Dark optical solitons with power law nonlinearity using G′/G-expansion

This paper studies the dynamics of dark optical solitons. The G′/G-expansion approach is utilized. The byproduct of this approach is the singular periodic solution of the governing nonlinear Schrödinger's equation for its corresponding parameter regime. The constraint conditions are also in place for the existence of dark solitons.     

Topological solitons of resonant nonlinear Schödinger'sequation with dual-power law nonlinearity by G′/G-expansion technique

This paper considers the resonant nonlinear Schrödinger's equation with dual-power law nonlinearity. The G′/G-expansion method is applied to integrate this equation. The soliton solutions are thus obtained. Both constant coefficients as well as time-dependent coefficients are considered. The results for parabolic law nonlinearity fall out as a special case.     

Removal of lead(II) by adsorption onto Viscumalbum L.: Effect of temperature and equilibrium isotherm analyses

The removal efficiency of Viscumalbum L. from lead containing aqueous solutions was investigated. The effect of adsorbent mass, pH of solution, initial Pb(II) concentration and temperature was investigated using a batch adsorption technique. The optimum pH for Pb(II) adsorption was found as 3.0 for Viscumalbum L. Results were analyzed by the Langmuir, Freundlich, Temkin and Harkins-Jura, equation using linearized correlation coefficient at different temperature. The characteristic parameters for each isotherm have been determined. The Langmuir model agrees very well with experimental data than the other models. According to Langmuir isoterm, the monolayer saturation capacity (Q_o) is 769.23 mg/g at 25 °C. Models and the isotherm constant were evaluated depending on temperature. Thermodynamic parameters such as ΔH^o, ΔS^o and ΔG^o were calculated. The adsorption process was found to be endothermic and spontaneous. The experimental data were analyzed using the first- and the second-order kinetic models. The rate constants of adsorption for both kinetics models have been calculated. The second-order model provides the best correlation of the data.     

Integral equations satisfied by the H- X- and Y-functions and the albedo problem

We come back to a nonlinear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab.     

Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity

We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G^′/G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before.     

Explicit solutions of nonlinear wave equation systems

We apply the (G’/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. We highlight the power of the (G’/G)-expansion method in providing generalized solitary wave solutions of different physical structures. It is shown that the (G’/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.     

n(G)-nonextendibility of linear positive maps

Linear positive maps of C¹-algebras into the algebra of all bounded operators acting on a Hilbert space are considered. A special class of n(G)-nonextendible maps, which contains the class of nonextendible positive maps introduced by S.L. Woronowicz [9], is defined and studied. A map is n(G)-positive if it is n-positive or covariant with respect to the action of some group G of automorphisms of a C¹-algebra. n(G)-nonextendible maps are those which are nonextendible in this class in the sense of [9].Any n(G)-positive map can be obtained from an n(G)-nonextendible one by restriction.     

Renormalized G-convolution of N-point functions in quantum field theory. II. Asymptotic behavior

This is the second paper of the series concerning the renormalized G-convolution product H_G^ren in the Euclidean space associated with a general graph G with n external lines. We establish the asymptotic behavior of H_G^ren(K) with respect to every subspace of the external momenta K of G in terms of the asymptotic coefficients of a precise class of Weinberg functions.     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

G-matrix effective interaction with the paris potential

An effective interaction is derived by fitting the oscillator matrix elements of the sum of the OBEP functions to the G-matrix elements derived from the Paris nucleon-nucleon interaction. The functional form, the mass dependence and the ambiguities of the effective interaction are discussed. For the application of the present effective interaction, we study the mass dependence of the G-matrices and estimate the Landau-Migdal parameter g′. We have obtained reasonable results for these cases.     

A note on the treatment of the projection-operator in the nuclear G-matrix equation

An alternative derivation of the new solution for the nuclear G-matrix obtained by Tsai and Kuo is presented.     

