Determinant and inverse of meet and join matrices.
Altinisik, Ercan, Tuglu, Naim, Haukkanen, Pentti (2007)
International Journal of Mathematics and Mathematical Sciences
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Altinisik, Ercan, Tuglu, Naim, Haukkanen, Pentti (2007)
International Journal of Mathematics and Mathematical Sciences
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Ishikawa, Masao, Kawamuko, Hiroyuki, Okada, Soichi (2005)
The Electronic Journal of Combinatorics [electronic only]
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Xin, Guoce (2011)
The Electronic Journal of Combinatorics [electronic only]
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Wen, Jia-Jin, Zhang, Zhi-Hua (2010)
Journal of Inequalities and Applications [electronic only]
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Shaofang Hong, Qi Sun (2004)
Czechoslovak Mathematical Journal
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Let be a finite subset of a partially ordered set . Let be an incidence function of . Let denote the matrix having evaluated at the meet of and as its -entry and denote the matrix having evaluated at the join of and as its -entry. The set is said to be meet-closed if for all . In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set . We also obtain necessary and sufficient conditions for...
Zeilberger, Doron (1996)
The Electronic Journal of Combinatorics [electronic only]
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Siao Hong, Shuangnian Hu, Shaofang Hong (2016)
Open Mathematics
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Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of...
Boris Kapitonov, Bernadette Miara, Gustavo Perla Menzala (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary...