Search results for "bracket"
showing 10 items of 99 documents
Singular quadratic Lie superalgebras
2012
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.
Star calculus on Jacobi manifolds
2002
Abstract We study the Gerstenhaber bracket on differential forms induced by the two main examples of Jacobi manifolds: contact manifolds and l.c.s. manifolds. Moreover, we obtain explicit expressions of the generating operators and the derivations on the algebra of multivector fields. We define star operators for contact manifolds and l.c.s. manifolds and we study some of its properties.
The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations
2010
Abstract In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V k to a decreasing family of k foliations F i on a manifold M . We have shown that there exists a ( 1 , 1 ) tensor J of V k such that J k ≠ 0 , J k + 1 = 0 and we defined by L J ( V k ) the Lie Algebra of vector fields X on V k such that, for each vector field Y on V k , [ X , J Y ] = J [ X , Y ] . In this note, we study the first Chevalley–Eilenberg Cohomology Group, i.e. the quotient space of derivations of L J ( V k ) by the subspace of inner derivations, denoted by H 1 ( L J ( V k ) ) .
Some remarks concerning Nambu mechanics
1996
The structure of Nambu-Poisson brackets is studied and we establish that any Nambu tensor is decomposable. We show that every Nambu-Poisson manifold admits a local foliation by canonical Nambu-Poisson manifolds. Finally, a cohomology for Nambu (Lie) algebras which is adapted to the study of formal deformations of Nambu structures is introduced.
On a possible origin of quantum groups
1991
A Poisson bracket structure having the commutation relations of the quantum group SLq(2) is quantized by means of the Moyal star-product on C∞(ℝ2), showing that quantum groups are not exactly quantizations, but require a quantization (with another parameter) in the background. The resulting associative algebra is a strongly invariant nonlinear star-product realization of the q-algebra Uq(sl(2)). The principle of strong invariance (the requirement that the star-commutator is star-expressed, up to a phase, by the same function as its classical limit) implies essentially the uniqueness of the commutation relations of Uq(sl(2)).
Effect of saliva contamination on cementation of orthodontic brackets using different adhesive systems
2017
Background The enamel condition and the quality of surface are points that need to be considered for achieving optimal efficiency in the treatment with orthodontic brackets. The aim of this study was to assess the immediate bond strength of metallic brackets cemented to dental. Material and Methods Forty human premolars were double-sectioned, placed in PVC matrices and randomly divided into 10 groups (n=8). They received artificial saliva contamination before or after the application of adhesive systems, except for the control groups. The metallic brackets were cemented using two orthodontic cements (Transbond™ Plus Color Change, 3M Unitek e Transbond™ XT Light, 3M Unitek). The specimens we…
Effectivity comparison between three different enamel remineralizing agent postfix orthodontic treatment
2019
Background This study aims to compare the effectiveness of topical fluoride application, a toothpaste containing synthetic hydroxyapatite with one containing calcium sodium phosphosilicate (CSPS) in remineralizing enamel after the debonding process. Material and methods The study constituted experimental laboratory research incorporating posttest-only control group design. A metal bracket was placed on the buccal surface of 40 premolar teeth and immersed in artificial saliva. After 1 month, the bracket was debonded. The teeth were then randomly divided into four groups, namely (n = 6) the control group (C), the 1st treatment group (T1), the 2nd treatment group (T2), and the 3rd treatment gr…
The Influence of Friction on Design of the Type of Bracket and Its Relation to OHRQoL in Patients Who Use Multi-Bracket Appliances: A Randomized Clin…
2021
Background and objectives: The aim of this study was to evaluate the influence of friction on design of the type of bracket, patients’ perception of pain and the impact on their oral health-related quality of life. Materials and Methods: A randomized clinical trial was carried out with 90 patients (62.2% women and 37.8% men) with three kinds of fixed multi-bracket appliances: Conventional (GC), fixed multi-bracket low friction (GS) and self-ligating (GA). The VAS (Visual Analogue Scale) was used to determine pain during the first seven days of treatment at different points in time. The patients were also given the OHIP-14 (Oral Health Impact Profile) questionnaire to analyse their oral heal…
Poisson-Nijenhuis structures and the Vinogradov bracket
1994
We express the compatibility conditions that a Poisson bivector and a Nijenhuis tensor must fulfil in order to be a Poisson-Nijenhuis structure by means of a graded Lie bracket. This bracket is a generalization of Schouten and Frolicher-Nijenhuis graded Lie brackets defined on multivector fields and on vector valued differential forms respectively.
Effect of surface treatment with sandblasting and Er,Cr:YSGG laser on bonding of stainless steel orthodontic brackets to silver amalgam
2011
Objectives: Satisfactory bonding of orthodontic attachments to amalgam is a challenge for orthodontists. The aim of this in vitro study was to compare the shear bond strength of stainless steel orthodontic brackets to silver amalgam treated with sandblasting and Er,Cr:YSGG laser. Study Design: Fifty-four amalgam discs were prepared, polished and divided into three groups: In group 1 (the control group) the premolar brackets were bonded using Panavia F resin cement without any surface treatment; in groups 2 and 3, the specimens were subjected to sandblasting and Er,Cr:YSGG laser respectively, before bracket bonding. After immersing in distilled water at 37°C for 24 hours, all the specimens w…