Temperature overshoots for a 4-velocity unidimensional discrete Boltzmann model

We propose a 4-velocity unidimensional discrete Boltzmann model with two different speeds 2, 1 and two different masses 1, 2. With the three conservation laws of mass, momentum, and energy satisfied, we can introduce a nontrivial temperature. First, we determine the similarity shock waves satisfying physical properties: positivity, shock stability, inequalities of the subsonic and supersonic flows, increase or decrease of both mass and temperature across the shock. It results that either the speed of the shock front is higher than the speed 1 of the slow particles and the shocks are compressive or less than 1 and the shocks are rarefactive. We observe overshoots of the temperature, across the shock, with bumps higher and higher as the shock front speed increases. Second, we study the (1+1)-dimensional shock waves. They represent the superposition and collision of two compressive shocks traveling in opposite directions and we observe temperature overshoots for not too large times.     

温盐双扩散系统非线性周期对流稳定性分析

提出一种研究流层中温盐对流的稳定性的方法。计算简单,且可应用于更广泛的一类系统。     

一类高阶线性混合型方程的定解问题

本文讨论了一类高阶线性混合型方程,并且证明了两个边值问题解的存在唯一性。     

一类Hill方程的渐近解的完全表达式

本文研究Ｈｉｌｌ方程其中ｆ（ｘ）是ｘ的以２π为周期的正则周期函数，在每个周期内有两个一阶零点。本文应用不同于Ｍｏｒｉｇｕｃｈｉ的方法，得到了方程在转向点附近的形式一致有效渐近解的完全表达式。     

Weak solutions of the forward problem in EEG for different conductivity values

The potential distribution on the scalp produced by current sources in the brain can be measured by an EEG recorder. The relationship between these sources and the scalp potential distribution may be described by a well-known mathematical model where some simplifications are usually introduced. The head is modeled as a multicompartment nested set and the conductivity of the different tissues is approximated by a positive piecewise constant function. This simplified model is used to solve the forward problem (FP), i.e., to calculate the scalp potential for a current source configuration. In this work, we prove that the weak solutions of the FP are continuous with respect to the conductivity values, that is, the difference between the scalp potentials is small if the conductivity values are closed enough. We present numerical examples that illustrates this property.     

Temperature dependent small-angle neutron scattering of CTABr—magnetic fluid emulsion

Small-angle neutron scattering studies have been carried out to check the structural integrity of citryltrimethylammonium bromide (CTABr) micelles in a magnetic fluid for different magnetic fluid concentrations at two different temperatures 303 and 333 K. It is found that the CTABr micelles grow with increasing magnetic fluid concentration and there is a decrease in the micellar size with increase in temperature.     

Spurious solutions of three-dimensional Faddeev equations

We obtain explicit spurious solutions of three-dimensional Faddeev equations written in the total angular momentum and total space parity representation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 227–242, August, 2006.     

ON THE EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR SINGULAR p-LAPLACE EQUATIONS

In this paper N-dimensional singular, p-Laplace equations of the following form are considered, where p ≥N, β > 0, and f : [0,∞)×(0,∞)×[0, ∞)→[0,∞) is a continuous function. Some sufficient conditions are obtained for the existence of infinitely many radially positive entire solutions of the equation which are asymptotic to positive constant multiples of |x|(p-N)/(p-1) for p > N or log|x| for N = p as |x|→∞.     

Coexistence states for systems of mutualist species

Coexistence states for a class of systems of mutualist species are obtained via bifurcation theory and monotone techniques.