Abelian varieties over cyclotomic fields with good reduction everywhere

 For every conductor f{1,3,4,5,7,8,9,11,12,15} there exist non-zero abelian varieties over the cyclotomic field Q(ζ _f ) with good reduction everywhere. Suitable isogeny factors of the Jacobian variety of the modular curve X ₁ (f) are examples of such abelian varieties. In the other direction we show that for all f in the above set there do not exist any non-zero abelian varieties over Q(ζ _f ) with good reduction everywhere except possibly when f=11 or 15. Assuming the Generalized Riemann Hypothesis (GRH) we prove the same result when f=11 and 15. Received: 19 April 2001 / Revised version: 21 October 2001 / Published online: 10 February 2003     

CONTINUOUS DEPENDENCE ON THE TERMINAL CONDITION OF SOLUTIONS TO NONLINEAR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper,we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator of a lower semi-continuous,proper and convex function under non-Lipschitz condition by means of the corollary of Bihari inequality.     

超声雾化法制取金属粉末方法研究

本文介绍了利用超声振动能量制取超细金属粉末的超声雾化方法，提出了超声制粉雾化室，等离子枪，阴极、阳极喷咀及换能器振动系统的最佳尺寸和工作参数，给出了实验结果及制得的粉末显微结构照片．实验结果表明，用本文所述方法制得的金属粉末组成为：－80目粉占84呢，－120目粉占63．7啪，而用PREP方法制得的粉末分别占19．5％和11．7％，由此看来，用本方法制取超细金属粉，在粒度组成方面优于PREP方法．文中还对粉末冷却速度做了估算，得到了粉末平均冷却速度大于1×10_5k/5     

Multiple positive solutions for discrete nonlocal boundary value problems

In this paper, we investigate a second-order nonlinear difference equation with sign-changing nonlinearity subject to two different sets of nonlocal boundary conditions. The explicit expressions of the associated Green's functions are presented. By using a recently developed fixed point theorem, we establish sufficient conditions for the existence of multiple positive solutions of the boundary value problem.     

平行四边形的3-剖分

It has been proved that if a rectangle is dissected into three congruent pieces,then those pieces must themselves be rectangles. In the present paper this result is generalized to the case of parallelogram.     

Characteristics of Quantum Radiation as Tunneling from a Cylindrically Symmetric Black Hole

Applying the semi-classical quantum tunneling model, we have studied the Hawking radiation via tunneling from a cylindrically symmetric black hole. The derived results show that the tunneling rate of at the event horizon of the black hole is related to Bekenstein–Hawking entropy and the factual radiation spectrum is not strictly pure thermal, but is consistent with the underlying unitary theory. PACS numbers: 04.20.-s, 97.60.Lf.     

二维平板光子晶体直波导的制备和光传输特性的测量

利用聚焦离子束刻蚀的方法在SOI(silicon on insulator)基片上制备了W3型二维光子晶体直波导.观察并测量了近红外激光通过光子晶体波导的散射图形和透过谱.实验结果说明，激光在有引入引出脊形波导的光子晶体直波导中具有很好的传输特性. 关键词： 光子晶体波导 光子带隙 脊型波导     

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.     

一个关于球面和环面上嵌入图的近-三角剖分嵌入的内插定理(I)

一个近-三角剖分嵌入是指一个曲面上的嵌入图使得几乎所有的面都是三角形,至多只有一个可能的例外.文中作者证明了如下结论:如果一个图G 在球面S₀(或环面S₁)上有近-三角剖分嵌入,那么G在每一个可定向曲面S_k有近-三角剖分嵌入,其中k=h,h+1,\cdots ,\lfloor\frac{\beta(G)}{2}\rfloor$, 而h=0(或1)并且β(G)是图G的Betti数.特别地,G是上可嵌入的.     

On the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups

The aim of this paper is to study the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups. We carry over a qualitative version of the Erdös-Rényi law of large numbers for Brownian motion to simply connected step 2-nilpotent Lie groups. The method applied gives rise to a proof for qualitative results concerning the modulus of continuity of Brownian motion on simply connected step 3-resp. step 2-nilpotent Lie groups without using the Ventsel-Freidlin theory as in Baldi.