查询词典 abscissa of uniform convergence

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。

In this thesis, various conventional and ill-conditioned load flow calculation methods have been fully analyzed and evaluated in the aspect of convergence, and the relationship between the convergence and the Jacobian matrix of polar type load flow equation has been discussed and evaluated.

本文对常规潮流算法和常用病态潮流计算方法进行了全面的算法、收敛性分析、评价、比较。

Then it compares these operators' performance through its convergence quality,and it demonstrates that this over-flow dealing method is effective through a group of experiments,the mutation operators used in single-objective optimization have the respectable distribution to polynomial mutation and achieve better convergence quality.

通过一组实验表明这种越界处理方法是非常有效的，单目标优化中的这些变异算子具有与多项式变异算子相当的分布性，同时取得了更好的收敛性能。

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。

And under suitable conditions,we establish the global convergence and locally superlinear/quadratic convergence of the method.

在适当条件下，建立了算法的全局和局部超线性/二阶收敛性

To the tangent distance minimization method,it's quadratic convergence for zero residual problems may not convergence at all.

对于切线距离最小方法，它是接近二次相交零余留的问题，也有可能没有相交。

During the iterations the trial step is truncated when necessary in order to keep the strict feasibility of the iteration points. It is shown that the LMTI approach and the STI approach have global convergence properties under some reasonable assumptions and will achieve local quadratic convergence rate under some even stronger conditions.

LMTI方法主要利用由有限内存BFGS公式的紧致形式获取的目标函数海色阵的近似矩阵构造信赖域问题模型并对其进行求解；而STI方法在构造的低维子空间上求信赖域子问题的解。

Zero residual and non-zero residual problems are discussed in different parts in this paper and the algorithm is proven quadratic convergence for zero residual problems and superlinear convergence for non-zero residual problems.

新方法将问题划分为零残量和非零残量来讨论，并证明了算法对零残量问题具有二次收敛性，对非零残量问题具有超线性收敛性。

The large-scale convergence for Newton-like iterative methods has quadratic convergence.

若为了放宽对初值的选择范围而采用Newton下IJJ法x，十1=x，一汀/flx。

We estab-lish,under some mild assumptions,a locally quadratic convergence theoremfor Method I and prove a semi-local convergence theorem for Method II.Applications of the two methods to complementarity,variational inequalityand optimization problems are investigated as well.

在某些适当的假设下，我们证明了方法I的局部二次收敛性和方法II的半局部收敛性；还研究了两个方法在求解互补问题，变分不等式问题及约束优化问题中的应用。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48