Functional differential equations with deviating arguments are studied for the first time in the framework of Karamata regularly varying functions. A sharp condition is established for the existence of slowly varying solutions for a class of second order linear equations of the form x′′ = q(t)x(g(t)), both in the retarded and in the advanced case.

Linear equality systems with fuzzy parameters and crisp variables defined by the extension principle are called possibilistic linear equality systems. The study focuses on the problem of stability (with respect to perturbations of fuzzy parameters) of the solution in these systems.

The feasibility to unambiguously determine the nature of the cosmic dark energy with future supernovae experimental data is investigated. We work with four kinds of quintessential components : a cosmological constant, a general barotropic fluid, a perfect fluid with a linear equation-of-state and a more physical model based on a pseudo-Nambu-Goldstone boson field. The standard χ method is used....

A linear equation on k unknowns is called a (k, h)-equation if it is of the form ∑k i=1 aixi = 0, with ai ∈ {−h, . . . , h} and ∑ ai = 0. For a (k, h)-equation E, let rE(n) denote the size of the largest subset of the first n integers with no solution of E (besides certain trivial solutions). Several special cases of this general problem, such as Sidon’s equation and sets without threeterm arit...

The paper describes improved analysis techniques for basis reduction that allow one to prove strong complexity bounds and reduced basis guarantees for traditional reduction algorithms and some of their variants. This is achieved by a careful exploitation of the linear equations and inequalities relating various bit sizes before and after one or more reduction steps.

A robust linear method for auto-calibration of a moving camera from image sequences is presented. Known techniques for auto-calibration have problems with critical motion sequences or biased estimates. The proposed approach uses known linear equations that are weighted by variable factors. Experiments show, that this modification reduces problems with critical motion sequences and that the esti...

The objective of this paper is to study a special family of Minkowski sums, that is of polytopes relatively in general position. We show that the maximum number of faces in the sum can be attained by this family. We present a new linear equation that is satisfied by f -vectors of the sum and the summands. We study some of the implications of this equation.

In the recent paper [2], the authors obtained new proofs on the existence and uniqueness of the solution of the Volterra linear equation. Applying their results, in this paper we express the exact and approximate solution of the equation in the field of Mikusi´nski operators, F, which corresponds to an integro–differential equation.

Fredholm Alternative is a classical tool of periodic linear equations, allowing to describe the existence of periodic solutions of an inhomogeneous equation in terms of the adjoint equation. A few partial extensions have been proposed in the literature for recurrent equations: our aim is to point out they have a common root and discuss whether such root gives rise to a general Fredholm–type Alt...