Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.     

Reduction and New Explicit Solutions of (2+1)-Dimensional Breaking Soliton Equation

By applying the Lie group method, the (2+1)-dimensional breaking soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.     

利用手征SU(3)夸克模型研究轻双Λ超核^6_ΛΛHe,^5_ΛΛHe,^5_ΛΛH,^4_ΛΛHe,和^4_ΛΛH的结合能

在手征SU(3)夸克集团模型下, 通过共振群方法(RGM)计算了双Λ超核^6_ΛΛHe,^5_ΛΛHe,^5_ΛΛH,^4_ΛΛHe,和^4_ΛΛH的结合能. 结果表明, 假定双Λ超核具有双Λ集团和壳心核集团构成的两集团结构, 得到的^6_ΛΛHe超核的结合能与实验值基本吻合, 表明手征SU(3)夸克集团模型不仅能较好地描述重子谱、N-N和Y-N相互作用及轻Λ超核的结合能, 也能较好地描述Y-Y相互作用及双Λ超核^6_ΛΛHe,^5_ΛΛHe,^5_ΛΛH,^4_ΛΛHe,和^4_ΛΛH的结合能, 指出了它们存在的可能性.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

对《二维六角形晶格伊辛模型的重正化群解》一文的进一步计算

针对《二维六角形晶格伊辛模型的重正化群解》一文中有关〈V〉0的计算进行了修正,给出了新的重正化群的变换、重正化群的线性化变换矩阵以及临界指数.     

光纤中高斯型伪随机序列码偏振度的理论分析和实验研究

推导了准单色光波情况下高斯脉冲伪随机序列偏振度的简洁数学表达式.理论分析结果表明,偏振度与差分群延迟之间的关系与线路啁啾和光纤色散无关,并且此关系可以由光信号频谱半宽度Δω和分光比γ唯一确定.用10 Gbit/s 7级m序列归零码进行的实验表明:实验结果与理论推导基本一致,从而验证了推导公式的正确性.     

Enabling arbitrary wavelength frequency combs on chip

A necessary condition for generation of bright soliton Kerr frequency combs in microresonators is to achieve anomalous group velocity dispersion (GVD) for the resonator modes. This condition is hard to implement in the visible as well as ultraviolet since the majority of optical materials are characterized with large normal GVD in these wavelength regions. We overcome this challenge by borrowing ideas from strongly dispersive coupled systems in solid state physics and optics. We show that photonic compound ring resonators can possess large anomalous GVD at any desirable wavelength, even if each individual resonator is characterized with normal GVD. Based on this concept, we design a mode‐locked frequency comb with thin‐film silicon nitride compound ring resonators in the vicinity of the rubidium D₁ line (794.6 nm) and propose to use this optical comb as a flywheel for chip‐scale optical clocks.

     

Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.     

有限自由度系统的定域Lie对称性和守恒量

研究有限自由度系统定域Lie对称性的正问题和逆问题。给出了定域Lie对称性的定义、确定方程、结构方程和守恒量。进一步从定域Lie对称性导出在有限连续群无限小变换下的Lie对称性。最后给出一个例子去说明这些结果。