On Solutions of Quantum Eigenvalue Problems: A Supersymmetric Approach

We study solutions of various quantum mechanical eigenvalue problems using the formalism of one dimensional supersymmetric quantum mechanics. The problems studied includes among other problems the non-polynomial oscillator and the doubly anharmonic oscillator potentials. The solutions obtained here are of two types — exact analytical solutions and approximate solutions. The method of obtaining exact solutions have been shown to be general enough to be applied to a large class of potentials. The method of obtaining approximate solutions have been studied in details and their accuracy have been compared with exact numerical results.     

Theory of paraxial lateral aberrations of electrostatic imaging electrostatic electron optics based on asymptotic solutions and its verification

In imaging electron optics, study of geometrical lateral aberrations of third order and paraxial lateral aberrations of second order has traditionally been paid more attention to, but the existence of paraxial chromatic aberrations of third order and paraxial chromatic aberrations of magnification of third order was almost ignored, and the general form of paraxial lateral aberration has not been studied theoretically.In the present paper, the paraxial lateral aberrations expressed in general form have been derived emphatically on the basis of asymptotic solutions of paraxial equation. The relationship between the coefficients of asymptotic solutions has been investigated, which proves that the coefficients of asymptotic solutions are related each other. Through a bi-electrode electrostatic spherical concentric system model, two special solutions expressed by asymptotic solutions and accurate solutions in a bi-electrode electrostatic spherical concentric system have been deduced, and the paraxial lateral aberrations have been verified and tested, in which the aberration coefficients are solved by asymptotic solutions of paraxial equation. Result completely proves that the approach based on asymptotic solutions to solve the paraxial lateral aberrations are practicable and accurate enough. The paraxial chromatic aberration of magnification of third order and the paraxial chromatic aberration of third order have been firstly derived, and the Recknagel-Artimovich formula of paraxial chromatic aberration of second order which possess an greatest part in the whole paraxial lateral aberrations has been deduced and confirmed. A simple and clear form for expressing paraxial lateral aberrations of imaging electron optics is suggested for practical use. Results of the present paper will have theoretical value for aberration theory of imaging electron optics and practical significance for the design of image tubes.     

RLC暂态电路的理论分析和数值模拟

利用Maple符号计算软件做RLC电路方程的拉普拉斯变换,得到电路的精确解,绘制解的图像,并且理论分析了这些解的特点,得到了一些有助于教学应用的结论.     

New soliton solutions of Davey–Stewartson equation with power-law nonlinearity

This study is related to new soliton solutions of Davey–Stewartson equation (DSE) with power-law nonlinearity. The generalized Kudryashov method which is one of the analytical methods has been used for finding exact solutions of this equation. By using this method, dark soliton solutions of DSE have been found. Also, by using Mathematica Release 9, some graphical representations have been done to analyze the motion of these solutions.     

Traveling wave solutions of conformable time-fractional Zakharov–Kuznetsov and Zoomeron equations

To model physical phenomena more accurately, fractional order differential equations have been widely used. Investigating exact solutions of the fractional differential equations have become more important because of the applications in applied mathematics, mathematical physics, and other areas. In this work, by means of the trial solution method and complete discrimination system, exact traveling wave solutions of the conformable time-fractional Zakharov–Kuznetsov equation and conformable time-fractional Zoomeron equation have been obtained and also solutions have been illustrated. Finding exact solutions of these equations that are encountered in plasma physics, nonlinear optics, fluid mechanics, and laser physics can help to understand nature of the complex phenomena.     

Viscosity of aqueous solutions of monocarboxylic acids

An attempt has been undertaken to apply viscosimetric measurements for the examination of incomplete dissociation of symmetric electrolyte solutions. For this purpose precise measurements of the viscosity and density of dilute aqueous solutions of monocarboxylic acids (formic, acetic, propionic and valeric) have been conducted at 298.15 K. Modified Jones–Dole equations have been proposed for incompletely dissociated electrolyte solutions of 1–1 type. The data have been analysed taking into account dimerization of carboxylic acids. The B coefficients for all chemical species in the solution have been determined.     

Finding Solutions to Equations for the Longitudinal Components of an Electromagnetic Field in a Biisotropic Medium in the Neighborhood of a Regular Singular Point as Generalized Power Series

For a system of equations that describe electromagnetic fields in a biisotropic medium, particular solutions have been constructed in the neighborhood of a regular singular point. The solutions are written in the form of generalized power series. For the coefficients of the power series, exponents and recursion relations have been found. It has been shown that the solutions of the wave equations are generalizations of well-known special cylindrical functions. The behavior of the particular solutions have been examined for varied material parameters of the medium. The solutions obtained allow one to formulate mathematical models which could be used to calculate and optimize the parameters of a wide spectrum of functional devices based on waveguide structures with biisotropic inserts.     

On some classes of exact solutions of scalar Born-Infeld equation

Some classes of exact solutions of scalar Born-Infeld equation have been found. Certain selected properties of these solutions have been presented.     

Volumetric, viscometric, acoustical, and optical studies of glutamic acid in aqueous zinc and copper chloride solutions

Ultrasonic velocity, density, viscosity and refractive index measurements of L-glutamic acid in aqueous zinc chloride and copper chloride solutions have been carried out at 303.15K. From these experimental data isentropic compressibility, acoustic impendence, relative association, free path length, apparent molar volume, apparent molar isentropic compressibility and molar refraction of L-glutamic acid in aqueous solutions of electrolytes are evaluated. These values have been used to explain molecular association, solutesolvent interaction through hydrogen bonding and solvation. Viscosity data have been analyzed in the light of Jones-Dole equation and the constants A and B have been estimated and interpreted in terms of ion-ion, ionsolvent and molecular interactions occurring in solutions.     

