在半局部环上表矩阵为初等阵之积

该文将半局部环上的矩阵表为初等阵之乘积.     

Photonic generation of microwave signals using dual-wavelength single-longitudinal-mode fiber lasers

Photonic generation of microwave signals is demonstrated with a dual-wavelength single-longitudinal-mode erbium-doped fiber ring laser. Microwave signal with a frequency of 21.07 GHz is obtained by aligning the reflection band of a uniform fiber Bragg grating to the two transmission peaks within a fiber Bragg grating-based Fabry-Perot filter. Stable dual-wavelength single-longitudinal-mode operation is guaranteed by means of the combined filtering effect of a saturable absorber and the Fabry-Perot filter. This approach provides an effective solution to the photonic generation of high-frequency microwave signals.     

非腔长匹配相干叠加脉冲锁模激光器的理论研究

提出了一个新的非腔长匹配相干叠加脉冲锁模激光器的物理模型,建立了它的数学方程,并进行了模拟计算.计算结果给出了各个参数对相干叠加脉冲锁模激光器运转的影响,以及脉冲宽度压缩速度和各参数之间的关系,获得了实现非腔长匹配相干叠加脉冲锁模激光器运转的最佳条件.     

均匀带电圆环片的空间电场计算

利用均匀带电圆环片电场的轴对称性,联合运用静电场的高斯定理和安培环路定理,以轴线上的场强值为初值,通过反复迭代的方式巧妙地导出了均匀带电圆环片空间电场的无穷级数表达式.     

单项导子的Darboux多项式和常数环

证明Moulin Ollagnier和Nowicki构造的四元多项式代数上的一个单项导子没有Darboux多项式当且仅当其常数环是平凡的.     

The Zero Divisor Graphs of Commutative Local Rings of Order p 4 and p 5

To each commutative ring R we can associate a zero divisor graph whose vertices are the zero divisors of R and such that two vertices are adjacent if their product is zero. Detecting isomorphisms among zero divisor graphs can be reduced to the problem of computing the classes of R under a suitable semigroup congruence. Presently, we introduce a strategy for computing this quotient for local rings using knowledge about a generating set for the maximal ideal. As an example, we then compute Γ(R) for several classes of rings; with the results in [4 Bloomfield , N. , Wickham , C. ( 2010 ). Local rings with genus 2 zero divisor graph . Comm. Alg. 38 ( 8 ): 2965 – 2980 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] these classes include all local rings of order p ⁴ and p ⁵ for prime p.     

Group Rings Whose Symmetric Units are Solvable

Let K be an infinite field of characteristic different from 2, and G a group. Under suitable restrictions upon G, we classify the groups such that the symmetric units of KG satisfy the solvability identity (x ₁, x ₂,…, x _{2 ⁿ} ) ^o  = 1, for some n.     

Group inverses for some 2 × 2 block matrices over rings

We first consider the group inverses of the block matrices (A0BC) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices (ACBD) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B^# and (B^πA) ^# both exist; (ii) B is invertible and m = n; (iii) A^# and (D - CA^#B)^# both exist, C = CAA^# , where A and D are m × m and n × n matrices, respectively.