Scaling violations for the spin-dependent structure function G1

With the formalism of Altarelli and Parisi, we study scaling violations for the spin dependent structure function G₁. We find that the variation of G₁ with Q² is essentially determined by that of the valence quarks helicity distributions, the antiquark densities contributing negligibly.     

带强迫项变系数组合KdV方程的无穷序列复合型类孤子新解

为了获得变系数非线性发展方程的无穷序列复合型新解,研究了G′(ξ)G(ξ)展开法.通过引入一种函数变换,把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题.在此基础上,利用Riccati方程解的非线性叠加公式,获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解.借助这些复合型新解与符号计算系统Mathematica,构造了带强迫项变系数组合KdV方程的无穷序列复合型类孤子新精确解.     

Exciton and polaron properties in GaxIn1−xAs ternary mixed crystals

Based on the pseudopotential method under the virtual crystal approximation that takes into account the effect of compositional disorder, the electron and heavy-hole effective masses and the dielectric constants in Ga_xIn_1−xAs (0≤x≤1) have been calculated. The results are firstly used in the Wannier equation, which allowed the determination of the exciton reduced mass, binding energy and Bohr radius; then, the polaron properties have been investigated. In this respect, the Fröhlich coupling parameter, Debye temperature and polaron effective mass are calculated and their dependence on the Ga concentration is examined. For InAs and GaAs, our results are generally in reasonable agreement with the known data in the literature, while for compositions x in the range 0-1, our treatment represents the first theoretical predictions. It is found that the exciton and polaron properties for compositions 0<x<1 differ from those of the parent compounds suggesting thus more diverse opportunities to describe most exciton and polaron properties in ternary mixed crystals of interest.     

The I-V characteristics of InAs/GaAs quantum dot laser

The I-V characteristics of an InAs/GaAs quantum dot (QD) laser diode have been investigated under both the high and low input current conditions. Under the low current condition, the I-V curve obeys the Shockley equation, from which the forbidden energy gap of the junction can be derived. On the other hand, in the high current range, the I-V characteristics violate the Shockley equation and the device tends to operate as a resistance. In addition, the I-V curve can be used to fit the temperature coefficient of the forward voltage, which is a critical parameter for determining the junction temperature of the laser diode.     

Spectroscopy of X2Y4 (D2h) molecules: tensorial formalism adapted to the O(3)⊃D2h chain, Hamiltonian and transition moment operators

A tensorial formalism adapted to the case of the X₂Y₄ molecules with D_2h symmetry has been developed in the same way as in the previous works on XY₄ (T_d) and XY₆ (O_h) spherical tops and XY₅Z (C_4v) symmetric tops. Here, we use the O(3)⊃D_2h group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain and used in the case of the Hamiltonian and transition moment operators.     

构造非线性发展方程的无穷序列复合型类孤子新解

为了构造非线性发展方程的无穷序列复合型类孤子新解, 进一步研究了G'(ξ)/G(ξ) 展开法. 首先, 给出一种函数变换, 把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题. 然后, 利用Riccati方程解的非线性叠加公式, 获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解. 在此基础上, 借助符号计算系统Mathematica, 构造了改进的(2+1)维色散水波系统和(2+1)维色散长波方程的无穷序列复合型类孤子新精确解. 关键词： G'(ξ)/G(ξ)展开法')" href="#">G'(ξ)/G(ξ)展开法 非线性叠加公式 非线性发展方程 复合型类孤子新解     

On the structure of the irreducible representation basis for the exceptional group G2

Using the method of projection operators we have constructed the basis of the irreducible representation D

of the exceptional Lie group G₂ corresponding to the reduction of this group to the subgroup SU₃. The basis is nonorthogonal but convenient for calculations. The matrices of the generators of the group G₂ in this basis have been found. The problem of additional quantum number ω required for the complete labelling of the basis vectors is considered. For this purpose we introduce the operator ω which is cubic with respect to the generators of the group G₂ and scalar with respect to the subgroup SU₃. The matrix of this operator has been calculated in the nonorthogonal basis. This matrix has a nondegenerate spectrum of eigenvalues ω which can be used as the missing quantum number.