Delta and singular delta locus for one‐dimensional systems of conservation laws

This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau‐type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd.     

Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems

Although the numerical solution of one-dimensional phase-change, or Stefan, problems is well documented, a review of the most recent literature indicates that there are still unresolved issues regarding the start-up of a computation for a region that initially has zero thickness, as well as how to determine the location of the moving boundary thereafter. This paper considers the so-called boundary immobilization method for four benchmark melting problems, in tandem with three finite-difference discretization schemes. We demonstrate a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution that is often used, and is numerically second-order accurate in both time and space, a point that has been consistently overlooked for this type of moving-boundary problem.     

Thermodynamic properties of the ternary system {yNH4Cl + (1 − y)MgCl2} (aq) at 298.15 K

The mixture {yNH₄Cl + (1 − y)MgCl₂} (aq) has been studied using the hygrometric method at the temperature 298.15 K. The water activities are measured at total molalities from 0.30 mol kg⁻¹ up to saturation for different ionic strength fractions y of NH₄Cl with y = 0.20, 0.50 and 0.80. The obtained data allow the deduction of osmotic coefficients. Experimental results are compared with the calculations using the models of Zdanovskii–Stokes–Robinson, Kusik and Meissner, Robinson and Stokes, Lietzke and Stoughton, Reilly–Wood and Robinson and Pitzer. Thermodynamic properties have been modeled using the Pitzer ion-interaction model with inclusion of an ionic strength dependence of the third virial coefficient for the binary systems. From these measurements and the obtained binary parameters β⁽⁰⁾, β⁽¹⁾, C⁽⁰⁾ and C⁽¹⁾, the mixing ionic parameters θNH₄Mg${\theta }_{\text{N}{\text{H}}_4\text{Mg}}$ and ψNH₄MgCl${\psi }_{\text{N}{\text{H}}_4\text{MgCl}}$ are determined by the standard Pitzer model. The results show that a good accuracy is obtained with the standard Pitzer model using extended binary parameters. The parameters θNH₄Mg${\theta }_{\text{N}{\text{H}}_4\text{Mg}}$ and ψNH₄MgCl${\psi }_{\text{N}{\text{H}}_4\text{MgCl}}$ were used for evaluation of activity coefficients in the mixture. The excess Gibbs energy is also determined.     

Periodic Solutions for a Class of Nonlinear Differential-Difference Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained.     

Recursions associated to trapezoid,symmetric and rotation symmetric functions over Galois fields

Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of ${\mathbb{F}}_2$, an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field ${\mathbb{F}}_q$. Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences.     

A note on global existence of weak solutions to the compressible magnetohydrodynamic equations with Coulomb force

In this note, for the case of , we prove the existence of global-in-time finite energy weak solution of the equations of a two-dimensional magnetohydrodynamics with Coulomb force, where γ denotes the adiabatic exponent. The value is the optimal lower bound of γ to establish global-in-time finite energy weak solution under current frame.     

New exact solutions for the nonlinear wave equation with fifth-order nonlinear term

The purpose of this paper is to reveal the dynamical behavior of the nonlinear wave equation with fifth-order nonlinear term, and provides its bounded traveling wave solutions. Applying the bifurcation theory of planar dynamical systems, we depict phase portraits of the traveling wave system corresponding to this equation under various parameter conditions. Through discussing the bifurcation of phase portraits, we obtain all explicit expressions of solitary wave solutions and kink wave solutions. Further, we investigate the relation between the bounded orbit of the traveling wave system and the energy level h. By analyzing the energy level constant h, we get all possible periodic wave solutions.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.     

一类弱耗散Camassa-Holm方程局部强解的适定性及弱解的存在性

使用Pseudoparabolic正则化方法和从弱耗散Camassa-Holm方程自身导出的估计式,在Sobolev空间Hs(R)(s3/2)中,证明了该Camassa-Holm方程解的局部适定性.同时给出了一个在空间Hs(R)(1s2\3)中确保该方程弱解存在的充分条件.