For a self{similar or self{aane tile in R n we study the following questions: 1) What is the boundary? 2) What is the convex hull? We show that the boundary is a graph directed self{aane fractal, and in the self{similar case we give an algorithm to compute its dimension. We give necessary and suucient conditions for the convex hull to be a polytope, and we give a description of the Gauss map of...

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of Γ-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of...

For a self similar or self a ne tile in R we study the following questions What is the boundary What is the convex hull We show that the boundary is a graph directed self a ne fractal and in the self similar case we give an algorithm to compute its dimension We give necessary and su cient conditions for the convex hull to be a polytope and we give a description of the Gauss map of the convex hull

Bone condensing as a technique to prepare an implant site is demonstrated on a patient who was to undergo orthodontic treatment utilizing a palatal implant as an anchor. Based on the anatomic constraints of the palate and the desire to load the implant as axially as possible, adapted-instrumentation for bone condensing is presented. Bone condensing for preparation of the implant site in soft ma...

In this paper level-cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied. Using the extensions of nonlinear compact operators, topological degree theory with respect to condensing operators is given in standard fuzzy normed spaces. As an application of degree theory, a fixed point theorem for condensing operators is presented. © 2009...

in this paper, the energy efficient resource allocation in noma-based heterogeneous cellular network(hcn) systems is investigated. since energy consumption and its limitations is one of the important challenges in fifth generation of cellular networks (5g), we propose a resource allocation problem which allocates power and subcarriers to multiple users to achieve the best system energy efficien...

This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat some transport problems, of independent interest, with a convex constraint on the displacement. As an illustration of our strategy, we prove existence of opt...

This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (R, ‖ · ‖) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f : X → X , converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm,...

This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat some transport problems, of independent interest, with a convex constraint on the displacement. As an illustration of our strategy, we prove existence of opt...