Mathematical induction,difference equations and divisibility

Many exercises in mathematical induction require the student to prove a divisibility property of a function of the integers. Such problems are generally presented as being independent of each other. However, many of these problems can be presented in terms of difference equations, and the theory of difference equations can be used to provide a uniform method for creating such divisibility problems. This article shows how a multitude of such problems can be created, and how standard problems from textbooks can be analysed in terms of difference equations.     

The most stable crystal structure and the formation processes of an order-disorder (OD) intermetallic phase in the Mg–Al–Gd ternary system

The most stable crystal structure for an 18R-type order-disorder (OD) intermetallic phase in the Mg–Al–Gd ternary system and its formation processes by annealing at 525?°C have been investigated by means of transmission electron microscopy and scanning transmission electron microscopy. The most energetically favourable polytype at 525?°C is found to be the structurally simplest one, a maximum degree of order polytype (monoclinic, 1M, space group: C2/m), described with a single stacking vector in stacking six-layer structural blocks. The formation of this simplest polytype occurs in the sequence of (i) enrichment of Gd and Al in four consecutive close-packed planes while keeping the hexagonal close-packed stacking of the AB-type, (ii) formation of Al₆Gd₈ clusters in the four consecutive atomic planes, introducing a stacking fault in the middle of the four consecutive atomic planes, (iii) thickening by the formation of Gd and Al-enriched four consecutive planes at a distance of two or three close-packed Mg atomic planes from the pre-existing Gd and Al-enriched four consecutive atomic planes so as to form six-layer and, sometimes seven-layer structural blocks, (iv) in-plane ordering of Al₆Gd₈ clusters in the four consecutive atomic planes and the stacking of structural blocks in the preferential stacking positions to form the OD structure, and (v) elimination of different structural blocks (other than six-layer ones) and the long-range ordering in the stacking of structural blocks.     

镀膜长周期光纤光栅耦合系数的研究

给出了镀膜长周期光纤光栅芯层模式和包层模式耦合的耦合系数的详细表达式,应用此表达式对镀膜长周期光纤光栅的耦合系数的特性进行了较为详细的研究。研究发现:1)同次模式的耦合系数随薄膜厚度变化而变化,在某些厚度下,奇次模式耦合的耦合系数与偶次模式耦合的耦合系数几乎相等;2)在某些厚度处,交流耦合系数会有跳变发生;3)交流耦合系数随环境折射率的变化而变化,并且当环境折射率靠近光纤包层折射率时交流耦合系数会有急剧跳变发生。     

The effect of annealing and temperature on transmission spectra of long period gratings written in hydrogen loaded standard single mode fiber

The influence of annealing and temperature on the transmission spectrum of Long Period Grating (LPG) is investigated by monitoring the wavelength shift and the intensity variation in the loss peaks. The LPGs are inscribed in a hydrogen loaded standard telecommunication fiber and experiments are performed at different annealing temperature and time to observe the spectral changes. The effect of temperature changes on the spectral profile of LPG is also studied.     

Novel bending sensor based on a meniscus shaped beam with LPG

A novel bending sensor based on a long period fiber grating (LPG) is presented. A LPG was glued into a V-shaped groove, which lies on the lower surface of a meniscus shaped beam. It is found that the transmission optical power of the LPG changed linearly with the variation of the bending of the beam. The bending applied on the beam can be measured by detecting the intensity variation of the LPG's resonant dip wavelength. Under a relative large bending measured range from 0 to 7.5 m^?1, the sensitivity of 3.003 dB m^?1 and curvature resolution of 0.001 m^?1 have been achieved for the proposed bending sensor.     

Pressure-induced crystallization of triacylglycerides

We report on the impact of high pressures on the crystallization of pure triolein and triolein–trilaurin mixtures. We detect growth rates and induction times of single crystals under a high pressure application with a polarization microscope. Statistical studies on the induction time were carried out studying light scattering and transmittance. Similar to supercooling in temperature-induced crystallization, we find a superpressuring in pressure-induced crystallization. In binary mixtures, the inverse induction time indicates a threshold concentration close to the melting point of one component, beyond which it depends linearly on concentration.     

