幂函数型完全非线性函数原像分布的特征

完全非线性函数是特征为奇数的有限域上抗差分密码攻击最优的函数,目前已有的六类完全非线性函数都是2-1的。当Π(x)为Fqm上的Dembowski-Ostrom函数或者Coulter-Matthews函数时,从Fqm到Fq的完全非线性函数tr(aΠ(x))的原像分布恰有两种取值,其中一种取值对应Fqm所有平方剩余元,另一种取值对应Fqm所有非平方剩余元。该结论在文中得到了证明。     

一类完全非线性函数的证明与计数

Helleseth等最近给出了一类二项式形式的完全非线性函数,这是至今为止所发现的第一类由两个互不等价的单项式组成的二项式形式的完全非线性函数。本文利用Frobinus自同构将其变形为一个新的二项式,给出了其完全非线性的简洁证明,指出了这类函数与x2是等价的,最后讨论了该类完全非线性函数的计数性质。     

广义Liénard方程Poincaré分岔极限环的唯一性和不存在性

讨论了一类广义Linard方程x¨+f1(x)x.2+εf2(x)x.+g(x)=0的Poincar分岔极限环的唯一性和不存在性。将不对Abel积分进行分项,而是利用一阶Mel′nikov函数直接从整体上进行分析讨论,得出了若干判别准则和充分条件。     

基于极大熵微粒群混合算法的非线性方程组求解

针对非线性方程组,给出了一个新的算法.该算法首先把非线性方程组转化为一个不可微优化问题,然后用一个称之为凝聚函数的光滑函数直接代替不可微的极大值函数,从而可把非线性方程组的求解转化为无约束优化问题,再利用微粒群算法对其进行求解.利用4个测试函数对其进行测试并与其他算法进行比较.计算结果表明,提出的算法在求解的准确性和有效性方面均优于其它算法.     

非平稳数据处理方法与瞬时频率

利用“经验模式分解”(EMD)方法,任何复杂的数集都能够被分解为有限且通常数量较少的“本征模式函数”。“本征模式函数”产生瞬时频率,最终结果表示为H ilbert谱规定的能量-频率-时间分布。应用“经验模式分解”方法表示自然现象中的传统非线性平衡系统及其数据的数值结果,同时给出实例展示了这种新方法的作用和效果。这种方法阐明了能量-频率-时间分布,进一步显示出对非线性非平稳系统的处理效果———精确化、形象化和可视化。     

高非线性度弹性S盒的构造

弹性S盒可应用于容错分布计算,量子密码密钥分配和流密码中伪随机序列产生.基于线性码和高非线性度的S盒,给出了一种构造具有高非线性度,且代数次数大于给定值的弹性S盒的方法.对于给定参数的线性码,构造的弹性S盒的非线性度是可以计算的.结果表明所构造的函数的非线性度优于已有的结果.     

一类非线性类薛定谔方程的有限差分格式

给出了一类非线性类薛定谔方程的有限差分格式,推导了这类非线性类薛定谔方程的积分形式,并得到积分形式下系统的2个守恒定理.通过对积分方程离散化,并对系统的守恒量进行有限差分,得到了这类非线性类薛定谔方程的有限差分格式.     

样条有限点法分析板的非线性动力响应问题

本文提出了用样条有限点法分析板的几何非线性动力响应问题。采用了三次B样条函数与梁的振型函数的乘积作为试函数,由虚位移原理的动力方程出发,建立起以样条函数结点参数表示的基本方程,推导了非线性刚度矩阵的精确显式,并用wilson-θ法求解动力增量方程,求得挠度响应曲线。本文给出了算例,并与文献结果进行比较。本文提出的方法具有计算量小、精度高等优点。是十分有效的方法。     

基于改进粒子群优化算法的发动机故障仿真

为对发动机的稳态故障特性进行有效分析,提出了一种基于改进粒子群优化算法的故障仿真方法。首先将描述系统性能的非线性方程组,转化为带约束的最优化形式,通过设置式中参数可以仿真不同状况下的系统故障。并且提出运用一种改进的粒子群优化算法来为解决描述系统的高维、非线性函数,该算法在初始化时,运用混沌的思想,使得粒子分布遍历所有状态;在进化时,运用的免疫的思想,设置了基于适应度的克隆算子与变异算子增加粒子的多样性;在免疫选择之后,对各个粒子的速度也进行了重新设置,增加了粒子寻找全局最优的能力。实验结果表明,改进的粒子群优化算法能够有效地求得最优解。     

