Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

强度解调型光纤光栅温度传感实验

光纤光栅在工程上应用广泛,但由于存在解调系统复杂、成本高,尤其是需要使用光纤光谱仪等波长解调仪器,使得光纤光栅很难走入本科教学的实验课堂.本文提出了一种基于窄线宽DFB激光器的强度解调方案,极大地简化了光纤光栅传感器的解调系统,完全满足较高分辨率和实时检测的系统要求.合理安排的温度传感实验可以非常直观地展示光纤光栅的线性传感性能,使得工程化的光纤光栅传感技术轻松走进本科教学课堂,具有极高的推广和应用潜力.     

思维导图促进分析化学课堂思政教学的探索——以“酸碱滴定法基本原理”为例

在分析化学课程的教学中,通过充分发掘其中的思政元素,将其与教学内容进行有机结合,达到育人的目的。通过引入思维导图教学法,搭建思政元素与教学内容的桥梁,学生可以快速把握所学知识。通过学生的表现,分析教学效果,存在的问题等,为课堂思政与本科化学教学有机结合提供一定的借鉴。     

Exceptional Cycles in the Bounded Derived Categories of Quivers

An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ)of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean quiver,then the length type of exceptional cycles in D^b(kQ)is exactly the tubular type of Q;if Q is a Dynkin quiver of type E_m(m=6,7,8),or Q is a wild quiver,then there are no exceptional cycles in D^b(kQ);and if Q is a Dynkin quiver of type An or D_n,then the length of an exceptional cycle in D^b(kQ)is either h or h/2,where h is the Coxeter number of Q.     

Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications

In this paper, we study certain interesting and useful properties of incomplete $\aleph$-functions. The incomplete $\aleph$-function is an extension of the $\aleph$-function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete $\aleph$-functions and point out several special cases. Finally, we give the applications of incomplete $\aleph$-functions in detecting glucose supply in human blood.     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.