群的Gorenstein同调维数

设$k$是一个弱维数有限的交换环, $G$是一个群. 本文讨论了群$G$具有有限的Gorenstein同调维数的标准.证明了群$G$的Gorenstein同调维数的有限性与群环$kG$的Gorenstein弱维数的有限性是一致的.进一步,我们给出了Serre定理的一个Gorenstein类比.推广了整环上$G$的Gorenstein同调维数的一些已知结果.     

单腔双光梳拍频信号包络提取方法

对单腔双光梳拍频信号的包络提取方法进行了实验研究。在单个光纤激光器中引入具有强双折射的保偏光纤,使脉冲沿偏振正交的两个方向进行复用传输和锁模。精细调节腔内偏振态,实现了重频差在337 Hz～2.33 kHz范围内连续可调的双光梳生成。通过激光器腔外偏振态调节和偏振分束,获得了消光比分别为28.5 dB和38.2 dB的两路光频梳。两路光频梳经过异步采样后,采用所设计的包络检波电路对拍频信号的包络进行提取,与采用基于样条插值和希尔伯特变换的包络提取算法计算结果相比,所提取的包络峰值位置基本保持一致,验证了该方法的可行性。双光梳拍频信号包络提取实验研究可以快速实时提取包络形状和包络峰值位置,可进一步应用于包络信号触发和精密测距等领域。     

Levi problem and semistable quotients

A complex space X is in class 𝒬 _G if it is a semistable quotient of the complement to an analytic subset of a Stein manifold by a holomorphic action of a reductive complex Lie group G. It is shown that every pseudoconvex unramified domain over X is also in 𝒬 _G .     

Classification of arithmetically Gorenstein divisors on some Fano varieties

We find all the arithmetically Gorenstein divisors on Fano varieties of dimension n and index r with 3 ≤ n ≤ 2r − 1 and ρ(Y) ≥ 2, where Y is smooth, connected, subcanonical and linearly normal.      

矩阵空间上保弱伴随矩阵的线性映射

为了刻画矩阵空间上保弱伴随矩阵的线性映射f,引入了保弱伴随矩阵的概念,以矩阵的弱伴随矩阵为不变量,得到了当n≥3时数域F上从线性矩阵空间Mn×n（F）到Mm×m（F）的保弱伴随矩阵的线性映射f的形式．     

Localization of injective modules over valuation rings

It is proved that is injective if is an injective module over a valuation ring , for each prime ideal . Moreover, if or is flat, then is injective, too. It follows that localizations of injective modules over h-local Prüfer domains are injective, too.

     

Pure projective modules and FP-injective modules over Morita rings

Let {\mathrm{\Lambda }}_{(0,0)}=\left(\begin{array}{cc}A& {}_A{N}_B\\ {}_B{N}_A& B\end{array}\right) be a Morita ring, where the bimodule homomorphisms \varphiand \psi are zero. We study the finite presentedness, locally coherence, pure projectivity, pure injectivity, and FP-injectivity of modules over {\mathrm{\Lambda }}_{(\mathrm{0},\mathrm{0})}. Some applications are then given.     

Using conical partition to globally maximizing the nonlinear sum of ratios

This article presents a global optimization algorithm for globally maximizing the sum of concave–convex ratios problem with a convex feasible region. The algorithm uses a branch and bound scheme where a concave envelope of the objective function is constructed to obtain an upper bound of the optimal value by using conical partition. As a result, the upper-bound subproblems during the algorithm search are all ordinary convex programs with less variables and constraints and do not grow in size from iterations to iterations in the computation procedure, and furthermore a new bounding tightening strategy is proposed such that the upper-bound convex relaxation subproblems are closer to the original nonconvex problem to enhance solution procedure. At last, some numerical examples are given to vindicate our conclusions.     

连通微分分次代数的Gorenstein性质

证明了由两个同调光滑的,Koszul,Gorenstein连通微分分次代数作张量得到的连通微分分次代数仍为同调光滑的,Koszul,Gorenstein连通微分分次代数;假设A是同凋光滑的连通微分分次代数使得H(A)是Koszul连通分次代数,则A是Gorenstein连通微分分次代数当且仅当H(A)是Gorenstein连通分次代数.