共查询到20条相似文献,搜索用时 15 毫秒
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We establish a stochastic nonlinear analogue of the Perron–Frobenius theorem on eigenvalues and eigenvectors of positive matrices.
The result is formulated in terms of an automorphism T of a probability space and a random transformation D of the non-negative cone of an n-dimensional Euclidean space. Under assumptions of monotonicity and homogeneity of D, we prove the existence of scalar and vector measurable functions α > 0 and x > 0 satisfying the equation αTx = D(x) almost surely. We apply the result obtained to the analysis of a class of random dynamical systems arising in mathematical
economics and finance (von Neumann–Gale dynamical systems). 相似文献
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Niushan Gao 《Positivity》2013,17(4):965-977
The classical Perron–Frobenius theory asserts that, for two matrices $A$ and $B$ , if $0\le B \le A$ and $r(A)=r(B)$ with $A$ being irreducible, then $A=B$ . It has been extended to infinite-dimensional Banach lattices under certain additional conditions, including that $r(A)$ is a pole of the resolvent of $A$ . In this paper, we prove that the same result holds if $B$ is irreducible and $r(B)$ is a pole of the resolvent for $B$ . We also prove some other interesting extensions of the theorem for infinite-dimensional Banach lattices. 相似文献
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This Note presents formulas to express the coordinates of Perron–Frobenius vectors of Cartan matrices (finite or affine) as products of Gamma values, for each finite irreducible root system of rank r. 相似文献
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Let P_k(p, A, B) be the class of functions f(z) = z~p-sum from n=k to ∞(|α_(n+′p|Z~((n+)~-)p) k≥2 analytic in the unit disc E={z:|z|<1} and satisfying the condition |(zf′(z)/f(z)-p)/(Ap-Bzf (z)/f(z))|<1. for z∈E and -1≤B相似文献
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Chris Bernhardt 《Journal of Difference Equations and Applications》2016,22(1):55-66
The goal of this paper is to describe the connections between Perron–Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron–Frobenius theory gives results about the sets of integers that can arise as periods of periodic orbits, about the concepts of transitivity and topological mixing and about horseshoes and topological entropy. 相似文献
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The Perron–Frobenius theorem for an irreducible nonnegative matrix is proved using the matrix graph and the ergodic theorem
of the theory of Markov chains. Bibliography: 7 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 5–16. 相似文献
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Recently, there have been many intriguing new developments in the study of hypermatrices and their associated eigenvalue problems. In particular, results coming from the matrix setting when studying the max algebra have shown especially attractive combinatorial features. We now extend this max algebra setting into the realm of hypermatrices. Considering that the max algebra has shown particular significance in optimization problems for the matrix setting, we look to examine and extend these results in the higher order conditions. Furthermore, we establish some algebraic properties for hypermatrices and then proceed to extend the Perron–Frobenius Theorem for this setting and prove the existence of a unique eigenvalue. We continue by stating a result from Nussbaum, that the Min–Max theorem holds, and provide a proof for completeness. For strongly increasing hypermatrices, an iterative algorithm which converges to our unique eigenvalue is given. Finally, we conclude with an analysis of our results in the hypergraph setting. 相似文献
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In this paper we study the non-existence problem of (nearly) perfect (almost) m-ary sequences via their connection to (near) Butson–Hadamard (BH) matrices and (near) conference matrices. We refine the idea of Brock on the unsolvability of certain equations in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain and get many new non-existence results for near BH matrices and near conference matrices. We also apply previous results on vanishing sums of roots of unity and self conjugacy condition to derive non-existence results for near BH matrices and near conference matrices. 相似文献
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On Graphs with Zero Determinant of Adjacency MatricesXuYinfeng(徐寅峰)(TheSchoolofManagement,Xi'anJiaotongUniversity,Xi'an,71004... 相似文献
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§1.IntroductionTheTeichmülerspacesdiscussedinthispaperareinfinitedimensionalTeichmülerspaceswithcomplexstructure.Thisimpliest... 相似文献
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V. M. Gordienko 《Siberian Mathematical Journal》2017,58(6):990-1003
We consider the matrices of Clebsch–Gordan coefficients. It turns out that these matrices are convenient in order to state, prove, and use many facts of the theory of representations of the groups SO(3) and SU(2). 相似文献
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Facundo Mémoli 《Discrete and Computational Geometry》2012,48(2):416-440
The Gromov?CHausdorff distance between metric spaces appears to be a useful tool for modeling some object matching procedures. Since its conception it has been mainly used by pure mathematicians who are interested in the topology generated by this distance, and quantitative consequences of the definition are not very common. As a result, only few lower bounds for the distance are known, and the stability of many metric invariants is not understood. This paper aims at clarifying some of these points by proving several results dealing with explicit lower bounds for the Gromov?CHausdorff distance which involve different standard metric invariants. We also study a modified version of the Gromov?CHausdorff distance which is motivated by practical applications and both prove a structural theorem for it and study its topological equivalence to the usual notion. This structural theorem provides a decomposition of the modified Gromov?CHausdorff distance as the supremum over a family of pseudo-metrics, each of which involves the comparison of certain discrete analogues of curvature. This modified version relates the standard Gromov?CHausdorff distance to the work of Boutin and Kemper, and Olver. 相似文献
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Ya. N. Shitov 《Journal of Mathematical Sciences》2009,163(5):598-624
Let GMr(A) be the row Gondran–Minoux rank of a matrix, GMc(A) be the column Gondran–Minoux rank, and d(A) be the determinantal rank, respectively. The following problem was posed by M. Akian, S. Gaubert, and A. Guterman: Find the minimal numbers m and n such that there exists an (m × n)-matrix B with different row and column Gondran–Minoux ranks. We prove that in the case GMr(B) > GMc(B) the minimal m and n are equal to 5 and 6, respectively, and in the case GMc(B) > GMr(B) the numbers m = 6 and n = 5 are minimal. An example of a matrix $ A \in {\mathcal{M}_{5 \times 6}}\left( {{\mathbb{R}_{\max }}} \right) $ such that GMr(A) = GMc(A t) = 5 and GMc(A) = GMr(A t) = 4 is provided. It is proved that p = 5 and q = 6 are the minimal numbers such that there exists an (p×q)-matrix with different row Gondran–Minoux and determinantal ranks. 相似文献
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OnSomePropertiesofLTypeIntuitionisticFuzzyFamilyYueShusong;(岳树松)WangJianping(王建平)(HenanNormalUniversity)(HenanUniversity)Abst... 相似文献
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The class of Artin-Rees modules is large.It contains modules satisfying (accr).In this paper, we investigate such modules and show that some properties of modules satisfying (accr) can be generalized to modules of this class. 相似文献