Fibonacci数列的模数列的周期的一个性质

Fibonacci数列的模数列是周期数列,并且是纯周期数列.利用模数列的定义,讨论了Fibonacci数列的模数列的周期的一个性质,证明了下列结果:假设m1与m2为不同的正整数,Fibonacci数列{Fn}的模数列{an(m1)}与{an(m2)}的最小正周期分别为T1与T2,则模数列{an([m1,m2])}的最小正周期为[T1,T2].     

Archaeometrical study of paleometallurgical materials from the archaeological site “Cerro de las Balsas — Chinchorro” (La Albufereta, Alacant, Spain)

An Iberian archaeological site located in the east of Spain is one of the most important cupellation centers found in the 4th century b.c. Different metallurgical materials were found in the archaeological site as minerals, cast slags, forged slags, metallic lead, cupella fragments and bronzes. Also was found reverbs remains used for cupper-based materials and cupellation procedure, and hearth forge remains for obtained iron material. The recuperated samples were studied by comparing samples of the same type of material by macroanalysis and microanalysis. The microanalysis and quantitation of the different archaeological materials was carried out by SEM/EDX. The information provides about the knowledge of a metallurgic process such as that of silver production by lead cupellation. The microanalysis results reflect the variety of elements that constitute the slags and other materials, and that come from the forge of the worked metallic materials. Also, the process cupellation was confirmed by the identification of lead and silver. The presence of forge slag corroborates the use of the great amount of recovered heart forges in the excavation like metallurgical structures for the iron work.     

含三次耦合项的两自由度Duffing系统的共振及混沌行为

研究了一类含三次耦合项的两自由度Duffing系统的动力学行为。首先应用多尺度方法近似求解系统的一阶稳态响应。通过讨论系统的主共振和1∶1内共振,分析了三次耦合项对系统响应的影响。随后研究系统随外加周期力强度变化的分岔过程,发现除了常见的倍周期分岔通向混沌外,还存在一种直接由周期运动进入混沌的突发路径。结合对系统的最大Lyapunov指数,相轨图及Poincar啨映射的分析验证了上述结论。     

双金属氰化物催化二氧化碳与环氧丙烷聚合

研究了双金属氰化配合物(DMC)催化剂催化二氧化碳(CO2)与环氧丙烷(PO)的共聚及PO的均聚反应,考察了DMC催化剂的诱导现象。结果表明,共聚时DMC催化的诱导期比均聚短,尤其是在低CO2压力(1.0MPa)下更明显,诱导期由均聚时的45min缩短为共聚时的15min。共聚时诱导期随CO2压力升高而增加,当反应压力由1.0MPa升高至7.0MPa时,诱导期由15min增至40min。PO与CO2共聚时的引发现象不同于PO均聚:共聚引发时温度和压力突然异常升高并迅速降低至引发前的状态,而均聚引发时温度突然升高后逐渐下降。由此可知CO2能促进DMC催化剂的活化。     

Detection and analysis of paraffin oil adulteration in coconut oil using fiber optic long period grating sensor

A fiber optic sensing system for the detection of adulteration of coconut oil by paraffin oil is experimentally demonstrated. The sensing mechanism is based on the sensitive dependence of the resonance peaks of a long period grating (LPG) on the changes of the refractive index of the environmental medium surrounding the cladding surface of the grating. The wavelength shift of the attenuation bands of the LPG was measured with the sensor immersed in a mixture of paraffin oil and pure coconut oil in different proportions. Detection limit of adulteration was found to be 3% for coconut oil-paraffin oil binary mixture.     

Controlling of symmetric and asymmetric mode coupling in long-period fiber gratings singe-side induced by long-pulse CO2 laser

We report a simple fabricating approach to control the mode couplings in long-period fiber gratings (LPFGs) through side exposing fiber to long-pulse-10.6-μm laser from a cheap, internally modulated CO₂ tube. By tuning focused-spot size on fibers, not only circularly symmetric mode coupling but also asymmetric mode couplings can be effectively achieved. Simulation of mode profiles in grating cross-section with Finite Element Method (FEM), and LPFG-cladding etching experiment with hydrofluoric acid (HF), support our explanation that asymmetric mode coupling in LPFGs depends on local refractive-index (RI) change within an azimuthally thin cladding layer, resulted from large-spot method induced deep melt flow on fiber surface during CO₂ laser irradiation.     

Analysis of statistical nature of electrical breakdown time delay in nitrogen at 6.6 mbar pressure in presence of positive ions and N(4S) atoms

On the basis of the mean value of electrical breakdown time delay and the standard deviation of electrical breakdown time delay σ dependence on the afterglow period τ, the mechanisms which dominantly influence to breakdown initiation in nitrogen were separated. It was shown that the positive ions formed in mutual collision of long‐lived metastable molecules have a dominant role in breakdown initiation for τ values up to 70 ms. The metastable molecules were derived from previous breakdown and discharge. In this case σ ≪ t_d and the total time delay t_d is approximately equal to formative time t_f which decreases in value with the increase of overvoltage. When positive ions have a dominant role in the breakdown initiation the Gaussian distribution describes data of t_d ≈ t_f very well. For τ > 1 s, N (⁴S) atoms formed in previous breakdown and discharge, have a dominant role in the breakdown initiation. Then, σ ≈ and Laue's distribution, which is valid for statistical time delay t_s, describes t_d data very well (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Duffing单边碰撞系统的混沌鞍合并激变

以典型的Duffing单边碰撞系统为研究对象,对系统中的混沌鞍进行了细致的分析.研究表明,系统的混沌鞍同样存在合并激变,合并激变是由连接两个混沌鞍的周期鞍的稳定流形与不稳定流形相切所诱发,相切使得边界上的混沌鞍与内部的混沌鞍发生碰撞而突然合并为一个较大的边界混沌鞍.混沌鞍的合并激变行为最终会诱导混沌吸引子的合并激变发生. 关键词： Duffing碰撞系统 混沌鞍 周期鞍 稳定与不稳定流形     

Mock period functions in higher level cases

Generalizing the results of Bringmann, Diamantis and Raum [3] we investigate a generating series of non-critical values which can be interpreted as a mock period function and prove that non-critical values can be encoded into a sesquiharmonic Maass form in higher level cases. Moreover we prove Eichler–Shimura-type isomorphism for the space of period polynomials and for that of mock period functions in level p   with p∈{2,3}$p\in \{2,3\}$.     

Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems

We study some monotonicity and iteration inequality of the Maslov-type index i-1of linear Hamiltonian systems.As an application we prove the existence of symmetric periodic solutions with prescribed minimal period for first order nonlinear autonomous Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity.This result gives a positive answer to Rabinowitz’s minimal period conjecture in this case without strictly convex assumption.We also give a different proof of the existence of symmetric periodic solutions with prescribed minimal period for classical Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity which was proved by Fei,Kim and Wang in 2001.