The Schrödinger equation is investigated in the Euclidean TaubNUT geometry. The bound states are degenerate and an extra degeneracy is due to the conserved Runge-Lenz vector. The existence of the extra conserved quantities, quadratic in four-velocities implies the possibility of separating variables in two different coordinate systems. The eigenvalues and the eigenvectors are given in both case...

We discuss causality properties of asymmetrically warped space-times and argue that such scenarios may allow for timelike curves which can be closed via paths in the extra-dimensional bulk. We find a metric where the null, weak and dominant energy conditions are violated in the bulk, but satisfied on the brane. Such scenarios are interesting, since in principle gravitons or gauge-singlet (“ster...

The Schrödinger equation is investigated in the Euclidean TaubNUT geometry. The bound states are degenerate and an extra degeneracy is due to the conserved Runge-Lenz vector. The existence of the extra conserved quantities, quadratic in four-velocities implies the possibility of separating variables in two different coordinate systems. The eigenvalues and the eigenvectors are given in both case...

Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators have order 2. If Q is power-associative and |Q| is finite and relatively prime to 6, then Q is a group. If Q is a finite non-associative extra loop, then 16 | |Q|.

The problem of gain-scheduled state feedback control for discrete-time linear systems with time-varying parameters is considered in this paper. The time-varying parameters are assumed to belong to the unit simplex and to have bounded rates of variation, which depend on the values of the parameters and can vary from slow to arbitrarily fast. An augmented state vector is defined to take into acco...

Convex polyhedra, commonly employed for the analysis and verification of both hardware and software, may be defined either by a finite set of linear inequality constraints or by finite sets of generating points and rays of the polyhedron. Although most implementations of the polyhedral operations assume that the polyhedra are topologically closed (i.e., all the constraints defining them are non...

This paper presents a new closed-form solution of the direct kinematic problem of nearly general parallel manipulators by using three linear extra sensors. The sensors are disposed at optimal location, connecting the planar base and the planar mobile platform at distinct points. The basic idea is to use the coordinates of the three distinct anchor points of the extra sensors on the mobile platf...

This paper explores the properties of adaptive systems with closed–loop reference models. Historically, reference models in adaptive systems run open–loop in parallel with the plant and controller, using no information from the plant or controller to alter the trajectory of the reference system. Closed–loop reference models on the other hand use information from the plant to alter the reference...