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.     

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.     

Comparison of Uniform and Non-uniform Pressure Approaches Used to Analyze an Adsorption Process in a Closed Type Adsorbent Bed

Heat and mass transfer in an annular adsorbent bed filled with silica gel particles is numerically analyzed by uniform and non-uniform pressure approaches. The study is performed for silica gel–water pair, particle radius from 0.025 to 1 mm and two bed radii of 10 and 40 mm. For uniform pressure approach, the energy equation for the bed and the mass transfer equation for the particle are solved. For non-uniform pressure approach, the continuity and Darcy equations due to the motion of water vapor in the bed are added, and four coupled partial differential equations are solved. The changes of the adsorbate concentration, pressure, and temperature in the bed throughout the adsorption process for both approaches are obtained and compared. The obtained results showed that the particle size plays an important role on the validity of uniform pressure approach. Due to the interparticle mass transfer resistance, there is a considerable difference between the results of the uniform pressure and non-uniform pressure approaches for the beds with small size of particles such as $r_\mathrm{{p}} =$ 0.025 mm.     

Radiostability of Allantoin by Using Electron Spin Resonance Spectroscopy

The radiosterilization potential and dosimetric feature of allantoin were investigated through the molecular degradations produced after ultraviolet and gamma irradiation using electron spin resonance, infrared, and ultraviolet spectroscopies and thermal measurement techniques (differential thermal analysis and the glass transition temperature). Although ultraviolet-irradiated allantoin presents no electron spin resonance signal, gamma irradiation exhibited an electron spin resonance signal of triplet appearance. Room temperature and high-temperature line intensity and spectrum area data and their variations with applied microwave power, storage time, annealing time, annealing temperature, and applied radiation dose were analyzed by assuming the production of two different types of radicals having different spectroscopic and decay characteristics. Based on its relatively stable nature toward gamma and ultraviolet radiations, it was concluded that allantoin itself and the products containing it can be sterilized by gamma and/or ultraviolet radiations without creating a great loss in its beneficial effects in the allowed radiosterilization dose limits.