球面上的分数次积分

设Ｓθ是ｎ维单位球面Ωｎ上的平移算子，ｐ〉１，定义平均意义下的Ｌｉｐｓｃｈｉｔｚ空间：Ａα＾ｐ＝｛ｆ（ｘ）：‖Ｓθ（ｆ）－ｆ‖ｐ〈Ｃｆ＾θα｝，０〈α〈１本文研究球面分数次积分在Λα＾ｐ中的性质。     

钴前驱体对掺杂TiO2微结构和可见光催化性能的影响

为发展可见光下破坏污染物的钴掺杂TiO2光催化剂,以CoCl2、Co(NO3)2和CoSO4为钴前驱体,采用溶胶-凝胶法制备了钴掺杂TiO2,通过X射线衍射、扫描电镜、BET表面积测试和紫外-可见吸收光谱对比研究了钴前驱体对样品的微观结构和吸光性能的影响．同时,以苯胺为降解目标物,比较了样品在可见光下的催化活性．结果表明,样品的TiO2晶相、形貌、比表面积和吸光性能都随着钴前驱体的不同而不同,其中以Co(NO3)2为前驱体制备得到的样品其光催化活性最高,特别是1％掺杂且400℃烧结得到的样品,并简要讨论了其可能原因．     

氦原子1snp组态的塞曼效应

利用塞曼哈密顿的球张量形式,采用将微扰理论与里兹变分方法相结合的方式,导出了氦原子1snp组态塞曼哈密顿矩阵元的一般形式,给出了氦原子1s3p组态塞曼效应之解,并绘出了不同磁场强度下氦原子1s3p组态的塞曼能级分裂图.     

The removal of sodium dodecylbenzene sulfonate surfactant from water using silica/titania nanorods/nanotubes composite membrane with photocatalytic capability

This paper reports experimental results on removal of sodium dodecylbenzene sulfonate (SDBS), using silica/titania nanorods/nanotubes composite membrane with photocatalytic capability. This multifunctional composite membrane has been successfully prepared from colloidal X-silica/titania sols (X denotes molar percent of silica) by the sol-gel technique. The prepared nanorods/nanotubes composite membranes were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), scanning probe microscope (SPM) and UV-vis diffuse reflectance spectra (DRS). XRD patterns confirmed that the embedding of amorphous silica into nanophase titania matrix helped to increase the thermal stability of titania and control the size of titania particles. The small size titania particles with anatase phase played an important role in formation of silica/titania nanorods/nanotubes composite membranes with photocatalytic capability. The percentage of anatase phase titania reached 93% when 20%-silica/titania nanorods/nanotubes composite membrane calcined at 400 °C for 2 h. Most (95%) of the pore volume was located in mesopores of diameters ranging from 1.4 to 10 nm. The experimental results showed that the removal of SDBS achieved 89% after 100 min by combining the photocatalysis with membrane filtration techniques. Although the SDBS was not completely decomposed by photocatalysis, the degradation of the SDBS helped to enhance composite membrane flux and prevent membrane fouling. It was possible to treat successfully surfactant wastewater using multifunctional silica/titania nanorods/nanotubes composite membrane by means of a continuous process; this could be interesting for industrial applications.     

Pickup lens inspection on the 5th order aberration using shearing interference by grating with curve fitting algorithm

An optical system based on shearing interference using diffraction grating was applied, to carry out the aberration inspection process of the pickup lens of a digital versatile disc (DVD) at high speed. An algorithm was devised that processes points allocated on certain lines on a fringe and fits relations between the distance from basis point to the measurement points, and phase data of the fringe at these points to an equation of higher degree as curve fitting. Aberration was numerically estimated as the size of a certain coefficient. Simulation showed that this algorithm could detect all 5th order aberrations independently. An inspection system developed based on this optical system and algorithm detected aberration as accurately as a conventional interferometer that has been used as the standard, attaining an inspection time of 1/10-1/20. In comparison with the spot method, this system has 5th order aberration detecting ability and 1/3 the inspection time.     

TiO_2纳米粉体的制备及光催化活性

以钛酸四丁酯为原料，采用溶胶凝胶过程超临界干燥法制备了 Ｔｉ Ｏ２ 纳米粉体，并通过 Ｘ Ｒ Ｄ、 Ｂ Ｅ Ｔ、 Ｔ Ｅ Ｍ 等方法对所得样品进行表征． 制备的 Ｔｉ Ｏ２ 气凝胶具有很高的比表面积（４８８ ｍ ２ ·ｇ－ １），平均粒径为 ４．６ ｎｍ ，具有锐钛矿型晶体结构，经５００℃煅烧２ ｈ 所得的纳米粉体，锐钛矿型晶体结构更为明显，平均粒径６．７ ｎｍ ，比表面积 １５８ ｍ ２ ·ｇ－ １． 将它用于甲基橙溶液的脱色反应，具有高的光催化活性     

Study on the Radius of an Electrical Spherical Micelle： Functional Theoretical Approach

For the purpose of eliminating restriction, the Poisson-Bokzmann (PB) equation, which represents the potential of the electrical double layer of spherical miceUes, can be solved analytically only under the lower potential condition, a kind of iterative method in functional analysis theory has been used. The radius of the spherical particle can be obtained from the diagram of the second iterative solution of the potential versus the distance from the center of the particle. The influences of the concentration of the ions, the charge number of ions, the aggregation number of the particle, the dielectric constant of solvent and the temperature of system on the radius also have been studied.     

Electromagnetic scattering theorems for interior dipole excitation of a layered obstacle

A layered scatterer is excited by a time‐harmonic spherical electromagnetic wave, generated by a dipole located either in the interior or in the exterior of the scatterer. The scatterer's core may be perfect conducting, impedance or dielectric. This paper initiates the investigation of scattering theorems corresponding to the excitation of a layered scatterer by a dipole in its interior. We establish reciprocity and general scattering theorems relating the total electric fields with the corresponding far‐field patterns. The optical theorem, relating the scattering cross‐section with the electric field in the layer containing the dipole, is recovered as a corollary of the general scattering theorem. Furthermore, for a scatterer excited by a spherical and a plane wave, mixed scattering theorems are derived. Besides, all the derived theorems recover known results, concerning the excitation of a homogeneous scatterer by an exterior dipole. We also analyze numerical implementations of the optical theorem in certain concrete scattering applications. Copyright © 2007 John Wiley & Sons, Ltd.     

Engineering Nanoarchitectures for Photonic Crystals

The detailed shape of the dense material network of inverse opals has a significant influence on the appearance of band gaps in these photonic crystals. One example of these topologically very similar networks is the skeleton structure, which can show two complete band gaps. Like all inverse opals, these structures are self‐standing and can be fabricated via self‐assembly strategies. The first step for obtaining these novel kind of photonic crystals has been achieved by synthesizing a titania skeleton structure.     

On the chromatic aberration of magnetic lenses with a field distribution in the form of an inverse power low (B(z) ∝ z)

The chromatic aberration of magnetic lenses with the field distribution in the forms of inverse law have been studied by analytical and digital methods. These aberrations can be expressed in terms of Bessel function of fraction order. Analytical expressions for chromatic aberration coefficients of the spherical field model, which is useful for the study of single-pole magnetic lenses, are given.