Conte Truncated Expansion and Applications

In the special Conte truncated expansion approach one obtains different solutions of the Prigogine–Lefever equation by use of various solutions of a type of Riccati equation, including the periodic soliton solutions and singular soliton solutions. In order to acquire conveniently the soliton solutions of the Boussinesq equation, a proper transformation is applied. Using the special Conte truncated expansion approach yields the known bell-shape solutions and some new soliton solutions like cot² × sec², tan² × c sec², tanh² × sech², etc. We also study the soliton solutions of the modified Burgers equation (MBE). Using leading term analysis, we find the exponent is a fraction, i.e., – . Therefore, the special Conte truncated expansion approach cannot be used directly. A transformation is first made to them another form of the MBE. Various soliton solutions of MBE are then presented, including the periodic solutions and singular soliton solutions.     

新颖的酸催化迈克尔型巯基荧光探针的机理

迈克尔加成反应通常为碱催化的反应,但是在本工作体系当中,2-(2-乙烯基,7-羟基喹啉)丙二酸(QMA)能够被酸催化检测巯基. 从实验和理论计算证明了QMA探测巯基是,且溶液pH值越低,活 性越强. 在碱性溶液中,它的负离子形式QMA[-2H⁺]2^-不能够与电离前或电离后的巯基反应. 与QMA相比,它的酯QME显示出相反的pH效应,这与一般的基于迈克尔加成的巯基荧光探针类似. DFT计算得到的活化焓支持上述两种探针的pH效应. 在酸性溶液中,质子化的QMA与中性和碱性溶液中的负离子形式相比更容易与亲核试剂发生加成,因此能够与低活性的未电离硫醇反应. 相反地,QME与未电离硫醇反应的能垒很高,与电离后的硫醇反应活化能很低. 理论计算研究显示QMA与未电离硫醇的反应为1,4-加成而QME与电离后的硫醇的反应为1,2-加成.     

Simplified analytic solutions and a novel fast algorithm for Yb-doped double-clad fiber lasers

In this paper, continuous wave Yb³⁺-doped double-clad fiber lasers (DCFLs) with linear-cavity are investigated theoretically and numerically using the rate equations. Under the steady state conditions, the simplified analytic solutions of Yb³⁺-doped DCFLs under considering the scattering loss are deduced in the strongly pump condition. Compared with the known analytic solutions in published literatures, our analytic solutions are more accurate, especially, at higher reflectivity of output mirror. In addition, a fast and stable algorithm based on the Newton-Raphson method is proposed to simulate numerically Yb³⁺-doped DCFLs. The results by simplified analytic solutions are in good agreement with those by the numerical simulation. Moreover, we have performed the optimization of an Yb³⁺-doped DCFL using the simplified analytic solutions and the numerical simulations, respectively.     

General Behaviour of Bianchi VI0 Solutions with an Exponential-Potential Scalar Field

The solutions to the Einstein-Klein-Gordon equations without a cosmological constant are investigated for an exponential potential in a Bianchi VI₀ metric. There exists a two-parameter family of solutions which have a power-law inflationary behaviour when the exponent of the potential, k, satisfies k² < 2. In addition, there exists a two-parameter family of singular solutions for all k² values. A simple anisotropic exact solution is found to be stable when 2 < k².     

Ionic reorientational motions in aqueous solutions: a depolarized light scattering study of NO3 - and SCN-

Depolarized Rayleigh scattering has been measured in the frequency range 0·2 cm^-1 to 200 cm^-1 using a triple monochromator and Fabry-Perot interferometry for solutions of ammonium, sodium and lithium nitrates, for nitric acid and ammonium and potassium thiocyanate over a range of concentrations and temperatures. From comparisons with scattering from water and alkali halide solutions it is concluded that the narrow central component of the scattering arises predominantly from anion reorientational motions. From intensity measurements there is no evidence for significant anion-anion correlations. Infinite dilution relaxation times are discussed in relation to the motions of water molecules in the hydration spheres. Except for very dilute solutions, a simple hydrodynamic model accounts for the temperature and concentration dependence of SCN^- reorientation. For NO₃ ^- it is necessary to assume that the boundary conditions are concentration dependent. In very concentrated nitrate solutions the lineshape is non-lorentzian due, it is argued, to specific cation-anion interactions.     

