In motion Kinematics, it is well-known that the time derivative of a 3 × 3 rotation matrix equals a skew-symmetric matrix multiplied by the rotation matrix where the skew symmetric matrix is a linear (matrix-valued) function of the angular velocity and the rotation matrix represents the rotating motion of a frame with respect to a reference frame. The equation is widely used in engineering, e.g...

Abstract In this paper, we consider skew-Hermitian solution of coupled generalized Sylvester matrix equations encompassing $$*$$ ∗ -hermicity over complex field. The compact formula the general system is presented in terms inverses when some necessary and sufficient conditi...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

0. Introduction 1. Borel decomposition and the 2-Toda lattice 2. Two-Toda τ -functions and Pfaffian τ̃ -functions 3. The Pfaffian Toda lattice and skew-orthogonal polynomials 4. The (s = −t)-reduction of the Virasoro vector fields 5. A representation of the Pfaffian τ̃ -function as a symmetric matrix integral 6. String equations and Virasoro constraints 7. Virasoro constraints with boundary terms...

In this paper we develop lower bounds for the spectral radius of symmetric , skew{symmetric, and arbitrary real matrices. Our approach utilizes the well{known Leverrier{Faddeev algorithm for calculating the co-eecients of the characteristic polynomial of a matrix in conjunction with a theorem by Lucas which states that the critical points of a polynomial lie within the convex hull of its roots....

for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. We prove under certain conditions that the maximal domain D(Ap) of the generator Ap belonging to the OrnsteinUhlenbeck semigroup coincides with the dom...

The present study is concerned with the propagation of Lamb waves in a homogeneous isotropic thermoelastic micropolar solid with two temperatures bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions. The generalized theory of thermoelasticity developed by Lord and Shulman has been used to investigate the problem. The secular equations for symmetric...

for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. As shown in a companion paper, one key assumption to prove resolvent estimates of L∞ in L (R,C ), 1 < p < ∞, is the following L-dissipativity condition...