In this talk, we will discuss the Ringel-Hall algebras of a hereditary abelian category. From the category of the $/mathbb{Z}/2$-graded complexes over a hereditary abelian category, we consider a certain quotient algebra and some localization of its Ringel-Hall algebra, which is called the modified Ringel-Hall algebra. When this hereditary abelian category is finitary, in particular the category of representations of a quiver and the category of coherent sheaves on a weighted projective line over a finite field, we prove that the modified Ringel-Hall algebra is isomorphic to the Drinfeld double of the extended Ringel-Hall algebra of the hereditary abelian category.

To study the well-known Schneider's projection problem, Lutwak, Yang and Zhang introduced a U-functional for polytopes, and posed two conjectures for this U-functional. In this paper, an affirmative answer for the second conjecture is given. As a by-product to prove our main theorem, a new sharp affine inequality characterizing simplices is established for the centered cone-volume measures.

We consider some sets of points whose codings have prescribed group frequencies and determine their Hausdorff dimensions. These sets can be used to describe orbit properties of some maps in the view of dynamical way. We shall also introduce some basic knowledge of fractals.

The paper studies the estimation and empirical likelihood for single-index models with missing covariates. A generalized estimating equations estimator for index parameter with missing covariates is constructed, and its asymptotic distribution is obtained. The local linear estimator for link function achieves optimal convergence rate. By using the bias-correction and inverse selection probability weighted methods, a class of empirical likelihood ratios is proposed such that each of our class of ratios is asymptotically chi-squared. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths/areas of confidence intervals/regions. An example of a real data set is illustrated.

Vascular access for haemodialysis is of paramount importance. Although studies have found that central venous catheter is often associated with poor outcomes and switching to arteriovenous fistula is beneficial, it has not been fully elucidated how the effect of switching of access on outcomes changes over time and whether the effect depends on switching time. Analysis of the longitudinal data needs to account for changes over multiple time indices. In this paper we propose a flexible model that jointly models the change over treatment time, the trend over calendar time, the change associated with treatment switching and time-varying effects of covariates. The effect of switching may depend on both the time of switching and time since switching. All unknown functions are modeled nonparametrically using local linear smoothers and estimated using a backfitting procedure.

题目：Compressed Sensing with Redundant Systems报告人：李松教授 (浙江大学)时间：2016年11月4日(星期五) 下午2：00—3：00地点：致远楼102室李松：教授，博士生导师，目前担任浙江大学必赢国际bwin登录副院长、浙江大学数学科学研究中心副主任、担任中国数学会理事、浙江省数学会副理事长等职务。他的研究方向包括；小波分析理论及其应用、压缩感知理论、低秩矩阵恢复理论等，是国内较早开展压缩感知领域的研究工作者之一，他关...

Analytical solutions of pharmacokinetic models are appealing since they provide a clear and direct way to reveal the relationship between different model components, and greatly improve the process of drug development and drug design. In this talk, I will present mathematical solutions, including time-course of drug concentration and estimation of key pharmacokinetics parameters, of some pharmacokinetic models where nonlinear elimination is an important factor for some drug disposition, typically hormone drugs such as granulocyte colony-stimulating factor (G-CSF). This is a joint work with Professors Fahima Nekka and Jun Li at Université de Montréal.

仿射Kac-Moody李代数是从单位圆到有限单李代数的多项式函数的中心扩张。将单位圆换成环面，就得到环面李代数。高维仿射李代数正是环面李代数的更一般的推广。它是由数学物理学家最先提出来的。这类李代数的根系恰好是Saito在研究奇异理论时引进的高维仿射根系。高维仿射李代数还与代数几何学家Slodowy的相交矩阵李代数，及Berman-Moody和Benkart-Zelmanov等学者研究的根系分次李代数有紧密的联系。其中A型高维仿射李代数有丰富的结构理论，比如它容许量子环面，凯莱环面和若当环面作为坐标代数。A型高维仿射李代数的分类还涉及到量子环面的Connes循环同调群。坐标代数是量子环面的A型高维仿射李代数被Ginzburg-Kapranov-Vasserot在研究代数曲面的Langlands Reciprocity时进行了量子化。这些代数的表示如顶点算子，酉表示，及源于Solvable lattice model的表示等已被许多学者研究。