Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...

The main purpose of this paper is to study various configurations of a magnetorheological (MR) damper valve and to evaluate their performance indices typically dynamic range, valve ratio, inductive time constant and pressure drop. It is known that these performance indices (PI) of the damper depend upon the magnetic circuit design of the valve. Hence, nine valve configurations are considered fo...

let be a set and let be the set of subsets of . the pair in which is a collection of elements of (blocks) is called a design if every element of appears in , times. is called a symmetric design if . in a symmetric design, each element of appears times in blocks of . a mapping between two designs and is an isomorphism if is a one-to-one correspondence and . every isomorphism of a design, , to it...

We construct two commuting sets of creation and annihilation operators for the PT-symmetric oscillator. We then build coherent states of the latter as eigenstates of such annihilation operators by employing a modified version of the normalization integral that is relevant to PT-symmetric systems. We show that the coherent states are normalizable only in the range (0, 1) of the underlying coupli...

We construct symmetric cubature formulae of degrees in the 1339 range for the surface measure on the unit sphere. We exploit a recently published correspondence between cubature formulae on the sphere and on the triangle. Specifically, a fully symmetric cubature formula for the surface measure on the unit sphere corresponds to a symmetric cubature formula for the triangle with weight function (...

We construct symmetric cubature formulae of degrees in the 13-39 range for the surface measure on the unit sphere. We exploit a recently published correspondence between cubature formulae on the sphere and on the triangle. Speciically, a fully symmetric cubature formula for the surface measure on the unit sphere corresponds to a symmetric cubature formula for the triangle with weight function (...

In the literature it is known that the decomposable numerical range W∧ k (A) of A ∈ Cn×n is not necessarily convex. But it is not known whether W∧ k (A) is star-shaped. We construct a symmetric unitary matrix A ∈ Cn×n such that the decomposable numerical range W∧ k (A) is not star-shaped and hence not simply connected. We then consider a real analog R∧ k (A) and show that R∧ k (A) is star-shape...