We prove that in the space of all Cr (r ≥ 1) partially hyperbolic diffeomorphisms, there is a C1 open and dense set of accessible diffeomorphisms. This settles the C1 case of a conjecture of Pugh and Shub. The same result holds in the space of volume preserving or symplectic partially hyperbolic diffeomorphisms. Combining this theorem with results in [Br], [Ar] and [PugSh3], we obtain several c...

Advanced 3D scanning technologies enable us to obtain dense and accurate surface sample point sets. From sufficiently dense sample point set, Crust algorithm, which is based on Voronoi diagram and its dual Delaunay triangulation, can reconstruct a triangle mesh that is topologically valid and convergent to the original surface. However, the algorithm is restricted in the practical application b...

We refer the reader to Jerrum's book [1] for the analysis of a Markov chain for generating a random matching of an arbitrary graph. Here we'll look at how to extend the argument to sample perfect matchings in dense graphs and arbitrary bipartite graphs. Both of these results are due to Jerrum and Sinclair [2]. Dense graphs We'll need some definitions and notations first: Definition 7.1 A graph ...

community detection is a task of fundamental importance in social network analysis. community structures enable us to discover the hidden interactions among the network entities and summarize the network information that can be applied in many applied domains such as bioinformatics, finance, e-commerce and forensic science. there exist a variety of methods for community detection based on diffe...

Consider the exterior boundary value problem (V* + k’) u = 0, in R, k > 0. u lr. = k where T is a smooth closed connected surface in Ip’, u exp(ik 1x1) Ixl-‘f(k, n) as Ix/ + co, n =x lx]-‘, f is called the radiation pattern. We prove that when h runs through any dense set in L’(r) the corresponding radiation pattern f(k, n) runs through a dense set in L*(S’) for any k > 0, where S* is the unit ...

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topolo...

and rðtÞ :1⁄4 sup{t , t : t [ T}; for all t [ T, where inf Y: 1⁄4 sup T and sup Y: 1⁄4 inf T, where Y denotes the empty set. We assume throughout that T has the topology that it inherits from the standard topology on the real numbers R. If s(t) . t, we say t is right-scattered, while if r(t) , t we say t is leftscattered. If s(t) 1⁄4 t and t , sup T we say t is right-dense, while if r(t) 1⁄4 t ...

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topolo...

Let X be a real Banach space and let K be a bounded closed convex subset of X. We prove that the set of strongly exposing functions K" of K is a (norm) dense G, in X* if and only if for any bounded closed convex subset C such that Kit C, there exists a point x in K which is a strongly exposed point of conv (C U K). As an application, we show that if X* is weakly compact generated, then for any ...

We find a necessary and sufficient condition for the Ruelle operator of a weakly Hölder continuous potential on a topologically mixing countable Markov shift to act with spectral gap on some rich Banach space. We show that the set of potentials satisfying this condition is open and dense for a variety of topologies. We then analyze the complement of this set (in a finer topology) and show that ...