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161.
本文介绍数学中“不变性”思想,讨论了线性代数中某种条件下秩数不变、特征多项式、特征值不变;对称性、半正定、正定性不变;以及度量性不变.以初等变换为首要方法,解决线性代数中一类重要问题.阐述了矩阵或线性方程组线性变换的本质 相似文献
162.
Alberto Cavicchioli Friedrich Hegenbarth Dusan Repovs 《Transactions of the American Mathematical Society》1997,349(10):4007-4019
We study the homotopy type of closed connected topological -manifolds whose fundamental group is that of an aspherical surface . Then we use surgery theory to show that these manifolds are -cobordant to connected sums of simply-connected manifolds with an -bundle over .
163.
A topological sphere theorem is obtained from the point of view of submanifold geometry. An important scalar is defined by the mean curvature and the squared norm of the second fundamental form of an oriented complete submanifold Mn in a space form of nonnegative sectional curvature. If the infimum of this scalar is negative, we then prove that the Ricci curvature of Mn has a positive lower bound. Making use of the Lawson–Simons formula for the nonexistence of stable k-currents, we eliminate Hk (Mn, Z) for all 1 ` k ` n – 1.We then observe that the fundamental group of Mn is trivial. It should be emphasized that our result is optimal. 相似文献
164.
In the present article, we aim at treating the existence of fundamental solutions of linear partial differential operators with constant coefficients from the viewpoint of setting up explicit formulae yielding fundamental solutions. 相似文献
165.
Compound matrices are encountered in many fields such as Matrix Theory, Systems Theory, Control Theory, etc. In the present
paper we develop an efficient algorithm computing the Smith normal form of compound matrices. This algorithm is based on a
new theorem establishing an equivalence relation between the Smith normal form of the compounds of a given matrix and the
compounds of the Smith normal form of the given matrix.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
166.
Masakiyo Miyazawa 《Queueing Systems》1997,25(1-4):45-75
We consider characterizations of departure functions in Markovian queueing networks with batch movements and state-dependent
routing in discrete-time and in continuous-time. For this purpose, the notion of structure-reversibility is introduced, which
means that the time-reversed dynamics of a queueing network corresponds with the same type of queueing network. The notion
is useful to derive a traffic equation. We also introduce a multi-source model, which means that there are different types
of outside sources, to capture a wider range of applications. Characterizations of the departure functions are obtained for
any routing mechanism of customers satisfying a recurrent condition. These results give a unified view to queueing network
models with linear traffic equations. Furthermore, they enable us to consider new examples as well as show limited usages
of this kind of queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
167.
作为H.F.Trotter[3]中一个结果的模拟,本文给出实二次函数域K中基本单位ε的范为N(ε)=g的一些充分必要条件,其中g为K的常数域Fq的非零乘法群Fq^*的生成元(2├q)。利用图论的语言,本文还给出了N(ε)=g的一些充分条件,这些条件对于数域也同样地适用,从而推广了Trotter[3]和前人工作中关于充分条件的结果。 相似文献
168.
Yu. S. Kolesov 《Mathematical Notes》1997,62(5):623-628
For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997.
Translated by O. V. Sipacheva 相似文献
169.
Dingxiong Wang 《中国科学A辑(英文版)》1997,40(8):872-878
The upper bounds on the entropy of a radiation system confined to a spherical box are calculated in six cases by using the
equation of state of radiation in flat spacetime and the equation of state of radiation near black-hole horizon, which was
derived by Li and Liu (hereafter the Li-Liu equation). It turns out that the Li-Liu equation does have unique advantage in
dealing with the entropy bound of critical self-gravitating radiation systems, while the usual equation of state will result
in entropy divergence. In the case of non-self-gravitating radiation systems and non-critical self-gravitating radiation systems,
there is no difference in the entropy bounds derived by these two equations of state. 相似文献
170.
Fully and partially observed stochastic control of systems with nonlinear dynamics and terminal and running costs are considered.
Measure changes are introduced which allow both state and observation dynamics to be thought of as linear. In the case when
the terms of the cost have a special form the measure change transformation “cancels out” the nonlinearities and changes the
original nonlinear problem into a classical LQG one and standard results can be applied. We also consider unnormalized conditional
densities of the whole path as state variables and obtain dynamic programming and verification results.
R. J. Elliott wishes to acknowledge support of the Natural Sciences and Engineering Research Council of Canada, Grant A7964. 相似文献