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The P_0^+-matrix completion problem
No full textA real n by n matrix B is a P_0^+ -matrix if for each k in {1, 2, . . . , n} every k by k principal minor of B is nonnegative, and at least one k by k principal minor is positive. A digraph D is said to have P_0^+-completion if every partial P_0^+-matrix specifying D can be completed to a P_0^+ -matrix. In this paper, we study the P_0^+-completion problem, give necessary conditions for a digraph to have P_0^+-completion, and single out those digraphs of order at most four that have P_0^+-completion
A norm inequality for pairs of commuting positive semidefinite matrices
No full textFor , let and be positive semidefinite matrices such that, for each , commutes with . We show that, for any unitarily invariant norm, The case was recently conjectured by Hayajneh and Kittaneh and proven by them for the trace norm and the Hilbert-Schmidt norm. A simple application of this norm inequality answers a question by Bourin in the affirmative
Orthogonal -basis of relative symmetry classes of polynomials
No full textIn this note, the existence of orthogonal â-basis of the symmetry classes of polynomials is discussed. Analogously to the orthogonal â-basis of symmetry classes of tensor, some criteria for the existence of the basis for finite groups are provided. A condition for the existence of such basis of symmetry classes of polynomials associated to symmetric groups and some irreducible characters is also investigated
Common reducing unitary subspaces and decoherence in quantum systems
No full textMaps of the form Phi(X) =sum_{i=1}^s A_iXA^*, where A_1, . . . ,A_s are fixed complex n by n matrices and X is any complex n by n matrix are used in quantum information theory as representations of quantum channels. This article deals with computable conditions for the existence of decoherence--free subspaces for Phi. Since the definition of decoherence-free subspace for quantum channels relies only on the matrices A1, . . . ,As, the term of common reducing unitary subspace is used instead of the original one. Among the main results of the paper, there are computable conditions for the existence of common eigenvectors. These are related to common reducing unitary subspaces of dimension one. The new results on common eigenvectors provide new effective condition for the existence of common invariant subspaces of arbitrary dimensions
Matrix functions that preserve the strong Perron-Frobenius property
No full textIn this note, matrix functions that preserve the strong Perron-Frobenius property are characterized, using the real Jordan canonical form of a real matrix
River Otter Distribution and Food Habits in Grand Teton National Park as Part of an Ongoing Project in the GYE
No full textGrand Teton National Park is part of the known range of the North American river otter, however not much is known about this semi-aquatic mammal within the park. The results presented here are part of a larger project to investigate the potential of the river otter (Lontra canadensis) to serve as an aquatic flagship (species that engender public support and action) for the Greater Yellowstone Ecosystem. River otters, known for their charismatic behavior have the potential to serve as an aquatic flagship species to promote conservation of aquatic ecosystems. The primary objective of this portion of the study was to identify river otter latrines on portions of the Snake River, between Flagg Ranch and Jackson Lake, and between Jackson Lake Dam and Pacific Creek, collect river otter scats to determine diet of the river otter, and employ remote cameras to determine activity patterns of the river otters. Between 20 June and 1 July 2015, 26 river otter latrines were identified during shoreline surveys, 186 river otter scats were collected, and cameras were deployed at 6 latrines between 7 July and 24 August 2015. River otter scats have been cleaned and prepared for analysis, but have not all been processed to date. Camera traps recorded 222 images, of which 7% (n = 14) were of carnivores, 70% (n = 155) were of non-carnivore mammals, and 9% (n = 22) were of birds. River otters were detected at 1 of the 6 latrines, a total of 5 independent times during the study
Geophysical and Geomorphological Analysis of the Teton Fault, Wyoming
No full textThis investigation applied geophysical and geomorphological analyses of the Teton Fault to assess its geometry, history, and influences on landscape evolution. This project builds on results from a preceding geophysical study completed one year ago (Thackray et al. 2014), a recent study of fault scarp morphology (Thackray and Staley, in review), and years of previous studies of the fault by many practitioners
Normalized rational semiregular graphs
No full textLet G be a graph and let A and D be the adjacency matrix of G and diagonal matrix of vertex degrees of G respectively. If each vertex degree is positive, then the normalized adjacency matrix of G is \hat{A} = D^(â1/2)AD^(â1/2). A classification is given of those graphs for which the all eigenvalues of the normalized adjacency matrix are integral. The problem of determining those graphs G for which \lambda \in Q for each eigenvalue of \hat{A}(G) is considered. These graphs are called normalized rational. It will be shown that a semiregular bipartite graph G with vertex degrees r and s is normalized rational if and only if every eigenvalue of A is a rational multiple of (rs)^{1/2}. This result will be used to classify the values of n for which the semiregular graph (with vertex degrees 2 and n â 1) obtained from subdividing each edge of K_n is normalized rational. Necessary conditions for the k-uniform complete hypergraph on n vertices to be normalized rational are also given. Finally, conditions for the incidence graphs of Steiner triple and quadruple systems to be normalized rational are given
Bounds for eigenvalues of nonsingular H-tensor
No full textThe bounds for the Z-spectral radius of nonsingular H -tensor, the upper and lower bounds for the minimum H-eigenvalue of nonsingular (strong) M -tensor are studied in this paper. The sharper bounds are obtained. Numerical examples illustrate that our bounds give tighter bounds
A Combinatorial Determinant Dual to the Group Determinant
No full textWe define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We give the following combinatorial example of a commuting algebra determinant. Let \Bq(n) denote the set of all subspaces of an -dimensional vector space over \Fq. The {\em type} of an ordered pair of subspaces, where U,V\in \Bq(n), is the ordered triple (\mbox{dim }U, \mbox{dim }V, \mbox{dim }U\cap V) of nonnegative integers. Assume that there are independent indeterminates corresponding to each type. Let be the \Bq(n)\times \Bq(n) matrix whose entry in row , column is the indeterminate corresponding to the type of . We factorize the determinant of into irreducible polynomials