收敛的阶

This paper,by means of a new method,the graph theory,reanalyses the stability of antisymmetric discrete Hopfield networks,avoiding the construction of energy function.The nessesary and sufficient conditions for a network to converge to a cycle of length 4 are presented,and the number of cycles of length 4 associated with a p-order antisymmetric discrete Hopfield network is discussed,with some suspicions presented.

本文应用一种新的方法——图论方法重新系统地研究了反对称离散Hopfield网络的稳定性理论，这种方法回避了构造能量函数的麻烦，本文给出了网络收敛于长度为4的环吸引子的充分及必要条件，讨论了p阶反对称离散Hopfield网络含有长度为4的环吸引子的数目，并提出了几个尚待解决的猜想。

We introduce the general sigma point selection framework, and give two kinds of efficient methods: a reducing the computing complexity by decreasing the number of the sigma point; b scaling the sigma points to influence the effects of the higher order moments, then improve the accuracy of the UT; c Convergence analysis of the UKF, when used as an observer for nonlinear deterministic discrete-time system, is presented. Based on the UKF that captures the posterior mean and covariance accurately to the second or third order term (in terms of Taylor series expansion) for any form of nonlinearity, sufficient conditions to ensure local asymptotic convergence are established.

论文介绍了sigma点的一般选取规则，并给出了两种有效的方法：a通过减少sigma点集合的元素的数目来减少计算复杂度，b通过增加参数来逼近泰勒展开的高阶项，从而提高UT变换的精度；c论文研究了UKF算法应用于非线性确定性离散时间系统时的收敛性问题。

This paper, considers conservative equation with periodic boundary value problem, and construct a difference scheme, Uses the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, proves that the scheme converges uniformly to the solution of differential equation with order one.

研究守恒型奇振动方程的周期边界问题，构造一个差分格式，利用分解解的奇性项的方法，结合问题的渐近展开，证明所构造的差分格式为一阶一致收敛。

We deal with the biharmonic equation and proved that under our assumptions, the week solution of the natural boundary value problem strongly converges (in H~2) to that of the first boundary value problem.

为克服这一困难，我们用具自然边界条件的边值问题(在二阶椭圆型方程情形为第三边值问题)去逼近相应的第一边值问题，并以重调和方程为例，证明了在一定条件下，其具自然边界条件的边值问题的弱解在H~2的意义下强收敛到相应的第一边值问题的弱解。

Under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were obtained by means of applying the Arzela-Ascoli theorem Lebesque control convergence theorem and disproof method.

在上下解存在的条件下，构造迭代序列，由Arzea-Ascoli定理和Lebesque控制收敛定理得到了二阶非线性Hammerstein型积分微分差分方程的线性边值问题的解的存在性。再利用反证法获得了解的唯一性。

We improved the merit function in quasi-feasible interior point method and used the exponential function that is the more general function to prove the existence of one order optimality point in feasible problem. We discussed the inner and outer algorithms and made the convergence theorem.

在算法中改进了拟可行内点法中的值函数，使用指数形式的更一般函数，用此值函数证明了可行性问题的一阶最优性点的存在性，并通过对内部算法及外部算法的讨论得到了算法的收敛性定理。

The first one is to study how the convergence properties of Newton-type methods change with convergent order. The second one is to study what will infects the computation of the inversion of Jacobi matrix.

本项目对其涉及计算复杂性的几个问题进行的研究，关心的问题是： 1）Newton型方法的收敛性随着阶变化的关系。2）寻找是什么影响着Jacobi矩阵逆的逼近。

The numerical techniques developed here, including the high accuracy method of using expansions in orthogonal functions in normal direction and the effective algebraic mapping to deal with the problem of infinite region, can raise the calculation precision and the convergence velocity greatly.

文中所发展的方法，如，在法向上采用高精度的高阶谱方法和对无限区域数值问题的更为有效的代数变换处理等，提高了计算精度和收敛速度；同时，通过预估校正迭代法，使抛物化稳定性方程中重要的正规化条件得到满足，保证了数值计算的稳定。

By use of first-order linear expansion of Taylor series, the linearization process of both nonlinear constraints and objective function of long-term optimal scheduling model are performed and an optimal scheduling model based on seccessive linear programming is built; an approach to solve Optimal scheduling of cascade hydropower station problem by seccessive linear programming is put forward, the scale-down factor of iteration step length is used to ensure that the algorithm can converge to the optimal solution of optimization problem quickly and accurately.

通过采用泰勒级数一阶描述形式，对优化调度目标函数和约束条件中的非线性约束进行线性化处理，建立了基于连续线性规划算法的优化调度数学模型，提出了用连续线性规划技术求解梯级水电站优化调度问题的算法，并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。

Based on the improved Atiken iterative method and dimidiate method, a new algorithm of searching zero of derivative function is given, the simulation results show that if using the new algorithm to find the zero of derivative function, the convergence speed is faster than the improved Atiken iterative method .

采用二分法预报、改进的Aitken迭代校正的方法，构造了一种求导数零点的一种新算法。新算法在迭代过程中不用计算导数，且二阶收敛。数值试验表明，该算法具有较高的精度和较大的初值选择范

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。