Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

应用级联倍频方法提高倍频系统输出稳定性研究

提出应用级联倍频方法提高倍频系统输出稳定性,并就该方法的有效性进行了理论分析和模拟计算.分析和计算结果不但证明级联倍频方法能实现倍频系统稳定输出,而且还表明可以通过仔细调节第一块倍频晶体中波矢方向 k 与光轴间夹角、两块倍频晶体间的间隔,能调节改变实现倍频系统最稳输出时所需第二块晶体的理论计算长度,使之与第二块倍频晶体的实际加工长度一致,最终实现系统稳定倍频输出.级联倍频方法在实现高输出稳定性的同时能实现高的倍频转换效率,对应用于光参量啁啾脉冲放大系统的高稳定抽运源系统的设计建造具有重要参考意义. 关键词： 级联倍频 稳定倍频输出 光参量啁啾脉冲放大     

Multiplesite structure and photoluminescence properties of Eu3+ doped MgO nanocrystals

MgO:Eu³⁺ nanocrystals with average diameter around 15 nm were prepared via a facile combustion method under a weak reductive atmosphere at temperature as low as 300°C. The photoluminescence spectra showed that the MgO:Eu³⁺ nanocrystals emit white light, the hypersensitive transition (⁵ D ₀→⁷ F _j of Eu³⁺) emission was prominent in the emission spectra resulting from the noinversion symmetry local site at which Eu³⁺ ions were located. Two kinds of luminescence sites of Eu³⁺ are identified by means of the fluorescence decay and site-selective spectroscopy. The excitation and absorption spectra indicated that the absorption of surface state decreased with the increase of Eu³⁺ concentration, meaning that the surface defect decreased through Eu³⁺ doping for some of them located at the disordered sites near the surface or absorbed at the surface of MgO host. Meanwhile, absorptivity and CIE chromaticity coordinates of all samples were measured; the results were in accordance with the excitation and absorption spectra and photoluminescence spectra, respectively.     

Electrical properties of neodymium doped CaBi4Ti4O15 ceramics

Neodymium doped bismuth layer structure ferroelectrics (BLSFs) ceramics CaBi_4−xNd_xTi₄O₁₅ (x=0, 0.25, 0.50, 0.75) were prepared by solid-state reaction method. X-ray diffraction pattern showed that single phase was formed when x=0-0.75. The refined lattice parameters showed that a (b) axes decrease at x=0.25 and increase with more Nd³⁺ dopant. The effects of Nd³⁺ doping on the dielectric and ferroelectric properties of CaBi₄Ti₄O₁₅ ceramics are studied. Nd³⁺ dopant decreased the Curie temperature linearly, and the dielectric loss, tan δ, as well. The remnant polarization of Nd³⁺ doped CaBi₄Ti₄O₁₅ ceramics was increased by 80% at x=0.25, while more Nd³⁺ dopant decreased the remnant polarization. CaBi_3.75Nd_0.25Ti₄O₁₅ ceramics had the largest piezoelectric constant d₃₃. The structure and properties of CaBi_4−xNd_xTi₄O₁₅ ceramics showed that Nd³⁺ may occupy different crystal locations when Nd³⁺ content x is less than 0.25 and more than 0.50.     

Photocatalytic performance of ZnO:Fe array films under sunlight irradiation

ZnO:Fe array thin films were prepared by the hydrothermal method using the sol-gel grown film as a seed layer. The samples were characterized by X-ray diffraction (XRD), ultraviolet/visible absorption spectra (UV-vis) and scanning electron microscopy (SEM). The photocatalytic activities of the prepared samples were investigated for the photodegradation of methylene blue (MB) under sunlight irradiation. The results show that the lattice constant a and the cell volume of ZnO:Fe film increase due to the substitution of Fe for Zn. The absorption edge of Fe-doped ZnO displays a red shift with a significant absorption between 600 and 700 nm. The ZnO:Fe array film is composed of disk particles with uniformity and compactness. Doping Fe ions enhances the photodegradation rate of ZnO array film for MB. 1.5% Fe doped ZnO sample exhibits the highest activity under irradiation time of 4 h. Its degradation rate increases about 1.6 times compared to the undoped ZnO.     

硬脂酸晶体压力效应的FT-IR光谱研究

 本文在0~4 GPa范围内研究了预压力对硬脂酸晶体的相关场劈裂和固态-熔融态相变过程的影响。通过γCH₂面内摇摆振动模和γ'CH₂相关场模的强度和频率变化,发现预压力对晶体内的相关场合分子链取向有明显的影响。预压力对硬脂酸的熔点虽然没有影响,但对γ'CH₂模有“硬化”作用。并且由此出发,对硬脂酸的预熔过程作了讨论。     

一种高分辨率的光纤光栅传感解调技术

报道了一种基于光纤激光器波长扫描寻址的高分辨率的光纤光栅传感解调方案。光纤激光器的扫描寻址过程由微机来控制。微机控制光纤激光器波长扫描的同时,同步采集、处理传感信号,并通过曲线拟合给出传感光栅的中心反射波长值。本解调方案的波长移动分辨率为０．１ｐｍ,可以实现高分辨率的温度及应变测量。     

间接原子吸收光谱法测定水样中的痕量硼

本文研究了四氟硼酸根与邻二氮菲银形成的络合物由MIBK萃取后,用火焰原子吸收光谱法间接测定硼,其线性范围为0.002-1μg/mL,检出限为0.41μg/mL,回收率为93%-101%,且K^ 、Na^ 等10个种离子不干扰测定,本方法用于地下水中痕量硼的测定,结果令人满意。     

苯并氧化呋咱稳定性和异构化的DFT和ab initio研究

运用B3LYP/6-31G(d)密度泛函理论（DFT）方法对苯并氧化呋咱、邻二亚硝基苯及其间的异构化反应进行了计算研究。结果表明,苯并氧化呋咱的分子总能量比邻二亚硝基苯的低;由苯并氧化呋咱异构为邻二亚硝基苯的正向反应活化能（Ea+=51.0kJ/mol）,与文献实测值（58.6kJ/mol）较接近,而其逆向反应活化能（Ea-=4.6kJ/mol）很小,从而揭示了苯并氧化呋咱比邻二亚硝基苯更稳定·此外,进行了HF/3-21G、HF/6-31G(d)和MP2/6-31G(d)//6-31G(d)水平下相应的计算,发现B3LYP-DFT的结果较abinitio为优。谐振动频率的B3LYP/6-31G(d)计算还支持了邻二亚硝基苯为苯并氧化呋咱“自-自”互变重排反应的中间体。     

光纤光栅力传感器的无源温漂补偿技术

将一光纤光栅沿轴向粘贴于两重叠等腰三角形悬臂梁的交界处进行力传感。理论和实验均证实该无源装置具有自动补偿布拉格波长温漂效应的功能。０￣０．３４Ｎ力范围内,实验表明其传感灵敏度ｎｍ／Ｎ。