A. This paper investigates the origin of divergence errors in MHD simulations. For that purpose, we introduce the concept of discrete involutions for discretized conservation laws. This is done in analogue to the concept of involutions for hyperbolic conservation laws, introduced by Dafermos. By exploring the connection between discrete involutions and resonance, especially for constrain...

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...

We define an excedance number for the multi-colored permutation group i.e. the wreath product (Zr1 × · · · ×Zrk) o Sn and calculate its multi-distribution with some natural parameters. We also compute the multi-distribution of the parameters exc(π) and fix(π) over the sets of involutions in the multi-colored permutation group. Using this, we count the number of involutions in this group having ...

We show that the principal order ideal of an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin...

In finite-dimensional simple Lie algebras and affine Kac-Moody algebras, Chevalley involutions are crucial ingredients of the modular theory. Towards establishing theory for extended we investigate existence “Chevalley involutions” tori algebras. We first discuss how to lift a involution from centerless core which is characterized be torus then entire algebra. prove by type-dependent argument t...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

Let In(π) denote the number of involutions in the symmetric group Sn which avoid the permutation π. We say that two permutations α, β ∈ Sj may be exchanged if for every k and ordering τ of j + 1, . . . , k, we have In(ατ) = In(βτ) for every n. Here we prove that 12 and 21 may be exchanged and that 123 and 321 may be exchanged. The first of these theorems gives a number of known results for patt...

In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to...