Matrix models without scaling limit

In the context of hermitean one--matrix models we show that the emergence of the NLS hierarchy and of its reduction, the KdV hierarchy, is an exact result of the lattice characterizing the matrix model. Said otherwise, we are not obliged to take a continuum limit to find these hierarchies. We interpret this result as an indication of the topological nature of them. We discuss the topological field theories associated with both and discuss the connection with topological field theories coupled to topological gravity already studied in the literature.Comment: Latex, SISSA-ISAS 161/92/E

The (N,M)-th KdV hierarchy and the associated W algebra

We discuss a differential integrable hierarchy, which we call the (N, M)$--th KdV hierarchy, whose Lax operator is obtained by properly adding$M$pseudo--differential terms to the Lax operator of the N--th KdV hierarchy. This new hierarchy contains both the higher KdV hierarchy and multi--field representation of KP hierarchy as sub--systems and naturally appears in multi--matrix models. The N+2M-1 coordinates or fields of this hierarchy satisfy two algebras of compatible Poisson brackets which are {\it local} and {\it polynomial}. Each Poisson structure generate an extended W_{1+\infty} and W_\infty algebra, respectively. We call W(N, M) the generating algebra of the extended W_\infty algebra. This algebra, which corresponds with the second Poisson structure, shares many features of the usual$W_N$ algebra. We show that there exist M distinct reductions of the (N, M)--th KdV hierarchy, which are obtained by imposing suitable second class constraints. The most drastic reduction corresponds to the (N+M)--th KdV hierarchy. Correspondingly the W(N, M) algebra is reduced to the W_{N+M} algebra. We study in detail the dispersionless limit of this hierarchy and the relevant reductions.Comment: 40 pages, LaTeX, SISSA-171/93/EP, BONN-HE-46/93, AS-IPT-49/9

A Tri-band-notched UWB Antenna with Low Mutual Coupling between the Band-notched Structures

A compact printed U-shape ultra-wideband (UWB) antenna with triple band-notched characteristics is presented. The proposed antenna, with compact size of 24×33 mm2, yields an impedance bandwidth of 2.8-12GHz for VSWR<2, except the notched bands. The notched bands are realized by introducing two different types of slots. Two C-shape half-wavelength slots are etched on the radiating patch to obtain two notched bands in 3.3-3.7GHz for WiMAX and 7.25-7.75GHz for downlink of X-band satellite communication systems. In order to minimize the mutual coupling between the band-notched structures, the middle notched band in 5-6GHz for WLAN is achieved by using a U-slot defected ground structure. The parametric study is carried out to understand the mutual coupling. Surface current distributions and equivalent circuit are used to illustrate the notched mechanism. The performance of this antenna both by simulation and by experiment indicates that the proposed antenna is suitable and a good candidate for UWB applications

The generalized KP hierarchy

We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.Comment: 12

MeV oxygen ion implantation induced compositional intermixing in AlAs/GaAs superlattices

We present in this letter an investigation of compositional intermixing in AlAs/GaAs superlattices induced by 2 MeV oxygen ion implantation. The results are compared with implantation at 500 keV. In addition to Al intermixing in the direct lattice damage region by nuclear collision spikes, as is normally present in low-energy ion implantation, Al interdiffusion has also been found to take place in the subsurface region where MeV ion induced electronic spike damage dominates and a uniform strain field builds up due to defect generation and diffusion. Uniform compositional intermixing of the superlattices results after subsequent thermal annealing when Al interdiffusion is stimulated through recovery of the implantation-induced lattice strain field, the reconstruction and the redistribution of lattice defects, and annealing of lattice damage

One-dimensional Ising model built on small-world networks: competing dynamics

In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result of rewiring-type is given because of the similarities of these two typical networks. We study the dynamical processes with competing Glauber mechanism and Kawasaki mechanism. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. By studying the phase diagram obtained in the present work, we can realize some dynamical properties influenced by the small-world effect.Comment: 5 pages, one figure, accepted for publication in Physical Review