Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford’s Geometric Invariant Theory. We obtain several new Hilbert-Mumford type theorems, and we extend a projectivity criterion of Bia lynicki-Birula and Świȩcicka for va...

2 Basic group theory 2 2.1 The definition of a group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Group homomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3 Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Cosets and quotient spaces . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford’s Geometric Invariant Theory. We obtain several new Hilbert-Mumford type theorems, and we extend a projectivity criterion of Bia lynicki-Birula and Świȩcicka for va...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

The characterization of normal subgroups M , N of free group F for which the quotient group F/[M, N ] is finitely presented is given.

background: to determine whether using mechanical ventilation in neonatal intensive care unit (nicu) influences motor development of low birth weight (lbw) infants and to compare their motor development with normal birth weight (nbw) infants at the age of 8 to 12 months using peabody developmental motor scale 2 (pdms-2). methods: this cross sectional study was conducted on 70 lbw infants in two...

BACKGROUND Speech problems are a common clinical feature of the 22q11.2 deletion syndrome. The objectives of this study were to inventory the speech history and current self-reported speech rating of adolescents and young adults, and examine the possible variables influencing the current speech ratings, including cleft palate, surgery, speech and language therapy, intelligence quotient, and age...

INTRODUCTION Besides dental and skeletal fluorosis, excessive fluoride intake can also affect the central nervous system without first causing the physical deformities associated with skeletal fluorosis. With the existence of widespread endemic fluorosis in India, the possible adverse effect of elevated fluoride in drinking water on the Intelligence Quotient (IQ) level of children is a potentia...

We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower affine Applications the theory include construction normal bundles for weighted submanifolds, as well pairs submanifolds with clean intersection.