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11月演講

創校85週年暨創系60週年系列演講, Michigan State University, Prof. Wei-Hsuan Yu (俞韋亘教授)
Tuesday, November 1, 16:10—17:00 數學系3174教室
Title: New Bounds for Equiangular Lines and Spherical Two-distance Sets
Abstract: The set of points in a metric space is called an $s$-distance set if pairwise distances between these points admit only $s$ distinct values. Two-distance spherical sets with the set of scalar products $\{\alpha, -\alpha\}$, $\alpha\in[0,1)$, are called equiangular. The problem of determining the maximal size of $s$-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding the size of an $s$-distance set in two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-distance set in $\mathbb{R}^n$ is $\frac{n(n+1)}2$ with possible exceptions for some $n=(2k+1)^2-3$, $k \in \mathbb{N}$. We also prove the universal upper bound $\sim \frac 2 3 n a^2$ for equiangular sets with $\alpha=\frac 1 a$ and, employing this bound, prove a new upper bound on the size of equiangular sets in an arbitrary dimension. Finally, we classify all equiangular sets reaching this new bound.

創校85週年暨創系60週年系列演講, Inha University, Prof. Hyeonbae Kang
Thursday, November 3, 16:10—17:00 數學系3174教室
Title: Recent Development in Spectral Theory of the Neumann-Poincare Operator
Abstract: No

PDE Seminar, 國家理論中心 Manas Kar博士
Tuesday, November 9, 14:10—15:00 數學系3F會議室
Title: Strong Unique Continuation Principle and Some Quantitative Estimates for p-Laplacian in Plane
Abstract: Link

創校85周年暨創系60週年系列演講, 台灣大學工科海洋暨數學系 許文翰終身特聘教授
Tuesday, November 10, 16:10—17:00 數學系3174教室
Title: Symplecticity Preserving Solution for the Two-Component Camassa-Holm Equation
Abstract: In this talk a new finite difference scheme for solving two-component Camassa-Holm (CH) equation will be presented in detail. To simulate shallow water accurately, high-order scheme will be developed for the equivalent system of CH equations which contains only the first order derivative terms. In the space, fifth-order accurate combined compact difference (CCD) scheme is developed together with the sixth-order accurate compact scheme developed in a three-point stencil is developed for the Helmholtz equation. In the time frame, a symplectic Runge-Kutta scheme with sixth-order accuracy is proposed to preserve infinite number of conservation laws embedded in the two-component CH equation.

創校85周年暨創系60週年系列演講, Hokkaido University, Prof. Gen Nakamura
Tuesday, November 15, 16:10—17:00 數學系3174教室
Title: Probe Type Method for Acoustic Wave Equations with Discontinuous Coefficients
Abstract: By adapting the idea of Belishev given in the paper below, we will show how the boundary control method abbreviated by BC method can be used to identify an unknown inclusion inside the medium. This idea is quite similar to the probing type argument for the Helmholtz equation and heat equation.
Belishev M 1987 Equations of the Gelfand-Levitan type in a multidimensional inverse problem for the wave equations Zap. Nauchn. Semin. LOMI 173 30–41 Belishev M 1991 J. Sov. Math. 55 1663 (Engl. transl.)

PDE Seminar, 京都大學 藤原宏志 教授
Thursday, November23, 15:10—16:00 數學系3174教室
Title: Design and Implementation of Multiple-Precision Arithmetic on MATLAB and Its Applications to Numerically Unstable Problems
Abstract: In this presentation, a new multiple-precision arithmetic environment on MATLAB is introduced. MATLAB is widely used in numerical computations, and double precision arithmetic which has approximately 16 decimal digits accuracy is used. In numerical treatments of unstable problems, rounding errors give serious influences to results. The proposed environment provides approximation and arithmetic of real numbers with arbitrary accuracy, and is effective to overcome numerical instability. Four basic rules are implemented in assembly language for the sake of fast computations, and it runs on MATLAB (2016b) on MacOSX and Windows at present. Comparisons between VPA (variable precision arithmetic) in MATLAB Symbolic Math Toolbox will be presented, and some demonstrations will be also exhibited.

創校85週年暨創系60週年系列演講, 台灣大學數學系 林太家 教授
Thursday, November 24, 16:10—17:00 數學系3174教室
Title: Nonlinear Schrödinger Equations with Square Root and Saturable Nonlinearities
Abstract: Nonlinear Schrödinger (NLS) equations with square root and saturable nonlinearities are well-known models to describe photorefractive mediums in nonlinear optics. Mathematically, such nonlinearities are different from power nonlinearity in many aspects. For instance, there is scaling invariant on the eigenvalue problem of NLS equations with power nonlinearity but neither square root nor saturable nonlinearity can give such a property. In this lecture, I’ll introduce some problems and results of NLS equations with square root and saturable nonlinearities.

   
 


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