A Category of Restricted Modules for the Ovisenko-Roger Algebra

In this paper, we study a category of restricted modules for the Ovsienko-Roger algebra, which is an extension of the Virasoro algebra of its tensor density module of degree one. We construct and characterize simple modules in this category and give natural free field realizations of certain restricted modules using the Weyl vertex algebra.

     

Design and fabrication of GeAsSeS chalcogenide waveguides with thermal annealing

We reported a chalcogenide glass-based rib waveguide fabricated using photolithography and dry etching method. A commercial software(COMSOL Multiphysics) was used to optimize the waveguide structure and the distribution of the fundamental modes in the waveguide based on the complete vector finite component. We further employed thermal annealing to optimize the surface and sidewalls of the rib waveguides. It was found that the optimal annealing temperature for Ge As Se S films is 220℃, and the roughness of the films could be significantly reduced by annealing. The zero-dispersion wavelength(ZDW) could be shifted to a short wavelength around ~2.1 μm via waveguide structural optimization, which promotes supercontinuum generation with a short wavelength pump laser source. The insertion loss of the waveguides with cross-sectional areas of 4.0 μm×3.5 μm and 6.0 μm×3.5 μm was measured using lens fiber and the cut-back method. The propagation loss of the 220℃ annealed waveguides could be as low as 1.9 d B/cm at 1550 nm.     

Introduction to Co-split Lie Algebras

In this work, we introduce a new concept which is obtained by defining a new compatibility condition between Lie algebras and Lie coalgebras. With this terminology, we describe the interrelation between the Killing form and the adjoint representation in a new perspective.     

不同配副下ZrB2-SiC复相陶瓷的摩擦学性能

以微米级ZrB_2和SiC粉末为原料,采用热压烧结制备ZrB_2-SiC复相陶瓷,考察了SiC含量,摩擦对偶,速度和载荷对ZrB_2-SiC复相陶瓷摩擦磨损特性的影响.结果表明:ZrB_2-SiC复相陶瓷的摩擦系数和磨损率对SiC含量和摩擦对偶的变化较为敏感,速度和载荷变化,摩擦系数和磨损率的波动较大;以WC为对偶,速度0.1 m/s,载荷5 N时的ZrB_2-SiC复相陶瓷的平均摩擦系数和磨损率分别仅为0.4和2.41×10–4 mm3/(N·m).ZrB_2-SiC复相陶瓷的磨损机制以机械磨损为主,伴有轻微摩擦氧化,摩擦层的形成有利于摩擦系数的减小.     

Finite dimensional modules over quantum toroidal algebras

For all generic q\mathrm{\in }{C}^{*}, when g is not of type A₁; we prove that the quantum toroidal algebra U_q(g_tor) has no nontrivial finite dimensional simple module.     

On the centers of quantum groups of <Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>-type

Let g be the finite dimensional simple Lie algebra of type An, and let U? = U _q (g,Λ) and U = U _q (g,Q) be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U? for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U? = U _q (g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U? = U _q (g,Λ) and U = U _q (g,Q).     

仿射李代数的水平零的Whittaker模

对任意的仿射李代数 \tsg, 作者构造了一类水平为零的 imaginary Whittaker \tsg{-}模.同时证明了这类模在某些给定条件下是单的.     

Simulation and experimental characterization of a dual-mode two-section amplified feedback laser with mode separation over 100 GHz

A tunable two-section amplified feedback laser, which employs an amplifier section as the integrated feedback cavity, is designed and fabricated for dual-mode operation with mode separation of 100 GHz. Detailed simulations and experimental characterizations on the performance of the laser are presented. Promising dual-mode emission with continuous tuning range over 16 GHz（87.41–103.64 GHz） is experimentally demonstrated.     

Majid conjecture: quantum Kac-Moody algebras version

Based on the n-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G_2^{(1)} , E_2^{(1)},and Tp,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.     

仿射Kac-Moody李代数的生成元配对问题

本文讨论仿射Kac-Moody李代数的生成元配对问题.对任意的X(k)l型仿射Kac-Moody李代数9(A)以及任意的非零虚根向量x,也证明了存在某个y∈g(A),使得g'(A)包含在由z和y所生成的李代数之中.