Let T be a tree with t vertices. Clearly, an n vertex graph contains at most n/t vertex disjoint trees isomorphic to T . In this paper we show that for every > 0, there exists a D( , t) > 0 such that, if d > D( , t) and G is a simple d-regular graph on n vertices, then G contains at least (1− )n/t vertex disjoint trees isomorphic to T .

We prove local injectivity near a boundary point for the geodesic X-ray transform an asymptotically hyperbolic metric even mod $O(\rho^5)$ in dimensions three and higher.

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f : C → C a contractive mapping or a weakly contractive mapping , and T : C → C nonexpansive mapping with the fixed point set F T / ∅. Let {xn} be generated by a...

We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state rho of two d-dimensional systems and completely depolarized noise, with respective weights p and 1-p. We first construct a local model for the case in which rho is maximally entangled and p at or below a certain bound. We then extend the model to arbitrary rho. Our results provide bounds on the...

We prove a global Lorentz estimate of the Hessian of strong solutions to a class of asymptotically regular fully nonlinear elliptic equations over a C1,1 smooth bounded domain. Here, the approach of the main proof is based on the Possion’s transform from an asymptotically regular elliptic equation to the regular one.

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}