Sectional bodies associated with a convex body

We define the sectional bodies associated to a convex body in and two related measures of symmetry. These definitions extend those of Grünbaum (1963). As Grünbaum conjectured, we prove that the simplices are the most dissymmetrical convex bodies with respect to these measures. In the case when the convex body has a sufficiently smooth boundary, we investigate some limit behaviours of the volume of the sectional bodies.

     

激光金属汽化汽离混合区状态参量的稳定性及其影响因素分析

在汽离混合区激光强度时空修正的基础上,近似求解了流体力学模型下的状态参数,找出了稳定状态参数的共同自洽参量,分析了自洽参量的取值方法,研究了相关参数对自洽参量的影响机制,结果发现:(1)汽离混合区内,状态参量的稳定性可用自洽参量的稳定性来表征;(2)当入射激光强度小于108W.cm-2时,自洽参量随入射激光强度变化相对较快,稳定性差;当激光强度大于108W.cm-2时,自洽参量随入射激光强度变化相对较慢,稳定性高;(3)汽离混合区各处的约化自洽参量随辐照激光的波长成变周期增加的变化,波长越长,约化自洽参量越大;(4)要使自洽参量稳定,纹波较小,宜采取短波激光辐照;(5)当蒸汽压强小于2.7×106Pa时,自洽参量随蒸汽压强成指数递减规律变化;当蒸汽压大于2.7×106Pa时,自洽参量与蒸汽压强之间没有对应关系.     

Performance limits of pico-cell systems using radio-over-fiber techniques with an electroabsorption modulator

We investigate the performance limits of a pico-cell system using the radio- over-fiber technique with an electroabsorption modulator (EAM) in a 2.4 GHz wireless local area network (WLAN) environment. To understand the performance limits of the system using an EAM as the optical transceiver, we vary the optical modulation index (OMI) of the transmitter for different bias voltages to the EAM. Power margins in the links are found to estimate a possible service range, and packet loss rates (PLRs) in the pico-cell system are measured to evaluate the transmission performance. The total service range can be extended up to 3 m by adjusting the OMI of the transmitter for different applied bias voltages to the EAM.     

用于脉冲γ强度测量的Ф60,1000μmPIN探测器

采用电阻率为10000—20000Ω.cm的高阻单晶硅材料,研制成功灵敏区尺寸为60mm,耗尽层厚度~1000μm的大面积厚PIN半导体探测器.设计了该类探测器厚度测量专用的反冲质子测量系统,对探测器的时间响应、γ灵敏度、漏电流、γ/n分辨等物理参数进行了测量和分析,结果表明,这类探测器可满足低强度裂变n/γ混合场中脉冲γ强度测量的需要.     

Dispersion and Confinement Loss Control in Modified Hexagonal Photonic Crystal Fibers

This paper presents a novel technique for the control of chromatic dispersion and confinement loss in hexagonal photonic crystal fibers (H-PCFs). It is demonstrated that it is possible to obtain very low chromatic dispersion of 0 ± 0:38 ps/(nm·km) in the wavelength range of 1.41 to 1.66 μm and confinement loss of less than 0.0001 dB/km from a six ring modified H-PCF (MH-PCF). The higher order dispersion at 1.55 μm is about −0.001 ps/(nm²-km).     

Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.     

The area within a curve

The area of a simple closed convex curve can be estimated in terms of the number of points of a square lattice that lie within the curve. We obtain the usual error bound without integration using a form of the Hardy—Littlewood—Ramanujan circle method, and also present simple estimates for the mean square error.     

Lp径向Blaschke-Minkowski同态的Lp对偶几何表面积

2006年，Schuster提出了径向Blaschke-Minkowski同态的概念.随后，汪卫等人将其推广到L_p径向Blaschke-Minkowski同态.本文结合L_p对偶几何表面积，建立了L_p径向Blaschke-Minkowski同态的若干不等式，包括Brunn-Minkowski型不等式和单调不等式.并给出了L_p径向Blaschke-Minkowski同态的Busemann-Petty问题的肯定和否定形式.     

Interfacial change on morphological transitions in styrene-isoprene diblock copolymer

The specific interfacial area (S/V) and interfacial thickness in each microstructure of styrene-isoprene diblock copolymer were estimated by analyzing the deviations from Porod’s law. The thermally induced phase transitions proceeded from lamellae (L) to hexagonally ordered cylinder (HEX), via hexagonally perforated layer (HPL) and gyroid (G). The S/V ratio increased stepwise at the order-order transition (OOT) from L to HEX, via HPL and G. The S/V data can be utilized for OOT determination.     

The affine Plateau problem

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.