求解武器目标分配问题的一个近似最优方法

文章研究在作战领域中应用非常广泛的武器目标分配(WTA)问题。这一问题研究如何将一类武器分配给打击目标,使得被打击目标总的损毁效果最大。WTA问题难以找到多项式时间解,目前不存在求最优解的精确算法。文章利用WTA模型中目标函数的特点,使用线性函数来替代原问题中的非线性目标函数,近而将非线性整数规划问题转化为线性整数规划问题。在CPLEX下的数值试验显示,在较短时间内,这一线性整数规划模型可以得到一个好的次优解。     

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew (PFGS) plates. The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate. A nonlinear finite element (FE) formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory (FSDT) in conjunction with von Karman’s nonlinear strain displacement relations. The governing equations of the PFGS plate are derived using the principle of virtual work. The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations. The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters. The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.     

Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous (FGP) variable-thickness plates by using an edge-based smoothed finite element method (ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index (k) and maximum porosity distributions (Ω) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.     

Optimal replacement of parts having observable correlated stages of deterioration

A single component system is assumed to progress through a finite number of increasingly bad levels of deterioration. The system with level i (0 ≤ i ≤ n) starts in state 0 when new, and is definitely replaced upon reaching the worthless state n. It is assumed that the transition times are directly monitored and the admissible class of strategies allows substitution of a new component only at such transition times. The durations in various deterioration levels are dependent random variables with exponential marginal distributions and a particularly convenient joint distribution. Strategies are chosen to maximize the average rewards per unit time. For some reward functions (with the reward rate depending on the state and the duration in this state) the knowledge of previous state duration provides useful information about the rate of deterioration.     

Dynamic pricing in a dual‐market environment

This article is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, for example, a long‐distance market and an on‐site market. The key difference between the two markets is that the long‐distance market provides for a one period delay in demand fulfillment. In contrast, on‐site orders must be filled immediately as the customer is at the physical on‐site location. We model the demands in consecutive periods as independent random variables and their distributions depend on the item's price in accordance with two general stochastic demand functions: additive or multiplicative. The firm uses a single pool of inventory to fulfill demands from both markets. We investigate properties of the structure of the dynamic pricing strategy that maximizes the total expected discounted profit over the finite time horizon, under fixed or controlled replenishment conditions. Further, we provide conditions under which one market may be the preferred outlet to sale over the other. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 531–549, 2015     

On the theory of semi-infinite programming and a generalization of the kuhn-tucker saddle point theorem for arbitrary convex functions

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.     

Maximizing the sum of certain quasiconcave functions using generalized benders decomposition

In this paper we consider the problem of maximizing the sum of certain quasi-concave functions over a convex set. The functions considered belong to the classes of functions which are known as nonlinear fractional and binonlinear functions. Each individual function is quasi-concave but the sum is not. We show that this nonconvex programming problem can be solved using Generalized Benders Decomposition as developed by Geoffrion.     

Optimal advertising and inventory control of perishable goods

The primary goal of this article is to extend the results of a previous article to the case where the effect of advertisement on sales lasts more than one period. Monotonicity of the optimal advertising and inventory policies in the various factors is investigated. Also, attention will be focused on the relationship between the fluctuations over time of the optimal policies and the variations over time of the factors involved, such as demand distributions and holding costs. For example, if over a finite interval the demand decreases from one period to the next, reaches a minimum, and then increases, then the optimal advertising policy will produce the opposite effect. The period of minimum demand never precedes that of maximum goodwill; moreover, the optimal inventory level decreases while the demand decreases. Finally, when demand distributions are just translates of one another, the results of this article can be extended to nonperishable goods.     

Fluctuations of the optimal advertising and inventory policy: A qualitative analysis

This paper discusses the properties of the inventory and advertising policy minimizing the expected discounted cost over a finite horizon in a dynamic nonstationary inventory model with random demand which is influenced by the level of promotion or goodwill. Attention is focused on the relation between the fluctuations over time of the optimal policies and the variations over time of the factors involved, i.e., demand distributions and various costs. The optimal policies are proved to be monotone in the various factors. Also, three types of fluctuations over time of the optimal policies are discussed according to which factor varies over time. For example, if over a finite interval, the random demand increases (stochastically) from one period to the next, reaches a maximum and then decreases, then the optimal inventory level will do the same. Also the period of maximum of demand never precedes that of maximum inventory. The optimal advertising behaves in the opposite way and its minimum will occur at the same time as the maximum of the inventory. The model has a linear inventory ordering cost and instantaneous delivery of stocks; many results, however, are extended to models with a convex ordering cost or a delivery time lag.