A Lagrangian or an affine Hamiltonian is called totally singular if it is defined by affine functions in highest velocities or momenta respectively. A natural duality relation between these Lagrangians and affine Hamiltonians is considered. The energy of a second order affine Hamiltonian is related with a dual corresponding Lagrangian of order one. Relations between the curves that are solution...

Bent functions (Dillon 1974; Rothaus 1976) are extremal objects in combinatorics and Boolean function theory. They have been studied for about 40 years; even more, under the name of difference sets in elementary Abelian 2-groups. The motivation for the study of these particular difference sets is mainly cryptographic (but bent functions play also a role in coding theory and sequences; and as di...

Planar functions were introduced by Dembowski and Ostrom ([4]) to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a question posed in [4]. These planar f...

Let (G, u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G, u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state...

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur’s P and Q functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine typ...

In [13] for a given vectorial Boolean function F from F2 to itself it was defined an associated Boolean function γF (a, b) in 2n variables that takes value 1 iff a 6= 0 and equation F (x) + F (x + a) = b has solutions. In this paper we introduce the notion of differentially equivalent functions as vectorial functions that have equal associated Boolean functions. It is an interesting open proble...

A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for functions of several arguments and identification min...

We study finite elements of arbitrarily high-order defined on pyramids for discontinuous Galerkin methods. We propose a new family of high-order pyramidal finite elements using orthogonal basis functions which can be used in hybrid meshes including hexahedra, tetrahedra, wedges and pyramids. We perform a comparison between these orthogonal functions and nodal functions for affine and non-affine...

We consider a supply function equilibrium (SFE) model of interaction in an electricity market. We assume a linear demand function and consider a competitive fringe and several strategic players all having capacity limits and affine marginal costs. The choice of SFE over Cournot equilibrium and the choice of affine marginal costs is reviewed in the context of the existing literature. We assume t...

Rotation symmetric Boolean functions have been extensively studied for about 15 years because of their applications in cryptography and coding theory. Until recently little was known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomia...