Browsing by Author "Hsu, YJ"

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A global pinching theorem for surfaces with constant mean curvature in S-3
(2001-01-01)
Hsu, YJ
;
Wang, TH
;
應用數學系
;
Department of Applied Mathematics
Let M be a compact immersed surface in the unit sphere S-3 with constant mean curvature H. Denote by phi the linear map from T-p(M) into Tp(M), phi = A - H/2 I, where A is the linear map associated to the second fundamental form and I is the identity map. Let Phi denote the square of the length of phi. We prove that if parallel to Phi parallel to (L2) less than or equal to C, then M is either totally umbilical or an H(r)-torus, where C is a constant depending only on the mean curvature H.
A global pinching theorem for surfaces with constant mean curvature in S-3
(2002)
Hsu, YJ
;
Wang, TH
;
應用數學系
;
Department of Applied Mathematics
Let M be a compact immersed surface in the unit sphere S-3 with constant mean curvature H. Denote by phi the linear map from T-p(M) into Tp(M), phi = A - H/2 I, where A is the linear map associated to the second fundamental form and I is the identity map. Let Phi denote the square of the length of phi. We prove that if parallel to Phi parallel to (L2) less than or equal to C, then M is either totally umbilical or an H(r)-torus, where C is a constant depending only on the mean curvature H.
Dual wavelength demultiplexing by coupling and decoupling of photonic crystal waveguides
(2004-03-22)
Chien, FSS
;
Hsu, YJ
;
Hsieh, WF
;
Cheng, SC
;
光電工程學系
We demonstrate that the fundamental mode of the two coupled photonic crystal waveguides (PCWs) can be odd parity in a triangular photonic crystal and their dispersion curves do intersect. Thus, the PCWs are decoupled at the crossing point. By employing the decoupling at the crossing-point frequency and ultra short coupling length for another frequency, we designed a dual-wavelength demultiplexer with a coupling length of only two wavelengths and output power ratio as high as 15 dB. A loop-shape PCW is adapted to eliminate the backward energy flow. (C) 2004 Optical Society of America.
Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials
(2004-08-15)
Hsu, YJ
;
Huang, YC
;
Lih, JS
;
Chern, JL
;
光電工程學系
Recently, structures called deformed split ring resonators have been proposed to achieve the smallest volume of a unit cell, while retaining negative permeability. With a combination of wire structures, the characteristics of a negative index of refraction, or left-handed meta-materials, can be seen from the transmission spectrum. This electromagnetic resonance, including its orientation tolerance and angular dependence on the incident beam, is explored in detail in the microwave range. (C) 2004 American Institute of Physics.
Inequalities between Dirichlet and Neumann eigenvalues for domains in spheres
(2001-12-01)
Hsu, YJ
;
Wang, TH
;
應用數學系
;
Department of Applied Mathematics
Let M be a domain in the unit n-sphere with smooth boundary. The purpose of this paper is to describe some inequalities between Dirichlet and Neumann eigenvalues for M under certain convex restrictions on the boundary. We prove that if the mean curvature of the boundary is nonpositive, then the kth nonzero Neumann eigenvalue is less than or equal to the kth Dirichlet eigenvalue for k = 1, 2, Furthermore, if the second fundamental form of the boundary is nonpositive, then the (k + [n-1/2])th nonzero Neumann eigenvalue is less than or equal to the kth Dirichlet eigenvalue for k = 1, 2, (. . .).
Multivariate polynomial spline spaces
(1999-09-01)
Chen, LA
;
Hsu, YJ
;
Chiang, YC
;
應用數學系
;
統計學研究所
In this paper we construct bases of certain spaces of multivariate polynomial splines defined on rectangular partitions. These bases are presented by polynomials, truncated power functions and products of these functions. This setting provides a natural generalization of the two-dimensional polynomial spline, proposed by Chui and Wang [3], to p variables.
Singlemode InAs quantum dot photonic crystal VCSELs
(2005-09-29)
Yang, HPD
;
Chang, YH
;
Lai, FI
;
Yu, HC
;
Hsu, YJ
An InAs quantum dot photonic crystal vertical-cavity surface-emitting laser (QD PhC-VCSEL) for fibre-optic applications is first demonstrated. Single fundamental mode CW output power of 0.2 mW has been achieved in the 1300 nm range, with a threshold current of 4.75 mA. Side-mode suppression ratio larger than 40 dB has been observed over the entire thermally limited operation range.
Thickness dependence of Co anisotropy in TbFe/Co exchange-coupled bilayers
(2004-06-01)
Lin, CC
;
Lai, CH
;
Wei, DH
;
Hsu, YJ
;
Shieh, HPD
The orientation of element-specific moments was determined by using x-ray magnetic circular dichroism spectroscopy to explore exchange anisotropy of TbFe/Co bilayers. Perpendicular anisotropy of 15 Angstrom Co was induced by TbFe through exchange coupling, resulting in the out-of-plane Co moments. With increasing the thickness, Co moments were gradually tilted to the in-plane orientation because of increasing planar anisotropy. In the bilayer with thick Co, interfacial Fe moments were unidirectionally aligned in the plane, leading to in-plane exchange bias of Co. The coercivity and exchange bias field of Co in the bilayers exhibited a strong dependence on Co thickness. (C) 2004 American Institute of Physics.
Transmission characteristics of smiling pattern resonators
(2004-05-15)
Hsu, YJ
;
Chern, JL
;
光電工程學系
;
Department of Photonics
We propose and experimentally verify a novel metallic-microstructure composite that consists of smiling-pattern resonators to broaden the bandwidth of resonance, in contrast to the well known narrow-band split ring resonators in the field of meta-materials and left-handed negative-index media. The underlying idea is to introduce multiple interaction scales to the resonator. Our microwave analog experiment shows that the range of resonant frequencies could also be extended apparently with double resonance bands. Furthermore, this smiling-Pattern resonator is superior in manufacturing for its simplicity in structure.
Willmore surfaces in the unit N-sphere
(2004-09-01)
Chang, YC
;
Hsu, YJ
;
應用數學系
;
Department of Applied Mathematics
Let M-2 be a compact Willmore surface in the n-dimensional unit sphere. Denote by phi(ij)(alpha) the tracefree part of the second fundamental form h(ij)(alpha) of M-2, and by H the mean curvature vector of M-2. Let Phi be the square of the length of phi(ij)(alpha) and H = H. We prove that if 0 < Phi < C(1 + (H2)/(8)), where C = 2 when n = 3 and C = (4)/(3) when n greater than or equal to 4, then either Phi = 0 and M-2 is totally umbilic or Phi = C(1 + (H2)/(8)) In the latter case, either n = 3 and M-2 is the Clifford torus or n = 4 and M-2 is the Veronese surface.