Letter: Global Hyperbolicity of Sliced Spaces

We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced spaces are timelike and null geodesically complete if and only if space is a complete Riemannian manifold.     

Propagation of elegant Laguerre–Gaussian beams through an annular apertured paraxial ABCD optical system

Based on the generalized Huygens–Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of elegant Laguerre–Gaussian beams passing through a paraxial ABCD optical system with an annular aperture is derived. Meanwhile, the corresponding closed-forms for the unapertured, circular apertured or circular black screen cases are also given. The obtained results provide more convenience for studying their propagation and transformation than the usual way by using diffraction integral formula directly. Some numerical examples are given to illustrate the propagation properties of elegant Laguerre–Gaussian beams.     

A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

Block transitive Steiner systems with more than one point orbit

For all ‘reasonable’ finite t, k, and s, we construct a t‐(?₀, k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2‐(?0, 4, 1) design with a block‐transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by‐product of a new way of looking at a model‐theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.     

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients

In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coefficients can be continued along this curve.

     

Predictive control of periodic-review production inventory systems with deteriorating items

In this paper a predictive control strategy is applied to a periodic-review dynamic inventory system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach is the use of future information of the inventory target level and the desired production rate, which are available, along the fixed horizon. The deterioration coefficient may be known or unknown and both cases are considered. In the case where it is unknown, the self-tuning predictive control is applied. The proposed control algorithms are illustrated by simulations.     

Dirac on Gauges and Constraints

We examine the relevance of Dirac's view on the use of transformation theory and invariants in modern physics to current reflections on the meaning of physical symmetries, especially gauge symmetries.     

Quadratic Integrals of Motion for the Systems of Identical Particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in Hamilton-Jacobi equation is clarified.