Non-commutative Chiral QCD2 Model

The effective action of chiral QCD₂ was studied in two-dimensional non-commutative space-time by using path integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a term corresponding to a Wess-Zumino-Witten-like term.     

2×2列联表中二属性相关的Bayes检验

2×2列联表中二属性相关的假设检验是定性数据分析中的热点问题,针对此问题的研究频率学派已做过大量的工作,其理论方法已趋于成熟.利用Bayes检验研究2×2列联表中二属性的相关性迄今为止国内外的相关文献还为数不多.将依据Bayes理论对此问题提出新的检验方法,推出其Bayes因子计算公式,利用正态近似研究三项假设计算出有关的后验概率,不仅解决了频率学派难以处理的问题,并且为吸烟有害健康提供了理论支撑.     

对流扩散方程的稳定化流线扩散法最小二乘非协调有限元分析

将最小二乘法和稳定化的流线扩散法相结合,研究了对流扩散方程的非协调有限元格式,用矩形EQ_1~(rot)元和零阶R-T元分别来逼近位移和应力,利用单元本身的特殊性质,证明了离散格式解的存在惟一性,得到了位移H~1-模和应力H(div)-模的最优误差估计.     

菲涅耳-基尔霍夫积分与半波带法分析衍射光谱

惠更斯菲 涅耳原理指出光的衍射本质是无穷多次波的相干叠加.在研究衍射光谱的强度时可使用菲涅耳-基尔霍夫衍射积分进行计算,但该积分的计算较为复杂.为了简化计算而引入菲涅耳半波带的概念,把积分运算简化为振幅矢量的叠加,从而在研究衍射时由菲涅耳-基尔霍夫衍射积分过渡到菲涅耳半波带法.在菲涅耳半波带法中波前上相邻两个半波带到达叠加点的光程差为半个波长,从而导致相位差π.因此相邻两个半波带引起的振动在叠加点发生相消,最终叠加点的光强由发出次波的半波带数目的奇偶性决定.奇数个半波带在叠加点的光强得到加强,偶数个半波带在叠加点的光强发生相消.     

Ion Viscosity Stabilization of Tokamak Resistive Internal Kink Modes

For most of small and medium sized Tokamaks, the unstable mode responsible for the sawtooth crash is the resistive internal kink mode. However, the plasma parameters can be in the ion kinetic regime. In this paper, we consider the dependence of the mode growth rate on the magnetic shear which is changeable during a sawtooth cycle and find that the ion viscosity effect can completely stabilize the mode only for shear smaller than some critical value, corresponding to the stable phase of the sawtooth evolution. This is consistent with one of the salient phenomena of the sawtooth, the sudden onset.     

拟线性双曲方程类Wilson非协调元的高精度分析

主要研究类Wilson元对拟线性双曲方程的逼近.首先证明了当问题的解u∈H~3(Ω)或u∈H~4(Ω)时,u与其双线性插值之差的梯度与类Wilson元空间任意元素的梯度,在分片意义下的内积可以达到O(h~2)这一重要结论.其次运用能量模意义下该元的非协调误差可以分别达到O(h~2)/O(h~3),即比插值误差高一阶/二阶这一性质,并利用对时间t的导数转移技巧,结合双线性元的高精度结果及插值后处理技术,获得了O(h~2)阶的超逼近性和整体超收敛性,从而进一步拓广了该元的应用范围.     

逆Walsh序p值Walsh变换的演化生成及快速算法

本文利用二分演化思想和矩阵分解技术 ,重点讨论逆Walsh序三值Walsh变换的演化生成和快速算法 ,并将之推广至p值情形 .     

300GHz超导SIS接收机系统的设计与构建

超导SIS(Superconductor-Insulator-Superconductor)混频技术是新兴的低噪声检测技术.其卓越的低噪声性能已使其成为毫米波和亚毫米波频段灵敏度最高的谱线接收设备,接收机的自动控制和稳定性有更高的要求,研制能够长期稳定工作的接收机有很重要的意义.本文主要讨论了我们自行研究设计工作在4K温度,准光学系统的毫米波超导SIS接收机的组成部件,根据我们制备的超导SIS隧道结器件的特性指标,计算设计了300GHz波段的超导接收机天线和结的集成芯片.     

Generalized Toda Mechanics Associated with Loop Algebras (L)(Cr) and (L)(Dr) and Their Reductions

We construct a class of integrable generalization of Toda mechanics with long-range interactions. These systems are associated with the loop algebras L(C_r) and L(D_r) in the sense that their Lax matrices can be realized in terms of the c=0 representations of the affine Lie algebras C⁽¹⁾_r and D⁽¹⁾_r and the interactions pattern involved bears the typical characters of the corresponding root systems. We present the equations of motion and the Hamiltonian structure. These generalized systems can be identified unambiguously by specifying the underlying loop algebra together with an ordered pair of integers (n,m). It turns out that different systems associated with the same underlying loop algebra but with different pairs of integers (n₁,m₁) and (n₂,m₂) with n₂<n₁ and m₂<m₁ can be related by a nested Hamiltonian reduction procedure. For all nontrivial generalizations, the extra coordinates besides the standard Toda variables are Poisson non-commute, and when either $n$ or m≥3, the Poisson structure for the extra coordinate variables becomes some Lie algebra (i.e. the extra variables appear linearly on the right-hand side of the Poisson brackets). In the quantum case, such generalizations will become systems with noncommutative variables without spoiling the integrability.     

一类差分方程性质的研究(英文)

This paper is concerned with the following rational difference equation xn+1=axn-bxn-1+ex2n/(cXn+dxn-1), with the initial conditions x-1 , x0 ∈ (0, +∞) and a, b, c, d, e ∈ R+ . Locally asymptotically stability, global attractively and boundedness character of the equilibrium point of the equation are investigated. Moreover, simulation is shown to support the results.