关于举行湖北大学文胜友教授和华中农业大学郭迎军博士学术报告会的通知

报告题目1：On thin carpets for doubling measures
报 告 人：文胜友 教授    （湖北大学）
报告时间：2017年04月22日（星期六）下午14:30-15:30

报告题目2：On the regularity of $/{/lfloor/log_b(/alpha n+/beta)/rfloor/}_{n/geq0}$
报 告 人： 郭迎军  博士 （华中农业大学）
报告时间：2017年04月22日（星期六）下午15:30-16:30

报告地点：4号楼4318室

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                                                                       数学学院
                                                                  2017年04月18日
报告1摘要：
    We study subsets of $/R^{d}$ which are thin for doubling measures or isotropic doubling measures. We show that any subset of $/R^{d}$ with Hausdorff dimension less than or equal to $d-1$ is thin for isotropic doubling measures. We also prove that a self-affine set that satisfies $OSCH$ (open set condition with holes) is thin for isotropic doubling measures. For doubling measures, we prove that Bara/'nski carpets are thin for doubling measures.

报告2摘要：
    Let $/alpha,/beta$ be real numbers and $b/geq2$ be an integer. Allouche and Shallit showed that the sequence $/{/lfloor/alpha n+/beta/rfloor/}_{n/geq0}$ is $b$-regular if and only if $/alpha$ is rational. In this paper, using a base-independent regular language, we prove a similar result that the sequence $/{/lfloor/log_b(/alpha n+/beta)/rfloor/}_{n/geq0}$ is $b$-regular if and only if $/alpha$ is rational, where $/alpha>0$. In particular, when $/alpha=/sqrt{2},/beta=0$ and $b=2$, we answer the question of Allouche and Shallit  that the sequence $/{/lfloor/frac{1}{2} + /log_2n/rfloor/}_{n/geq 1}$ is not $2$-regular, which has been proved by Bell, Moshe and Rowland respectively.