Note on the Blow-up Set for A Semilinear Parabolic Differential System

ＮｏｔｅｏｎｔｈｅＢｌｏｗ－ｕｐＳｅｔｆｏｒＡＳｅｍｉｌｉｎｅａｒＰａｒａｂｏｌｉｃＤｉｆｆｅｒｅｎｔｉａｌＳｙｓｔｅｍ￥ＣｈｅｎＦｕｊｕｎ（陈富均）（ＳｈａｎｇＱｉｕＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ４７６０００）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｎｏｔｅｄ...     

Thermodynamics of interaction between sodium bis(2‐ethylhexyl) sulfosuccinae and polymers in aqueous solutions by isothermal titration microcalorimetry

The interactions between sodium bis(2‐ethylhexyl) sulfosuccinae (AOT) and two nonionic water‐soluble polymers, including polyvinyl pyrrolidone (PVP) and polyethylene glycol (PEG) have been investigated by using isothermal titration microcalorimetry in aqueous solutions at 298.15 K. The results show that the critical aggregation concentration, which corresponding to the first turning point in the curve of experimental interaction heat versus concentration of the surfactant, is lower than the critical micellar concentration (cmc), confirming the existence of polymer‐surfactant interactions. The value of cac is not sensitive to the relative amount of polymer in low concentration range of the polymer. The mono‐layer saturated adsorption concentration, which corresponding to the second turning point, rises as the polymer concentration is increased. The interaction between PVP and AOT is stronger than that between PEG and AOT. The results also indicate that the aggregation of AOT in water and polymers solutions is entropically driven. The observed thermal effects have been interpreted in terms of the interactions of the polymer molecules with AOT monomers or the molecular clusters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 275–283, 2006     

Laser beam alignment by fast feedback control of both linear and angular drifts

A new way to enhance the directional stability of laser beams with alternating intensity by fast feedback control of both linear and angular drifts has been proposed for alignment of laser beams at higher accuracy. Both linear and angular drifts of laser beams, processed through light intensity modulation and primary alignment using single-mode optical fiber (SMOF), are separated using light path arrangement and detected using phase-lock technique, and are controlled using fast feedback control mechanisms according to their detected magnitudes, so that both linear and angular drifts are suppressed to enhance the directional stability of the emitting laser beams. Theoretical analyses and preliminary experimental results indicate that the approach proposed can be used to achieve an alignment accuracy of more than 10⁻⁸ rad.     

FIR spectroscopy of ethyl bromide and trioxane: New laser transitions and assignments

Eight new optically pumped far infrared laser transitions from ethyl bromide and 22 from trioxane are presented. For each new line we give the wavelength, the polarization relative to that of the pump laser and the absorption offset relative to the CO₂ center frequency. The assignment of the rotovibrational states for the pump and the emission transitions of ethyl bromide are calculated. We also partly assigned the rotational levels of trioxane.     

管范畴上的算子及其应用

本文定义了管范畴上的一些算子,研究了它们的一些性质,给出了循环单列代数的Ringel-Hall代数H(T)的结构常数FML,N的一个计算公式．利用这些算子和这个公式,我们得到了其合成代数C(T)及半单模[l(?)i=1nSi](t∈Z+)在H(T)中的一些中心化子．事实上,它们是H(T)的中心元素,且是H(T)在其合成代数C(T)上代数无关的生成元．     

Self-catalytic synthesis and light-emitting property of highly aligned Mn-doped Zn2SiO4 nanorods

Highly aligned Mn-doped Zn₂SiO₄ nanorods were fabricated by using a modified vapor-phase evaporation method. Their microstructure and chemical bond configurations were investigated with the help of X-ray diffraction, scanning electron microscopy, transmission electron microscopy, Fourier-transform infrared absorption spectroscopy, and X-ray photoelectron spectroscopy. The formation process of the Mn-doped Zn₂SiO₄ nanorods can be elucidated on the basis of a self-catalytic vapor–liquid–solid growth mechanism in which Mn chloride hydrate acts as the catalyst and impurity source. Photoluminescence measurements revealed that an intensive green luminescence peak appears at 523 nm, which corresponds to the electronic transition ⁴T₁(⁴G)→⁶A₁(⁶S) of Mn²⁺ ions. Our experimental results provide a useful approach to directly fabricate Si-based nanoscale light-emitting materials using ZnO–Zn₂SiO₄ composite. PACS 81.05.-t; 81.10.Bk; 81.07.-b     

Impulsive loading of clamped monolithic and sandwich beams over a central patch

An analytical model is developed for the response of clamped monolithic and sandwich beams subjected to impulse loading over a central loading patch. A number of topologies of sandwich core are investigated, including the honeycomb core, pyramidal core, prismatic diamond core and metal foam. The various cores are characterised by their dependencies of through-thickness compressive strength and longitudinal tensile strength upon relative density. Closed-form expressions are derived for the deflection of the beam when the ratio r of length of loading patch to the beam span exceeds 0.5. In contrast, an ordinary differential equation needs to be solved numerically for the choice r<0.5. Explicit finite element calculations show that most practical shock loadings can be treated as impulsive and the accuracy of the impulsive analytical predictions is confirmed. The analytical formulae are employed to determine optimal geometries of the sandwich beams that maximise the shock resistance of the beams for a given mass. The optimisation reveals that sandwich beams have a superior shock resistance relative to monolithic beams of the same mass, with the prismatic diamond core sandwich beam providing the best performance. Further, the optimal sandwich beam designs are only mildly sensitive to the length of the loading patch.     

An approach to achieve lateral superresolution for small probe confocal measurement system and its element

A shaped annular beam superresolution approach is proposed to improve a lateral resolution of a small probe laser confocal measurement system (LCMS). The approach proposed enables lateral superresolution measurement of LCMS to be achieved by using a binary optical diffractive element to shape a He–Ne Gaussian laser beam into an annular beam with an inner diameter of 0.87 mm and an outer diameter of 1.8 mm required for superresolution measurement, and shift the beam spatial frequency from low to high. And a binary optical element (BOE) with 16 phase levels is designed and fabricated to shape a Gaussian laser beam into an annular beam. Preliminary experimental results indicate that an intensity distribution of a shaped annular beam is in agreement with simulation results, the diffractive efficiency is 87.2%; LCMS lateral and axial resolutions of 0.2 μm and 3 nm are achieved, respectively, and its measurement range is expanded nearly to double, when BOE is used in LCMS and , NA=0.85.     

n阶全矩阵环(代数)的极小生成集

证明了下面的结论：１．若Ｒ是有单位元１的环，则Ｍｎ（Ｒ）作为环与Ｒ－模可由两个元生成；２．设Ｆ是域，Ｍｎ（Ｆ）作为Ｆ－代数可由两个元生成，且Ｍｎ（Ｆ）的任意非中心元皆可作为极小生成集中的一员；３．设Ｆ是特征为零的域，则Ｍｎ（Ｆ）的上三角矩阵子代数可由两个元生成