DSpace Collection:
https://scholars.lib.ntu.edu.tw/handle/123456789/29389
2019-09-19T04:35:45Z
2019-09-19T04:35:45Z
Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats
Hung, Li Chang
Wu, Chang Hong
Huang, Yin Liang
CHIUN-CHUAN CHEN
https://scholars.lib.ntu.edu.tw/handle/123456789/418812
2019-09-09T00:46:23Z
2020-01-01T00:00:00Z
Title: Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats
Authors: Hung, Li Chang; Wu, Chang Hong; Huang, Yin Liang; CHIUN-CHUAN CHEN
Abstract: © 2020 American Institute of Mathematical Sciences. All rights reserved. We are concerned with the coexistence states of the diffusive Lotka-Volterra system of two competing species when the growth rates of the two species depend periodically on the spacial variable. For the one-dimensional problem, we employ the generalized Jacobi elliptic function method to find semi-exact solutions under certain conditions on the parameters. In addition, we use the sine function to construct a pair of upper and lower solutions and obtain a solution of the above-mentioned system. Next, we provide a sufficient condition for the existence of pulsating fronts connecting two semi-trivial states by applying the abstract theory regarding monotone semiflows. Some numerical simulations are also included.
2020-01-01T00:00:00Z
On Algebro-Geometric Simply-Periodic Solutions of the KdV Hierarchy
CHANG-SHOU LIN
Chen, Zhijie
https://scholars.lib.ntu.edu.tw/handle/123456789/418811
2019-09-09T00:46:23Z
2019-01-01T00:00:00Z
Title: On Algebro-Geometric Simply-Periodic Solutions of the KdV Hierarchy
Authors: CHANG-SHOU LIN; Chen, Zhijie
Abstract: © 2019, Springer-Verlag GmbH Germany, part of Springer Nature. In this paper, we show that as τ→-1∞, any zero of the Lamé function converges to either ∞ or a finite point p satisfying Rep=12 and e2πip being an algebraic number. Our proof is based on studying a special family of simply-periodic KdV potentials with period 1, i.e. algebro-geometric simply-periodic solutions of the KdV hierarchy. We show that except the pole 0, all other poles of such KdV potentials locate on the line Rez=12. We also compute explicitly the eigenvalue set of the corresponding L2[0 , 1] eigenvalue problem for such KdV potentials, thus extends Takemura’s works (Commun Math Phys 235:467–494, 2003) and (Electron J Differ Equ 2004(15):1–30, 2004). Our main idea is to apply the classification result for simply-periodic KdV potentials by Gesztesy et al. (Trans Am Math Soc 358:603–656, 2006) and the Darboux transformation.
2019-01-01T00:00:00Z
On the determinants and permanents Of matrices with restricted entries over prime fields
Pham, Thang
CHUN-YEN SHEN
Vinh, Le Anh
Koh, Doowon
https://scholars.lib.ntu.edu.tw/handle/123456789/418813
2019-09-09T00:46:23Z
2019-01-01T00:00:00Z
Title: On the determinants and permanents Of matrices with restricted entries over prime fields
Authors: Pham, Thang; CHUN-YEN SHEN; Vinh, Le Anh; Koh, Doowon
Abstract: © 2019 Mathematical Sciences Publishers. Let A be a set in a prime field F[double-struck]p. We prove that d × d matrices with entries in A determine almost |A|3+ 1/45 distinct determinants and almost |A|2-1/6 distinct permanents when |A| is small enough. Our proofs rely on recent advances in additive combinatorics and incidence machinery.
2019-01-01T00:00:00Z
E <inf>1</inf> -degeneration of the irregular Hodge filtration
Esnault, Hélène
Sabbah, Claude
JENG-DAW YU
Saito, Morihiko
https://scholars.lib.ntu.edu.tw/handle/123456789/412262
2019-07-02T02:41:47Z
2017-08-01T00:00:00Z
Title: E <inf>1</inf> -degeneration of the irregular Hodge filtration
Authors: Esnault, Hélène; Sabbah, Claude; JENG-DAW YU; Saito, Morihiko
Abstract: © De Gruyter 2017. For a regular function f on a smooth complex quasi-projective variety, J.-D. Yu introduced in [35] a filtration (the irregular Hodge filtration) on the de Rham complex with twisted differential d C df , extending a definition of Deligne in the case of curves. In this article, we show the degeneration at E1 of the spectral sequence attached to the irregular Hodge filtration, by using the method of [26].We also make explicit the relation with a complex introduced by M. Kontsevich and give details on his proof of the corresponding E1-degeneration, by reduction to characteristic p, when the pole divisor of the function is reduced with normal crossings. In Appendix E, M. Saito gives a different proof of the E1-degeneration.
2017-08-01T00:00:00Z