ON A KAHLER VERSION OF CHEEGER-GROMOLL-PERELMAN＇S SOUL THEOREM

In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.     

完备正曲率凯拉流形的体积增长与曲率衰减

在Cn上构造了一族全纯截曲率为正的凯拉度量,并证明所构造的度量具有如下性质当测地距离ρ趋于无穷时,测地球的体积增长为O(ρ2(β+1)n/β+2),而黎曼标量曲率的衰减为O(ρ-2(β+1)β+2),其中β≥0.     

Wideband Antireflection Film Fabricated by Glancing Angle Deposition

Graded-index ZrO2 films has been fabricated on K9 glass by glancing angle deposition. Because the index mismatch at the interface has been reduced, the film results in wideband high-transmission antireflection. From 400nm to 1200nm, the film reflection is lower than 0.8% and the lowest value is 0.2% at 432nm.     

Design of internal Brewster guided-mode resonance filter

An internal Brewster guided-mode resonance （GMR） filter is designed. For this kind of GMR filter, the Brewster reflection occurs at the interface of grating/waveguide layers rather than at the interface of air/grating layers. At Brewster angle of 60~, the GMR filter owns almost 100% reflection at the resonance wavelength of 800 nm with the full-width at half-maximum （FWHM） of 0.2 nm. Its angle response changing with the fabrication deviation is also discussed.     

Wideband film polarizer design

The reflection and transmittance of s- and p-polarized lights should be treated separately at nonzero angle incidence. By choosing two special film materials whose refractive indices meet the Brewster condition in a given incident angle, the reflection of p-polarized light can be eliminated. When the two materials are fabricated into multilayer stacks, the reflection of s-polarized light can be largely increased while the reflection of p-polarized light keeps low. According to this principle, a film polarizer with bandwidth of 198 nm or even more is designed.     

ZrO_2 films with variable refractive index by glancing angle deposition

When optical film is deposited at oblique angle incidences, the film becomes porously, and the film effective refractive index will decrease. Six porous ZrO2 films are fabricated by the glancing angle deposition (GLAD) technique with the different incidence angles. By changing the substrate tilt angle from 0° to 85°. the film refractive index varies from 1.92 to 1.27.     

Design of single-material guided-mode resonance filter

In this letter, a guided-mode resonance （GMR） filter with the same material for both the grating layer and the waveguide layer is designed, and its optical properties are investigated. The GMR filter owns almost 100% reflection at the resonance wavelength of 800 nm with the full-width at half-maximum （FWHM） of 20 nm, and its sideband reflection from 700 to 1000 nm is less than 5%. As the resonance wavelength is influenced by more than one parameter during the fabrication process, GMR filter with the same resonance wavelength can be obtained by adjusting other parameters or even one parameter to deviate from the design value.     

空间（Lμ^p）^m的弱Banach-Saks性质

证明了由m个Lμp空间产生的Banach向量空间（Lμp）m的弱Banach-Saks性质,其中m是自然数, 1 p 〈＋∞.当m= 1时,这就是著名的Banach-Saks-Szlenk定理.运用该性质,还给出了定义在向量空间Rm的一个凸集上的非负连续凸函数与取值在空间（Lpμ）m的一个弱紧子集中的向量值函数的复合函数的积分不等式.当这些向量值函数属于由m个Lμ∞空间产生的积空间（Lμ∞）m的一个弱＊紧子集时,类似的积分不等式还是成立的.     

VOLUME GROWTH ESTIMATES OF MANIFOLDS WITH NONNEGATIVE CURVATURE OUTSIDE A COMPACT SET

In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is at least half of the real dimension. The authors also give a brief proof of a generalized Yau＇s theorem.