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41.
Thomas H. Pate 《Linear and Multilinear Algebra》2003,51(3):263-278
If 1≤k≤n, then Cor(n,k) denotes the set of all n×n real correlation matrices of rank not exceeding k. Grone and Pierce have shown that if A∈Cor (n, n-1), then per(A)≥n/(n-1). We show that if A∈Cor(n,2), then , and that this inequality is the best possible. 相似文献
42.
Several models have been developed in order to categorize the numerous expressions that people use in order to describe their emotional experiences. The focus of the present study is on one of these theoretical classifications proposed by Pekrun (1992) specifically concerning emotions which are directly related to learning and achievement in mathematics. In his model, emotions are classified according to their valence (positive vs. negative) and their level of activation. In testing the assumptions of this model, we investigated students' enjoyment, anxiety, anger and boredom experienced before, during, and after the completion of a math test. Correspondence analyses which were used to generate a graphical illustration of structural interrelationships between these emotions provide empirical support for the theoretical classification. 相似文献
43.
The capability of a modern interpretation system for IR spectra has been tested, in which the process of structural assignment
is modelled by methods of fuzzy logic. Figures of merit were generated for different interpretation algorithms. These figures
of merit permit the validation as well as a comparison of independent interpretation systems. The influence of the sample
preparation practice onto the information content of the resulting spectrum has been evaluated as well. Automatically generated
band tables show only restricted reliability.
Received: 13 February 1997 / Revised: 1 April 1997 / Accepted: 3 April 1997 相似文献
44.
45.
46.
Regularity of multiwavelets 总被引:7,自引:0,他引:7
The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields. 相似文献
47.
The large N phase transition point is investigated in the heat kernel on the U(N) group with respect to arbitrary boundary conditions. A simple functional relation is found relating the density of eigenvalues of the boundary field to the saddle point shape of the typical Young tableaux in the large N limit of the character expansion of the heat kernel. Both strong coupling and weak coupling phases are investigated for some particular cases of the boundary holonomy. 相似文献
48.
We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd-dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber-Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber-Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology. 相似文献
49.
Guy Schmitz 《国际化学动力学杂志》2007,39(1):17-21
At bromide concentrations higher than 0.1 M, a second term must be added to the classical rate law of the bromate–bromide reaction that becomes ?d[BrO3?]/dt = [BrO3?][H+]2(k1[Br?] + k2[Br?]2). In perchloric solutions at 25°C, k1 = 2.18 dm3 mol?3 s?1 and k2 = 0.65 dm4 mol?4 s?1 at 1 M ionic strength and k1 = 2.60 dm3 mol3 s?1and k2 = 1.05 dm4 mol?4 s?1 at 2 M ionic strength. A mechanism explaining this rate law, with Br2O2 as key intermediate species, is proposed. Errors that may occur when using the Guggenheim method are discussed. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 39: 17–21, 2007 相似文献
50.
A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum,
the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without
the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in
the square. Our results differ from previous ones because we require that the entries in the square all be different from
each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from
set systems to rational linear forms.
Dedicated to the memory of Claudia Zaslavsky, 1917–2006
Received August 10, 2005 相似文献