Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

The derivative nonlinear Schrödinger (DNLS) equation, which governs the propagation of the femtosecond optical pulse in a monomodal optical fiber, is analytically studied in this Letter. Breather and double-pole solutions are derived from the two-soliton solution with the choice of parameters. It is found that the parameters in the DNLS equation cannot only control the phase and propagation direction of the breather and double pole, but also influence the interaction period of the breather. Elastic collisions between a breather and a dark/anti-dark soliton are studied by the qualitative analysis and graphical illustration. The stability of the breather and double-pole solutions is also analyzed.     

Simultaneous Determination of Two Synthetic Dyes Erytrosine and Sunset Yellow in a Pharmaceutical Syrup By First Derivative Visible Spectrophotometry

ABSTRACT.

A rapid first derivative spectrophotometric method for simultaneous determination of two synthetic dyes, erytrosine (E 127) and sunset yellow (E 110), in a mixture is proposed. The procedure does not require any separation step. The method was applied for determining the two compounds in a pharmaceutical syrup. Good linearity, accuracy, precision and selectivity were found, and the method is proposed for routine quality control purposes.     

A WAVELET TRANSFORM AND ITS APPLICATION TO SPECTROSCOPIC ANALYSIS

ABSTRACT

An introduction to the wavelet transform and its applications in spectroscopy analysis are presented. Owing to the property of the dual localization both in time and in frequency domains, the wavelet transform exhibits several useful characteristics. With the wavelet transform a signal can be decomposed into series of contributions according to the frequency difference, these contributions are respectively called discrete approximations and discrete details. By applying certain treatment to the discrete approximations (the low frequency part) or the discrete details (the high frequency part), a part of the original signal within a certain frequency range can be obtained. The wavelet transform has been applied in various fields of the analytical chemistry, including removal of high frequency noise, information extraction, resolution of overlapping signals, and data compression etc. Research concerning application in analytical chemistry are introduced in respect of photoacoustic spectroscopy, EXAFS spectrum, NMR analysis, and Raman spectrum.     

The Pfaff/Cauchy derivative identities and Hurwitz type extensions

More than 200 years ago, Pfaff found two generalizations of Leibniz’s rule for the nth derivative of a product of two functions. Thirty years later Cauchy found two similar identities, one equivalent to one of Pfaff’s and the other new. We give simple proofs of these little-known identities and some further history. We also give applications to Abel-Rothe type binomial identities, Lagrange’s series, and Laguerre and Jacobi polynomials. Most importantly, we give extensions that are related to the Pfaff/Cauchy theorems as Hurwitz’s generalized binomial theorems are to the Abel-Rothe identities. We apply these extensions to Laguerre and Jacobi polynomials as well. Dedicated to Dick Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—05A19; Secondary—33C45     

白杨黄酮的单扫描示波极谱法测定及应用

在0.1 mol.L-1的NH4Cl-氨水(pH 9.4)溶液中白杨黄酮于-1.22 V(vs.SCE)处产生一个灵敏的极谱波,其二阶导数峰峰电流i″p与白杨黄酮浓度在3.7×10-7~2.6×10-5mol.L-1范围内呈良好的线性关系(r=0.997 2,n=9),检出限为1.0×10-7mol.L-1(S/N=3),9次测定5.0×10-6mol.L-1白杨黄酮的相对标准偏差为1.2%;研究了一些常见离子及有机物对测定的影响。通过循环伏安法等方法证明白杨黄酮在汞电极上为受吸附控制的不可逆过程,并通过试验推导出其电极反应。该方法应用于木蝴蝶种子提取物中白杨黄酮的测定,其回收率在96.7%~103.0%之间。     

导数-可变角同步荧光法用于1-萘酚和2-萘酚的同时测定

同步扫描和导数光谱法是两类很有用的荧光分析新技术。固定波长或恒能量同步荧光法和导数技术的结合可进一步提高光谱分辨率和排除基体干扰。本文将导数技术和可变角同步荧光法结合起来,用于1-萘酚和2-萘酚的同时分析,效果良好。研究表明,导数-可变角同步荧光法可望发展为荧光分析复杂样品的新技术。     

N-氧化吡啶-2-甲醛单缩1,2-丙二胺Schiff碱镍配合物的晶体结构

由于N-氧化吡啶及其衍生物具有独特的配位性质~[1]以及其金属配合物可作为药物~[2],因此人们对其进行了广泛的研究~[3～8]. 本文继合成N-氧化吡啶-2-甲醛与1,2-丙二胺的双缩Schiff碱铜配合物并测定了其晶体结构之后~[8],又得到了一个新的N-氧化吡啶-2-甲醛单缩1,2-丙二胺镍的配合物.经X射线     

导数-恒能量同步荧光法同时测定芴、苊、蒽和苝

恒能量同步荧光法［’j是同步荧光洁的一个新分支．该法在激发和发射波长的同时扫描过程中,可保持两者之间的一个恒定的能量差关系．苟、危、惠和完均属多环芳烃（PHAS）,其振动能层间隔在1400～1600cm‘之间．采用固定能量差凸9一1600cm－’,对4种物质的混合体系进行恒能量同步荧光法测定,可简化谱图,达到混合物体系各组分同时测定的目的．导数技术能放大窄带的灵敏度,对恒能量同步荧光光谱的窄带应用很有利［’j．两者联用可使检测限更低,对各组分的分辨更有效”‘,采用一阶导数一恒能量同步荧光法对药、危、意和芬的检出限依次…     

比值导数波谱法分析食品中混合色素

利用混合物的波谱除以干扰组分的波谱得比值波谱,对波长求导得比值导数波谱,由此可消除干扰组分的吸光度叠加效应。该法能有效地对三组分混合体系进行分析。利用此法对亮蓝、日落黄、胭脂及柠檬黄等色素所组成的二组分和三组分混合体系进行分析,取得满意效果。     

Simultaneous First Derivative Spectrophotometric Determination of Palladium and Nickel Using 2-(2-Thiazolylazo)-5-Dimethylaminobenzoic Acid as an Analytical Reagent

 A simple, rapid, selective, sensitive and economical method has been developed for the simultaneous determination of trace amounts of palladium and nickel in aqueous methanolic medium using 2-(2-thiazolylazo)-5-dimethylam inobenzoic acid as an analytical reagent by first derivative spectrophotometr y. Palladium is determined by measuring base to peak distance at λ=695.0 nm while nickel is estimated by zero crossing method in the mixture. The linearity is maintained between 0.12–1.75 μg mL⁻¹ for palladium and 0.07–1.60 μg mL⁻¹ for nickel in the pH range 2.8–7.2 and 3.4–8.8 respectively. Seven replicate determinations of 1.0 μ g mL⁻¹ of palladium and 0.8 μg mL⁻¹ of nickel in a mixture give a mean signal height of 0.391 for Pd and 0.541 for Ni with relative standard deviations of 0.9% and 1.2%, respectively. The sensitivity of the proposed method is 0.391 (dA/dλ)/(μg mL⁻¹) for palladium and 0.685 (dA/dλ)/(μg mL⁻¹) for nickel. Various parameters have been optimised for the simultaneous determination of palladium and nickel in various complex samples. Received March 30, 1999. Revision November 25, 1999.