歷史演講 PAST TALKS

Abstract In this talk, the asymptotic probability for the deviations of dependent bootstrap means from the sample mean is obtained, without imposing any assumptions on joint distribution of the original sequence of random variation form which the dependent bootstrap sample is selected. A nonrestrictive assumption of stochastic domination by a random variation is imposed on the marginal distribution of this sequence.

Abstract Geometry and Analysis have been around for centuries. Technological software packages have helped us in teaching, learning and research in recent years. In this talk, we will show why exploring mathematics with technology should be a FACT-Fun, Accessible, Challenging and Theoretical. a) Many examples from calculus to advanced calculus will be demonstrated with the help of dynamic geometry software and CAS. b) We will see when to incorporate various software packages so mathematical problems can be made accessible to most but challenging to some. c) A shrinking sphere problem, Mean Value, Cauchy Mean Value Theorems and their converses, Taylor Theorem, and etc. will be explored.

Abstract We consider the loop of neural network with one-way distributed delay coupling. Each cell is coupled to the the convolution of a cell-dependent kernel function with the output of its neighboring cell over the past time interval of a cell-dependent length. We focus on constant type of kernel functions. The parameter space consisting of the product of coupling strength between cells and the length of time intervals for the convolution. We split the parameter space into disjoint regions with boundaries where the stability may switches and bifurcation occurs. The Hopf and Pitchfork bifurcations are analyzed by normal form for functional differential equation.

Abstract We will apply the theory of dynamical system to calculate some characteristics of experimental data acquired from human brains of normal subjects and patients. In the theory of dynamical system, Takens had developed the theory of delay coordinates and embedding theorem to reconstruct the phase space of the system we considered. Therefore, some characteristics like correlation dimension, Lyapunov exponents, entropy, synchronization and phase synchronization can be calculated. These characteristics can help us to detect transient state of some diseases and doctors can take some therapies early.

Abstract Let be a finite von Neumann algebra on a complex Hilbert space . We consider some analytic properties of operator subalgebras of , maximal subdiagonal algebras and analytic operator algebra determined by a flow on by use of Tomita-Tadesaki theory in operator algebras. We will concern on the invariance under modular automorphism groups for subdiagonal algebras, noncommutative space, operator fractorization, relative invariant subspace lattices and algebraic commutants of analytic operator algebras.

Abstract: The Selberg trace formula is an important tool for computing the trace of a linear operator in the regular representation of a group G. In this talk, we will use representation theory to reprove some of the classical trace formula on classical modular forms. We will also discuss how to obtain new formula using this setting. Some applications to number theory will be discussed.