收敛

Compared with GDQR and FEM, the error of displacement was 2.4 percent and the error of force was 4.2 percent in the solutions.

介绍了广义微分求积法的一般原则，对比了用传统DQ法与GDQR在处理截面突变问题中的优劣，研究了用DQ法试解静水压力作用下变截面环向加箍贮液罐圆筒问题，由于变截面处的奇异性问题，所得到的结果不收敛，而采用GDQR重解该问题则得到收敛解。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

According to poisson distribution and percolation theory, we construct stock price model, and use characteristic function to prove the convergence of this model, we can get that the characteristic function of the constructed model converge on the characteristic function of the Black-Scholes function.

根据泊松分布和渗流理论构造了股票价格的随机模型，并利用特征函数的性质论证了该模型的收敛性，得出所构造的股票价格随机模型的特征函数收敛到某一个Black-Scholes公式的特征函数的结论。

The chattering mode in the dynamic process of the unforced switched systems isinvestigated. The relations between the rotation directions of trajectory, the increase ordecrease the polar radius of trajectory, and the convergent chattering mode are revealed.

分析了二阶切换线性系统的收敛震颤现象与相轨迹的旋向以及相轨迹极半径增减趋势之间的关系，进而得到忽略切换延迟时二阶切换线性系统出现收敛震颤模态的充分条件。

Some examples are calculated and by comparing the results with those obtained by the power series method, the validity and some excellences of the B-spline function method, such as wider convergent range, higher precision and less amount of computing time, are demonstrated.

所得结果很理想，验证了样条函数在此问题上的有效性，并在收敛速度、收敛范围、计算精度等方面体现了此法的优越性。

To settle the contradictory between convergence speed and precocity and stagnation in ant colony algorithm, an adaptive ant colony algorithm, which is based on the equilibrium of the ant distribution, is presented.

针对蚁群算法加速收敛和早熟停滞现象的矛盾，提出一种基于分布均匀度的自适应蚁群算法，以求在加速收敛和防止早熟、停滞现象之间取得很好的平衡。

The Paper introduces prepotency and variance operator and new individuals , so the arithmetic a-voids premature and improves convergent speed and capability .

在遗传算法中引入了优生算子，变异算子和新个体，避免了局部早熟，提高了收敛速度和全局收敛能力。

Finally, it has been proved that a step learning function, which satisfies the condition of LMS algorithm, could make network weight converge with probability 1 to the feature vector.

并证明了SOFM网络的学习存在一表征特征矢量的稳定解，最后证明了一个满足LMS随机逼近收敛算法条件的步幅函数可使网络权值以概率1收敛于特征矢量。

Until recently, the convergence of the Rosen"s arithmetic has been proved. The projection gradient method is the generalization of Steepest decent method to constraint problem. So it does have a faster convergence speed that the fastest decent method . To solve the problem, many researchers have generalizat the well-developed optimization with unconstraint to the Rosen"s gradient method. The conjugate gradient method is one of success to solve the problem.

投影梯度法是最速下降法对约束问题的推广，因此没有较快的收敛速度，为了解决这个问题很多中外学者把发展得比较成熟的无约束最优化算法作类似的推广，其中共轭梯度方法是近年发展的很成熟的方法，它具有计算简单，算法结构好，计算量少，具有良好的收敛性等优点，而Rosen投影梯度法的提出使寻找下降方向变得简单。

The proposed algorithm is convergent to the solution through the solutions of a series of condensation trust region subproblems. It is proved that the method is globally convergent and that the convergence rate is quadratic.

算法通过求解序列压缩信赖域子问题来获得原问题的最优解，并具有全局收敛性和局部二阶收敛速度。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。