We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

Suppose q is a prime power and f ∈ Fq[x] is a univariate polynomial with exactly t nonzero terms and degree <q−1. To establish a finite field analogue of Descartes’ Rule, Bi, Cheng and Rojas (2013) proved an upper bound of 2(q − 1) t−2 t−1 on the number of cosets in F∗ q needed to cover the roots of f in F∗ q . Here, we give explicit f with root structure approaching this bound: For q a t power...

Eye movements are crucial in understanding complex scenes. By predicting where humans look in natural scenes, we can understand how they percieve scenes and priotriaze information for further high-level processing. Here, we study the effect of a particular type of scene structural information known as vanishing point and show that human gaze is attracted to vanishing point regions. We then buil...

Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak solutions and on the convergence of vanishing viscosity approximations. 2000 Mathematics Subject Classification: 35L60, 35L65.

A new technique to automatically detect the vanishing points in digital images is presented. The proposed method borrows several ideas from various papers on vanishing point detection and segmentation in sparse images and recombines them with a new intersection point neighborhood on Z.

We provide results on the smoothness of normalisers in connected reductive algebraic groups G over fields k of positive characteristic p. Specifically we we give bounds on p which guarantee that normalisers of subalgebras of g in G are smooth, i.e. so that the Lie algebras of these normalisers coincide with the infinitesimal normalisers. One of our main tools is to exploit cohomology vanishing ...

We analyse the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application of these theorems, we give the first example of non-affine, non-product...