The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to start with, we obtain the natural analytic generalization of some semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we give a simple and...

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

The diameter of a set S of points is the maximal distance between a pair of points in S. The center of S is the set of points that minimize the distance to their furthest neighbours. The problem of nding the diameter and center of a simple polygon with n vertices for diierent distance measures has been studied extensively in recent years. There are algorithms that run in linear time if the geod...

We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajtasz Sobolev spaces, weighted Sobolev spaces, Upper-gradients, etc). We then introduce the notion of variational p-capacity and discuss its relation with the geometric properties of the metric space. The notions of p-parabolic ...

Doust and Weston [8] introduced a new method called “enhanced negative type” for calculating a non trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). (In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be non trivial.) In this paper we refine the technique of enhanced negative type and show how it may be applied more...

Fisher information and natural gradient provided deep insights and powerful tools to artificial neural networks. However related analysis becomes more and more difficult as the learner’s structure turns large and complex. This paper makes a preliminary step towards a new direction. We extract a local component from a large neural system, and define its relative Fisher information metric that de...