Michael Fowler 03/07/06 The Interaction Representation Recall that in the first part of this course sequence, we discussed the Schrödinger and Heisenberg representations of quantum mechanics here. In the Schrödinger representation, the operators are time-independent (except for explicitly time-dependent potentials) the kets representing the quantum states develop in time. In the Heisenberg repr...

Various existing techniques are discussed and combined to form a compound algorithm for the heuristic solution of large Travelling Salesman Problems. Improvements are then offered for two of its key components; one for general use and one for the Euclidean special case.

The higher-order singular values for a tensor of order d are defined as the singular values of the d different matricizations associated with the multilinear rank. When d ≥ 3, the singular values are generally different for different matricizations but not completely independent. Characterizing the set of feasible singular values turns out to be difficult. In this work, we contribute to this qu...

the present research attempts to explain dynamic pull-in instability of functionally graded micro-cantilevers actuated by step dc voltage while the fringing-field effect is taken into account in the vibrational equation of motion. by employing modern asymptotic approach namely homotopy perturbation method with an auxiliary term, high-order frequency-amplitude relation is obtained, then the infl...