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超导-介质型Fibonacci光子晶体的透射谱与滤波特性分析
Fibonacci光子晶体 超导 传输矩阵法 温控调谐
2013/9/28
目前广泛应用的可调谐光滤波器通过调节干涉腔长度来实现波段的调谐。它需要制备高反射悬浮膜,而悬浮膜在驱动电压的影响下其运动会受到限制,且较窄的透射峰与较大的调谐范围二者不可兼得。为此,本文将光子晶体中的其中一种介质以超导材料取而代之。基于超导理论,利用传输矩阵法对一维超导-介质型Fibonacci光子晶体的透射谱进行了计算,讨论了厚度、折射率以及温度对透射谱的影响。结果表明,受光子带隙的影响,超导体...
A determinant of generalized Fibonacci numbers
generalized Fibonacci numbers Cassini’s identity determinant evaluation
2012/4/18
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of the...
关于Fibonacci 数中含有形如4p+1的素因子
Fibonacci数 素数 二项式定理
2011/9/18
本文将用初等数学的方法证明下标素数 p为何值的情况下，Fibonacci数 F_p具有形如 4p+1的素因子。本文给出如下的结论：如果素数p>7 ，p=2(mod5) ，4p+1 也是素数，且-5(F_p)^2+4<>0(mod4p+1) ，则4p+1|F_p 。
Golden Quantum Oscillator and Binet-Fibonacci Calculus
Golden Quantum Oscillator Binet-Fibonacci Calculus Quantum Algebra
2011/9/19
Abstract: The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases $q=\phi$ and $Q=-1/\phi$. Quantum harmonic oscillator for this Golden calc...
本文构建了含有电光材料LiNbO3的一维对称广义Fibonacci光子晶体结构,提出并设计了一种基于该结构的可调谐滤波器,并利用传输矩阵法对设计的滤波器的可调谐滤波特性进行了理论研究.数据模拟结果表明:保持对称广义Fibonacci光子晶体的几何结构不变,通过改变电极所在处施加在电光介质(LiNbO3)层上的外加电场,即可实现滤波器的滤波通道波长的调节,滤波通道波长的改变与外加电压呈线性关系,随着...
Categorification of the Fibonacci numbers using representations of quivers
Categorification of the Fibonacci numbers representations of quivers Representation Theory
2011/8/31
Abstract: In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the ...
利用谱范数与 Frobenius 范数之间的不等式和 Toeplitz矩阵的表示式, 给出了关于 Fibonacci和Lucas数的 Toeplitz矩阵的谱范数的上界和下界, 并改进了 Akbulak M 等相关结论中谱范数的上界.
A Metis design is one for which v = r + k + 1. This paper deals with Metis designs that are quasi-residual. The parameters of such designs and the corresponding symmetric designs can be expressed by F...
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
generalized Fibonacci numbers renewal theory
2011/2/25
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell’s renewal theorem we find an approximation to the generalized Fibonacci n...
We show that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density
Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci
fast simple O(lg n) algorithm math
2010/11/24
Two very fast and simple O(lg n) algorithms for individual Fibonacci numbers are given and compared to competing algorithms. A simple O(lg n) recursion is derived that can also be applied to Lucas. A...
Generalized Compositions and Weighted Fibonacci Numbers
Compositions Fibonacci numbers Polynomial coefficients
2010/12/8
In this paper we consider particular generalized compositions of a nat-ural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized composit...
花瓣Fibonacci数的生存函数研究
花瓣 Fibonacci数 Lucas数 生存函数
2009/12/7
花瓣与Fibonacci数有着密切关系，根据Fibonacci数与Lucas数的递归关系，给出了关于Fibonacci数的生存函数F(r,x)和S(r,n,x)的定义，得到了关于Fibonacci数的生存函数，揭示了Fibonacci数的内在联系。
用特征矩阵法研究了由正常色散SiO2/TiO2薄膜组成的Fibonacci序列一维光子晶体在可见光波段的传输特性，并与无色散时的传输特性做了对比。结果表明,随序列项数的增加，相应的前一序列的透射谱中透射率较低的凹带逐渐变成禁带，禁带数增加；初始介质是低折射率的SiO2薄膜时比高折射率的TiO2薄膜时各序列的透射谱中的禁带数多，各禁带的宽度和中心波长基本相同；在总厚度一定的条件下，随SiO2薄膜的厚...
Rational Identities and Inequalities involving Fibonacci and Lucas Numbers
Rational Identities and Inequalities Sequences of Integers Fibonacci and Lucas numbers
2008/6/27
In this paper we use integral calculus, complex variable techniques and some classical inequalities to establish rational identities and inequalities involving Fibonacci and Lucas numbers.