Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

硬件锁中的无线USB

无线USB的前途似乎无与伦比——它能消除那些把大家桌面弄得像鼠窝一样小小的不怎么灵便的电缆。但事实上,只有需要大量的外设时无线USB设备才有优势,而且它必须非常微型而廉价,否则带来的麻烦远多于缠绕的电缆。因此,插在PC USB端口作为无线基站的硬件锁就必须有尽可能高的集成度。但一片芯片中要包含USB有线接口、控制器、无线基带和RF电路,技术上还无法实现。下面我们将看到一家供应商Wisalr的一种可量产参考设计,它是如何接近于解决这个问题的。     

Magnetic effects of direct ion implantation of Mn and Fe into p-GaN

In p-GaN implanted with Mn (3×10¹⁶ cm⁻² at 250 keV), the material after annealing shows ferromagnetic properties below 250 K. Cross-sectional transmission electron microscopy (TEM) revealed the presence of platelet structures with hexagonal symmetry. These regions are most likely Ga_xMn_1−xN, which produce the ferromagnetic contribution to the magnetization. In p-GaN implanted with Fe, the material after annealing showed ferromagnetic properties at temperatures that were dependent on the Fe dose, but were below 200 K in all cases. In these samples, TEM and diffraction analysis did not reveal any secondary phase formation. The results for the Fe implantation are similar to those reported for Fe doping during epitaxial growth of GaN.     

Heuristic Solution Methods for the Multilevel Generalized Assignment Problem

The multilevel generalized assignment problem is a problem of assigning agents to tasks where the agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. Two heuristic solution methods are presented for the problem. The heuristics are developed from solution methods for the generalized assignment problem. One method uses a regret minimization approach whilst the other method uses a repair approach on a relaxation of the problem. The heuristics are able to solve moderately large instances of the problem rapidly and effectively. Procedures for deriving an upper bound on the solution of the problem are also described. On larger and harder instances of the problem one heuristic is particularly effective.     

On the critical exponents of random k‐SAT

There has been much recent interest in the satisfiability of random Boolean formulas. A random k‐SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known that when the number of variables n is large, there is a sharp transition from satisfiability to unsatisfiability; in the case of 2‐SAT this happens when m/n → 1, for 3‐SAT the critical ratio is thought to be m/n ≈ 4.2. The sharpness of this transition is characterized by a critical exponent, sometimes called ν = ν_k (the smaller the value of ν the sharper the transition). Experiments have suggested that ν₃ = 1.5 ± 0.1. ν₄ = 1.25 ± 0.05, ν₅ = 1.1 ± 0.05, ν₆ = 1.05 ± 0.05, and heuristics have suggested that ν_k → 1 as k → ∞. We give here a simple proof that each of these exponents is at least 2 (provided the exponent is well defined). This result holds for each of the three standard ensembles of random k‐SAT formulas: m clauses selected uniformly at random without replacement, m clauses selected uniformly at random with replacement, and each clause selected with probability p independent of the other clauses. We also obtain similar results for q‐colorability and the appearance of a q‐core in a random graph. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 182–195, 2002     

Simulation of magnetic component models in electric circuitsincluding dynamic thermal effects

It is essential in the simulation of power electronics applications to model magnetic components accurately. In addition to modeling the nonlinear hysteresis behavior, eddy currents and winding losses must be included to provide a realistic model. In practice the losses in magnetic components give rise to significant temperature increases which can lead to major changes in the component behavior. In this paper a model of magnetic components is presented which integrates a nonlinear model of hysteresis, electro-magnetic windings and thermal behavior in a single model for use in circuit simulation of power electronics systems. Measurements and simulations are presented which demonstrate the accuracy of the approach for the electrical, magnetic and thermal domains across a variety of operating conditions, including static thermal conditions and dynamic self heating     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

PSL2(59) is a Subgroup of the Monster

A computer construction of the Monster is used to prove thatPSL(2, 59) is a subgroup of the Monster.