|Colloquium, 中興大學數學系 陳鵬文教授|
Thursday, November 5, 16:10—17:00 數學系3174
Title: Arnoldi Algorithms with Structured Orthogonalization
Abstract:This is one joint work with Chung Kuan Cheng and Xinyuan Wang.
We study a stability preserved Arnoldi algorithm for matrix exponential in the time domain simulation of large-scale power delivery networks (PDN), which are formulated as semi-explicit differential algebraic equations (DAEs). The solution can be decomposed to a sum of two projections, one in the range of the system operator and the other in its null space. The range projection can be computed with one shift-and -invert Krylov subspace method. The other projection can be computed with the algebraic equations. Differing from the ordinary Arnoldi method, the orthogonality in the Krylov subspace is replaced with the semi-inner product induced by the positive semi-definite system operator. With proper adjustment, numerical ranges of the Krylov operator lie in the right half-plane, and we obtain theoretical convergence analysis for the modified Arnoldi algorithm in computing phi-functions. Simulations on RLC networks are demonstrated to validate the effectiveness of the Arnoldi algorithm with structured-orthogonalization.
|Colloquium, 國立師範大學數學系 陳界山教授|
Thursday, November 12, 16:10—17:00 數學系3174
Title: Decompositions and Projections with Respect to Some Classes of Non-Symmetric Cones
Abstract: It is known that the analysis to tackle with non-symmetric cone optimization is quite different from the way to deal with symmetric cone optimization due to the discrepancy between these types of cones. However, there are still common concepts for both optimization problems, for example, the decomposition with respect to the given cone, smooth and nonsmooth analysis for the associated conic function, conic-convexity, conic-monotonicity and etc. In this talk, we focus on issues of decompositions and projections w.r.t some classes of non-symmetric cones. These concepts and the obtained results pave a way to deal with non-symmetric cone optimization.
|Colloquium, 清華大學理學院 蔡孟傑院長|
Thursday, November 19, 15:10—16:00 理學院 36102教室
Abstract:日常生活中處處可見對稱現象,它點綴了生活中的美感。 我們從這些經驗中漸進探討對稱的意義和發展過程, 以及它在現代數學中扮演真與美的角色。
|Colloquium, 中央研究院數學研究所 李元斌 所長|
Thursday, November 19, 16:10—17:00 數學系3174
Title: What is a Moduli Space?
Abstract: I will discuss the concept of the moduli space through a few examples from geometry, physics and (if time allows) number theory.
|Colloquium, 國立高雄師範大學數學系 葉均承助理教授|
Thursday, November 26, 15:10—16:00 數學系3174
Title: Chen’s Grammars and Several Applications in Combinatorics (I)
Abstract:In this talk, we present a survey of our work on the study of Chen’s grammars (which is also known as context-free grammars). We first present the grammars for Eulerian polynomials of types A and B, the q-Eulerian polynomials, derangement polynomials of types A and B, the 1/k Eulerian polynomials. We then present the study on the 1/k Eulerian polynomials. Some problems are also discussed.
|Colloquium, 中央研究院數學研究所 葉永南研究員|
Thursday, November 26, 16:10—17:00 數學系3174
Title: Chen’s Grammars and Several Applications in Combinatorics (II)
Abstract:In this talk, we first apply the change of grammars method to study gamma-positivity and partial gamma-positivity of descent-type polynomials. We then show the symmetry of the coefficients polynomials of the Jacobi elliptic function sn(u,k). At last, we show the semi-gamma-positivity of the alternating runs polynomials of dual Stirling permutations.