In this paper we study the static Einstein–Maxwell space when it is conformal to an n-dimensional pseudo-Euclidean space, which invariant under action of $$(n-1)$$ -dimensional translation group. We also provide a complete classification such space.

The Alesker product turns the space of smooth translation-invariant valuations on convex bodies into a commutative associative unital algebra, satisfying Poincaré duality and hard Lefschetz theorem. In this article, version Hodge-Riemann relations for algebra is conjectured, conjecture proved in two particular situations: even valuations, 1-homogeneous valuations. latter result then used to ded...

Given a real and invertible d×d matrix C, we define for k ∈ Zd a generalized translation operator TCk acting on f ∈ L 2(Rd) by (TCkf)(x) = f(x − Ck), x ∈ R . A generalized shift-invariant system is a system of the type {TCjkφj}j∈J,k∈Zd , where {Cj}j∈J is a countable collection of real invertible d×d matrices, and {φj}j∈J ⊂ L 2(Rd). Generalized shift-invariant systems contain the classical wavel...

In this work a complete access control system based on a biometric code formed by invariant geometric features extracted from the hand’s image, a hardware key and a vital sign detector. The feature extraction process is based on the analysis of the curvature profile of the image, making the system invariant to the rotation and translation of the hand. This makes unnecessary the use of any kind ...