Fast algorithms for spherical harmonic expansions,III

We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on “Fast algorithms for spherical harmonic expansions”. The requisite precomputations become manageable when organized as a “depth-first traversal” of the program’s control-flow graph, rather than as the perhaps more natural “breadth-first traversal” that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples.     

${\mathbb{Z}}/3{\mathbb{Z}}$-量子群的Gr\"{o}bner-Shirshov 基

通过计算合成, 我们证明了Yamane 给出的关系是 ${\mathbb{Z}}/3{\mathbb{Z}}$-量子群的一个Gr\"{o}bner-Shirshov 基.     

前放滤波对红外探测器光谱测试的影响

傅里叶变换红外光谱仪有着测试效率高、分辨率高等优点,一般比棱镜式或光栅式在实用波段分辨率要高上40倍,对红外探测器进行测试,受到动态范围、光敏元面积、外部接口要求等影响,必须通过电流放大器进行连接.通过测试对比,研究了前放波率的不同设置对光谱测试的影响,分析了影响机理,得到了前放较佳的设置波段.     

傅里叶变换红外光谱仪光阑孔径及扫描速率设置探讨

傅里叶变换红外光谱仪辐射通量大,特别适用于测量弱信号光谱,从而具有很高的灵敏度.因此也对处理系统有着苛刻的要求,在实际测试中,博里叶光谱仪光阑孔径及扫描速率设置是相关联的,直接影响到采集及数据处理的精度.通过试验,研究探讨了傅里叶光谱仪光阑孔径及扫描速率设置极限及平衡点,兼顾快与准.     

热红联用技术在森林火灾烟气测试中的应用

探索了一套基于热重分析仪-红外光谱分析仪联用（热红联用）技术的森林火灾烟气测试方法.该方法在对森林可燃物燃烧的热失重过程进行热重分析的同时,同步地对热解气体成分进行傅里叶红外光谱（FTIR）分析,从而实现了对燃烧过程诸因素的跟踪分析.     

水溶性CdTe:Mn量子点的双光子吸收

采用激发波长800 nm、脉宽50 fs、重复频率1 kHz的Ti:sapphire放大飞秒激光器作为激发光源,利用开孔Z扫描技术研究了不同粒径的CdTe:Mn量子点的非线性吸收性质。理论计算结果表明,同一生长时间CdTe:Mn量子点的双光子吸收系数是CdTe量子点的1.1倍,其双光子吸收系数随量子点尺寸的减小而增大,这是由于CdTe:Mn量子点非线性吸收属于反饱和吸收,掺杂了Mn元素,减小了表面缺陷浓度,表明掺杂量子点具有很好的双光子吸收现象。     

The Pseudo-differential Operator hμ,a on Hankel Invariant Spaces

Using Hankel transform the symbol 'a' is defined and the pseudo-differential operator (p.d.o.) h_μ,a associated with the Bessel operator d ²/dx ² + (1 ? 4μ ²)/4x ² in terms of this symbol is defined. It is shown that the operator h_μ,a is a continuous linear map of a Hankel invariant space into itself. A special pseudo-differential operator called the Hankel potential is defined and some of its properties are investigated.     

Existence of subharmonic solutions and homoclinic orbits for a class of even higher order differential equations

Using the variational structure and the Z ₂ group index theory we establish the existence of subharmonic solutions and homoclinic solutions for a class of even higher order differential equation.     

Copula理论在复合期权定价中的应用

本文使用风险中性评价方法分三部分计算了复合期权的价值,针对需要计算联合分布的第二部分,通过选取边缘分布为GARCH模型的二元正态Copula模型进行推理验证,结果求得的联合分布与使用风险中性评价方法的计算结果一致.进一步计算得到了时间相依的复合期权的价值,并且给出了使用Bayes时序诊断法和Z检验来诊断期权定价时其出现价格大的波动时的局部拐点的方法.     

An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle

We present "one-dimensional" Fourier theory on commutative groups T hH , 0 h h < X , 0< H h X within the framework of the so-called calculus on measure chains (or time scales). Depending on certain values of the graininess h and length H of the group the four classical types of Fourier transform are covered: Fourier integral ( T 0 X = R ), Fourier series ( T 1 X = Z ), Fourier analysis of periodic functions ( T 0,2 ~ = S 1 (0) unit circle) and discrete Fourier transform ( T 1 N = Z N ). We will present Fourier theory on these groups in a unified manner. This also allows to closely track the roles of the graininess h and length H of the group--especially for h M 0 and H M X . In the final part of the paper, we investigate the solution of a fundamental equation on T hH , which can be considered as a generalization of the Gauss function. It finally leads to a version of the Heisenberg uncertainty principle, which extends the classical one, valid for T 0 X = R , to the case T hH , where either h >0 or H < X .