Microhardness of crystals of KBr-KI solid solutions with Sr2+ and OH− impurities

The microhardness, conductivity, and dielectric-loss angle have been studied in KBr and KI single crystals and in their solid solutions with Sr²⁺ and OH^– impurities. It is shown that the Sr²⁺ impurity dissolves only slightly in KI crystals and in KBr-KI solid solutions having a large KI content. Addition of the anionic OH^– impurity to the molten salts reduces the micro-hardness of KBr but it does not affect that of KI crystals or KBr-KI solid solutions having a large KI content. The composition dependence of the microhardness for KBr-KI solid solutions is constructed on the basis of the microhardness values for the corresponding crystals purified of cationic impurities of different valence.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 18–21, October, 1969.     

The decay of the gravitational field

The asymptotic behaviour of Einstein-Rosen waves, a class of nonstationary solutions of Einstein's vacuum equations, is investigated. It is established that solutions of this type exist which admit part ofI ⁺ and a regularI ⁺ in the sense of Penrose.     

Soliton-like solutions of some nonlinear theories and transformations among them

The observation that the soliton-like solutions of a given second-order nonlinear differential equation define the separatrix of the equivalent autonomous system is used to obtain the one-soliton solutions for theφ ⁴ theories (the usual and the one with the wrong sign of the mass term), theφ ⁶, theφ ⁸, the sine-Gordon theories and the KdV equation. Transformations are given which transform the sine-Gordon equation into an equation belonging to theφ ²ⁿ class of theories. A procedure is evolved for obtaining the two-soliton solutions for the sine-Gordon theory without the use of Backlund transformations; it is suggested that this procedure may be useful for investigating the existence of similar solutions for theories of the polynomial type.     

Spectroscopy of silver complexes in solutions of inorganic compounds

The absorption, photoluminescence, and photoexcitation spectra of a number of inorganic solid solutions with a silver ion impurity have been examined. The influence of the temperature on the spectral characteristics of haloid and oxygen-containing solutions activated with Ag⁺ ions has been investigated. The temperature dependences of the luminescence quantum yield of solid solutions with Ag⁺ impurity in the temperature range 77-150 K have been studied. It is shown that the spectra under observation are conditioned by electron transition between energetic levels of Ag⁺ ion which are deformed because of the interaction with environment.     

A NOTE ON TRAVELING WAVE SOLUTIONS TO THE TWO COMPONENT CAMASSA–HOLM EQUATION

In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa–Holm equation are distributional traveling wave solutions to the Camassa–Holm equation provided that the set u^-1(c), where c is the speed of the wave, is of measure zero. In particular there are no new peakon or cuspon solutions beyond those already satisfying the Camassa–Holm equation. However, the two component Camassa–Holm equation has distinct from Camassa–Holm equation smooth traveling wave solutions as well as new distributional solutions when the measure of u^-1(c) is not zero. We provide examples of such solutions.     

Proton relaxation times in 7LiCl and 6LiCl solutions

Measurements of the proton spin-lattice relaxation times have been made as a function of concentration and temperature in aqueous solutions of ⁷LiCl and ⁶LiCl. The difference in the relaxation times for two isotopic solutions of the same concentration and temperature is small, corresponding to a difference n reciprocal relaxation times of 0·004 sec^-1. c at 25°c, where c is the molarity of the solutions. This value decreases with increasing temperature. It is shown that the difference in relaxation times arises solely from the magnetic dipole interaction between the ⁷Li ion nucleus and water protons. The concept of a long-lived, rigid hydrated complex around the Li ion is shown to be inconsistent with the results.     

Fast degradation of azo dye by nanocrystallized Fe-based alloys

Exploring new alloys with high efficiency in degrading organic pollutants in aqueous solutions is of wide interests. Here, we report that the nanocrystallized Fe_(82.65)Si_4B_(12)Cu_(1.35) alloy exhibits higher efficiency in decolorizing azo dye solutions compared to its amorphous counterpart. The increased efficiency is attributed to the formation of numerous microbatteries between the α-Fe(Si)and Fe_2 B nanocrystalline phases, which exhibit different corrosion potentials. These results suggest that nanocrystallized Fe-based amorphous composites hold promising application potential in degrading azo dyes solutions.     

