Search results for "Quotient"

Correction parameters in X-ray fluorescence analysis applying the limit dilution method (LDM)

1992

This paper is a study of the interelemental effect and its correction based on the mathematical model used to develop LDM in XRF analysis. A “compensation coefficient” is defined which is obtained from the quotient of the mass absorption coefficients of the problem and the standard (μs*/μp*). This coefficient compensates the effects produced by interactions between the analyt and the interferences and therefore acts as a correction factor for the interelemental effect within this theoretical model. The model itself establishes a simple relation of the “compensation coefficient” and the Y/H correction parameters for the unknown and the standard. An algorithm is proposed for calculating the “…

On the classification of Kim and Kostrikin manifolds

2006

International audience; We completely classify the topological and geometric structures of some series of closed connected orientable 3-manifolds introduced by Kim and Kostrikin in [20, 21] as quotient spaces of certain polyhedral 3-cells by pairwise identifications of their boundary faces. Then we study further classes of closed orientable 3-manifolds arising from similar polyhedral schemata, and describe their topological properties.

HOMFLY-PT skein module of singular links in the three-sphere

2012

For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in 𝕊3. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in 𝕊3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.

Compressed Drinfeld associators

2004

Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.

Finite index subgroups of mapping class groups

2011

Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n is 2g−1(2g − 1). AMS Subject Classification. Primary: 57M99. Secondary: 20G40, 20E28. 0 Introduction and statement of results The interaction between mapping class groups and finite groups has long been a topic of interest. The famous Hurwitz bound of 1893 showed that the mapping class group of a clo…

Rational solutions to the mKdV equation associated to particular polynomials

2021

International audience; Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.

The mKdV equation and multi-parameters rational solutions

2021

Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .

A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups

2018

Sensitivity and Specificity of Stability Criteria for Immediately Loaded Splinted Maxillary Implants

2014

Background To assess the suitability of dental implants for immediate loading, primary stability is usually evaluated intraoperatively. Purpose This retrospective study aimed to assess the suitability of three stability parameters – namely, insertion torque (IT), implant stability quotient (ISQ; measured by resonance frequency analysis), and Periotest (PT) values – as potential predictors for the risk of nonosseointegration of immediately loaded splinted implants. The stability parameters were routinely collected under immediate loading. Materials and Methods Nineteen patients with 11 edentulous and 8 partially edentulous maxillae were treated with 105 dental implants, which were immediatel…

PREMORBID ADJUSTMENT AND CANNABIS USE IN FIRST-EPISODE-PSYCHOSIS PATIENTS. A CROSS-EUROPEAN CASE-CONTROL STUDY

The harmful effects of cannabis use and possible neuropsychological impairment associated with its use are a contentious topic of debate in both research and public health,as is thefact that cannabis use has been repeatedly shown to be a risk factor for the development of psychosis. Surprisingly, three different meta-analyses on cognition and cannabis, among schizophrenic patients, found better cognitive performance in patients with a lifetime use of cannabis (Potvin, Joyal, Pelletier, & Stip, 2008; Rabin, Zakzanis, & George, 2011; Yücel et al., 2012). This counterintuitive finding, coupled with the fact that most psychotic patients suffer from cognitive impairment (Reichenberg et al., 2009…