In this paper, we study a new flexible method to extend linearly the graph of nonlinear, and usually not bijective, function so that resulting extension is bijection. Our motivation comes from cryptography. Examples symmetric cryptography are given as how was used implicitly in construction some well-known block ciphers. The heavily relies on ideas brought linear coding theory secret sharing. W...

A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns integer from $\{1, \ldots, k \}$ to every vertex so that, in edge, the (multi)set colours has a unique maximum. Equivalently, for $r=3$, if two vertices edge are assigned same colour, then third is larger colour (as opposed different as classic non-monochromatic colouring). Barto, Battistelli, and Berg [STACS'21] studied...

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

The aim of this paper is to study the convergence properties of the gradient projection method and to apply these results to algorithms for linearly constrained problems. The main convergence result is obtained by defining a projected gradient, and proving that the gradient projection method forces the sequence of projected gradients to zero. A consequence of this result is that if the gradient...