Geometrical interpretation of the photon position operator with commuting components

Operator Radii of Commuting Products

Operator radii wp(T) for a bounded linear operator T on a Hubert space were introduced in connection with unitary p-dilations. We shall be concerned with universal estimates for the ratios wp(ST)/(wa(S)wl,(T)) for commuting operators S, T and o, p > 0. 1. All operators in this paper are bounded linear operators on a complex Hubert space §. We say an operator T belongs to the class G (0 < p < oo...

Operators commuting with the Volterra operator are not weakly supercyclic

We prove that any bounded linear operator on Lp[0, 1] for 1 6 p < ∞, commuting with the Volterra operator V , is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with V . ...

Geometrical Interpretation of Constrained Systems

The standard approach to classical dynamics is to form a Lagrangian which is a function of n generalized coordinates qi, n generalized velocities q̇i and parameter τ . The 2n variables qi, q̇i form the tangent bundle TQ. The passage from TQ to the cotangent bundle T ∗Q is achieved by introducing generalized momenta and a Hamiltonian. However, this procedure requires that the rank of Hessian matrix

A geometrical interpretation of the inverse matrix

Geometrical Interpretation of the Arc-length Method

The arc-length method is a powerful solution technique becoming increasingly popular among researchers and engineers. This method is presented here as a particular case of a more general formulation which includes all other solution strategies. The arc-length method is derived in its continuous and discrete formulations. Two versions of the arc-length method (Crisfield and Ramm) are presented a...