Linear functions are used to model a broad range of real-world problems. The ability to solve linear equations and inequalities is an essential skill for analysing these models. This section covers ...

Abstract: This paper addresses the correspondence between linear inequalities for Shannon entropy and differential entropy for sums of independent group-valued random variables. We show that any ...

Abstract: In this article, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality ...

ABSTRACT: The known Fourier-Chernikov algorithm of linear inequality system convolution is complemented with an original procedure of all dependent (redundant) inequalities deletion. The concept of ...

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that ...

ABSTRACT: This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two ...

\({\textless}\) \({y}~{\textless}~{x}\) reads as ‘\({x}\) is greater than \({y}\)’ or ‘\({y}\) is less than \({x}\)’ \({\textgreater}\) \({7}~{\textgreater ...

Given a homogeneous k-th order differential operator A(D) on ℝn between two finite dimensional spaces, we establish the Hardy inequality ${\int }_{{\mathrm{\mathbb ...