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131.
基于对积和式性质的讨论,给出了积和式的"化长为方"计算方法;基于对积和式概念的研究,作为行列式的推广,给出了一般m×n矩阵的行式定义,讨论了行式的性质和计算方法,推广了克莱姆法则. 相似文献
133.
Wendy L. Poston Edward J. Wegman Carey E. Priebe Jeffrey L. Solka 《Journal of computational and graphical statistics》2013,22(3):300-313
Abstract The existence of outliers in a data set and how to deal with them is an important problem in statistics. The minimum volume ellipsoid (MVE) estimator is a robust estimator of location and covariate structure; however its use has been limited because there are few computationally attractive methods. Determining the MVE consists of two parts—finding the subset of points to be used in the estimate and finding the ellipsoid that covers this set. This article addresses the first problem. Our method will also allow us to compute the minimum covariance determinant (MCD) estimator. The proposed method of subset selection is called the effective independence distribution (EID) method, which chooses the subset by minimizing determinants of matrices containing the data. This method is deterministic, yielding reproducible estimates of location and scatter for a given data set. The EID method of finding the MVE is applied to several regression data sets where the true estimate is known. Results show that the EID method, when applied to these data sets, produces the subset of data more quickly than conventional procedures and that there is less than 6% relative error in the estimates. We also give timing results illustrating the feasibility of our method for larger data sets. For the case of 10,000 points in 10 dimensions, the compute time is under 25 minutes. 相似文献
134.
本文对在单位圆盘U={z∈C:l│z│〈1}内解析且满足(1-λ)f(z)/z+λf^1(z)〈1+Az/1+Bz(-1≤B<A≤1;z∈U的函数f所对应的Hankel行列式│a2a4-a^23│,利用Toeplitz行列式的性质得到了其上界估计。 相似文献
135.
George Seifert 《Journal of Difference Equations and Applications》2013,19(3):295-299
In this paper we use a method due to Carvalho (A method to investigate bifurcation of periodic solution in retarded differential equations, J. Differ. Equ. Appl. 4 (1998), pp. 17–27) to obtain conditions for the existence of nonconstant periodic solutions of certain systems of hybrid delay-differential equations. We first deal with a scalar equation of Lotka–Valterra type; then a system of two equations in two unknowns that could model the interactions of two identical neurons. It will be seen that such solutions are determined by solutions of corresponding difference equations. Another paper in which this method is used is by Cooke and Ladeira (Applying Carvalho's method to find periodic solutions of difference equations, J. Differ. Equ. Appl. 2 (1996), pp. 105–115). We first state Carvalho's result. 相似文献
136.
Xiang-Ke Chang Xing-Biao Hu Guo-Fu Yu 《Journal of Difference Equations and Applications》2013,19(7):1093-1107
A Hankel type determinant solution for an integrable semi-discrete equation is presented. As an application, the relations between the solution and combinatorial numbers are discussed, which lead to new combinatorial numbers. The so-called Motzkin-like numbers are obtained, and the corresponding combinatorial interpretation is given. Additionally, it is also shown that some lattice paths have connections with the special solution. 相似文献
137.
Thotsaporn ‘Aek’ Thanatipanonda 《Journal of Difference Equations and Applications》2013,19(9):1344-1349
Using the methodology of (rigorous) experimental mathematics, we give a simple and motivated solution to Zudilin's question concerning a q-analogue of a problem posed by Asmus Schmidt about a certain binomial coefficients sum. Our method is based on two simple identities that can be automatically proved using the Zeilberger and q-Zeilberger algorithms. We further illustrate our method by proving two further binomial coefficient sums. 相似文献
138.
Utilizing the Wronskian technique, a combined Wronskian condition is established for a (3+1)-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed. 相似文献
139.
Caili Sang 《Linear and Multilinear Algebra》2013,61(12):2399-2409
ABSTRACTBy excluding some proper subsets, which do not include any eigenvalues of tensors, from an existing eigenvalue localization set provided by Zhao and Sang, a new eigenvalue localization set for tensors is given. As an application, a sufficient condition such that the determinant of a tensor is not zero is provided. 相似文献
140.
Mari Sano 《Linear and Multilinear Algebra》2013,61(4):474-485
We give an explicit formula for the first non-trivial boundary map of the Akin–Buchsbaum–Weyman resolution (Schur functors and Schur complexes, Adv. Math 1982;44:207-278). The role of the Laplace expansion formula is emphasized. 相似文献