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
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
Sets of range uniqueness for multivariate polynomials and linear functions with rank k. [PDF]
Linear Multilinear Algebra, 2022 Halbeisen L +3 more
europepmc +1 more source
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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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
europepmc +1 more source
Maternal and Early Postnatal Diet Supplemented with Conjugated Linoleic Acid Isomers Affect Lipid Profile in Hearts of Offspring Rats with Mammary Tumors. [PDF]
Animals (Basel), 2020 Białek M, Białek A, Czauderna M.
europepmc +1 more source
Modified fish diet shifted serum metabolome and alleviated chronic anemia in bottlenose dolphins (Tursiops truncatus): Potential role of odd-chain saturated fatty acids. [PDF]
PLoS One, 2020 Venn-Watson S +4 more
europepmc +1 more source
Yeast lipids from cardoon stalks, stranded driftwood and olive tree pruning residues as possible extra sources of oils for producing biofuels and biochemicals. [PDF]
Biotechnol Biofuels, 2018 Tasselli G +12 more
europepmc +1 more source