基于混合变异的果蝇优化算法

果蝇算法是新提出一种的群智能优化算法,它存在一些不足尤其是在收敛性和求解精度方面.基于以上提出了一种基于混合变异算子的果蝇优化算法,充分利用柯西变异算子所具有全局搜索能力强的特点和高斯变异算子的局部搜能力强的优点,将这两个算子结合在一起来更新果蝇的位置从而很好的避免了各自算子的缺点.为了验证算法的性能通过测试7个标准多元非线性函数同果蝇优化算法及参考文献中算法结果相比较,实验表明该算法的收敛速度和求解的精度都得到了提高.     

模糊推理的α-三I算法

三I算法是针对模糊推理的FMP与FMT模型的一种新的推理方法。本文借助蕴涵算子的性质,针对满足一定条件的较一般蕴涵算子,建立了FMP与FMT模型的α-三I算法,并讨论了算法的还原性。     

模糊推理三Ⅰ算法的还原性

模糊推理算法的还原性是判断蕴涵算子与推理方法配合效果的一个重要标准,只有蕴涵算子与推理方法搭配适当,才能使模糊推理有一个好的效果。本文对模糊推理三I算法具备还原性的条件进行了研究。首先,当与蕴涵算子相伴随的三角模为连续三角模时,给出了FM P问题三I算法具有还原性的充要条件;其次,当蕴涵算子为连续的正则蕴涵算子时,给出了FM T问题的三I算法具有还原性的充要条件;最后,当正则蕴涵算子关于补运算满足对合律时,给出了FM T问题三I算法满足还原性的一个充分条件。     

建立模糊诊断矩阵的一种新方法

本文首先提出了一个新的模糊逻辑算子——模糊加权综合算子“#”,进而给出建立模糊诊断矩阵的新方法——网络法 ,并给出了相应的算法     

基于S蕴涵算子的区间值模糊推理的三I算法

针对S蕴涵算子讨论了FM P模型及FM T模型的区间值模糊集三I推理,借助S蕴涵算子的性质,给出相应的推理算法,并讨论了算法的还原性。     

参数Kleene系统的三Ⅰ算法与反向三Ⅰ支持算法

提出基于参数蕴涵算子θp模糊推理的思想,给出了在模糊推理的每一步都使用蕴涵运算pθ的三I算法与反向三I支持算法理论,得到了三I上确界算法、模糊取式算法(FM P)与模糊拒取式算法(FM T)的计算公式,这将有助于提高模糊推理结果的可靠性。     

θp型三I算法与反向三I算法支持度分析

研究了基于蕴涵算子以θp模糊推理的三Ⅰ算法与反向三Ⅰ算法的支持度理论，分析了支持度的性质，得到了α-三Ⅰ算法的FMP（FMT）计算公式与α-反向三Ⅰ算法的FMP（FMT）计算公式。     

基于Lukasiewicz蕴涵算子的反向三I算法

三Ⅰ算法是针对模糊推理的FMP与FMT模型的一种新的推理方法。本文针对Lukasiewicz蕴涵算子讨论FMP模型及FMT模型的反向三Ⅰ推理及反向α-三Ⅰ推理,借助该蕴涵算子的性质,给出相应的推理算法。     

基于蕴涵算子族L-λ-G的模糊推理三Ⅰ支持算法

提出了基于蕴涵算子族L-λ-G的模糊推理的思想,这将有助于提高推理结果的效果.针对蕴涵算子族L-λ-G给出了模糊推理的FMP模型及FMT模型的三Ⅰ支持算法、α-三Ⅰ支持算法。     

基于蕴涵算子族L-λ-G的模糊推理三I支持算法

提出了基于蕴涵算子族L -λ-G的模糊推理的思想,这将有助于提高推理结果的效果.针对蕴涵算子族L-λ-G 给出了模糊推理的FMP模型及FMT模型的三I支持算法、α-三I支持算法.     