Quantum Cosmology in Higher Derivative and Scalar-Tensor Gravity

The Bicknell theorem states that a non-linear Lagrangian can be recast in the form of a scalar-tensor theory, with a suitable potential, through a conformal transformation. In this paper, we first show that such classical equivalence remains valid at the level of the Wheeler—deWitt equation. Then, we consider a specific case, represented by a Lagrangian f(R) = R + l^–2(l²R)^4/3 whose vacuum cosmological solutions describe a non-singular Universe. The corresponding scalar-tensor theory and its cosmological solutions are written down. We find again non-singular solutions. The Wheeler—deWitt equation for this case is analyzed. The application of the Bicknell theorem leads to the interpretation of the behaviour of the scale factor in terms of the matter content, represented by the scalar field, and consequently to the energy conditions. The problem of classical and quantum regime is discussed and the classical behaviour is recovered, from the quantum solutions, near the maximum of the scale factor where the strong energy condition is satisfied.     

Reflection K-matrices for 19-vertex models

We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or A₁⁽¹⁾ model, Izergin-Korepin or A₂⁽²⁾ model, sl(2|1) model and the osp(2|1) model. We find that there is a general solution for A₁⁽¹⁰⁾ and sl(2|1) models. In both models it is a complete K-matrix with three free parameters. For the A₂⁽²⁾ and os(2|1) models we find three general solutions, being two complete reflection K-matrices solutions and one incomplete reflection K-matrix solution with some null entries. In both models these solutions have two free parameters. Integrable spin-1 Hamiltonians with general boundary interactions are also presented. Several reduced solutions from these general solutions are presented in the appendices.     

Inhomogeneous mixmaster universes: Some exact solutions

Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S³ topology of spatial sections, are developed. The known exact vacuum and stiff-fluid solutions with S³ topology are used as an input. The methods developed are further applied to derive inhomogenous generalizations of Bianchi type IX solutions and inhomogeneous S³ Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy of the rate of growth of density perturbations is studied in detail.     

Stationary D = 4 black holes in supergravity: The issue of real nilpotent orbits

The complete classification of the nilpotent orbits of SO(2,2)² in the representation (2,2,2,2) , achieved in 14 , is applied to the study of multi‐center, asymptotically flat, extremal black hole solutions to the STU model. These real orbits provide an intrinsic characterization of regular single‐center solutions, which is invariant with respect to the action of the global symmetry group SO(4,4), underlying the stationary solutions of the model, and provide stringent regularity constraints on multi‐centered solutions. The known almost‐BPS and composite non‐BPS solutions are revisited in this setting. We systematically provide, for the relevant SO(2,2)²‐nilpotent orbits of the global Noether charge matrix, regular representatives thereof. This analysis unveils a composition law of the orbits according to which those containing regular multi‐centered solutions can be obtained as combinations of specific single‐center orbits defining the constituent black holes. Some of the SO(2,2)²‐orbits of the total Noether charge matrix are characterized as “intrinsically singular” in that they cannot contain any regular solution.     

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity (II)

It is shown that all torsion-free vacuum solutions of the model of de Sitter (dS) gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian (F ² + T ²), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.     

Convergence to diffusion waves of solutions to nonlinear viscoelastic model with fading memory

We study the large time behavior inL ² of solutions to a model for the motion of an unbounded, homogeneous, viscoelastic bar with fading memory. Decay rates for the solutions are obtained under the assumption that the initial data and histories are smooth and small. Moreover, convergence of the solutions to diffusion waves, which are solutions of Burgers equations, is proved and rates are obtained. Our method is based on the study of properties of the solutions to the linearized system in the Fourier space.     

Spherically Symmetric Solutions and Dark Matter on the Brane

It has recently been suggested that our universe is a three-brane embedded in a higher dimensional spacetime. In this paper I examine static, spherically symmetric solutions that satisfy the effective Einstein field equations on a brane embedded in a five dimensional spacetime. The field equations involve a term depending on the five dimensional Weyl tensor, so that the solutions will not be Schwarzschild in general. This Weyl term is traceless so that any solution of ⁽⁴⁾ R = 0 is a possible four dimensional spacetime. Different solutions correspond to different five dimensional spacetimes and to different induced energy-momentum tensors on the brane. One interesting possibility is that the Weyl term could be responsible for the observed dark matter in the universe. It is shown that there are solutions of the equation ⁽⁴⁾ R = 0 that can account for the observed rotation curves of spiral galaxies.