Exact solutions of nonlinear Schrödinger equation by using symbolic computation

The (G′/G,1/G)‐expansion method and (1/G′)‐expansion method are interesting approaches to find new and more general exact solutions to the nonlinear evolution equations. In this paper, these methods are applied to construct new exact travelling wave solutions of nonlinear Schrödinger equation. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. It is shown that the proposed methods provide a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Copyright © 2015 John Wiley & Sons, Ltd.     

Sufficient conditions for the invertibility of adapted perturbations of identity on the Wiener space

Let (W, H, μ) be the classical Wiener space. Assume that U = I _W  + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration of W. We give some sufficient analytic conditions on u which imply the invertibility of the map U. In particular it is shown that if ${u\in {\rm ID}_{p,1}(H)}$ is adapted and if ${\exp(\frac{1}{2}\|\nabla u\|_2^2-\delta u)\in L^q(\mu)}$ , where p ^?1 + q ^?1 = 1, then I _W  + u is almost surely invertible. With the help of this result it is shown that if ${\nabla u\in L^\infty(\mu,H\otimes H)}$ , then the Girsanov exponential of u times the Wiener measure satisfies the logarithmic Sobolev inequality and this implies the invertibility of U = I _W  +  u . As a consequence, if, there exists an integer k ≥  1 such that ${\|\nabla^k u\|_{H^{\otimes(k+1)}}\in L^\infty(\mu)}$ , then I _W  +  u is again almost surely invertible under the almost sure continuity hypothesis of ${t\to\nabla^i \dot{u}_t}$ for i ≤  k ? 1.     

Dynamic collision-induced dissociation (DCID) in a quadrupole ion trap using a two-frequency excitation waveform: I. Effects of excitation frequency and phase angle

This study describes the application of a two-frequency excitation waveform to the end-cap electrodes of a quadrupole ion trap (QIT) during the mass acquisition period to deliberately fragment selected precursor ions. This approach obviates the need for a discrete excitation period and guarantees on-resonant excitation conditions without any requirement for resonant tuning; it is therefore faster than the conventional approach to collision-induced dissociation (CID) in QITs. The molecular ion of n-butylbenzene is used as thermometer molecule to determine the energetics of the new excitation procedure. The excitation waveform, consisting of two closely spaced sinusoidal frequencies, has an interference pattern that displays nodes and crests in the time domain. The energetics (determined by the product ion ratios of 91/92 Th) and CID efficiencies are highly dependent on the excitation amplitude, the relative position of the excitation frequencies in the Mathieu stability diagram, and whether the ions come into resonance during a node or crest of the excitation waveform. Under highly energetic conditions, ratios of 91/92 as large as 15 can be obtained at concomitant CID efficiencies of 10%, indicating internal energies in excess of 10 eV at the time of fragmentation. These extremely high internal energies far exceed the energetics achievable using conventional on-resonance excitation in QITs, indicating that the collisional heating rate is very fast in the new approach. Under less energetic conditions CID efficiencies as high as 70% are possible, which compares favorably with results obtained by conventional on-resonance excitation. Correlation analyses are used to determine the conditions that simultaneously optimize energetic and efficient fragmentation conditions.     

Synthesis by radical cyclization and cytotoxicity of highly potent bioreductive alicyclic ring fused [1,2-a]benzimidazolequinones

The key step in the synthesis of new five, six and seven-membered alicyclic ring [1,2-a]-fused bioreductive benzimidazolequinones was radical cyclisation. Six and seven-membered tributyltin hydride-mediated homolytic aromatic substitutions of nucleophilic N-alkyl radicals onto the benzimidazole-2-position occurred in high yields (63-70 %) when quaternising the pyridine-like 3-N of imidazole with camphorsulfonic acid and using large excesses of the azo-initiator, 1,1'-azobis(cyclohexanecarbonitrile), to supplement the non-chain reaction. Elaboration of benzimidazoles to the benzimidazolequinones occurred in excellent yields. The IC50 values for the cytotoxicity of benzimidazolequinones towards the human skin fibroblast cell line GM00637 were in the nanomolar range, as determined by using the MTT assay. The benzimidazolequinones were much more cytotoxic than indolequinone analogues. 1,2,3,4-Tetrahydropyrido[1,2-a]benzimidazole-6,9-dione was the most potent compound prepared being more than 300 times more cytotoxic than the clinically used bioreductive drug, mitomycin C. The latter benzimidazolequinone was more potent under hypoxic conditions (associated with solid tumors), being 4.4 times more cytotoxic than under aerobic conditions, while mitomycin C was 1.8 times more selective towards hypoxia. The cyclopropane fused pyrido[1,2-a]benzimidazolequinone, 1a,2,3,9b-tetrahydro-1H-cyclopropa[3,4]pyrido[1,2-a]benzimidazole-5,8-dione was less cytotoxic and selective than the five-membered ring analogue, 1,1a,8,8a-tetrahydrocyclopropa[3,4]pyrrolo[1,2-a]benzimidazole-3,6-dione. Modifying the structure of the most potent pyrido[1,2-a]benzimidazolequinone by attaching methyl substituents onto the quinone moiety increased reductive potentials and decreased cytotoxicity and selectivity towards hypoxia.     

