Vectorial Boolean functions play an important role in cryptography, sequences and coding theory. Both affine equivalence EA-equivalence are well known relations between vectorial functions. In this paper, we give exact formula for the number of classes, asymptotic classes

Denotational semantics often make invariants explicit which are implicit in the structure of a proof theoretic system. Asperti’s Light Affine Logic is a proof theoretic system, which can be viewed as a computation model. It was shown by Asperti and Roversi that, as a computation model, it captures the feasible functions. Light Affine Logic is a simplification of Girard’s Light Linear Logic, to ...

We study the possibility of extending the Rackoff technique to Affine nets, which are Petri nets extended with affine functions. The Rackoff technique has been used for establishing Expspace upper bounds for the coverability and boundedness problems for Petri nets. We show that this technique can be extended to strongly increasing Affine nets, obtaining better upper bounds compared to known res...

Based on ideas of W. M. Tulczyjew, a geometric framework for a frame-independent formulation of different problems in analytical mechanics is developed. In this approach affine bundles replace vector bundles of the standard description and functions are replaced by sections of certain affine line bundles called AV-bundles. Categorial constructions for affine and special affine bundles as well a...

We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasiaffine counterparts a...

In this paper, we determine theWalsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by Göloğlu is affine equivalent to Gold functions.

A Boolean function f :F2 → F2 is called an affine disperser of dimension d, if f is not constant on any affine subspace of F2 of dimension at least d. Recently Ben-Sasson and Kopparty gave an explicit construction of an affine disperser for sublinear d. The main motivation for studying such functions comes from extracting randomness from structured sources of imperfect randomness. In this paper...

We study affine Jacobi structures (brackets) on an affine bundle π : A→M , i.e. Jacobi brackets that close on affine functions. We prove that if the rank of A is non-zero, there is a one-to-one correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A = ⋃ p∈M Aff(Ap,R) of affine functionals. In the case rank A = 0, it is shown that there is a one-t...

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.