时滞线性系统时滞独立稳定的劳斯-赫维茨方法

本文研究了滞后型线性时滞系统,给出了一个完全可计算的时滞独立稳定的代数充要条件,这个条件判别的全过程仅仅只需要计算二次劳斯表和一次赫维茨行列式,并且所有运算均在实数域中,具有简单性和实用性。     

基于因式分解的代理群签名方案

目前基于离散对数问题（如ElGamal或Schnorr）的代理群签名算法都要进行大数的模指数运算,效率一般不高,尤其是当群用户数目很多时问题将更加严重。利用有限域中二次方程的一些特性,提出了一种基于因式分解的代理群签名方案,该算法以乘法或求逆等简单运算形式为基础,计算效率有显著提高,能够满足群用户较多时对群签名的需求。     

借助游程运算实现多边形叠置分析

考虑到基于直接编码的栅格数据在计算效率和存储能力上的不足,提出一种便于代数操作的游程编码数据结构,以优化基于直接编码栅格数据的代数运算。介绍了基于该数据结构的游程“交”运算的实现方法,并在算法实现过程中完成游程属性的各种代数运算。提出使用这种游程的“交”运算完成多边形的叠置分析,其基本思路是：分别将两个图层中的多边形数据转换为游程集合,在栅格场中的任一行上使用叠加图的游程单元与底图上该行的游程集合执行“交”运算,逐行执行这种游程“交”运算得到两个图层之间多边形相交的结果游程集合,并根据“Union”、“Erase”等不同的叠置方式提取满足条件的游程单元,最后将游程矢量化为多边形数据输出。在叠置运算过程中,通过游程的“交”运算即能够实现图层间多边形的各种叠置方式,表明该运算具有很强的通用性。     

基于分数阶非线性各向异性扩散的图像去雾算法

针对大多数各向异性扩散方程在去雾过程中容易模糊边缘细节的问题,提出一种基于分数阶非线性各向异性扩散的去雾算法。使用从模糊图像中提取的大气光作为各向异性扩散过程中的初始值,通过迭代扩散过程计算精细的大气光传输图。使用分数阶导数的Riemann-Liouville模型,将各向异性扩散过程推广到1~2之间的任何实数阶数,而且在空间域中执行迭代过程使得算法在计算方面能够简单快速的实现。实验结果表明,该算法能够有效地突出去雾图像的细节,而且在多个评价指标上比其他算法都有更优的性能体现。     

椭圆曲线密码体制中快速标量乘方法研究

椭圆曲线标量乘是椭圆密码体制中最耗时的运算,其中求逆运算的次数直接决定了标量乘法的性质。转换求逆为乘法运算能够降低求逆次数。根据这个思想,给出在素数域Fp上用仿射坐标直接计算5P的算法,比传统方法节省了两次求逆运算。同时还给出直接计算5kP的算法,比重复计算k次5P更有效。最后结合多基链把这两个新算法应用到标量乘中。实验结果表明,该方法与以往的标量乘算法相比,效率可提高6.5%~14%,相交处I/M可降到1.1。     

改进的多目标遗传算法在营养决策中应用

将多目标遗传算法NSGA-Ⅱ应用于营养决策优化。采用多维实数向量的编码方式,使用状态转移表对遗传算子进行描述。对NSGA-Ⅱ算法进行改进,在进化操作中增加了随机变换运算和删除运算,加快了算法的收敛并避免了早熟。仿真结果证明该算法能逼近Pareto域,并在该域中均匀分布,经一次运行便可提供更多科学合理的营养决策优化候选方案。     

一个基于图像代数的并行图像处理环境

系统可用性和应用程序可移植性差是许多现有的并行图像处理计算结构难以获得实际应用的重要原因，基于Ritter提出的图像代数理论，研究、实现了一个并行图像处理环境．用户在并行计算结构上进行程序设计时，只需用图像处理环境提供的图像代数运算描述算法即可，处理环境能够根据用户算法的描述，依据一个时间开销模型，自动从并行实现函数库中提取出最优或近似最优的并行代码完成算法的运行，算法的并行实现和并行计算结构的硬件细节对用户透明。     

