On the bounded generation of arithmetic ${\rm SL}_2$
, 2019 Let $K$ be a number field and ${\mathcal O}$ be the ring of $S$-integers in $K$. Morgan, Rapinchuck, and Sury have proved that if the group of units ${\mathcal O}^{\times}$ is infinite, then every matrix in ${\rm SL}_2({\mathcal O})$ is a product of at ...
Jordan, Bruce W., Zaytman, Yevgeny
core
On the elementary symmetric functions of a sum of matrices
, 2009 Often in mathematics it is useful to summarize a multivariate phenomenon with a single number and in fact, the determinant -- which is represented by det -- is one of the simplest cases.
Costas-Santos, R. S.
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On some determinants involving the tangent function
, 2019 Let $p$ be an odd prime and let $a,b\in\mathbb Z$ with $p\nmid ab$. In this paper we mainly evaluate $$T_p^{(\delta)}(a,b):=\det\left[\tan\pi\frac{aj^2+bk^2}p\right]_{\delta\le j,k\le (p-1)/2}\ \ (\delta=0,1).$$ For example, in the case $p\equiv3\pmod4 ...
Sun, Zhi-Wei
core
GCD matrices, posets, and nonintersecting paths
, 2004 We show that with any finite partially ordered set one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives.
Altinisik, Ercan +2 more
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miR-497 Regulates LATS1 through the PPARG Pathway to Participate in Fatty Acid Synthesis in Bovine Mammary Epithelial Cells. [PDF]
Genes (Basel), 2023 Chu S, Yang Y, Nazar M, Chen Z, Yang Z.
europepmc +1 more source
Determinants of Toeplitz–Hessenberg Matrices with Generalized Leonardo Number Entries
Annales Mathematicae SilesianaeLet un = un(k) denote the generalized Leonardo number defined recursively by un = un−1 + un−2 + k for n ≥ 2, where u0 = u1 = 1. Terms of the sequence un(1) are referred to simply as Leonardo numbers.
Goy Taras, Shattuck Mark
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Sets of range uniqueness for multivariate polynomials and linear functions with rank k. [PDF]
Linear Multilinear Algebra, 2022 Halbeisen L +3 more
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The development of surgical risk score and evaluation of necrotizing soft tissue infection in 161 Naja atra envenomed patients. [PDF]
PLoS Negl Trop Dis, 2022 Lai CS +12 more
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Dietary Melatonin and Omega-3 Fatty Acids Induce Human Cancer Xenograft Regression In Vivo in Rats by Suppressing Linoleic Acid Uptake and Metabolism. [PDF]
Comp Med, 2021 Dauchy EM +6 more
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