where τ, σ , and c are constants in R with τ ≥ 0, σ ≥ 0, |c| < 1, g(t,x) is a T(> 0)-periodic function in t > 0, and for an arbitrary bounded domain E ⊂ R, g(t,x) is a Lipschitz function in [0,T] × E, p ∈ C(R,R), p(t +T) = p(t), and ∫ T 0 p(t)dt = 0. They obtained some sufficient conditions to guarantee the existence, at least a T-periodic solution, for this system. But, for the existence of pe...

The classical billiard system describes the motion of a point in a plane domain subject to the elastic reflection off the boundary, described by the familiar law of geometrical optics: the angle of incidence equals the angle of reflection; see, e.g., [13, 14] for surveys of mathematical billiards. For every n ≥ 2, the billiard system inside a circle has a very special property: every point of t...

Fast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, a...

Keywords: Schauder fixed point principle Exponentially stable Acquistapace–Terreni conditions Evolution families Almost periodic Higher-order differential equation with operator coefficients Wave equation with fractional damping a b s t r a c t In this paper, we make extensive use of the well-known Schauder fixed point principle and the exponential stability of the evolution family involved to ...

Let M be a compact connected oriented surface. The surface M is called a translation surface if it is equipped with a translation structure, that is, an atlas of charts such that all transition functions are translations in R2. It is assumed that the chart domains cover all surface M except for finitely many points called singular. The translation structure induces the structure of a smooth man...

The Turing machine is studied with new methods motivated by the notion of recurrence in classical dynamical systems theory. The state cycle of a Turing machine is introduced. It is proven that each consecutive repeating state cycle in a Turing machine determines a unique periodic configuration (point) and vice versa. This characterization is a periodic point theorem for Turing machines. A Turin...

We introduce a parameter space for periodic point sets, given as a union of m translates of a point lattice. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a denser periodic sphere packing. This in particular ...

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of perio...

This paper is concernedwith a periodic system dependent on parameter. We study differentiability with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the results regarding parameters for C0-semigroups, we obtained some convenient conditions for determining differentiability with parameters of the periodic solution. The paper is concluded with an ...