A sequence in an additively written abelian group is called a minimal zero-sum sequence if its sum is the zero element of the group and none of its proper subsequences has sum zero. The structure of the longest minimal zero-sum sequences in the group C2 ⊕C2k is known. Their length is equal to 2k + 1. We characterize the minimal zero-sum sequences in C2 ⊕ C2k (k ≥ 3) with lengths at least 2�k/2�...

We show that the existence of a Fredholm element of the zero calculus of pseudodifferential operators on a compact manifold with boundary with a given elliptic symbol is determined, up to stability, by the vanishing of the Atiyah-Bott obstruction. It follows that, up to small deformations and stability, the same symbols have Fredholm realizations in the zero calculus, in the scattering calculus...

Let A be a finite, nonempty subset of an abelian group. We show that if every element is sum two other elements, then has zero-sum subset. That is, (finite, nonempty) sum-full group not zero-sum-free.

The problem of high-speed penetration a non-deformable cylinder into steel plate is considered. defining system equations formulated in Lagrange variables three-dimensional formulation. equation motion derived from virtual work capacities balance. Kinematic relations are recorded the metric current state. flow theory with kinematic and isotropic hardening used as contact interaction modeled by ...

The goal of this paper is to investigate the spectral element method (SEM), a grid-based computational approach, and the grid-free particle strength exchange method (PSEM) for solving the advection-diffusion-reaction equation in a microfluidic channel. We identify the dimensionless parameter regimes at which each algorithm provides a satisfactory solution in terms of accuracy and computational ...

The results in this paper were motivated by the case when the inverse semigroup is the McAlister monoid MX on a set X. In [1] we considered some very large convolution algebras on MX , including some C ∗-algebras. Our main focus in [1] was deciding on the primitivity of the algebras, and one key tool was the use of generalized Rukolaine idempotents. To define these very large convolution algebr...

Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work,...

A finite subset A of an abelian group G is said to be zero-free if the identity element of G cannot be written as a sum of distinct elements from A. In this article we study the structure of zero-free subsets of Z/pZ, the cardinalities of which are close to the largest possible. In particular, we determine the cardinality of the largest zero-free subset of Z/pZ, when p is a sufficiently large p...

Interesting properties of the partitions of a finite field Fq induced by the combination of involutions and trace maps are studied. The special features of involutions of the form u z , u being a fixed element of Fq, are exploited to generate pseudorandom numbers, the randomness resting on the uniform distribution of the images of zero-trace elements among the sets of non-zero trace elements of...