切的联系.因此对某些解析微分系统建立其逆积分因子的结构定理是重要的.对于一类时间可逆解析微分系统,建立了逆积分因子的系数递推公式.利用此递推公式得到其具有给定形式逆积分因子的充要条件.为了说明我们的结论,对于一个具体的时间可逆五次微分系统,利用系数递推公式直接给出系统的多项式型逆积分因子和初等首次积分.     

电力系统计算坐标系的变换研究

电力系统分析中常利用坐标变换来简化问题的数学描述 ,且不同的问题应选用不同的坐标系及相应的坐标变换。其特点、适用范围及其与a、b、c系之间的两种变换关系做了详细研究。     

一类广义系统的能控性

能控性是现代控制论的基本问题,广义系统的能控性是难题之一,引起许多专家学者的重视和探究。通过一个定理,在系统正则的条件下,将系统分为快、慢两个子系统并分别讨论了它们的能控问题,得到了一类广义系统能控的充要条件,最后给出了一个范例。