scholarly journals EXTREME PRESERVERS OF TERM RANK INEQUALITIES OVER NONBINARY BOOLEAN SEMIRING

2014 ◽  
Vol 51 (1) ◽  
pp. 113-123
Author(s):  
LeRoy B. Beasley ◽  
Seong-Hee Heo ◽  
Seok-Zun Song
Keyword(s):  
Boolean Semiring ◽  
Term Rank

Minimal Term Rank of a Class of (0, 1)-Matrices

1963 ◽  
Vol 15 ◽  
pp. 188-192 ◽  
Author(s):  
Robert M. Haber
Keyword(s):  
Term Rank

Let be the class of m × n matrices all of whose entries are either 0 or 1 where every matrix A in the class satisfies the conditions that row i of A has ri ones, i = 1, 2, . . . , m; and column j of A has sj ones, j = 1, 2, . . . , n. We let R = (r1 . . . , rm), S = (s1, . . . , sn), and assume that r1 ≥ r2 ≥ . . . ≥ rm ≥ 0; s1 ≥ s2 ≥ . . . ≥ sn > 0. When this is the case we say the class is normalized.

Light Therapy for Seasonal Affective Disorder the Effects of Timing

1995 ◽  
Vol 166 (5) ◽  
pp. 607-612 ◽  
Author(s):  
Y. Meesters ◽  
J. H. C. Jansen ◽  
D. G. M. Beersma ◽  
A. L. Bouhuys ◽  
R. H. Van Den Hoofdakker
Keyword(s):  
Affective Disorder ◽  
Seasonal Affective Disorder ◽  
Response Rates ◽  
Light Therapy ◽  
Light Treatment ◽  
Therapeutic Outcome ◽  
Short Term ◽  
Rank Ordering ◽  
Term Rank

BackgroundSixty-eight patients with seasonal affective disorder participated in a 10 000-lux light treatment study in which two questions were addressed: do response rates differ when the light is applied at different times of the day and does short-term rank ordering of morning and evening light influence response rates?MethodThree groups of patients received a 4-day light treatment: (I) in the morning (8.00–8.30 a.m., n = 14), (II) in the afternoon (1.00–1.30 p.m., n = 15) or (III) in the evening (8.00–8.30 p.m., n = 12). Two additional groups of patients received two days of morning light treatment followed by two days of evening light (IV, n = 13) or vice versa (V, n = 14).ResultsResponse rates for groups I, II and III were 69, 57 and 80% respectively, with no significant differences between them. Response rates for groups IV and V were 67 and 50% respectively; this difference was not significant and these percentages did not differ significantly from those of groups I and III.ConclusionsThe results indicate that the timing of light treatment is not critical and that short-term rank ordering of morning and evening light does not influence therapeutic outcome.

The Term and Stochastic Ranks of a Matrix

1959 ◽  
Vol 11 ◽  
pp. 269-279 ◽  
Author(s):  
N. S. Mendelsohn ◽  
A. L. Dulmage
Keyword(s):  
Real Number ◽  
Stochastic Matrix ◽  
Real Numbers ◽  
Doubly Stochastic Matrix ◽  
Doubly Stochastic ◽  
The Matrix ◽  
Term Rank ◽  
Square Matrix

The term rank p of a matrix is the order of the largest minor which has a non-zero term in the expansion of its determinant. In a recent paper (1), the authors made the following conjecture. If S is the sum of all the entries in a square matrix of non-negative real numbers and if M is the maximum row or column sum, then the term rank p of the matrix is greater than or equal to the least integer which is greater than or equal to S/M. A generalization of this conjecture is proved in § 2.The term doubly stochastic has been used to describe a matrix of nonnegative entries in which the row and column sums are all equal to one. In this paper, by a doubly stochastic matrix, the, authors mean a matrix of non-negative entries in which the row and column sums are all equal to the same real number T.

scholarly journals Term-rank, permanent, and rook-polynomial preservers

1987 ◽  
Vol 90 ◽  
pp. 33-46 ◽  
Author(s):  
LeRoy B. Beasley ◽  
Norman J. Pullman
Keyword(s):  
Term Rank

Linear preservers of Hadamard majorization

2016 ◽  
Vol 31 ◽  
pp. 593-609 ◽  
Author(s):  
Sara Motlaghian ◽  
Ali Armandnejad ◽  
Frank Hall
Keyword(s):  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Graph Theoretic ◽  
Doubly Stochastic ◽  
Linear Preservers ◽  
Linear Maps ◽  
Term Rank

Let $\textbf{M}_{n }$ be the set of all $n \times n $ realmatrices. A matrix $D=[d_{ij}]\in\textbf{M}_{n } $ with nonnegative entries is called doubly stochastic if $\sum_{k=1}^{n} d_{ik}=\sum_{k=1}^{n} d_{kj}=1$ for all $1\leq i,j\leq n$. For $ X,Y \in \textbf{M}_{n}$ we say that $X$ is Hadamard-majorized by $Y$, denoted by $ X\prec_{H} Y$, if there exists an $n \times n$ doubly stochastic matrix $D$ such that $X=D\circ Y$.In this paper, some properties of$\prec_{H}$ on $\textbf{M}_{n}$ are first obtained, and then the (strong) linear preservers of$\prec_{H}$ on $\textbf{M}_{n }$ are characterized. For $n\geq3$, it is shown that the strong linear preservers of Hadamard majorization on $\textbf{M}_{n}$ are precisely the invertible linear maps on $\textbf{M}_{n}$ which preserve the set of matrices of term rank 1.An interesting graph theoretic connection to the linear preservers of Hadamard majorization is exhibited. A number of examples are also provided in the paper.

Sign in / Sign up

Export Citation Format

Share Document