多变量系统信号流图的简化及应用

本文运用信号流图矩阵代数和节点原理,提出了多变量系统基本环节的信号流图的简化法则。分析和计算表明,文中提出的法则可用于求解传递矩阵,对建立多变量系统的数学模型具有一定的参考价值。同时也可应用在信息处理,矩阵代数的运算等领域。     

基于IDL的栅格地图代数实现与应用

ArcGIS提供了功能强大的地图代数计算功能,可以有效地针对栅格数据进行空间分析。但是,由于其运算效率较低而成为一些项目应用的瓶颈。研究认为ArcGIS进行地图代数计算效率比较低的主要原因在于它在计算时首先对数据进行重采样。通过使用IDL提供的栅格数据处理功能,对数据进行预处理,建立进行地图代数计算时的模版,将进行地图代数计算的各个图层依照地图代数模版重新进行范围的分割,并根据原始栅格数据及研究内容确定像元大小,对栅格数据进行重采样,得到可以用IDL进行地图代数运算的栅格数据集。根据不同研究领域的内容,设计地图代数的算法,实现地图代数运算。最后,以使用USLE方程计算三江平原土壤侵蚀模数为例,验证了方法的有效性。     

分数阶控制器的数字实现及其特性

针对分数阶控制器数值计算和应用难的问题,研究了分数阶控制器的数字实现方法和控制特性．取Grunwald-Letnikov定义有限项,并直接离散化,得到有限记忆数字实现法;利用Tustin算子生成函数把分数阶微分由复频域变换到Z域,然后用连分式展开式CFE(continued fraction expansion)近似展开,可得到Tustin CFE数字实现法．两种方法的频域对比分析表明Tustin CFE法优于有限记忆法．采用设计的分数阶控制器的数字实现方法,对分数阶控制器和传统PID控制器的控制性能进行了对比实验分析．研究结果表明:分数阶控制器对非线性具有较强的控制能力．     

一种新的语言信息计算模型

语言的可计算性问题是理论计算机科学的一个基本问题，字母文字信息的计算模型已经有数十年的历史，而适合汉语信息的计算模型尚未见到．中文信息处理与信息安全的研究迫切需要有适合汉语信息的数学计算模型，提出了两个新的字符串计算模型．在模型1的基础上定义了几个函数运算．利用这两个模型可以将任何汉语信息的处理转换为相应的数值进行处理，对汉语信息处理、汉语程序设计理论的建立和信息安全的研究具有一定的实际意义。     

Ten reasons to use divisible load theory

During the past decade, divisible load theory has become a powerful tool for modeling data-intensive computational problems. DLT emerged from a desire to create intelligent sensor networks, but most recent applications involve parallel and distributed computing. Like other linear mathematical models such as Markovian queuing theory and electric resistive circuit theory, DLT offers easy computation, a schematic language, and equivalent network element modeling. While it can incorporate stochastic features, the basic model does not make statistical assumptions, which can be the Achilles' heel of a performance evaluation model.     

一种求解Ramsey数的DNA计算机算法

Ramsey理论是组合数学中一个庞大而又丰富的领域,在集合论、逻辑学、分析以及代数学上具有极重要的应用.Ramsey数的求解是非常困难的,迄今为止只求出9个Ramsey数的准确值.探讨了DNA生物分子超级计算在求解这一困难数学问题的可能性.将Adleman-Lipton模型生物操作与粘贴模型解空间相结合的DNA计算模型...     

