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In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl, 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest Ω-stable matrix problem: given an LMI region $ \Omega \subseteq {\mathbb C} $ Ω ⊆ C and a matrix $ A \in {\mathbb R}^{n \times n} $ A ∈ R n × n , find the nearest matrix to A whose eigenvalues belong to Ω. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices. [ABSTRACT FROM AUTHOR]

Sloshing in coaxial shells partially filled with liquid is investigated using reduced boundary element method. Conical shells are considered as storage tanks. An ideal and incompressible fluid is assumed in the shells. The spectral boundary problem for the liquid vibrations in rigid shells is solved. The results demonstrate the high accuracy of the presented approach. [ABSTRACT FROM AUTHOR]

This research investigates liquid sloshing in a 3D rigid rectangular tank. The impact of rigid baffle on sloshing frequencies has been studied. The mathematical model has been developed using potential theroy. The boundary value problem has an analytical solution in terms of velocity potential with undetermined frequency. We get a system of homogeneous algebraic equations using boundary and free surface conditions. The frequencies are calculated using the non-trivial solution condition. Frequencies of baffled tank are computed for various filling levels. The effects of filling level on frequencies are identified. ANSYS software is used to report the liquid domain and rigid baffle mode forms. [ABSTRACT FROM AUTHOR]