pH-Sensitive Oscillatory Motion of a Urease Motor on the Urea Aqueous Phase

A self-propelled object coupled with an enzyme reaction between urease and urea was investigated at the air/aqueous interface. A plastic object that was fixed to a urease-immobilized filter paper was used as a self-propelled object, termed a urease motor, placed on an aqueous urea solution. The driving force of the urease motor is the difference in the surface tension around the object. Oscillatory motion or no motion was triggered depending on the initial pH of the urea solution. Both the frequency and maximum speed of the oscillatory motion varied depending on the initial pH of the water phase. The mechanisms underlying the oscillatory motion and no motion were discussed in relation to the bell-shaped enzyme activity of urease in the enzyme reaction and the surface tension around the urease motor.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

On Oscillation Criteria of Fourth Order Linear Differential Equations

The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.     

Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor

Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.

     

关于多线性振荡奇异积分在加权Hardy-型空间上的一致估计

本文对一类具有光滑位相函数的多线性振荡奇异积分算子建立了一致的加权（H^1(R^n),L^1(R^n))估计及一致的加权（HKp(R^n),Kp(R^n)估计。     

Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.     

第三类Painlevé方程(δ=0或γ=0)解的渐近性态

对带有一般实参数第三类Painlevé方程,已有γ<0,δ>0时,解的有界性以及振荡渐近解的表达形式的结论.在本文中,我们给出当δ=0或γ=0时其振荡渐近解的表达形式.     

HCHO-(DL-苹果酸)-BrO-3-Mn2+-H2SO4体系化学振荡反应动力学研究

研究了HCHO参与下的(DL-苹果酸)-BrO-3-Mn2+-H2SO4化学振荡反应体系的非线性动力学行为,考察了该体系中各反应物的初始浓度范围及主要影响因素. 结果表明,在5.0×10-5～1.0×10-2 mol·L-1范围内, HCHO对振荡反应的诱导期和周期有较大影响,且HCHO浓度的对数lnc(HCHO)与诱导期倒数的对数ln(1/tin)及周期倒数的对数ln(1/tp)均存在线性关系. 诱导期和周期的表观活化参数分别为70.87,55.71 kJ·mol-1. 另外还对HCHO参与下的可能振荡反应机理进行了探讨.     

Frequent oscillation in a nonlinear partial difference equation

This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.      

Theory of oscillatory experiments with a coaxial cylinder viscometer

Equations are derived for the coaxial cylinder system in the combined oscillatory and steady-state shear mode. The limitations of the use of the various equations are presented. If the usual linear equations are used, the main limitation, in the case of oscillatory shear only, is that the frequency of measurement should be below 0.016 | ^*|/(r ₂ –r ₁ )². Here | ^*| is the modulus of the complex viscosity, is the density of the liquid andr ₁ andr ₂ are the radii of the cylinders. Furthermore it is shown that there is a small error in the numerical factor of the usually applied equations. The calculations are set up in such a way that extension to higher harmonics follows in a natural way. An experimental example illustrates the use of the derived equations.