关于Fujita类方程组解的有界性和Blow up的一些结论

对Fujita类方程组解的整体存在性和如何在有限时间内发生Blow up现象的研究,具有实际意义.M.Escobedo等人对其二元情形曾做过研究,即在[1]中对非线性项单一如v~(?)或u~(?)的Cauchy问题进行了讨论,本文意在上述基础上作些推广:修改非线性项如u~(?)v~(?)或u~qv~n情形,利用上、下解的方法,证明了在一定条件下,推广后的Cauchy问题亦有[1]中指出的类似的结果.     

Asymptotics of solutions for sub critical non‐convective type equations

We study the Cauchy problem for non‐linear dissipative evolution equations (1) where ?? is the linear pseudodifferential operator and the non‐linearity is a quadratic pseudodifferential operator (2) û ≡ ?<sub>x→ξsub> u is the Fourier transformation. We consider non‐convective type non‐linearity, that is we suppose that a(t,0,y) ≠ 0. Let the initial data , are sufficiently small and have a non‐zero total mass , where is the weighted Sobolev space. Then we give the main term of the large time asymptotics of solutions in the sub critical case. Copyright © 2004 John Wiley & Sons, Ltd.     

弱吸收基底上弱吸收薄膜的光学常数计算方法

采用一种相对简单而又精确的光度法来计算弱吸收基底上弱吸收薄膜的光学常数,为低损耗紫外薄膜的设计与实现提供了理论基础。采用JGS1型熔融石英基底,制备了MgF2与LaF3材料的单层膜,获得了JGS1型熔融石英基底及MgF2与LaF3薄膜的光学常数色散曲线。结果显示:在200 nm左右处,JGS1型熔融石英基底的吸收已经比较明显,消光系数在10-8量级,因此,应考虑基底的弱吸收,以提高薄膜光学常数的计算精度。     

预处理对355nm激光作用下熔石英损伤增长的影响

测试了经化学蚀刻、紫外激光预处理及其共同处理后的熔石英355 nm激光损伤阈值;研究了处理前后其损伤斑面积随激光辐照脉冲数的增长情况。结果表明,处理后熔石英355 nm激光损伤阈值得到了提高,且损伤斑面积增长变慢。利用CO2激光对熔石英表面损伤点进行了修复处理,修复后的损伤点R-on-1抗损伤阈值和基底阈值相当,损伤增长得到有效抑制。     

纳米TiO_2薄膜的低温等离子体制备技术

以四氯化钛为源物质,氩气为载气,氧气为反应气体,利用低温等离子体增强化学气相沉积在硅基表面制备出了TiO2薄膜。使用场发射扫描电子显微镜、X射线衍射仪等检测分析表征TiO2薄膜的性能与性质,并探讨了工艺条件如基片材料、沉积时间和基片温度对薄膜性能的影响。结果表明:制备的薄膜表面光滑均匀,结构致密,最小晶粒尺寸约15 nm;薄膜的晶型主要依赖于沉积温度,低于300℃沉积的薄膜是无定形的,300℃之上沉积的薄膜是锐钛矿结构。     

J0相干角向偏振涡旋光束的深聚焦

通过矢量德拜理论,研究了J0相干角向偏振涡旋光束深聚焦的性质。推导了在焦点区域的光强分布、光谱相干度和偏振度的表达式。数值模拟结果表明,光强分布、相干度和偏振度不仅依赖于相干长度和数值孔径最大角,而且依赖于拓扑电荷数。这种光束在焦平面还可获得非常小的焦点和焦洞。     

On sub‐Riemannian geodesics on the Engel groups: Hamilton's equations

We study the sub‐Riemannian geometry on the Engel group which is a step 3 nilpotent Lie group on . Our main result is to solve the Hamiltonian equations associated with the bi‐characteristic curves and express the solutions in terms of elliptic functions. Our model covers both the Heisenberg group and the Martinet case when setting certain parameters to be zero.     

A Nonlinear Diffusion Problem with Localized Large Diffusion

Abstract

This paper is concerned with a nonlinear parabolic problem, with nonlinear boundary conditions, for which the diffusion coefficient becomes very large in a sub-region of the physical domain.     

Sub‐picosecond Raman spectrometer for time‐resolved studies of structural dynamics in heme proteins

We describe a pump–probe Raman spectrometer based on a femtosecond Ti:sapphire laser, an optical parametric generator and two optical parametric amplifiers for time‐resolved studies, with emphasis on the structural dynamics in heme proteins. The system provides a 100‐fs pump pulse tunable in the range 500–600 nm and a transform‐limited sub‐picosecond probe pulse tunable in the range 390–450 nm. The spectrometer has spectral (25 cm⁻¹) and temporal (∼0.7 ps) resolutions which constitute an effective compromise for identifying transient heme protein species and for following their structural evolution by spontaneous Raman scattering in the time range 0.5 ps to 2 ns. This apparatus was applied to time‐resolved studies of a broad range of heme proteins, monitoring the primary dynamics of photoinduced heme coordination state and structural changes, its interaction with protein side‐chains and diatomic gaseous ligands, as well as heme vibrational cooling. The treatment of transient Raman spectra is described in detail, and the advantages and shortcomings of spontaneous resonance Raman spectroscopy for ultrafast heme proteins studies are discussed. We demonstrate the efficiency of the constructed spectrometer by measuring Raman spectra in the sub‐picosecond and picosecond time ranges for the oxygen‐storage heme protein myoglobin and for the oxygen‐sensor heme protein FixLH in interaction with the diatomic gaseous ligands CO, NO, and O<sub>2sub>. Copyright © 2010 John Wiley & Sons, Ltd.     

Hybrid Battery-Capacitor System based on Li4Ti5O12Anode and PTPAn Cathode北大核心CSCD

Owing to its high safe, high rate and long life characteristics, lithium titanate (Li4Ti5O12) anode material has attracted extensive attention in recent years, and many efforts are being made to develop the Li4Ti5O12based high performance hybrid supercapacitors and Li-ion batteries. Herein, we prepared the organic cathode material polytriphenylamine (PTPAn) through chemical oxidation and polymerization of triphenylamine (TPAn), and investigated its charge storage mechanism and electrode kinetics with the typical electrochemical methods in an organic electrolyte. It was demonstrated that the PTPAn exhibited the reversible capacity of 85 mA·g-1. The charge storage depended on the reversible adsorption/desorption of anion, which is not controlled by the diffusion process, and thus, can be considered as the pseudocapacitive behavior. Then, the PTPAn cathode was coupled with the Li4Ti5O12anode to form a hybrid capacitor/battery system with high power and improved energy density. Finally, the inherent drawback and the challenge for practical application of such an organic cathode are briefly discussed. © Journal of Electrochemistry 2018.