基于聚合经验模态分解方法的OJ 287 射电流量变化周期分析

BL Lac 天体OJ 287 是一个重要的Blazar天体, 光变具有准周期特点. 本文从密歇根大学射电天文台数据库收集了OJ 287射电波段4.8, 8.0和 14.5 GHz超过30年时间的观测数据. 由于天文观测资料的复杂性, 一些传统寻找周期的方法不是太理想. 近几年迅速发展起来的聚合经验模态分解(EEMD) 特别适合于具有非线性和非平稳动态变化特性的Blazar天体光变规律的研究. 运用EEMD方法对OJ 287 的3个射电波段流量分别进行多时间尺度分解, 各获得6个代表不同时间尺度局部特征信息的本征模态函数分量和一个趋势项. 研究结果表明: 4.8 GHz射电流量变化的主要周期是18.9, 11.9, 5.7 和2.4年; 8.0 GHz 的主要周期是12.2, 5.2和2.4 年; 14.5 GHz的主要周期是21.8, 12.0, 4.3和 2.4 年. 尽管3个波段流量变化主要周期大小有一定的差别, 但是存在着近似相同的变化周期12.0 和2.4年, 说明这3个波段可能来源于相同的辐射机制, 也证实了OJ 287 射电波段和光学波段具有相同的长光变周期12.0 年. 这些结论表明: EEMD 作为一种全新的非线性、非平稳信号处理方法, 可以更精确地提取Blazar天体中不同光变周期的分量. 关键词： OJ 287 光变周期 聚合经验模态分解     

The Suppression of Isothermal Cold Crystallization in PET Through Nano‐Silica Incorporation

Isothermal crystallization from the glassy state of pure poly(ethylene terephthalate)(PET) and PET/Silica nanocomposites films was studied. The results showed that addition of nano‐silica increased the crystallinity of filled PET compared to pure PET, suggesting that nano‐silica is an effective nucleating agent. However, the induction period prior to crystallization was prolonged and the overall crystallization rate decreased through nano‐silica incorporation. This is a result of the cold crystallization rate being primarily controlled by diffusion of PET chains, rather than being controlled by the nucleation rate. The strong interaction between the nanoparticles and PET chains confined the movement of the macromolecular chains and decreased the cold crystallization rate.     

基于近红外光谱技术的小麦条锈病菌潜伏侵染的检测

为实现对受到小麦条锈病菌侵染而尚未表现明显症状的小麦叶片进行早期检测,利用近红外光谱技术结合定性偏最小二乘法建立了小麦条锈病潜育期叶片定性识别模型。获取健康叶片30片、条锈病潜育期叶片330片(每天取30片,共11天)和发病叶片30片,扫描获得其近红外光谱曲线。采用内部交叉验证法建模,研究了不同谱区、建模比(建模集∶检验集)、光谱预处理方法和主成分数对建模识别效果的影响。在5 400~6 600和7 600~8 900cm-1组合谱区内,建模比为4∶1、预处理方法为"散射校正"和主成分数为14时,所建模型识别效果较理想,建模集的识别准确率、错误率和混淆率分别为95.51%,1.28%和3.21%;检验集的识别准确率、错误率和混淆率分别为100.00%,0.00%和0.00%。结果表明,利用近红外光谱技术可在接种1天后(即提前11天)识别出健康小麦叶片和受到条锈病菌侵染的小麦叶片,并且可以识别不同潜育期天数的叶片。因此,利用近红外光谱技术对条锈病菌潜伏侵染检测是可行的,为该病早期诊断提供了一种新途径。     

基于CATIA的固体火箭发动机系统设计

发动机图形绘制与性能计算是火箭设计的关键步骤,通过对固体火箭发动机设计过程的分析,提出CATIA参数化图形绘制技术;以单孔管状装药发动机为例,建立了发动机燃烧室与喷管模型,在VC环境下利用CATIA Automation二次开发技术实现了燃烧室与喷管参数化设计,完成了两者装配与动态显示;利用Matcom实现内弹道压力时间曲线计算,发射段轨道分析;最后完成系统软件编制;实际使用情况表明,使用该软件可快速构造发动机,进行全面的性能分析,为固体火箭发动机方案论证与初步设计提供了有力的工具。