scholarly journals A new characterization of inverse-positive matrices

1991 ◽  
Vol 154-156 ◽  
pp. 45-58 ◽  
Author(s):  
Josep E. Peris
Keyword(s):  
Positive Matrices

scholarly journals Sequence Characterization of 3-Dimensional Riordan Arrays and Some Application

2019 ◽  
Vol 74 (4) ◽  
Author(s):  
Roksana Słowik
Keyword(s):  
Sequence Characterization ◽  
3 Dimensional ◽  
Riordan Arrays ◽  
Totally Positive ◽  
Positive Matrices ◽  
Totally Positive Matrices

Abstract We propose the characterization of 3-dimensional Riordan arrays with use of three sequences that is analogous to the representation of 2-dimensional Riordan arrays with use of A and Z-sequence. We also suggest an application of this representation for finding totally positive matrices.

scholarly journals On standard quadratic programs with exact and inexact doubly nonnegative relaxations

2021 ◽  
Author(s):  
Y. Görkem Gökmen ◽  
E. Alper Yıldırım
Keyword(s):  
Positive Semidefinite ◽  
Quadratic Program ◽  
Algebraic Characterization ◽  
Nonnegative Matrices ◽  
Quadratic Programs ◽  
Optimal Value ◽  
Positive Matrices ◽  
Doubly Nonnegative Relaxation ◽  
Standard Quadratic Program

AbstractThe problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices. Replacing the intractable cone in this formulation by the larger but tractable cone of doubly nonnegative matrices, i.e., the cone of positive semidefinite and componentwise nonnegative matrices, one obtains the so-called doubly nonnegative relaxation, whose optimal value yields a lower bound on that of the original problem. We present a full algebraic characterization of the set of instances of standard quadratic programs that admit an exact doubly nonnegative relaxation. This characterization yields an algorithmic recipe for constructing such an instance. In addition, we explicitly identify three families of instances for which the doubly nonnegative relaxation is exact. We establish several relations between the so-called convexity graph of an instance and the tightness of the doubly nonnegative relaxation. We also provide an algebraic characterization of the set of instances for which the doubly nonnegative relaxation has a positive gap and show how to construct such an instance using this characterization.

A Characterization of Positive Matrices

Positivity ◽  
2005 ◽  
Vol 9 (1) ◽  
pp. 149-150 ◽  
Author(s):  
Charles R. Johnson ◽  
Pablo Tarazaga
Keyword(s):  
Positive Matrices

scholarly journals Strict Positivity of Operators and Inflated Schur Products

2018 ◽  
Vol 10 (6) ◽  
pp. 30
Author(s):  
Ching-Yun Suen
Keyword(s):  
Main Diagonal ◽  
Completely Positive ◽  
Strict Positivity ◽  
Linear Maps ◽  
Positive Matrices ◽  
Positive Linear Maps ◽  
Invertible Elements ◽  
Equivalent Conditions

In this paper we provide a characterization of strictly positive matrices of operators and a factorization of their inverses. Consequently, we provide a test of strict positivity of matrices in . We give equivalent conditions for the inequality . We prove a theorem involving inflated Schur products [4, P. 153] of positive matrices of operators with invertible elements in the main diagonal which extends the results [3, P. 479, Theorem 7.5.3 (b), (c)]. We also discuss strictly completely positive linear maps in the paper.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

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