Abstract:The conjugate direction method for solving the unconstrained optimization problem is extended to solving the constrained optimization problem by method of differential geomtry.By inducing a new class of affine connections on a constrained sub-manifold, the primary constrched optilnhation problem is converted to a unconstrained local quadratic programming problem.Based on the definition and construction of a new class of generalized conjugate directions, it isproved that optimum value of the primary constrained optimization problem must be located on thegeodesic line which is formed by the conjugate directions mentioned above and can be reached withinfinite searching step. Therefore a new curve search algorithm with generalized conjugate directions isput forward.

Abstract:The exponential dynamic neural network proposed.by T.D.Chiuch and R.M.Goodman in 1988 is investigated. A concise sufficient condition for the given standard patterns to bestable is presented. A one-step conversence radius of such a stable state is obtained. It is also shownthat there do not exist sporious stable states in the probabilistic sense.

Abstract:When the vertices fail independently with each other by a constant probability,the reliability of a sraph is defined to be the probability that the graph results from deleting thefailed venices together with the incidence edges is connected. The Harary graph,a class of graphswith the best connectivity is considered in this paper,the bound of it's reliability is obtained,and theasymptotic property of reliability is also analysed.

Abstract:The compact explicit formulation of the Back-poopagation is presented,based onwhich the robustness of the feed-forward neural networks is analysed,and some reference priciplesfor desisning a robust feed-forward net are provided.

Abstract:A jumping sequence is proposed,so that a class of r-uniform hypergraphs with nvenices and n edges is constructed. Then by analysing the connectivity of its two-section (graph),this class of hypergraphs is proved to have the best connectivity. The class of hypergraphs can beused to desisn the optimal fault-tolerant multibus computer systems.

Abstract:This paper trains the multilayer neural networks using dynamical programming.The weithts are adjusted layer by layer. The optimal weishts of each layer are calculated using OBPalgorithm proposed in the related reference. The globally optimal weights of each layer can be obtained by finite iterations.

Abstract:阐明了具有Ｌｉｐｓｃｈｉｔｚ指数的地震道信号奇异性的数学特征。对油气勘探区的人工地震资料，选取具有紧支集的二次样条函数作为小波基。然后将采样所得的数据作离散二进小波变换，采用Ｍａｌｌａｔ塔式算法对地震波信号进行分散与重构。

Abstract:通过对现有单机Ｅ／Ｔ排序问题的研究，建立了一类相 应的多机并行加工系统的Ｅ／Ｔ排序模型，模型的优化目标为工件排序的提前与拖期损失的总罚值为极小。还给出了一个工程实用型启发 式排序算法。

Abstract:Based on the algorithms proposed before,a model and new heuristic algorithmfor solving the load balance in a parallel processing system (cell) is put forward by authors in thispeper. The optimal goal of the propsed model benefits the minimum of the load of equipment withlargest load and the difference between and two equipments in the system. The complexity ofalogrithm is not higher than O(n2). The computational experiments show that it is a practical algorithmof engineering.

Abstract:This paper uses the discrete Marquardt algorithm to determine the values of parameters in the logistic equation of Evergreen Needle plant-Fokinenia hodginsii. The Marquardt algorithm is,perhaps,superior than the Gauss-Newton algorithm.

Abstract:The wavelet analysis are used in the detection of edges within the cross sectionfrom projections of parallel beams. This method can be applied in computerized tomography (CT) inorder to reduce the noise and the number of projections.

Abstract:This paper generalizes all known results on Rabinowitz's minimal periodic solution conjecture under the assumption that Hamiltonian function is C2 strictly convex.

Abstract:给出临界点理论中的一个定理：设＞０，水平集Ｆｃ＋ｅ≠φ，则对任意满足Ｆｃ＋ｅ∩Ｕ≠φ的开集Ｕ．或者１）存在ｘｅ∈使得Ｆ（ｘｅ）＜Ｃ－ε，或者２）存在ｘ使得．据此简化了几个熟知定理的证明。

Abstract:under the assumptions that (r)=O(rb)as r and*

Abstract:A minimax theorem is proved by taking advantage of Ekeland's variationalprinciple and the P. S. condition. This theorem can be regarded as an improvement of the theoremdue to Manasevich.

Abstract:We prove the existence of the singular direction related to differential polynomial f'--afn with concerning exceptional set.