The Primitive Exponent of a Class of Special Nonnegative Matrix Pairs

2014 ◽  
Vol 915-916 ◽  
pp. 1296-1299
Author(s):  
Mei Jin Luo
Keyword(s):  
Graph Theory ◽  
Nonnegative Matrix ◽  
One To One

There is a one-to-one relationship between nonnegative matrix pairs and two-colored digraph, so the problem of matrices can be changed into that of graphics to be solved. With the knowledge of graph theory, by studying the associated directed digraph of a class of special nonnegative matrix pairs, that is a class of two-colored digraphs whose uncolored digraph have vertices and consists of one-cycle and one-cycle are considered. The exponent and characteristic of extreme two-colored digraphs are given.

The Upper Bound of Primitive Exponent of a Class of Special Nonnegative Matrix Pairs

2014 ◽  
Vol 1061-1062 ◽  
pp. 1100-1103
Author(s):  
Mei Jin Luo
Keyword(s):  
Graph Theory ◽  
Upper Bound ◽  
Nonnegative Matrix ◽  
N Cycle ◽  
One To One

There is a one-to-one relationship between nonnegative matrix pairs and two-colored digraph. With the knowledge of graph theory, by studying the associated directed digraph of a class of special nonnegative matrix pairs, that is a class of two-colored digraphs whose uncolored digraph have 3n-1 vertices and consists of one (3n-1)-cycle and one n-cycle are considered. The exponent and characteristic of extreme two-colored digraphs are given.

Finding the shortest path for a Hypergraph

2021 ◽  
pp. 2150120
Author(s):  
G. H. Shirdel ◽  
B. Vaez-Zadeh
Keyword(s):  
Graph Theory ◽  
Shortest Path ◽  
Complex Structure ◽  
Dijkstra Algorithm ◽  
Clique Graph ◽  
One To One

A hypergraph is given by [Formula: see text], where [Formula: see text] is a set of vertices and [Formula: see text] is a set of nonempty subsets of [Formula: see text], the member of [Formula: see text] is named hyperedge. So, a hypergraph is a nature generalization of a graph. A hypergraph has a complex structure, thus some researchers try to transform a hypergraph to a graph. In this paper, we define two graphs, Clique graph and Persian graph. These relations are one to one. We can find the shortest path between two vertices in a hypergraph [Formula: see text], by using the Dijkstra algorithm in graph theory on the graphs corresponding to [Formula: see text].

scholarly journals On the maximal angle between copositive matrices

2014 ◽  
Vol 27 ◽  
Author(s):  
Felix Goldberg ◽  
Naomi Shaked-Monderer
Keyword(s):  
Graph Theory ◽  
Variational Approach ◽  
Related Problem ◽  
Nonnegative Matrix ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrix ◽  
Algebraic Graph Theory ◽  
Copositive Matrices ◽  
Maximal Angle ◽  
Semidefinite Matrix

Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle θ_{max}(C_n) between two copositive matrices of order n [J.-B. Hiriart-Urruty and A. Seeger. A variational approach to copositive matrices. SIAM Rev., 52:593–629, 2010.]. They have proved that θ_{max}(C_2) = (3/4)pi and conjectured that θ_{max}(C_n) is equal to (3/4)pi for all n ≥ 2. In this note, their conjecture is disproven by showing that lim_{n→∞} θ_{max}(C_n) = pi. The proof uses a construction from algebraic graph theory. The related problem of finding the maximal angle between a nonnegative matrix and a positive semidefinite matrix of the same order is considered in this paper.

A Support Program

1994 ◽  
Vol 25 (2) ◽  
pp. 112-114 ◽  
Author(s):  
Henna Grunblatt ◽  
Lisa Daar
Keyword(s):  
Hearing Aids ◽  
School Counselor ◽  
Support Program ◽  
Educational Audiology ◽  
Part Program ◽  
One To One

A program for providing information to children who are deaf about their deafness and addressing common concerns about deafness is detailed. Developed by a school audiologist and the school counselor, this two-part program is geared for children from 3 years to 15 years of age. The first part is an educational audiology program consisting of varied informational classes conducted by the audiologist. Five topics are addressed in this part of the program, including basic audiology, hearing aids, FM systems, audiograms, and student concerns. The second part of the program consists of individualized counseling. This involves both one-to-one counseling sessions between a student and the school counselor, as well as conjoint sessions conducted—with the student’s permission—by both the audiologist and the school counselor.

Review of One to One: The Experience of Psychotherapy.

1989 ◽  
Vol 34 (10) ◽  
pp. 958-958
Author(s):  
No authorship indicated
Keyword(s):  
One To One
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