Browsing by Author "Lin, Yi-Hsuan"

Now showing 1 - 8 of 8

Criterion for Deciding Zeta-Like Multizeta Values in Positive Characteristic
(2016)
Kuan, Yen-Liang
;
Lin, Yi-Hsuan
;
應用數學系
;
Department of Applied Mathematics
Multizeta values for F-q [theta] were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present article, we give an effective algorithm for determining whether a given multizeta value is zeta-like, namely, those whose ratio with the zeta value of the same weight is rational. Moreover, we state conjectures on certain families of zeta-like multizeta values. We provide the data in support of these guesses.
MONOTONICITY-BASED INVERSION OF THE FRACTIONAL SCHODINGER EQUATION II. GENERAL POTENTIALS AND STABILITY
(2020-01-01)
Harrach, Bastian
;
Lin, Yi-Hsuan
;
應用數學系
;
Department of Applied Mathematics
In this work, we use monotonicity-based methods for the fractional Schrodinger equation with general potentials q is an element of L-infinity(Omega) in a Lipschitz bounded open set Omega subset of R-n in any dimension n is an element of N. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness result for the fractional Calderon problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Schrodinger equation, and we prove uniqueness and Lipschitz stability from finitely many measurements for potentials lying in an a priori known bounded set in a finite dimensional subset of L-infinity(Omega).
Quaternionic loci in Siegel's modular threefold
(2020-06-01)
Lin, Yi-Hsuan
;
Yang, Yifan
;
應用數學系
;
Department of Applied Mathematics
Let QD be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order O in an indefinite quaternion algebra of discriminant D over Q such that the Rosati involution coincides with a positive involution of the form alpha & x21a6;mu-1 alpha over bar mu on O for some mu is an element of O with mu 2+D=0. In this paper, we first give a formula for the number of irreducible components in QD, strengthening an earlier result of Rotger. Then for each irreducible component of genus 0, we determine its rational parameterization in terms of a Hauptmodul of the associated Shimura curve.
Reactivity of graphene oxide and reduced graphene oxide toward Tetrabromobisphenol A, Bisphenol A, and phenol from water: Reaction mechanism and thermodynamic effects
(2018-08-19)
Catherine, Hepsiba
;
Lin, Yi-Hsuan
;
Shih, Yang-Hsin
;
Doong, Ruey-An
;
環境工程研究所
Serum repressing efflux pump CDR1 in Candida albicans
(2006-07-13)
Yang, Yun-Liang
;
Lin, Yi-Hsuan
;
Tsao, Ming-Yang
;
Chen, Chia-Geun
;
Shih, Hsin-I
Background: In the past decades, the prevalence of candidemia has increased significantly and drug resistance has also become a pressing problem. Overexpression of CDR1, an efflux pump, has been proposed as a major mechanism contributing to the drug resistance in Candida albicans. It has been demonstrated that biological fluids such as human serum can have profound effects on antifungal pharmacodynamics. The aim of this study is to understand the effects of serum in drug susceptibility via monitoring the activity of CDR1 promoter of C. albicans. Results: The wild-type C. albicans cells ( SC5314) but not the cdr1/cdr1 mutant cells became more susceptible to the antifungal drug when the medium contained serum. To understand the regulation of CDR1 in the presence of serum, we have constructed CDR1 promoter-Renilla luciferase ( CDR1p-RLUC) reporter to monitor the activity of the CDR1 promoter in C. albicans. As expected, the expression of CDR1p-RLUC was induced by miconazole. Surprisingly, it was repressed by serum. Consistently, the level of CDR1 mRNA was also reduced in the presence of serum but not N-acetyl-D-glucosamine, a known inducer for germ tube formation. Conclusion: Our finding that the expression of CDR1 is repressed by serum raises the question as to how does CDR1 contribute to the drug resistance in C. albicans causing candidemia. This also suggests that it is important to re-assess the prediction of in vivo therapeutic outcome of candidemia based on the results of standard in vitro antifungal susceptibility testing, conducted in the absence of serum.
THE CALDERON PROBLEM FOR A SPACE-TIME FRACTIONAL PARABOLIC EQUATION
(2020-01-01)
Lai, Ru-Yu
;
Lin, Yi-Hsuan
;
Rueland, Angkana
;
應用數學系
;
Department of Applied Mathematics
In this article we study an inverse problem for the space-time fractional parabolic operator (partial derivative(t) -Delta)(s) +Q with 0 < s < 1 in any space dimension. We uniquely determine the unknown bounded potential Q from infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on Runge approximation and the dual global weak unique continuation properties of the equation under consideration. In discussing weak unique continuation of our operator, a main feature of our argument relies on a new Carleman estimate for the associated degenerate parabolic Caffarelli- Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.
The Calderon problem for the fractional Schrodinger equation with drift
(2020-04-24)
Cekic, Mihajlo
;
Lin, Yi-Hsuan
;
Rueland, Angkana
;
應用數學系
;
Department of Applied Mathematics
We investigate the Calderon problem for the fractional Schrodinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does not enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many generic measurements is discussed. Here the genericity is obtained through singularity theory which might also be interesting in the context of hybrid inverse problems. Combined with the results from Ghosh et al. (Uniqueness and reconstruction for the fractional Calderon problem with a single easurement, 2018. ), this yields a finite measurements constructive reconstruction algorithm for the fractional Calderon problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension n >= 1.
Twisted Kloosterman sums
(2015-02-01)
Lin, Yi-Hsuan
;
Tu, Fang-Ting
;
應用數學系
;
Department of Applied Mathematics
In this report, we prove identities among the second, third and fourth twisted moments of twisted Kloosterman sums, and certain hypergeometric functions over finite fields. In some cases, the moments can be expressed in terms of Hecke characters of imaginary quadratic fields. (C) 2014 Elsevier Inc. All rights reserved.