Sharif Digital Repository

Boundary stabilization of vibrating three-dimensional Cosserat elastic solids are studied using mathematical tools, such as operator theory and semigroup techniques. The advantages of the boundary control laws for both boundary stabilization problems are investigated. The boundary stabilization problems are studied using a Lyapunov stability method and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme. © 2017 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd  

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time...