Genetic Algorithm Optimisation of Mathematical Models Using Distributed Computing

In this paper, a process by which experimental, or historical, data are used to create physically meaningful mathematical models is demonstrated. The procedure involves optimising the correlation between this real world data and the mathematical models using a genetic algorithm which is constrained to operate within the physics of the system. This concept is demonstrated here by creating a structural dynamic finite element model for a complete F/A-18 aircraft based on experimental data collected by shaking the aircraft when it is on the ground. The processes used for this problem are easily broken up and solved on a large number of PCs. A technique is described here by which such distributed computing can be carried out using desktop PCs within the secure computing environment of the Defence Science & Technology Organisation without compromising the PC or network security.     

Neurocomputing method based on structural finite element analysis of discrete model

Based on structural finite element analysis of discrete models, a neurocomputing strategy is developed in this paper. Dynamic iterative equations are constructed in terms of neural networks of discrete models. Determination of the iterative step size, which is important for convergence, is investigated based on the positive definiteness of the finite element stiffness matrix. Consequently, a method of choosing the step size of dynamic equations is proposed and the computational formula of the best step size is derived. The analysis of the computing model shows that the solution of finite element system equations can be obtained by the method of neural network computation efficiently. The proposed method can be used for parallel computation of structural finite element in a large-scale integrated circuit (LSI).     

Calculi for synchrony and asynchrony

A calculus for distributed computation is studied, based upon four combinators. A central idea is an Abelian group of actions which models the interfaces between components of a distributed computing agent. Using a notion of bisimulation, congruence relations are defined over computing agents, and thence an algebraic theory is derived. The calculus models both synchronous and asynchronous computation. In particular, it is shown that the author's Calculus of Communicating Systems (1980), which is an asynchronous model, is derivable from the calculus presented here.     

An approximation algorithm for box abstraction of transition systems on real state spaces

Predicate abstraction is a powerful technique for extracting finite-state models from infinite-state systems such as computer software, and is applied to verification of safety properties. Predicate abstraction is also applied to verification of dynamical systems on real state spaces such as hybrid dynamical systems. In this paper, we propose a fast algorithm for computing entire abstract state spaces of transition systems on real state spaces. The method is based on the box abstraction of state spaces, and requires a relatively smaller number of reachability checks and Boolean operations. We also propose a fast method for computing the set of boxes that intersect a given convex polyhedron. This computation is a part of the proposed state-space generation algorithm. Effectiveness of the algorithm is evaluated by the computation time and by the difference of the approximated state space from the exact state space.     

Coinductive Models of Finite Computing Agents

This paper explores the role of coinductive methods in modeling finite interactive computing agents. The computational extension of computing agents from algorithms to interaction parallels the mathematical extension of set theory and algebra from inductive to coinductive models. Maximal fixed points are shown to play a role in models of observation that parallels minimal fixed points in inductive mathematics. The impact of interactive (coinductive) models on Church's thesis and the connection between incompleteness and greater expressiveness are examined. A final section shows that actual software systems are interactive rather than algorithmic. Coinductive models could become as important as inductive models for software technology as computer applications become increasingly interactive.     

Computing Representations of a Lie Group via the Universal Enveloping Algebra

We present an algorithm for the computation of representations of a Lie algebra acting on its universal enveloping algebra. This is a new algorithm which permits the effective computation of these representations and of the matrix elements of the corresponding Lie group. The approach is based on a mathematical formulation originated by the authors. An interesting feature is the efficient computation of the adjoint representation of the corresponding Lie group. The methods are implemented using a symbolic computation program such as MAPLE.     

Performance modeling of pipelined linear algebra architectures on FPGAs

The potential design space of FPGA accelerators is very large. The factors that define performance of a particular implementation include the architecture design, number of pipelines, and memory bandwidth. In this paper we present a mathematical model that, based on these factors, calculates the computation time of pipelined FPGA accelerators and allows for quick exploration of the design space without any implementation or simulation. We evaluate the model and its ability to identify design bottlenecks and improve performance. Being the core of many compute-intensive applications, linear algebra computations are the main contributors to their total execution time. Hence, five relevant linear algebra computations are selected, analyzed, and the accuracy of the model is validated against implemented designs.