Multiplicative preservers of C-numerical ranges and radii on certain groups and semigroups of complex n × n matrices are characterized. The general and special linear groups are considered, as well as the semigroups of matrices having ranks not exceeding k, with k fixed in advance. For a fixed C, it turns out that typically the multiplicative preservers of the C-numerical range (or radius) have...

Abstract. The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular, it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI), an affine section of the semidefinite cone, is always dual to the numerical range of a matrix, which is therefore an affine projection of the semid...

We show that, for any 2n+ 2 distinct points a1, a′ 1, a2, a′ 2, . . . , an+1, a′ n+1 (in this order) on the unit circle, there is an n-by-n matrix A, unique up to unitary equivalence, which has norm one and satisfies the conditions that it has all its eigenvalues in the open unit disc, In − A∗A has rank one and its numerical range is circumscribed by the two (n+ 1)-gons a1a2 · · · an+1 and a′ 1...

in the present paper, a 3d numerical model has been applied to predict the flow hydrodynamics around power intakes within the dez dam reservoir. the dez dam is a 203 m high, double arch concrete dam which is constructed by italians in 1962. since then, sedimentation in reservoirhas continued and since the dam does not have bottom outlet, the reservoir bed level is raising by a rate of about 2.5...

A family of one-dimensional nonlinear dispersive wave equations is introduced as a model for assessing the validity of weak turbulence theory for random waves in an unambiguous and transparent fashion. These models have an explicitly solvable weak turbulence theory which is developed here, with Kolmogorov-type wave number spectra exhibiting interesting dependence on parameters in the equations....

Given a complex semisimple Lie algebra g = k+ ik, we consider the converse question of Kostant’s convexity theorem for a normal x ∈ g. Let π : g → h be the orthogonal projection under the Killing form onto the Cartan subalgebra h := t+it where t is a maximal abelian subalgebra of k. If π(Ad(K)x) is convex, then there is k ∈ K such that each simple component of Ad(k)x can be rotated into the cor...

Let L be a degree 2 Galois extension of the field K and M an n×n matrix with coefficients in L. Let 〈 , 〉 : Ln × Ln −→ L be the sesquilinear form associated to the involution L −→ L fixing K. We use 〈 , 〉 to define the numerical range Num(M) of M (a subset of L), extending the classical case K = R, L = C and the case of a finite field introduced by Coons, Jenkins, Knowles, Luke and Rault. There...

Numerical study of heat transfer and fluid flow over vertical double forward facing step were presented. The k-w model with finite volume method was employed to solve continuity, momentum, and energy equations. Different step heights were adopted for range of Reynolds number varied from 10000 to 40000, and range of temperature varied from 310K to 340 K. The straight side of duct is insulated wh...