Problem 1.(The Mapping Cone is a Homotopy Limit and a Homotopy Colimit) Let A be an Abelian category. Let A● and B● be objects in Ch●(A). Let f ● ∶ A● → B● be a morphism in Ch●(A). For every object T ● of Ch●(A), a left homotopy annihilator to T ● is a pair (Q●, σ●) of a morphism Q● ∶ B● → T ● in Ch●(A) and a nullhomotopy (σn ∶ An → T n−1)n∈Z of Q● ○ f ●, i.e., for every n ∈ Z, Q ○ f = dn−1 T ○...

LFSR-based stream ciphers with nonlinear filters or combiners are susceptible to algebraic attacks using linearization methods to solve an overdefined system of nonlinear equations. And this process is greatly enhanced if the filtering or combining function has a low degree annihilator. To prevent such an attack, one would choose the parameters of that function so that the degree of its annihil...

In this paper we generalize the Skjelbred–Sund method, used to classify nilpotent Lie algebras, in order triple systems with non-zero annihilator. We develop method purpose of classifying systems, obtaining from it algebraic classification up dimension four. Additionally, obtain geometric variety

Double aggregation operators are introduced and several basic properties are studied, as neutral and annihilator elements, idempotency, etc., which are illustrated by some examples. The classes of additive and comonotone additive double aggregation operators are characterized.

This paper formulates the problem of determining the degrees of all polynomial entries in a minimal polynomial basis of a polynomial matrix by using only the degree structure of the given matrix. Using a block Toeplitz matrix structure corresponding to the given polynomial matrix, it is shown that the degrees of the elements in its minimal polynomial basis, in the generic case, depend only on t...