离散余弦变换的一种推广

离散余弦变换(DCT)在数字信号、图像处理、频谱分析、数据压缩和信息隐藏等领域有着广泛的应用.推广离散余弦变换,给出一个包含三个参数的统一表达式,并证明在许多情形新变换是正交变换.最后给出一种新型离散余弦变换,并证明它是正交变换.     

离散三角子模

为了构造离散三角模,引入了离散三角子模的概念,给出了生成离散三角(子)模的方法;然后讨论了光滑离散三角子模的结构.     

计算一类数字变换的收缩阵列

本文以DFT的收缩（Systolic）阵列结构为基础，给出了一类数字变换的收缩阵列，这些变换包括离散富里叶变换，离散余弦变换，离散正弦变换，离散Hartley变换，数论变换和多项式变换．     

《离散多元分析:理论与实践》

原著名:DiscreteMultivariateAnalysis:TheoryandPractice原著作者:[美]YvonneM.M.Bishop,StephenE.Fienberg,PaulW.Holland主译人员:张尧庭校译人员:史宁中书评:本书是国际上有关离散数据统计分析的最著名的著作之一。在离散多元分析领域,它可作为一本权威的著作和教科书,对离散多元分析的理论研究和方法应用起了重要的推动作用。随着我国改革开放的深入,市场经济的发展,以及社会的进步,各种各样的市场调查,社会调查和民意测验,以及各种医学、临床试验、健康卫生和生物等领域里的试验研究和观察研究越来越重要。离散多元分析就是针…     

Zd中离散分形指标的线性不变性质

研究欧几里得格 Zd 内离散分形指标的线性不变性质 ,即证明了上、下离散质量维数的线性不变性质 ,离散 Hausdorff维数的线性不变性质以及离散填充维数的线性不变性质 .     

用伯努利试验研究离散型随机变量的分布

将常见的离散型随机变量的分布用一个与伯努利试验有关的题目加以整合,揭示了怎样由伯努利试验构造离散型随机变量的分布．并举出了基于伯努利试验的离散型随机变量的分布在解决相关问题中的例子．实例表明用伯努利试验研究离散型随机变量的分布及相关问题．会起到事半功倍的效果．     

关于人口发展方程半离散算法的研究

利用半离散的方法将人口发展方程的边界条件进行离散,离散后得到两个相应的偏微分方程模型,然后利用算子半群的理论证明了离散后的解都逼近原方程的解,从而证明这种半离散方法是可行的.     

离散模糊数直觉模糊广义系统

为了进一步研究模糊数直觉模糊广义系统,在离散区间值模糊系统和规则两面性的基础上首次提出了离散直觉模糊数广义系统。然后研究了这类系统的稳定性,讨论了离散区间值模糊系统、离散T-S模糊广义系统和离散直觉模糊数广义系统的两种关系。其次,深入研究了离散直觉模糊数控制器和离散直觉模糊数广义系统的稳定性。离散直觉模糊数广义系统将是一个新的研究方向,将成为解决实际问题的一种通用方法。最后,通过实例说明了该方法的有效性。     

三阶有势Markov过程的离散骨架

本文是关于三阶嵌入问题的一系列研究的一个阶段性结果,讨论三阶有势 Markov过程的离散骨架的判定问题:在§2中我们首次对三阶 Q-矩阵及其对应的 Q-过程和离散骨架进行分类并得到各类三阶离散骨架的表现定理,从而对全部三阶离散骨架作出了十分细致的完整的刻划,这一表现定理实际上已为一般三阶嵌入问题的彻底解决奠定了基础,在§3中我们给出了各类三阶有势 Markov 过程的离散骨架的判定准则,从而使这一特殊类型的离散骨架的判定问题彻底解决。     

离散算子差分法的单元函数

给出了弹性力学离散算子差分法的离散格式,并给出了该方法的几个板弯曲单元和平面四边形单元,通过对它们的考察,分析了离散算子差分方法中的离散格式对单元位移函数的反映能力。在离散算子差分方法中,无论单元位移函数是否协调,其位移函数均能在离散格式中得到十分好的再现,说明了离散算子差分方法的离散格式是一种性能很优良的离散格式。     

A critical review of discrete filled function methods in solving nonlinear discrete optimization problems

Many real life problems can be modeled as nonlinear discrete optimization problems. Such problems often have multiple local minima and thus require global optimization methods. Due to high complexity of these problems, heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems. One of the more recent global optimization tools is known as the discrete filled function method. Nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given. Some of the most promising filled functions are tested on various benchmark problems. Numerical results are given for comparison.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

Continuity correction for discrete barrier options with two barriers

Discrete barrier options are the options whose payoffs are determined by underlying prices at a finite set of times. We consider the discrete barrier option with two barriers. Broadie et al. (1997) [16] proposed a continuity correction for the discretely monitored barrier option. We extend this idea to barrier option with two barriers. The proof for discrete chained barrier option is provided and numerical results show the continuity correction approximation is remarkably accurate.     

Exterior Difference System on Hypercubic Lattice

Based on the exterior differential calculus, we define the exterior difference system on the hypercubic lattice. The pairing formula, bracket, contract operator and Lie derivative operator for this system are also constructed. The discrete H. Cartan formulas are obtained too. After those preparations, we prove the discrete Frobenius Theorem, discrete retraction theorem and discrete Cartan–Kähler theorem.     

离散哈密顿系统多个周期解的存在性

本文利用临界点理论,建立了一类离散哈密顿系统存在多个周期解的一些充分条件.     

Representation formula for discrete indefinite affine spheres

We present a representation formula for discrete indefinite affine spheres via loop group factorizations. This formula is derived from the Birkhoff decomposition of loop groups associated with discrete indefinite affine spheres. In particular we show that a discrete indefinite improper affine sphere can be constructed from two discrete plane curves.     

A flexible model and efficient solution strategies for discrete location problems

Flexible discrete location problems are a generalization of most classical discrete locations problems like p-median or p-center problems. They can be modeled by using so-called ordered median functions. These functions multiply a weight to the cost of fulfilling the demand of a customer, which depends on the position of that cost relative to the costs of fulfilling the demand of other customers.In this paper a covering type of model for the discrete ordered median problem is presented. For the solution of this model two sets of valid inequalities, which reduces the number of binary variables tremendously, and several variable fixing strategies are identified. Based on these concepts a specialized branch & cut procedure is proposed and extensive computational results are reported.     

Discrete exact solutions of modified Volterra and Volterra lattice equations via the new discrete sine-Gordon expansion algorithm

Recently, we have presented a sine-Gordon expansion method to construct new exact solutions of a wide of continuous nonlinear evolution equations. In this paper we further develop the method to be the discrete sine-Gordon expansion method in nonlinear differential-difference equations, in particular, discrete soliton equations. We choose the modified Volterra lattice and Volterra lattice equation to illustrate the new method such as many types of new exact solutions are obtained. Moreover some figures display the profiles of the obtained solutions. Our method can be also applied to other discrete soliton equations.