In algebraic geometry one often encounters the problem of taking the quotient of a scheme by a group. Despite the frequent occurrence of such problems, there are few general results about the existence of such quotients. These questions come up again and again in the theory of moduli spaces. When we want to classify some type of algebraic objects, say varieties or vector bundles, the classifica...

This file contains additional information relating to the article: “A Search for Solvable Weighing Matrices,” submitted to Journal of Combinatorial Mathematics and Combinatorial Computing Feb. 25, 2005. In that article, we describe a computer search for group-developed weighing matrices of order 60 and weight 25, which we abbreviate as W (60, 25). Generally speaking, we view weighing matrices a...

The Hunter–Saxton equation is the Euler equation for the geodesic flow on the quotient space of the infinite-dimensional group of orientation preserving diffeomorphisms of the unit circle modulo the subgroup of rigid rotations equipped with a right-invariant metric. We establish several properties of this quotient space: it has constant sectional curvature equal to 1, the Riemannian exponential...

OBJECTIVE Delay and impairment of motor development is reported in patients with congenital heart disease. This pilot study addressed the feasibility and effect of a low-dose motor training programme of 60 min once per week on motor ability in preschool children with congenital heart disease. PATIENTS AND METHODS In all, 14 children--including four girls, in the age group of 4-6 years--with v...

Subclinical organ damage precedes the occurrence of cardiovascular events in individuals with obesity and hypertension. The aim of this study was to assess the relationship between fuel utilization and subclinical cardiovascular damage in overweight/obese individuals free of established cardiovascular disease receiving the same diet and pharmacological intervention. In this retrospective study ...

CONTENTS This article proposes to represent subgroups of finitely presented 1 . Creation of Quotient Representations and Easy Calculations g r o u p s b y t h e i r i m a g e i n a quo t ient. It gives algorithms for basic 2. Subdirect Products operations in this representation and investigates how iteration 3. Iterated Quotient Representations of this approach can be used to extend known quoti...

Motivated by the recently introduced concept of a pseudosymmetric braided monoidal category, we define the pseudosymmetric group PSn, as the quotient of the braid group Bn by the relations σiσ −1 i+1 σi = σi+1σ −1 i σi+1, with 1 ≤ i ≤ n − 2. It turns out that PSn is isomorphic to the quotient of Bn by the commutator subgroup [Pn, Pn] of the pure braid group Pn (which amounts to saying that [Pn,...

0 //K ⊂ //E q //Q //1. Here K stands for kernel and Q stands for quotient. She assumed that K is abelian (= commutative), so she wrote its product as + with identity element 0. She did not assume that Q is abelian, so she wrote its product as · with identity element 1. That explains the joke notation with 0 at the left and 1 at the right. The sequence is exact, which means that K is a normal su...