复杂边界旋转Navier-Stokes方程的几何方法及二度并行算法

本文提出了一种求解复杂边界旋转Navier-Stokes方程的微分几何方法及其二度并行算法.此方法可用于求解透平机械内部叶片间流动和飞行器外部绕流等复杂流动问题.假设流动区域可以用一系列光滑曲面■_k,k=1,2,…,K分割为一系列子区域(称作流层),通过应用微分几何的方法,三维N-S算子可以分解为两类算子之和:建立在曲面■_k切空间上"膜算子"和曲面■_k法线方向的"挠曲算子",将挠曲算子应用欧拉中心差商来逼近,由此得到建立在■_k上的"2D-3C"N-S方程.求解2D-3C N-S方程并且反复迭代直到收敛.我们得到"二度并行算法",它是2D-3C N-S方程并行算法与k方向的同时并行.这个算法的优点在于,(1)可以改进由于复杂边界造成的不规则三维网格引起的逼近解的精度;(2)为克服边界层的数值效应,在边界层内可以构造很密的流层,形成三维多尺度的网格,是一个很好的边界层算法;(3)这个方法不同于经典的区域分解算法,这里的每个子区域只需要求解一个"2D-3C"N-S方程,而经典区域分解方法要在每个子区域上求解三维问题.     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

A Regularization Method for the Proximal Point Algorithm

A regularization method for the proximal point algorithm of finding a zero for a maximal monotone operator in a Hilbert space is proposed. Strong convergence of this algorithm is proved.Hong-Kun Xu: Supported in part by NRF     

Separation of Variables and Integral Relations for Special Functions

We show that the method of separation of variables gives a natural generalization of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the quadratic integral relations for the continuous q-ultraspherical polynomials. The separating integral operator M expressed in terms of the Askey-Wilson operator is studied in detail: apart from writing down the characteristic (separation) equations it satisfies, we find its spectrum, eigenfunctions, inversion, invariants (invariant q-difference operators), and give its interpretation as a fractional q-integration operator. We also give expansions of the A₁ Macdonald polynomials into the eigenfunctions of the separating operator M and vice versa.     

Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

Multilevel Additive Schwarz Method for the Version of the Galerkin Boundary Element Method

We study a multilevel additive Schwarz method for the - version of the Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind are considered. As it is well known the - version with geometric meshes converges exponentially fast in the energy norm. However, the condition number of the Galerkin matrix in this case blows up exponentially in the number of unknowns . We prove that the condition number of the multilevel additive Schwarz operator behaves like . As a direct consequence of this we also give the results for the -level preconditioner and also for the - version with quasi-uniform meshes. Numerical results supporting our theory are presented.

     

基于不确定多属性群决策方法的装甲武器战力评估

针对方案的属性权重为实数、属性值为不确定语言,通过定义不确定语言的"依可能度不差于"关系和对影响装甲武器战斗潜力的几个属性进行分析,探讨了不确定语言之间"依可能度不差于"关系比较大小的充要条件,提出了一种基于该关系的多属性群决策方法,并给出了实例仿真.实例表明:方法进行评估步骤少,计算简单,容易施行.     

A MULTI-GRID ALGORITHM FOR MIXED PROBLEMS WITH PENALTY BY C°-PIECEWISE LINEAR ELEMENT APPROXIMATION

In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.     

The Liouville Field Theory Zero-Mode Problem

We quantize the canonical free-field zero modes p, q on the half-plane p > 0 for both Liouville field theory and its reduced Liouville particle dynamics. We describe the particle dynamics in detail, calculate one-point functions of particle vertex operators, deduce their zero-mode realization on the half-plane, and prove that the particle vertex operators act self-adjointly on the Hilbert space L ²(₊) because of symmetries generated by the S-matrix. Similarly, we obtain the self-adjointness of the corresponding Liouville field theory vertex operator in the zero-mode sector by applying the Liouville reflection amplitude, which is derived by the operator method.