Consider the n-dimensional nonautonomous system x(t) = A(t)G(x(t)) B(t)F(x(t r(t))) Let ( ) J, 1. EM I i 1. EM . 1 F (j ' j n ) F U U"...,Un, a lmllull-a lIull' 00 Imllull-oo lIull' Z ,...,n, ,..., , amaxi=l,...,nUJ} and Foo = maxi=l,...,n{f~}. Under some quite general conditions, we prove that either Fa = 0 and F 00 = 00, or Fa = 00 and F 00 = 0, guarantee the existence of positive periodic so...

Bent functions f : F2 → F2 achieve largest distance to all linear functions. Equivalently, their spectrum with respect to the Hadamard-Walsh transform is flat (i.e. all spectral values have the same absolute value). That is equivalent to saying that the function f has optimum periodic autocorrelation properties. Negaperiodic correlation properties of f are related to another unitary transform c...

The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...

Let T be a tree and f : T → T be continuous. Denote by P (f) and ω(x, f) the set of periodic points of f and ω-limit set of x under f respectively. Write Λ(f) = ⋃ x∈T ω(x, f). In this paper, we show that if x ∈ Λ(f)−P (f), then ω(x, f) is an infinite minimal set.

Denote x t x1 t , x2 t , . . . , xn t , xt x1t, x2t, . . . , xnt , xit s xi t s i 1, 2, . . . , n , s ∈ −τ, 0 , τ is a positive constant or τ ∞, the norm of a bounded continuous function space C −τ, 0 , R is defined as ‖φ‖ maxs∈ −τ,0 |φ s |, where |φ| max{|φi|, i 1, 2, . . . , n}, C −τ, 0 , R {φ ∈ C −τ, 0 , R : for all θ ∈ −τ, 0 , φ θ > 0}. We call an almost periodic function is positive if and...