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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Mathematics Faculty Articles
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which expands the range of matrices to which our decomposition can be applied. Our decomposition leads us to a number of related results, allowing us to prove that for tridiagonal doubly stochastic matrices, positive semidefiniteness is equivalent to complete positivity (rather than merely being implied by complete positivity). We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete …
A Classification Of Hull Operators In Archimedean Lattice-Ordered Groups With Unit, Ricardo Enrique Carrera, Anthony W. Hager
A Classification Of Hull Operators In Archimedean Lattice-Ordered Groups With Unit, Ricardo Enrique Carrera, Anthony W. Hager
Mathematics Faculty Articles
The category, or class of algebras, in the title is denoted by W. A hull operator (ho) in W is a reflection in the category consisting of W objects with only essential embeddings as morphisms. The proper class of all of these is hoW. The bounded monocoreflection in W is denoted B. We classify the ho’s by their interaction with B as follows. A “word” is a function w : hoW → WW obtained as a finite composition of B and x a variable ranging in hoW. The set of these,“Word”, is in a natural …
Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang
Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang
Mathematics Faculty Articles
Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (CrI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R0 of COVID-19 to be 4.79(95% CrI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to Rc ≈ 0.32(95% CrI …
Pattern-Avoiding (0,1)-Matrices, Richard Brualdi, Lei Cao
Pattern-Avoiding (0,1)-Matrices, Richard Brualdi, Lei Cao
Mathematics Faculty Articles
We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have. We also give algorithms when carried out in all possible ways, construct all of the pattern-avoiding matrices of these two types.
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Emrah Paksoy
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Emrah Paksoy
Mathematics Faculty Articles
In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.
A Short Note On Extreme Points Of Certain Polytopes, Lei Cao, Ariana Hall, Selcuk Koyuncu
A Short Note On Extreme Points Of Certain Polytopes, Lei Cao, Ariana Hall, Selcuk Koyuncu
Mathematics Faculty Articles
We give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly substochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.