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It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分,主要研究了线性互补问题的几个相关的公开问题以及猜想:(1)研究了Murthy等在[2]中提出的公开问题,即对任意的矩阵A,其扩充矩阵是否为Q_0-矩阵,给出了肯定的回答,得到充分矩阵的扩充矩阵是充分矩阵,并讨论了Graves算法,证明了若A是双对称的P_0-矩阵时,LCP可由Graves算法给出;(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想,给出了半正定矩阵的一些充分条件,并研究了Pang~-猜想,得到了只R_0-矩阵与Q-矩阵的二个等价条件,以及E_0∩Q-矩阵的一些性质;(3)研究了Danao在[25]中提出的Danao猜想,即,若A为P_0-矩阵,则,我们给出了反例证明了此猜想当n≥4时不成立,指出了Murthy等在[20]中的一些错误,得到n=2,3时,即[25]中定理3.2中A∈P_0的条件可以去掉。

In the fourth chapter, the testing of variance component in semiparametric generalized linear model is studied.

第四章系统研究了半参数广义线性模型的方差成分检验。

In the fifth chapter, the testing of variance component in semiparamtric generalized linear model for longitudinal data is studied.

第五章系统研究了基于纵向数据的半参数广义线性模型的方差成分检验。

Further, it is proved that the semi-implicit Euler method is convergent with order 1/2 in mean square sense for the linear test equation by virtue of properties of the conditional expectation.

在此基础上由条件期望的性质证明了半隐式Euler方法应用于线性试验方程时在均方意义下是l/2阶收敛的。

Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann给出的,早期的有关类流形的研究与物理和力学密切相关,自从1991年金行壮二发表了陪集空间上存在不变仿凯勒结构的代数化结果后,李群及李代数理论在这类流形的研究中起着主要作用,特别地,李代数的双极化与这类流形密切相关,半单李代数的双极化的相关几何,金行壮二,候自新和邓少强等人已作了研究,二次李代数是比半单李代数更广且带有非退化不变双线性型的李代数,本文主要研究了二次代数的双极化及相关几何。

The results of orthogonal experiments show that of the three factors affecting the dispersion, sample volume is of the first importance, flow rate the second, and the tube length the last.

随着进样体积的增大,半峰宽和峰面积成正比例地增大,而峰高值开始时线性增大,随后增加幅度逐渐减慢。

Firstly, we obtain the well-posedness of the system by the semigroup theory of bounded linear operators.

首先, 利用有界线性算子半群理论得到了系统的适定性。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后,采用基于次微分的半光滑L-M法求解,该方法属于牛顿法范畴,可通过对L-M参数的调整保证迭代系数矩阵的正定性,克服了系数矩阵的奇异引起的"病态",且该方法在确定搜索方向时只需求解线性系统的加热器近似解,适用于大规模系统的求解。

The resulting vertical and horizontal slant angular displacement of bullet in half constraint region was presented during gun-firing, and the influence of rotor rotational speed and barrels clamp cone angle on initial ballistic dispersion were also discussed.

结果表明,半约束期内旋转离心力和身管组半锥夹角导致的科氏力对弹丸起始扰动有影响,同时弹丸偏角将随着身管转速的增加而线性增加,特别是高射速时,弹丸的偏角更大,这些可为转管武器的射击精度研究提供参考。

In this paper, a new algorithm relaxation-strategy-based for a class of linear semi-infinite programming is developed, called the modification algorithm.

对于一类线性半无限规划问题给出一种我们称之为修正算法的一种新算法。

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