In this paper we examine the initial-boundary value problems (a) limu__.-q,(u)= +o. For problem (a) we show that there is a positive number Lo such that if L<-L o, u(x,t)<_l-8 for some 8>0 for all t>0, while if L>Lo, u(L,t) reaches one in finite time while ut(L,t becomes unbounded in that time. For problem (fl) it is shown that if L is sufficiently small, then u(L, t)_<-8 for all t>0 while if L...

The global ?-synchronization problem for nonlinear multi-weighted complex dynamical networks with uncertain parameter perturbation and mixed time-varying delays is investigated in this paper. Unlike other existing works, all delays, including sampling internal coupling are assumed to be unbounded, making the considered model more general practical. Based on generalized impulsive comparison prin...

In this paper, we establish a coupling lemma for standard families in the setting of piecewise expanding interval maps with countably many branches. Our method only requires that map satisfies three assumptions: (H1) Chernov’s one-step expansion at q-scale; (H2) dynamically Hölder continuity log Jacobian (on each branch); (H3) eventually covering over magnet interval, which are much weaker than...

We introduce the quasi-hyperbolicity constant of a metric space, rough isometry invariant that measures how space deviates from being Gromov hyperbolic. This number, for unbounded spaces, lies in closed interval $[1,2]$. The an hyperbolic is equal to one. For CAT$(0)$-space, it bounded above by $\sqrt{2}$. Banach at least two dimensional below $\sqrt{2}$, and non-trivial $L_p$-space exactly $\m...

The notion of tight (wavelet) frames could be viewed as a generalization of orthonormal wavelets. By allowing redundancy, we gain the necessary flexibility to achieve such properties as “symmetry” for compactly supported wavelets and, more importantly, to be able to extend the classical theory of spline functions with arbitrary knots to a new theory of spline-wavelets that possess such importan...

let $c_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{d}$. each function $f in c_{0}(alpha)$ maps the unit disk $mathbb{d}$ onto the complement of an unbounded convex set. in this paper, we study the mapping properties of this class under integral operators.