厦门大学-吉林大学数学联合学术报告会

日期：2018年10月28日，地点：海韵园实验楼105会议室

学术报告题目和摘要

The instrituion fuction in income gap evolution

高丽媛（吉林大学）

In our new income distribution framework, we emphasize the function of distribution power in a bargain model. And we find out the institution plays an important role in distribution. If the hypothesis of homogenous individuals is released into heterogenous ones with different altruism distribution concept，our simulation show that the gini coefficient change a lot. So not only the formal distribution institution, but also the informal one which is ignored in system design affect the income gap evolution together.

Empirical Likelihood for Differentiable Functionals under Doubly Censorship

梁薇（厦门大学）

In this paper, we consider making inference for the parameters defined by differentiable functionals of the distribution function when the lifetimes are doubly censored. We utilize the efficient influence function of the parameter of interest to define an empirical likelihood ratio, and find that the log likelihood ratio asymptotically follows a standard chi-square distribution. Based on the result, we can construct the confidence interval for the parameter. The simulations are conducted to investigate the performance of the proposed method.

Inference on Semiparametric Transformation Model with General Interval-censored Failure Time Data

王培洁（吉林大学）

Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model.  Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases.  In this paper, we consider this class of models when one faces a general type of censored data, case K informatively censored data,for which there does not seem to exist an established inference procedure. For the problem,we present a two-step estimation procedure that is quite flexible and can be easily implemented,and the consistency and asymptotic normality of the proposed estimators of regression parameters are established.  In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations.  An application is also provided.

Perturbation Problems of Continuous Subsonic-Sonic Flows in Convergent Nozzles

聂元元（吉林大学）

In this talk, we will discuss the perturbation problems of isentropic, irrotational, steady compressible and continuous Euler subsonic-sonic flows in a 2-D convergent nozzle: finitely convergent nozzles, finitely and infinitely long symmetric convergent nozzle. The problems we consider can be described as the free boundary problem of nonlinear degenerate elliptic equations with nonlocal boundary value conditions and degeneracy at free boundary, whose free boundary is sonic curve. The main methods we use to solve the problem are the Schauder fixed point theorem and energy estimates.

Incompressible inviscid resistive MHD surface waves in 2D

王焰金（厦门大学）

This talk considers the dynamics of a layer of an incompressible electrically conducting fluid interacting with the magnetic field. The upper boundary is in contact with the atmosphere, and the lower boundary is a rigid flat bottom. We prove the global well-posedness of the inviscid and resistive problem with surface tension around a non-horizontal uniform magnetic field in a two-dimensional horizontally periodic setting; moreover, the solution decays to the equilibrium almost exponentially. One of the key observations here is an induced damping structure for the fluid vorticity due to the resistivity and transversal magnetic field. This is a joint work with Professor Zhouping Xin (CUHK).

Transfer and Its Applications

于浩然（吉林大学）

In this talk, by developing the strategy of Gagola and Isaacs, we not only prove some new results, but also use the most basic theory of transfer homomorphism to make a unified approach to some exciting theorems which were originally proved by different methods. The residuals play an important role in our work. By our results, we also answer a problem posed by Murray and Tent. Then we introduce a new subgroup, namely, the generalized p-supersolvable residual. We combine the generalized p-supersolvable residual with the generalized normal subgroups, and study the generalized normality from a different view. We obtain some new results and establish the connections of these results. Our results generalize and simplify a large number of existing results.

Riemannian optimization and averaging symmetric positive definte matrices

黄文（厦门大学）

Symmetric positive definite matrices have become fundamental computational objects in many areas. It is often of interest to average a collection of symmetric positive definite matrices. In this presentation, we investigate different averaging techniques for symmetric positive definite matrices. We use recent developments in Riemannian optimization to develop efficient and robust algorithms to handle this computational task. We provide methods to produce efficient numerical representations of geometric objects that are required for Riemannian optimization methods on the manifold of symmetric positive definite matrices. In addition, we offer theoretical and empirical suggestions on how to choose between various methods and parameters. In the end, we evaluate the performance of different averaging techniques in applications.

Linearized Alternating Direction Method of Multipliers with Adaptive Stepsize

李欣欣（吉林大学）

The linearized alternating direction method of multipliers(LADMM) is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, LADMM requires the user to choose stepsize parameters, and the speed of convergence is sensitive to this choice. In this talk, we introduce a new adaptive LADMM scheme that automatically tunes the stepsize parameters for fast convergence without user’s inputs. We prove rigorous convergence results for our method, and identify the conditions required for convergence. Numerical experiments show that adaptive LADMM has advantages over non-adaptive implementations in terms of both efficiency and simplicity for the users.