Stepanov ergodic perturbations for some neutral partial functional differential equations

In this work, we give sufficient conditions for the existence and uniqueness of μ?pseudo almost periodic integral solutions for some neutral partial functional differential equations with Stepanov μ?pseudo almost periodic forcing functions. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main results, we give applications to a neutral model arising in physical systems, as well as an application to heat equations with discrete and continuous delay. Copyright © 2015 John Wiley & Sons, Ltd.     

On the asymptotics of the number of reduced integral quadratic forms with a condition of divisibility of the first coefficients

For the quadratic forms mentioned in the title, we use the discrete ergodic method to obtain asymptotic formulas with remainders depending on the L-Dirichlet function L(s, χ) and its behavior under some hypotheses.     

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(φ)=(1+k)sinφ/1+kcosφ.     

具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

本文利用非均匀网格和指数型拟合差分方法给出了具有非光滑边界层函数的线性抛物型方程关于小参数ε一致收敛的差分格式.文章还给出了误差估计和数值结果.     

A mean ergodic theorem on vector spaces

A mean ergodic theorem for a matrix is first proved from which a mean ergodic theorem for affine operators on a vector space without any topological structure is obtained.     

Minimality and unique ergodicity of homogeneous actions

Consider a connected Lie groupG, a lattice Γ inG, a connected subgroupH ofG, and the adjoint representation Ad ofG on its Lie algebra g. Suppose that Ad(H) splits into a semidirect product of a reductive subgroup and the unipotent radical. We prove that the minimality of the leftH-action onG/Γ then implies its unique ergodicity. Simultaneously, we suggest a reduction of the study of finite ergodic measures for an arbitrary action (G/Γ,H), where the subgroupH∈G is connected and Γ∈G is discrete, to the case of an Abelian subgroupH. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 293–301, August, 1999.     

Non-ergodicity of Two Particles Interacting via a Smooth Potential

We examine two point particles interacting via a smooth Lennard-Jones-type potential of finite range on a two-dimensional torus. We find situations under which this system contains a stable, elliptic periodic orbit and hence is not ergodic. This result is in contrast to the case of hard spheres interacting via inelastic collision, which are always ergodic for two particles, are conjectured to be ergodic for arbitrarily many particles, and can never contain elliptic periodic orbits.     

一类具有红灯环境下随机游动的极限性态

就某类红灯随机环境下随机游动{Xn}n∈Z ,建立相应的Markov-双链{ηn}n∈Z ={(Xn,Tn)}n∈Z ;并给出在该红灯环境下,{Xn}n∈Z 的发展受红灯环境影响的关系式;以及由此关系式得出:由于红灯环境的影响减缓了{Xn}n∈Z 的发展速度.     

有限域上遍历矩阵的特性

通过对有限域上遍历矩阵性质的分析, 给出了有限域上遍历矩阵的计数定理, 并在此基础上给出了遍历矩阵与不可约多项式的相关结果及有限域上遍历矩阵与线性反馈移位寄存器之间的关系.