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      學術交流

      學術交流

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      報告時間 2023年1月11日14:00 報告地點 騰訊會議ID:516-216-115
      報告人

      第七屆華山青年學者國際論壇——數統院分論壇

      11114:00騰訊會議ID516-216-115

      時間

      開幕式(馬如云院長介紹學院情況)

      14:00-14:10

      時間

      報告人

      報告題目

      主持人

      14:10-14:40

      張寧寧

      Quantied conditional variance, skewness, and   kurtosis by Cornish-Fisher expansion

      薄立軍

      14:40-15:10

      劉金鵬

       

      Matrix-analytic methods for solving  Poisson's   equation  with applications to  Markov chains of GI/G/1-type

      歇(15:10-15:20

      15:20-15:50

      周嘉偉

       

      Symplectically flat connections

      馬如云

      15:50-16:20

      黃林哲

       

      Complete positivity of comultiplication and primary   criteria for unitary categorification

      歇(16:20-16:30

      16:30-17:00

      付世丘

      Critical Elliptic Boundary Value Problems with   Singular Trudinger-Moser Nonlinearities

      吳事良 

      17:00-17:30

      殷會敏

      Cascading processes, breather and   Fermi-Pasta-Ulam-Tsingou recurrence






       



      報告題目與摘要  

      Quantied conditional variance, skewness, and kurtosis by Cornish-Fisher expansion

      張寧寧 博士在讀香港大學統計學

      A picture containing person, clothing, posing, suit描述已自動生成

      The conditional variance, skewness, and kurtosis play a central role in time series analysis. These three conditional moments (CMs) are often studied by some parametric models but with two big issues: the risk of model mis-specification and the instability of model estimation. To avoid the above two issues, this paper proposes a novel method to estimate these three CMs by the so-called quantiled CMs (QCMs). The QCM method first adopts the idea of Cornish-Fisher expansion to construct a linear regression model, based on n different estimated conditional quantiles that can be obtained without assuming any parametric forms of the CMs. Next, it computes the QCMs simply and simultaneously at each fixed timepoint by using the ordinary least squares estimator of this regression model. Under regular conditions, the QCMs are shown to be consistent with the convergence rate n?1/2. Simulation studies indicate that the QCMs perform well under different scenarios of estimated conditional quantiles. In the application, the study of QCMs for eight major stock indexes demonstrates the effectiveness of financial rescue plans during the COVID-19 pandemic outbreak, and unveils a new non-zero kink phenomenon in the news impact curve function for the conditional kurtosis.

        

       Matrix-analytic methods for solving  Poisson's equation  with applications to  Markov chains of GI/G/1-type

      劉金鵬 博士研究生 中南大學

      In this talk, we are devoted to developing matrix-analytic methods for solving Poisson's equation for irreducible and positive recurrent discrete-time Markov chains (DTMCs). Two special solutions, including the deviation matrix D and the expected additive-type functional matrix K, will be considered. The results are applied to Markov chains of GI/G/1-type and MAP/G/1 queues with negative customers. Further extensions to continuous-time Markov chains (CTMCs) are also investigated. This talk is based on a joint with professors Yuanyuan Liu and Yiqiang Q. Zhao (Carleton University).

       

      Symplectically flat connections 



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      周嘉偉 博士后北京雁棲湖應用數學研究院 

      Over a symplectic manifold, we call a connection symplectically flat if its curvature is proportional to the symplectic form and this proportion is covariantly a constant. Such connections can be viewed as a generalization of flat connections. We will go through the relationship between these two types of connections, and give a classification of symplectically flat connections.


       

      Complete positivity of comultiplication and primary criteria for unitary categorification 





      黃林哲   博士后   清華大學丘成桐數學科學中心 

      In this talk, I will introduce our recent work on quantum Fourier analysis. We provide a family of analytic criteria for fusion rings’ unitary categorification, which are stronger than the Schur product criterion. Various examples of fusion rings will be given. Many variations of the criteria such as localized criteria are introduced. These criteria could also be applied as obstructions for principal graphs of subfactors. This work is joint with Zhengwei Liu, Sebastien Palcoux and Jinsong Wu.

       

      Critical Elliptic Boundary Value Problems with Singular Trudinger-Moser Nonlinearities

      付世丘 博士 美國佛羅里達理工大學

      In this talk, I will introduce two classes of elliptic problems that are critical with respect to singular Trudinger-Moser embedding. The proofs are based on compactness and regularity arguments.
       

      Cascading processes, breather and Fermi-Pasta-Ulam-Tsingou recurrence

      殷會敏 博士后 香港大學

      Modulation instability, breather formation, and the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena are studied. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schr?dinger equations. The Darboux transformation is used to calculate a class of breathers. A cascading mechanismis utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. An analytical formula for the time or distance of breather formation is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed.

       

       

       

       

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