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- Doubly substochastic matrices (2)
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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Eigenvalue Continuity And Gersgorin's Theorem, Chi-Kwong Li, Fuzhen Zhang
Eigenvalue Continuity And Gersgorin's Theorem, Chi-Kwong Li, Fuzhen Zhang
Mathematics Faculty Articles
Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.
Inequalities For Permanents And Permanental Minors Of Row Substochastic Matrices, Zhi Chen, Jiawei Li, Lizhen Yang, Zelin Zhu, Lei Cao
Inequalities For Permanents And Permanental Minors Of Row Substochastic Matrices, Zhi Chen, Jiawei Li, Lizhen Yang, Zelin Zhu, Lei Cao
Mathematics Faculty Articles
In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.
On The Linear Independence Of Finite Wavelet Systems Generated By Schwartz Functions Or Functions With Certain Behavior At Infinity, Abdelkrim Bourouihiya
On The Linear Independence Of Finite Wavelet Systems Generated By Schwartz Functions Or Functions With Certain Behavior At Infinity, Abdelkrim Bourouihiya
Mathematics Faculty Articles
One of the motivations to state HRT conjecture on the linear independence of finite Gabor systems was the fact that there are linearly dependent Finite Wavelet Systems (FWS). Meanwhile, there are also many examples of linearly independent FWS, some of which are presented in this paper. We prove the linear independence of every three point FWS generated by a nonzero Schwartz function and with any number of points if the FWS is generated by a nonzero Schwartz function, for which the absolute value of the Fourier transform is decreasing at infinity. We also prove the linear independence of any FWS …
Centrosymmetric Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Centrosymmetric Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Mathematics Faculty Articles
We consider the convex set Γm,n of m×n stochastic matrices and the convex set Γπm,n ⊂Γm,n of m×n centrosymmetric stochastic matrices (stochastic matrices that are symmetric under rotation by 180 degrees). For Γm,n, we demonstrate a Birkhoff theorem for its extreme points and create a basis from certain (0,1)-matrices. For Γπm,n, we characterize its extreme points and create bases, whose construction depends on the parity of m, using our basis construction for stochastic matrices. For each of Γm,n and Γπm,n, we further characterize their extreme …
A Note On Multilevel Toeplitz Matrices, Lei Cao, Selcuk Koyuncu
A Note On Multilevel Toeplitz Matrices, Lei Cao, Selcuk Koyuncu
Mathematics Faculty Articles
Chien, Liu, Nakazato and Tam proved that all n × n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only depends on the parity of n. In this paper we extend their result to multilevel Toeplitz matrices that any multilevel Toeplitz matrix is unitarily similar to a complex symmetric matrix. We provide a method to construct the unitary matrices that uniformly turn any multilevel Toeplitz matrix to a complex symmetric matrix by taking tensor products of these two types of unitary …
Non-Finitely Based Finite Involution Semigroups With Finitely Based Semigroup Reducts, Edmond W. H. Lee
Non-Finitely Based Finite Involution Semigroups With Finitely Based Semigroup Reducts, Edmond W. H. Lee
Mathematics Faculty Articles
Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup reducts---has so far been published. In the present article, a sufficient condition is established under which an involution semigroup is non-finitely based. This result is then applied to exhibit several examples of the desired opposite type.
Neuroevolutional Methods For Decision Support Under Uncertainty, Nina Komleva, Olga Khlopkova, Matthew He
Neuroevolutional Methods For Decision Support Under Uncertainty, Nina Komleva, Olga Khlopkova, Matthew He
Mathematics Faculty Articles
The article presents a comparative analysis of the fundamental neuroevolutional methods, which are widely applied for the intellectualization of the decision making support systems under uncertainty. Based on this analysis the new neuroevolutionary method is introduced. It is intended to modify both the topology and the parameters of the neural network, and not to impose additional constraints on the individual. The results of the experimental evaluation of the performance of the methods based on the series of benchmark tasks of adaptive control, classification and restoration of damaged data are carried out. As criteria of the methods evaluation the number of …
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Mathematics Faculty Articles
Let Ωn denote the convex polytope of all n x n doubly stochastic matrices, and ωn denote the convex polytope of all n x n doubly substochastic matrices. For a matrix A ϵ ωn, define the sub-defect of A to be the smallest integer k such that there exists an (n + k) x (n + k) doubly stochastic matrix containing A as a submatrix. Let ωn,k denote the subset of ωn which contains all doubly substochastic matrices with sub-defect k. For π a permutation of symmetric group of degree …
The Duals Of *-Operator Frames For End*A(H), Abdelkrim Bourouihiya, M. Rossafi, H. Labrigui, A. Touri
The Duals Of *-Operator Frames For End*A(H), Abdelkrim Bourouihiya, M. Rossafi, H. Labrigui, A. Touri
Mathematics Faculty Articles
Frames play significant role in signal and image processing, which leads to many applications in differents fields. In this paper we define the dual of ∗-operator frames and we show their propreties obtained in Hilbert A-modules and we establish some results.