A longitudinal single-bunch instability [1] in the damping rings at the Stanford Linear Collider (SLC) is thought to contribute to pulse-to-pulse orbit variations in downstream accelerator sections. To better understand this instability, we measured the beam phase and bunch length under harmonic modulations of the rf phase and rf voltage. For small phase-modulations the measured response can be...

This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ-complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

Computer algebra systems often have to deal with piecewise continuous functions. These are, for example, the absolute value function, signum, piecewise defined functions but also functions that are the supremum or infimum of two functions. We present a new algebraic approach to these types of problems. This paper presents a normal form for a function ring containing piecewise polynomial functio...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings.

A class of ring-like structures events (RLSEs) is studied that generalizes Boolean rings. Quantum logics represented by orthomodular lattices are characterized within this and the correspondence between algebras rings enlarged to lattices. The structure RLSEs various subclasses analyzed classical especially identified. Moreover, sets numerical different contexts physical problems described. eve...

Within local-spin-density functional theory, we have investigated the “dissociation” of few-electron circular vertical semiconductor double quantum ring artificial molecules at zero magnetic field as a function of interring distance. In a first step, the molecules are constituted by two identical quantum rings. When the rings are quantum mechanically strongly coupled, the electronic states are ...

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

The evolution of non-stationary localized states jCðt 1⁄4 0Þi is investigated in two-dimensional tight binding systems of N potential wells with and without a homogeneous field perpendicular to the plane. Most results are presented in analytical form, what is almost imperative if the patterns are as complex as for rings in a magnetic field, where the qualitatively different features arise depen...