### A Pfaffian-Hafnian analogue of Borchardt's identity.

Ishikawa, Masao, Kawamuko, Hiroyuki, Okada, Soichi (2005)

The Electronic Journal of Combinatorics [electronic only]

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Ishikawa, Masao, Kawamuko, Hiroyuki, Okada, Soichi (2005)

The Electronic Journal of Combinatorics [electronic only]

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Puninagool, W., Leeratanavalee, S. (2007)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Xin, Guoce (2011)

The Electronic Journal of Combinatorics [electronic only]

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Singh, Kuldip (1978)

International Journal of Mathematics and Mathematical Sciences

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Papaschinopoulos, G., Schinas, C.J., Stefanidou, G. (2007)

Advances in Difference Equations [electronic only]

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Zhongxue, Lü, Hongzheng, Xie (2002)

International Journal of Mathematics and Mathematical Sciences

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Changjian, Zhao, Chen, Chur-Jen, Cheung, Wing-Sum (2009)

Journal of Inequalities and Applications [electronic only]

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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...

Lin, Lai-Jiu, Chen, Hsin I (2003)

Abstract and Applied Analysis

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Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

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Let $S=\{{x}_{1},\cdots ,{x}_{n}\}$ be a finite subset of a partially ordered set $P$. Let $f$ be an incidence function of $P$. Let $\left[f({x}_{i}\wedge {x}_{j})\right]$ denote the $n\times n$ matrix having $f$ evaluated at the meet ${x}_{i}\wedge {x}_{j}$ of ${x}_{i}$ and ${x}_{j}$ as its $i,j$-entry and $\left[f({x}_{i}\vee {x}_{j})\right]$ denote the $n\times n$ matrix having $f$ evaluated at the join ${x}_{i}\vee {x}_{j}$ of ${x}_{i}$ and ${x}_{j}$ as its $i,j$-entry. The set $S$ is said to be meet-closed if ${x}_{i}\wedge {x}_{j}\in S$ for all $1\le i,j\le n$. In this paper we get explicit combinatorial formulas for the determinants of matrices $\left[f({x}_{i}\wedge {x}_{j})\right]$ and $\left[f({x}_{i}\vee {x}_{j})\right]$ on any meet-closed set $S$. We also obtain necessary and sufficient conditions for...

Wen, Jia-Jin, Zhang, Zhi-Hua (2010)

Journal of Inequalities and Applications [electronic only]

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