投入产出反问题的优化模型及算法

本文从反问题的角度讨论了修订直接消耗系数的几种优化方法，通过引入“投入产出反问题”的概念，建立了拉格朗日优化，二次规划，熵优化等三个优化模型，同时给出了算法和算例，并且比较了各种方法的计算结果。     

演化均匀优化算法

针对演化算法，使用随机法产生初始点带来的缺陷和均匀设计方法的优点，提出了演化均匀优化算法，进行了算法收敛性分析，并把它应用于多峰函数的数值优化计算，给出了计算示例，结果表明该方法是一种可行而且有效的优化算法．     

清江某拖拉机厂生铁最佳存贮策略的研究

本文分析了清江某拖拉机厂生铁需求及订货规律，建立了该厂生铁需求的概率分布函数，推导并建立了该厂生铁的存贮费用模型，经优化迭代运算，得出了最佳订货点和订货批量的订货策略，最后对优化计算结果进行了灵敏度分析和经济效益计算，证明此策略具有较强的适应性和显著的经济效益．     

一种新型的多属性决策权重计算方法

如何科学、合理地确定指标权重，关系到多属性决策结果的可靠性与正确性。现有多属性决策方法大多不能反映不同决策矩阵规范化方法对指标权重计算的影响，针对这一问题，本文提出了基于不同规范化矩阵确定指标权重的思想，进而推导了一种以全部方案总体效能最小为目标的指标权重模糊优化迭代算法。以向量规范法和线性变换法为例，对某战斗机性能多属性决策问题进行了权重计算。计算结果表明，该方法能够快速收敛到优化权重，从而为多属性决策的权重计算问题提供了新的解决方案。     

非线性二维导热反问题的混沌-正则化混合解法

考虑传导系数随温度变化，建立了非线性二维稳态导热反应题数值计算模型。并把混沌优化方法和梯度正则化方法相结合，构成一种混沌－正则化混合算法求该计算模型的全局解。以热传导系数随温度线性变化为例，由布置在结构边界上的观测点温度信息确定了结构材料热传导系数及其随温度变化规律。结果表明混合算法计算结果与初值无关，具有很好的全局寻优性能，而且计算量远比经典遗传算法和单纯采用混沌优化方法小。     

平稳过程在牙轮钻头井底模式分析中的应用

为了提高石油钻井速度，本文应用平稳过程于牙轮钻头井底模式分析，给出了分析方法和计算步骤，其结果直接服务于优化站井和钻头的优化设计。     

求解一类约束优化问题的Newton分裂算法

本文给出了求解一类约束优化问题的一个Newton分裂算法，并证明了算法的局部平方收敛性，该算法与已有算法相比，具有计算量小的特点，因而特别适合于求解大规模问题，为进一步降低算法的计算复杂性，我们结合Broyden算法，给出了两类Broyden类分裂算法。     

二重奇异积分近似计算的一种优化算法

本文对于矩形区域上某一内点为奇点的奇异积分的近似计算给出了优化中心数值算法，它在迭代计算过程中避免了函数值的重复计算．采用外推法减少迭代次数．     

二重奇异积分近似计算的一种优化算法

本文对于矩形区域上某一内点为奇点的奇异积分的近似计算给出了优化中心数值算法，它在迭代计算过程中避免了函数值的重复计算．采用外推法减少迭代次数．     

用Hopfield网络计算约束条件下系统熵的最小值

有约束条件时系统熵的最小值问题是ＮＰ 完全问题，该文利用Ｈｏｐｆｉｅｌｄ人工神经网络解决组合优化问题的能力计算了此问题，得到了较好的结果．     

Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbances

In this article, we propose a robust tube-based MPC formulation for a class of hybrid systems, namely autonomously switched PWA systems, with bounded additive disturbances. The term tube-based refers to those control techniques whose objective is to maintain all possible trajectories of the uncertain system inside a tube which is a set around the nominal (or reference) system trajectory, that is free from disturbances. Common methods in tube-based control systems consider an error dynamical system as the difference between the state of the nominal system and the state of the perturbed system. However, this definition of the error dynamical system leads to a complicated switched affine system for PWA systems. Therefore, we use a new notion of the reference system similar to the nominal system except that the switching between the various modes of the PWA system is driven by the state of the real system. Using this reference system instead of the nominal system leads us to an error dynamical system that can be modeled as a switched linear system. We employ a switched linear controller to stabilize this error system under arbitrary switching. This auxiliary controller forces the states of the uncertain system to remain in a tube confined to the invariant set around the state of the reference system. We add new constraints and tighten some other constraints of the nominal hybrid MPC for the reference system, in order to ensure convergence of the uncertain system and to guarantee robust exponential stability of the closed-loop system.     

模块化可靠性系统的Signature计算方法研究

系统Signature是体现结构设计优良性的一组向量,描述系统设计对系统故障率的影响,在诸如系统可靠性指标分析、系统设计、系统寿命比较、寿命极限行为以及系统设计优化等方面展现出了强大的功能,成为可靠性研究领域越来越强有力的研究工具。而如何求解一个系统的Signature往往成为分析的关键一步,当系统庞大而复杂时,Signature计算难度将随着元件数目的增加呈指数增加,出现维数爆炸问题,这无疑对后续的分析造成巨大的障碍. 本文为了解决此问题,建立了基于模块化思想的系统Signature求解方法,并给出了基于模块化思想的模块化串、并联系统与模块化备份系统的求解方法,对比于传统算法,运用模块化思想大大减少了计算Signature的复杂度,能够有效减小计算量,缩减计算时间,并拓展了可求解Signature的系统范围。     

Bifurcation of limit cycles at the equator

This paper studies center conditions and bifurcation of limit cycles from the equator for a class of polynomial differential system of order seven. By converting real planar system into complex system, we established the relation of focal values of a real system with singular point quantities of its concomitant system, and the recursion formula for the computation of singular point quantities of a complex system at the infinity. Therefore, the first 14 singular point quantities of a complex system at the infinity are deduced by using computer algebra system Mathematica. What’s more, the conditions for the infinity of the real system to be a center or 14 degree fine focus are derived, respectively. A system of order seven that bifurcates 12 limit cycles from the infinity is constructed for the first time.     

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.     

Reduced systems in Markov chains and their applications in queueing theory

A reduced system is a smaller system derived in the process of analyzing a larger system. While solving for steady-state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability matrix. In this paper, we catagorize reduced systems as standard and nonstandard and explore the existence of reduced systems and their properties relative to the original system. We also discuss first passage probabilities and means for the standard reduced system relative to the original system. These properties are illustrated while determining the steady-state probabilities and first passage time characteristics of a queueing system.     

Poisson冲击下的$k/n(G)$系统的可靠性分析

本文研究了一类Poisson冲击下的$k/n(G)$系统(即$k$-out-of-$n$: $G$系统). 假定冲击的到达数形成一个参数为$\lambda$的Poisson过程, 且冲击的量服从某一分布. 当每次冲击到达时, 对系统中工作的部件独立地产生影响. 进而假定每一部件以一定的概率故障, 概率值是冲击量的函数. 且各次冲击独立地对系统造成损失, 直到工作部件数少于$k$系统故障为止. 在这些假定下, 我们获得了系统的可靠度函数和系统的平均工作时间. 进一步, 假定系统是可修的, 系统中有一个维修工, 并根据``先坏先修’’的维修规则对故障部件进行维修. 在维修时间服从指数分布的假设下, 系统状态转移服从Markov过程. 对该系统我们建立了状态转移方程, 并求得了系统可用度、稳态下的平均工作时间、平均停工时间和系统失效频率等可靠性指标. 最后, 我们还给出了一个简单例子来演示讨论的模型.     

Model Dirac-Maxwell equations with pseudounitary symmetry

We introduce a new system of equations called a model system of Dirac-Maxwell equations, reproducing the main properties of the standard system. At the same time, the model system of equations differs from the standard system in several ways; in particular, it is a tensor system and has a new symmetry with respect to the pseudounitary group. We also propose a version of the model system of Dirac-Maxwell equations with local (gauge) pseudounitary symmetry. We show that any spinor solution of the standard system of Dirac-Maxwell equations can be obtained from the corresponding tensor solution of the model system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 425–435, December, 2008.     

交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

Singularity Structure of Third-Order Dynamical Systems. II

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point. An algorithm for transforming the given third-order system to a third-order Briot–Bouquet system is presented. The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot–Bouquet system. The results of Horn for the third-order Briot–Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured. This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka–Volterra system, and the May–Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.     

Possibly non-unital operator system structures on a possibly non-unital function system

In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.