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51.
伸缩张量率的抽象表示 总被引:2,自引:0,他引:2
本文用“主轴内蕴法”给出右-左伸缩张量 U 和 V 的时间导数 U 和 V 的抽象表示。文中引进所谓“分离技巧”,使能有效地应用张量函数的标准表示。V 的表达式是新的。还给出U 和 V 的两个新关系式。 相似文献
52.
First, some linear techniques in multivariate time-series analysis in EEG research are reviewed to highlight the problem of estimating the dimensionality of the state space (embedding dimension), the reconstruction of an attractor, and the evaluation of invariant properties of the attractor. The traditional linear techniques included the usual spectral and cospectral measures of power, phase, and coherence to which stepwise discriminant analysis was applied for canonical representation of the attractor. Then, some traditional nonlinear techniques of attractor reconstruction and dimensional analysis which use the time-lagged univariate approach of Ruelle and Takens (Takens, 1981) are reviewed. Next, updates and multivariate generalizations that use singular-value decomposition (Broomhead & King, 1986) are reviewed. Finally, Stewart's (1995, 1996) multivariate generalization of the method of false nearest neighbors (Abarbanel, Brown, Sidorowich, & Tsimring, 1993; Kennel, Brown, & Abarbanel, 1992) is reviewed. These are particularly relevant for evaluating multivariate coherence in research on the complex cooperative dynamical systems found in neuroscience, psychology, and social science when time series of sufficient length are investigated. 相似文献
53.
We introduce a family of reductions for removing proper and homogeneous pairs of cliques from a graph G. This family generalizes some routines presented in the literature, mostly in the context of claw-free graphs. These reductions can be embedded in a simple algorithm that in at most |E(G)| steps builds a new graph G′ without proper and homogeneous pairs of cliques, and such that G and G′ agree on the value of some relevant invariant (or property). 相似文献
54.
Bülent Karaszen Süleyman Yldz Murat Uzunca 《Mathematical Methods in the Applied Sciences》2021,44(1):476-492
In this paper, we present two different approaches for constructing reduced‐order models (ROMs) for the two‐dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After integration in time by the fully implicit average vector field method, ROMs are constructed with proper orthogonal decomposition(POD)/discrete empirical interpolation method that preserves the Hamiltonian structure. In the second approach, the SWE as a partial differential equation with quadratic nonlinearity is integrated in time by the linearly implicit Kahan's method, and ROMs are constructed with the tensorial POD that preserves the linear‐quadratic structure of the SWE. We show that in both approaches, the invariants of the SWE such as the energy, enstrophy, mass and circulation are preserved over a long period of time, leading to stable solutions. We conclude by demonstrating the accuracy and the computational efficiency of the reduced solutions by a numerical test problem. 相似文献
55.
Let T be an extension of a one to one normal operator A by a nilpotent operator N. In this paper we calculate the defect of reflexivity of T. We give a necessary and sufficient condition to insure the reflexivity of such extensions. In particular, it is shown that T is reflexive when N is reflexive. 相似文献
56.
M. Halic 《Commentarii Mathematici Helvetici》2002,77(1):145-191
Given a complex, projective variety and a connected, reductive group acting on it, we investigate the relationship between
the Gromov-Witten invariants of the variety and those of its invariant quotient for the group action. Certain so-called Hamiltonian
invariants naturally appear in the context.
Received: May 25, 2000; revised version: December 5, 2000 相似文献
57.
58.
We study the existence of solutions to a system of two inclusions involving Fredholm operators of nonnegative (Fredholm) index
and the so-called c-admissible maps: upper semicontinuous maps with values being continuous images of cell-like sets. The presented approach
resembles the substitution technique, i.e. applies the so-called solution map. The appearance of the ‘dimension defect’ reflecting
the nonnegativity of Fredholm indices requires the use of algebraic tools based on the cohomotopy theory, different from the
usual homological ones present in the fixed point theory. An application to boundary value problems is provided as well as
the brief exposition of basic facts from the cohomotopy theory.
Mathematics Subject Classifications (2000) 47H04, 47A53, 55M20, 55Q55, 34A60. 相似文献
59.
M. Azram 《Acta Mathematica Hungarica》2003,101(3):217-226
A theoretic and diagrammatic relationship between knots and planar graphs has enabled us to establish necessary condition
for achirality. It is shown that the regions, crossings and consequently the number of vertices, edges, and faces in the corresponding
LR-graph are same and invariant. Establishment of new but pivotal moves such as R*-move, 2π-twist and π-twist enabled us to prove that the black regions can be changed into white regions via Reidemeister
moves. Consequently, the equivalence of the companion graphs, necessary and sufficient conditions for achirality.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
60.
Regina Aragn 《Mathematical Logic Quarterly》1995,41(4):485-504
We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order language and α is a linear order with least element, then we let Sentalg(T) be the Lindenbaum-Tarski algebra with respect to T, and we let intalg(α) be the interval algebra of α. Using rank diagrams, we show that Sentalg(Thprin) ? intalg(ω4), Sentalg(Thmax) ? intalg(ω3) ? Sentalg(Thac), and Sentalg(Thsa) ? intalg(ω2 + ω2). For Thmax and Thac we use Ershov's elementary invariants of these theories. We also show that the algebra of formulas of the theory Tx of Boolean algebras with finitely many ideals is atomic. 相似文献