光纤水听器解调技术研究进展

光纤水听器是水声研究领域的关键技术,在实际应用中具有显著优势,广泛应用于AUV导航定位、资源勘探、海水警戒等场景.光纤水听器将声信号转化为光信号传播,在接收信号时就需要对光信号进行解调提取出声压信号.总结了几种常用的信号解调算法及关键技术,包括PGC解调法、3×3耦合器解调法和外差解调法;介绍了各种解调算法的基本原理和...     

Solvent Effect upon Ion-pair Extraction of Different Sodium Dyes Using Some Crown Ethers

Liquid-liquid extractive-spectrophotometric studies of sodium ion complexes of 18-crown-6(18C6), dibenzo-18-crown-6(DB18C6), 15-crown-5(15C5), and 12-crown-4(12C4) and anionic dyes [4-(2-pyridylazo)-resorcinol monosodium salt monohydrate (PAR), Eriochrom Black T (EBT), and methyl orange (MOR)] and sodium picrate (PICRAT) as the counter ion are described. The overall extraction equilibrium constants for the 1 : 1 complexes of the above crown ethers with sodium dyes between different organic solvents and water have been determined at 25deg;C. They were conducted in various solvent-water systems maintaining an identical initial cation concentration in water, [M0+]w, and macrocyclic ligand concentration in the organic phase, [L0]org}, so that in all extractions [M0+]w : [L0]org ratios were 1 : 1, 1 : 10, 1 : 20, 1 : 50, and 1 : 62.5. An ion association complex formed between the sodium-crown ether complex ion and a dye anion was extracted into the organic solvent, and then the dye concentration of the separated aqueous phase was measured with an ultraviolet-visible spectrophotometer. PAR was the best associated dye with all crown ethers sodium-dyes and the extracted dye occurs as the ion-pair complex. Methylene chloride was found to be better than other extractive solvents used in this study.     

Amperometric Determination of Norepinephrine Based on Dual-Film Modified Graphite Electrode

Norepinephrine (NE) is one of the most important biochemical messengers. The oxidation of NE at various electrodes has been extensively studied. The ease of NE oxidation lead to the development of convenient and rapid procedures for measuring NE levels using various electrochemical methods. A serious problem is that ascorbic acid (AA) often co-exists with NE, resulting in interference in NE determinations. This work describes the electrocatalytical activity of[Os(bpy)₂(PVP)₁₀Cl]⁺/Nafion modified graphite electrode for trace NE determination. The modified electrode can eliminate the interference from AA and uric acid (UA) in NE determinations,thus could be used as an amperometric sensors for the detection of NE levels.     

Vibrational spectroscopic and thermal studies of some 3-phenylpropylamine complexes

Four new Hofmann–3-phenylpropylamine (3PPA) type complexes with chemical formulae M(3PPA)₂Ni(CN)₄ (M = Ni, Co, Cd, and Pd) have been prepared and their vibrational spectra are reported in the region of 4000–60 cm⁻¹. The vibrational bands arising from 3PPA ligand molecule, the polymeric sheet and metal–ligand bands of the compounds are assigned. The thermal behaviour of these complexes is also provided using the DTA and TGA along with the magnetic susceptibility data. The results indicate that the monodentate 3PPA ligand molecule bonds to the metal atom of |M–Ni(CN)₄|_∞ polymeric layers and hence the compounds are similar in structure to Hofmann-type complexes.     

Development and Validation of Selective Spectrophotometric Methods for the Determination of Pregabalin in Pharmaceutical Preparation

Three simple, quick and sensitive methods are described for the spectrophotometric determination of pregabalin (Pgb) in pharmaceutical preparations. Among them, the first two methods are based on the reaction of Pgb as n-electron donors with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) and 7,7,8,8-tetracyanoquinodimethane (TCNQ) as π-acceptors to give highly colored complex species. The colored products were quantitated spectrophotometrically at 494 and 841 nm for DDQ and TCNQ, respectively. Optimization of the different experimental conditions was conducted. Beer’s law was obeyed in the concentration ranges 2.0—30.0 and 1.5—10 µg•mL－1 for DDQ and TCNQ methods, respectively. The third method is based on the interaction of ninhydrin (NN) with primary amine present in the pregabaline. This reaction produces a blue coloured product in N,N-dimethylformamide (DMF) medium, which absorbs maximally at 573 nm. Beer’s law was found in the concentration range 40.0—180.0 μg•mL－1. The methods were applied successfully to the determination of this drug in pharmaceutical dosage forms.