A smoothing method for mathematical programs with equilibrium constraints

Received May 3, 1996 / Revised version received November 19, 1997 Published online January 20, 1999     

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.     

Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.     

Properly immersed minimal disks bounded by straight lines

Let and be two distinct parallel planes in . Let and denote two points such that the segment meets and orthogonally. Let be a straight line containing , and denote as the set of straight lines in containing . Then there exists an analytic family of proper pairwise non congruent minimal immersions satisfying: 1. is homeomorphic to , where 2. , where . 3. is contained in the slab determined by and . 4. If and are the two connected components of , then is injective, . 5. The parameter is an analytic determination of the angle that the orthogonal projection of on makes with and is invariant under the reflection around a straight line not contained in the surface. 6. If is a proper minimal immersion satisfying 1, 2, 3 and4, then, up to a rigid motion, . Received December 28, 1997 / Revised November 20, 1999 / Published online October 11, 2000     

Orlicz function spaces without complemented copies ofl p

This paper proves the existence of Orlicz function spaces Lφ (0, 1) containing no complemented subspaces isomorphic tol ^p for anyp ≠ 2. Some properties of minimal Orlicz function spaces Lφ (0, 1) are also given. Supported in part by CAICYT grant 0338-84.     

Multiobjective routing problems

Summary Many network routing problems, particularly where the transportation of hazardous materials is involved, are multiobjective in nature; that is, it is desired to optimise not only physical path length but other features as well. Several such problems are defined here and a general framework for multiobjective routing problems is proposed. The notion of “efficient solution” is defined and it is demonstrated, by means of an example, that a problem may have very many solutions which are efficient. Next, potentially useful solution methods for multiobjective routing problems are discussed with emphasis being placed on the use of shortest/k-shortest path techniques. Finally, some directions for possible further research are indicated. Invited by B. Pelegrin     

Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

An alternative formulation for the set packing problem in a higher dimension is presented. The addition of a new family of binary variables allows us to find new valid inequalities, some of which are shown to be facets of the polytope in the higher dimension. We also consider the Winner Determination Problem, which is equivalent to the set packing problem and whose special structure allows us to easily implement these valid inequalities in a very easy way. The computational experiments illustrate the performance of the valid inequalities and obtain good results.