Almost Perfect Nonlinear (APN) functions are very useful in cryptography, when they are used as S-Boxes, because of their good resistance to differential cryptanalysis. An APN function f : F2n → F2n is called exceptional APN if it is APN on infinitely many extensions of F2n . Aubry, McGuire and Rodier conjectured that the only exceptional APN functions are the Gold and the Kasami-Welch monomial...

In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach chosen goal subspace. The questions studied in are motivated by recent results dynamics graphs, most particularly Markov chains. We focus describing how and times can be obtained, main novelties res...

is irreducible. Irreducibility here and throughout this paper refers to irreducibility over the rationals. Some condition, such as ja0j = janj = 1, on the integers aj is necessary; otherwise, the irreducibility of all polynomials of the form above would imply every polynomial inZ[x] is irreducible (which is clearly not the case). In this paper, we will mainly be interested in relaxing the condi...

The criterion of irreducibility of multi–loop Feynman integrals. Abstract The integration by parts recurrence relations allow to reduce some Feynman inte-grals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as by-product provides wit...

In this paper, by analyzing the Chalmers-Searle debate about Chalmers’ zombie thought experiment, I attempt to determine the implications that the irreducibility of consciousness has for the truth of materialism. While Chalmers claims that the irreducibility of consciousness forces us to embrace dualism, Searle claims that it has no deep metaphysical im­ port and, in particular, that it is full...

I Abstract n this paper we prove by entirely elementary means a very effective version of the Hilbert Irreducibility-n Theorem. We then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate poly omials over arbitrary perfect fields. For the usual coefficient fields the test runs in polynomial time in the input K size.

In this article, we give two different sufficient conditions for the irreducibility of a polynomial more than one variable, over an algebraically closed field, that can be written as sum polynomials which depend on mutually disjoint sets variables. These are derived from analyzing Newton polytope such and then applying ‘Irreducibility criterion’ introduced by Gao.

We prove the irreducibility of ceratin polynomials whose coefficients are in arithmetic progression with common difference 2 . We use Sylvester type of results on the greatest prime factor of a product with terms in an arithmetic progression and irreducibility results based on Newton Polygons.