Solutions for the propagation of light in nonlinear optical media with spatially inhomogeneous nonlinearities

In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions.     

Wormholes in higher dimensions with Gauss-Bonnet terms

A class of wormhole solutions permitted in a theory with Gauss-Bonnet terms in the gravitational action in higher dimensions have been studied. The case of de-Sitter type instantons, with a compact inner space, are of particular interest here. Some of the configurations, when continued analytically to the Lorentzian metric lead to the standard inflationary universe. Some multiple-sphere configurations of the type studied by Myers have also been noted. The Euclidean action for the solutions has been calculated and the relevance of the solutions in the quantum creation of the universe has been considered.     

非线性LC电路方程的显式精确行波解

理论上考察了具有耗散的非线性LC电路中的行波. 借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程. 一致地获得了丰富的显式精确解析行波解, 包括精确冲击波解和奇异的行波解, 和三角函数有理形式的周期波解. 关键词： LC电路')" href="#">非线性LC电路 非线性耗散波动方程 冲击波 周期波     

Exact solutions of the field equations for Charap’s chiral invariant model of the pion dynamics

The field equations for the chiral invariant model of pion dynamics developed by Charap have been revisited. Two new types of solutions of these equations have been obtained. Each type allows infinite number of solutions. It has also been shown that the chiral invariant field equations admit invariance for a transformation of the dependent variables.     

Apparent molar volumes and transport behavior of glycine and l-valine in aqueous solutions of tripotassium citrate at T = (308.15 and 318.15) K

Densities and viscosities of glycine and l-valine have been measured at 308.15 and 318.15 K in aqueous tripotassium citrate solutions ranging from 0.2 to 0.8 mol kg^− 1 of tripotassium citrate. The viscosity data have been analyzed by Jones-Dole equation. The activation parameters of viscous flow have been obtained to throw light on the mechanism of viscous flow. The values of apparent molar volume, partial molar volume at infinite dilution and relative viscosities of each amino acid in various aqueous tripotassium citrate solutions have been evaluated from the density and viscosity data. The partial molar volumes of transfer from water to aqueous tripotassium citrate solution at infinite dilution have also been calculated. Transfer volume data have been used to calculate the pair and triplet interactions. The results have been discussed in terms of solute-solute and solute-solvent interactions and the structural changes of the solutes in solutions.     

Uniqueness of Topological Solutions and the Structure of Solutions for the Chern-Simons System with Two Higgs Particles

The existence of topological solutions for the Chern-Simons equation with two Higgs particles has been proved by Lin, Ponce and Yang [16]. However, both the uniqueness problem and the existence of non-topological solutions have been left open. In this paper, we consider the case of one vortex at origin. Among others, we prove the uniqueness of topological solutions and give a complete study of the radial solutions, in particular, the existence of some non-topological solutions.     

Infrared Spectra of Water in Aqueous Solutions Using Internal Reflection Spectroscopy

Abstract

There has been a continuing interest in the structure of water and of aqueous solutions, and many studies have employed spectroscopic techniques. These have frequently involved absorption spectroscopy in the near-IR range, and Raman scattering. In general, however, the normal IR range has been but little used except for studies of HDO-containing solutions, and the region near 3500 cm^?1 of the intense H₂O absorption has been almost completely avoided. Transmission techniques have been exclusively employed with absorption spectroscopy. Internal reflection spectroscopy (IRS) techniques have been employed to examine aqueous solutions, but the emphasis was placed on studying the solute rather than the solvent. Also, the solute concentrations which had been employed in transmission studies have been rather high. We now suggest the feasibility of carrying out structural studies of aqueous solutions by using IRS techniques to record spectra in the IR range, employing solutions of relatively low concentrations. For example, the lowest concentration of aqueous HCl solution examined by Ackermann¹ was 2.5 M by transmission techniques in the 4000-1100 cm^?1 range; in contrast, using IRS, the perturbations of the O-H stretching and deformation bands of H₂O could be observed with 0.1 M HCl.     

Theory of spherulitic domains in cholesteric liquid crystals with positive dielectric anisotropy

New localized axisymmetric nonsingular solutions minimizing the Frank functional have been found for a cholesteric layer with homeotropic anchoring. They have a continuous distribution of the director field and are characterized by a convex shape. These solutions describe the so-called spherulitic domains which have been observed in a large-pitch cholesteric near the unwinding transition.     

Non-static non-conformally flat fluid plates of embedding class one

In the present article four non-static perfect fluid solutions have been derived by considering a plane symmetric metric of embedding class one. Out of the solutions so obtained two solutions possess an acceleration free velocity vector field while the other two have flow with acceleration. As far as the authors are aware the solutions with non-vanishing acceleration are new.     

Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime. In this research, we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves. We extend the modified expansion function method (MEFM) to obtain abundant solutions, as well as to find new solutions. By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM. Also, numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement. Besides, the instability modulation of the governing equations are explored through the linear stability analysis function. All new solutions satisfy the main coupled equation after they have been put into the governing equations.