4,703 research outputs found
Representations of hom-Lie algebras
In this paper, we study representations of hom-Lie algebras. In particular,
the adjoint representation and the trivial representation of hom-Lie algebras
are studied in detail. Derivations, deformations, central extensions and
derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used,
Algebra and Representation Theory, 15 (6) (2012), 1081-109
Hom-quantum groups I: quasi-triangular Hom-bialgebras
We introduce a Hom-type generalization of quantum groups, called
quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative
analogues of Drinfel'd's quasi-triangular bialgebras, in which the
non-(co)associativity is controlled by a twisting map. A family of
quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular
bialgebra, such as Drinfel'd's quantum enveloping algebras. Each
quasi-triangular Hom-bialgebra comes with a solution of the quantum
Hom-Yang-Baxter equation, which is a non-associative version of the quantum
Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained
from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page
Higher cyclic operads
We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees . We prove a nerve theorem exhibiting colored cyclic operads as presheaves on which satisfy a Segal condition. Finally, we produce a Quillen model category whose fibrant objects satisfy a weak Segal condition, and we consider these objects as an up-to-homotopy generalization of the concept of cyclic operad
The Electrochemical Oxidation of Organic Selenides and Selenoxides
The electrochemical oxidation of alkyl and aryl selenides was investigated in acetonitrile. The oxidation of diphenyl selenide and di(4‐methylphenyl) selenide led primarily to the formation of their respective selenoxides, which were identified by exhaustive coulometric oxidation and and analysis of the products. The selenoxide itself was not observed in the cyclic voltammetry of the selenide for two reasons: first, the protonation of the selenoxide by the acid formed from the reaction of water with the cation radical and second, the formation of a selenoxide hydrate. The formation of the hydrate with diphenyl selenoxide was verified by isolation of the dimethoxy derivative. In addition to the selenoxide, selenonium compounds, formed by the coupling of the oxidized material, were also observed. The alkyl selenides were generally oxidized at a lower potential than the aryl selenides. This trend is different from the sulfur analogues, where the aryl sulfides are easier to oxidize than their alkyl counterparts. As a result, the difference in their redox potentials is relatively small. These differences may occur because the oxidation of aryl sulfides is more likely to take place on the aromatic ring, which leads to a greater yield of the coupled products (about 100%) when compared to the selenide analogue
Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept
[[abstract]]Using conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yang et al.'s simplified geometric stiffness matrix [kg]12×12 of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14 of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14 matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14 matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]GB
Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from
n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns
out that the implications of the compatibility conditions, that are necessary
for this construction, can be understood in terms of the kernel of the trace
function and the range of the twisting maps. Furthermore, we investigate the
possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form
satisfying certain conditions
Positivity of Quasilocal Mass
Motivated by the important work of Brown adn York on quasilocal energy, we
propose definitions of quasilocal energy and momentum surface energy of a
spacelike 2-surface with positive intrinsic curvature in a spacetime. We show
that the quasilocal energy of the boundary of a compact spacelike hypersurface
which satisfies the local energy condition is strictly positive unless the
spacetime is flat along the spacelike hypersurface.Comment: 4 pages; final published versio
Deformation of dual Leibniz algebra morphisms
An algebraic deformation theory of morphisms of dual Leibniz algebras is
obtained.Comment: 10 pages. To appear in Communications in Algebr
Exploring the potential function of dimethylsulfoniopropionate and its by-product acrylate within the coral holobiont
Geoffrey Yau studied the potential function of dimethylsulfoniopropionate (DMSP) and acrylate in coral recruits. He found hosting Symbiodiniaceae enhanced Acropora growth and DMSP level. This study provided fundamental understanding of DMSP production in coral recruits and highlights the potential function of DMSP and acrylate in coral calcification
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