Some remarks on Liouville type results for quasilinear elliptic equations

For a wide class of nonlinearities satisfying

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we show that any nonnegative solution of the quasilinear equation over the entire must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.

     

Monomial bases for -Schur algebras

Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of and its associated monomial basis, we investigate -Schur algebras as ``little quantum groups". We give a presentation for and obtain a new basis for the integral -Schur algebra , which consists of certain monomials in the original generators. Finally, when , we interpret the Hecke algebra part of the monomial basis for in terms of Kazhdan-Lusztig basis elements.

     

Geometric structure in stochastic approximation

1. IntroductionLet f: Re -- R be a differelltiable fUnction. f reaChes its extremes on the setJ = {x E R"lfx(x) = 0}, (1.1)where,x(X) = (V,..., V)". (1.2)If jx can be observed exactly at any x e R", then there are various numerical methods toconstruct {xh}, xk E Re such that the distance d(xk, J) between uk and J tends to zero ask -- co. However, in many application problems jx can only be observed with noise, i.e.,the observation at time k 1 isYk 1 = fi(~k) (k 1, (1'3)where xk is …     

Submicron External Electro-optic Measuring System Based on an Electro-optic Solid Immersion Lens

In this paper, all electro-optic solid immersion lens (EOSIL) is introduced, which is made of GaAs. A reflecting external electro-optic measuring system based on the EOSIL is built. With a hemispherical GaAs EOSIL used as the external probe, 0.7 µm spot size is obtained when the wavelength of the probing beam from a laser diode is 1.3 µm and a microscope objective with 0.3 numerical aperture is used. The principle of the measuring system is analyzed by Jones matrix. By using the system, the electrical signals propagating on a microstrip transmission line are successfully measured. The voltage sensitivity about 5 mV/ is measured when 10 kHz sinusoidal electric signal is applied on the microstrip line.     

New class of magnetoresistance oscillations: interaction of a two-dimensional electron gas with leaky interface phonons

We report on a new class of magnetoresistance oscillations observed in a high-mobility two-dimensional electron gas (2DEG) in GaAs-Al(x)Ga(1--x)As heterostructures. Appearing in a weak magnetic field ( B < 0.3 T) and only in a narrow temperature range ( 2 K < T < 9 K), these oscillations are periodic in 1/B with a frequency proportional to the electron Fermi wave vector, k(F). We interpret the effect as a magnetophonon resonance of the 2DEG with leaky interface-acoustic phonon modes carrying a wave vector q = 2k(F). Calculations show a few branches of such modes existing on the GaAs-Al(x)Ga(1--)xAs interface, and their velocities are in quantitative agreement with the observation.     

Giant room-temperature magnetoresistance in polycrystalline Zn(0.41)Fe(2.59)O4 with alpha-Fe2O3 grain boundaries

A tunneling-type magnetoresistance (MR) as large as 158% is observed at T = 300 K in a polycrystalline Zn0.41Fe2.59O4 sample, in which the Zn0.41Fe2.59O4 grains are separated by insulating alpha-Fe2O3 boundaries. The huge room-temperature MR is attributed to the high spin polarization of Zn(0.41)Fe(2.59)O4 grains and antiferromagnetic correlations between magnetic domains on both sides of the insulating alpha-Fe2O3 boundary. The MR exhibits strong temperature dependence below 100 K and its magnitude is enhanced to reach 1280% at 4.2 K, which may arise from the Coulomb blockade effect.     

A trace formula for Weyl transforms with radial symbols

A trace formula for Weyl transforms onL ² () with radial symbols is given.This research has been partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0008562.     

双模最小关联混合态作为量子信道实现量子隐形传态的保真度

基于Braunstein和Kimble提出的B-K方案以双模最小关联混合态作为量子信道实施对未知量子态的隐形传送，并以传送相干态为例进行了研究.结果表明：双模最小关联混合态作为一种广义的Einstein-Podolsky-Rosen型纠缠态在实现量子隐形传态中能很好地担当量子信道的角色，在纠缠度和压缩度选择适当的条件下被传送未知量子态的保真度可以达到1.这是比双模压缩真空态更优越的量子信道. 关键词： 量子隐形传态 双模最小关联混合态 保真度     

左右手系材料界面处全反射行为的特性

基于电磁场理论，推导了左右手系材料界面处发生全反射时的物理特性，分析了相位变化情况.提出利用左右手系材料构成周期性结构，观测全反射时介质中隐失波干涉的实验设想，并从理论上计算了干涉条纹的分布. 关键词： 左手材料 负折射率 全反射 隐失波