Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Publication
- Publication Type
Articles 1 - 7 of 7
Full-Text Articles in Entire DC Network
Some Results On Injectivity And Multistationarity In Chemical Reaction Networks, Murad Banaji, Casian Pantea
Some Results On Injectivity And Multistationarity In Chemical Reaction Networks, Murad Banaji, Casian Pantea
Faculty & Staff Scholarship
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic results also mentioned. Several results appear in, or are close to, results in the literature. Here, we emphasise the connections between the results, and where possible, present elementary proofs which rely solely on basic linear algebra and calculus. A number of examples …
Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the 2v — j minors, j = 0, 1, 2 of D-optimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of either two SBIBD(2s2 + 2s + 1, s2, s2-s/2) or 2 — {2s2 + 2s + 1; s2, s2; s(s–1)} sds. This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth greater than 2(2s2 + 2s + 1) but experimentation has not …
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the v j minors, j = 0, 1,2 of (1, -1) incidence matrices of SBIBD(v, k, λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remains to establish whether the (1, -1) CP incidence matrices of SBIBD(v, k, λ), can have growth greater than v for families other than Hadamard families.
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We give an algorithm to obtain formulae and values for minors of Hadamard matrices. One step in our algorithm allows the (n – j) x (n – j) minors of an Hadamard matrix to be given in terms of the minors of a 2j-1 x 2j-1 matrix. In particular we illustrate our algorithm by finding explicitly all the (n – 4) x (n – 4) minors of an Hadamard matrix.
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We give an algorithm to obtain formulae and values for minors of Hadamard matrices. One step in our algorithm allows the (n – j) x (n – j) minors of an Hadamard matrix to be given in terms of the minors of a 2j-1 x 2j-1 matrix. In particular we illustrate our algorithm by finding explicitly all the (n – 4) x (n – 4) minors of an Hadamard matrix.
Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We obtain explicit formulae for the values of the 2v — j minors, j = 0, 1, 2 of D-optimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of either two SBIBD(2s2 + 2s + 1, s2, s2-s/2) or 2 — {2s2 + 2s + 1; s2, s2; s(s–1)} sds. This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth greater than 2(2s2 + 2s + 1) but experimentation has not …
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We obtain explicit formulae for the values of the v j minors, j = 0, 1,2 of (1, -1) incidence matrices of SBIBD(v, k, λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remains to establish whether the (1, -1) CP incidence matrices of SBIBD(v, k, λ), can have growth greater than v for families other than Hadamard families.