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121.
We define an S1-Euler characteristic, S
1(X), of a circle action on a compact manifold or finite complex X. It lies in the first Hochschild homology group HH
1(G) where G is the fundamental group of X. This S
1(X) is analogous in many ways to the ordinary Euler characteristic. One application is an intuitively satisfying formula for the Euler class (integer coefficients) of the normal bundle to a smooth circle action without fixed points on a manifold. In the special case of a three-dimensional Seifert fibered space, this formula is particularly effective. 相似文献
122.
This paper treats multidimensional discrete input-output systems from the constructive point of view. We adapt and improve recursive algorithms, derived earlier by E. Zerz and the second author from standard Gröbner basis algorithms, for the solution of the canonical Cauchy problem for linear systems of partial difference equations with constant coefficients on the lattices N = r1 × r2. These recursive algorithms, in turn, furnish four other solution methods for the initial value problem, namely by transfer operators, by canonical Kalman global state equations, by parametrizations of controllable systems and, for systems with proper transfer matrix and left bounded input signals, by convolution with the transfer matrix. In the 2D-case N = 2 the last method was studied by S. Zampieri. Minimally embedded systems are studied and give rise to especially simple Kalman equations. The latter also imply a useful characterization of the characteristic or polar variety of the system by eigenvalue spectra. For N = r we define reachability of a system and prove that controllability implies reachability, but not conversely. Moreover we solve, in full generality, the modelling problem which was introduced and partially solved by F. Pauer and S. Zampieri. Various algorithms have been implemented by the first author in axiom, and examples are demonstrated by means of computer generated pictures. Related work on state space representations has been done by the Padovian and Groningian system theory schools. 相似文献
123.
本文把文[2]中关于 R D D E 解空间为有限维的结果完整地推广到 N D D E 和 C D D E 上去,给出了相应的充要条件 相似文献
124.
N. Mukhopadhyay 《Journal of multivariate analysis》1999,68(2):463
We consider the classical fixed-size confidence region estimation problem for the mean vectorμin theNp(μ, Σ) population where Σ is unknown but positive definite. We writeλ1for the largest characteristic root of Σ and assume thatλ1is simple. Moreover, we suppose that, in many practical applications, we will often have available a numberλ*(>0) and that we can assumeλ1>λ*. Given this addi- tional, and yet very minimal, knowledge regardingλ1, the two-stage procedure of Chatterjee (Calcutta Statist. Assoc. Bull.8(1959a), 121–148;9(1959b), 20–28;11(1962), 144–159) is revised appropriately. The highlight in this paper involves the verification ofsecond-order propertiesassociated with such revised two-stage estimation techniques, along with the maintenance of the nominal confidence coefficient. 相似文献
125.
把实轴上具一阶奇性解的特征奇异积分方程及其相联方程的求解化为实轴上具一阶奇性解的Riemann边值问题讨论,对后者在提法、奇点的对待和典则函数的理解方面作了与传统有所不同的处理,对前者通过对解和可解条件的简化及等价性的讨论,得到解和可解条件的简化形式及推广的Noether定理。 相似文献
126.
通过文献分析,概述了认知心理学关于汉字识别过程及其加工机制研究的几种主要的加工模型,即经成分识别模型、多层次交互激活模型、连接主义模型、合体汉字字形识别模型和汉字识别的多层次格式塔双向加工模型. 相似文献
127.
128.
The mixed covolume method for the regularized long wave equation is developed and studied. By introducing a transfer operator γh , which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes. 相似文献
129.
A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of difference operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l 2 norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section. 相似文献
130.
Zbigniew J. Jurek 《Journal of multivariate analysis》1983,13(4):578-604
Let
= {Ut: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set
(X) of all probability measures on X. By
(Q;
) we denote the class of all limit measures of {Utn(μ1 * μ2*…*μn)*δxn}, where {μn}Q, {xn}X and measures Utnμj (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes Lm(
) as follows: L0(
)=
(
(X);
), Lm(
)=
(Lm−1(
);
) for m=1, 2,… and L∞(
)=m=0∞Lm(
). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from Lm(
), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators. 相似文献