Discrete transformation hypergroups and transformation hypergroups with phase tolerance space

Tolerance spaces and algebraic structures with compatible tolerances play an important role in contemporary algebra and its applications. In this contribution we present transformation hyperstructures, namely semihypergroups and hypergroups, acting on tolerance spaces. Some basic concepts concerning the mentioned structures are introduced and their fundamental properties are examined on suitable constructions.     

Moment functions on polynomial hypergroups

The study of moment functions on commutative topological groups leads to the study of systems of functional equations. Systems of functional equations characterizing moment functions and sequences of moment functions are closely related to exponential functions and additive functions. Here we describe moment functions and generalized moment functions on polynomial hypergroups.Received: 23 May 2003; revised: 20 September 2004     

Compact groups having almost discrete orbit hypergroups

LetG be a compact group of automorphism acting continuously on a compact groupH. Then the orbit spaceH ^G is a compact hypergroup. We characterize, all solvable groupsH and compact automorphism groupsG for whichH ^G is almost discrete, i.e.,H ^G is homeomorphic to the one-point-compactification of . It turns out that thenH is isomorphic either to the infinite direct product (p) of the cyclic groups (p) or to _p ⁿ ( _p the group of allp-adic numbers) for some primep and some . The almost discrete orbit hypergroupsH ^G are determined explicitly for some examples.     

Spectral synthesis on multivariate polynomial hypergroups

In a recent paper [16] we presented some results concerning spectral analysis and spectral synthesis on polynomial hypergroups in a single variable. Now we show that using Hilbert’s Nullstellensatz, the Noether-Lasker-theorem and the Ehrenpreis-Palamodov-theorem the ideas of [16] can be extended to prove spectral analysis and spectral synthesis on any multivariate polynomial hypergroup. Author’s address: Institute of Mathematics, University of Debrecen, Egyetem tér 1, 4032 Debrecen, Hungary     

A note on Bol loops of order 2 n k

It is shown that, for eachn 2 and k 3, there exist at least 2 ⁿ -3 non-isomorphic loops of order 2 ⁿ k which are Bol but not Moufang. In most cases this bound can be improved.     

On order of elements in hypergroups and p-Sylow subhypergroups

In this paper we define a left order, right order and order of an element in a hypergroup, which has a left scalar identity, right scalar identity and scalar identity, respectively. Using left and right orders, we define and investigate some classes of subhypergroups, especially p-Sylow subhypergroups of a hypergroup. Moreover, some examples have been proposed to show that the Sylow theorems do not hold for polygroups.     

Flat cyclotomic polynomials of order three

We say that a cyclotomic polynomial Φn has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of Φn. For each pair of primes p<q, we give an infinite family of r such that A(pqr)=1. We also prove that A(pqr)=A(pqs) whenever s>q is a prime congruent to .     

Block SSOR preconditionings for high order 3d fe systems

For solving 3D high order hierarchical FE systems the block SSOR preconditioned CG algorithms based on new stripwise block two-color orderings of degrees of freedom and providing for efficient concurrent/vector implementation are suggested. As demonstrated by numerical results for the 3D Navier equations approximated using hierarchical orderp, 2 p 5, FE's the convergence rate of such BSSOR-CG algorithms is only slightly dependent onp and mesh nonunformity.     

Crown multiplications and a higher order Hopf construction

We describe a ternary function (multiplication) from the product of three 12-point crowns into a 4-point crown in the category of partially ordered sets. The ternary map illustrates a version, in the context of posets, of associative multiplication. A higher order analogue of Hopf's construction applied to σ yields a poset model of a certain homotopy class, which we identify, in π₅(S³).     

On the α-amenability of hypergroups

Let UC(K) denote the Banach space of all bounded uniformly continuous functions on a hypergroup K. The main results of this article concern the α-amenability of UC(K) and quotient and product of hypergroups. It is also shown that a Sturm-Liouville hypergroup with a positive index is α-amenable if and only if α = 1. Author’s address: Dietlinden Stra?e 16, 80802 München, Germany     

Convergence estimates for an higher order optimized Schwarz method for domains with an arbitrary interface

Optimized Schwarz methods form a class of domain decomposition methods for the solution of elliptic partial differential equations. Optimized Schwarz methods employ a first or higher order boundary condition along the artificial interface to accelerate convergence. In the literature, the analysis of optimized Schwarz methods relies on Fourier analysis and so the domains are restricted to be regular (rectangular). In this paper, we express the interface operator of an optimized Schwarz method in terms of Poincare-Steklov operators. This enables us to derive an upper bound of the spectral radius of the operator arising in this method of 1−O(h^1/4) on a class of general domains, where h is the discretization parameter. This is the predicted rate for a second order optimized Schwarz method in the literature on rectangular subdomains and is also the observed rate in numerical simulations.     

Strong Morita equivalence of semigroups with local units

In this paper we study Morita contexts for semigroups. We prove a Rees matrix cover connection between strongly Morita equivalent semigroups and investigate how the existence of a unitary Morita semigroup over a given semigroup is related to the existence of a ‘good’ Rees matrix cover of this semigroup.     

On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

Mixed finite elements for second order elliptic problems in three variables

Summary Two families of mixed finite elements, one based on simplices and the other on cubes, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. These spaces are analogues of those introduced by Brezzi, Douglas, and Marini in two space variables. Error estimates inL ² andH ^–s are derived.     

On c-normality of certain subgroups of prime power order of finite groups

In this paper, we study the structure of the finite group G given that certain subgroups of prime power order are well-situated, which means that they are normally complemented modulo their normal core.Received: 14 October 2004; revised: 12 January 2005     

Amenability notions of hypergroups and some applications to locally compact groups

Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study the Leptin condition for discrete hypergroups derived from the representation theory of some classes of compact groups. Studying amenability of the hypergroup algebras for discrete commutative hypergroups, we obtain some results on amenability properties of some central Banach algebras on compact and discrete groups.     

Sobolev regularity for first order mean field games

In this paper we obtain Sobolev estimates for weak solutions of first order variational Mean Field Game systems with coupling terms that are local functions of the density variable. Under some coercivity conditions on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity conditions on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [23]. Our methods apply to a large class of Hamiltonians and coupling functions.     

A proximal-like method for a class of second order measure-differential inclusions describing vibro-impact problems

We are interested in the study of discrete mechanical systems subjected to frictionless unilateral constraints. The dynamics is described by a second order measure-differential inclusion for the unknown positions, completed by a Newton's impact law describing the transmission of the velocities when the constraints are saturated.By using another formulation of the problem at the velocity level, we introduce a time-stepping algorithm, inspired by the proximal methods for differential inclusions, and we prove the convergence of the approximate solutions to a solution of the Cauchy problem.     

High order explicit methods for parabolic equations

This paper discusses explicit embedded integration methods with large stability domains of order 3 and 4. The high order produces accurate results, the large stability domains allow some reasonable stiffness, the explicitness enables the method to treat very large problems, often space discretization of parabolic PDEs, and the embedded formulas permit an efficient stepsize control. The construction of these methods is achieved in two steps: firstly we compute stability polynomials of a given order with optimal stability domains, i.e., possessing a Chebyshev alternation; secondly we realize a corresponding explicit Runge-Kutta method with the help of the theory of composition methods. This work was supported by the Russian Fund Fundamental Researches and the Swiss National Science Foundation 20-43.314.95.