3,741 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
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
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
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
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
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
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
In this paper we construct ternary -Virasoro-Witt algebras which
-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie
and Zachos using enveloping algebra techniques. The ternary
Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a
parameter and are not Nambu-Lie algebras for all but finitely many values of
this parameter. For the parameter values for which the ternary Virasoro-Witt
algebras are Nambu-Lie, the corresponding ternary -Virasoro-Witt algebras
constructed in this article are also Hom-Nambu-Lie because they are obtained
from the ternary Nambu-Lie algebras using the composition method. For other
parameter values this composition method does not yield Hom-Nambu Lie algebra
structure for -Virasoro-Witt algebras. We show however, using a different
construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and
Zachos, as well as the general ternary -Virasoro-Witt algebras we construct,
carry a structure of ternary Hom-Nambu-Lie algebra for all values of the
involved parameters
Spintronic single qubit gate based on a quantum ring with spin-orbit interaction
In a quantum ring connected with two external leads the spin properties of an
incoming electron are modified by the spin-orbit interaction resulting in a
transformation of the qubit state carried by the spin. The ring acts as a one
qubit spintronic quantum gate whose properties can be varied by tuning the
Rashba parameter of the spin-orbit interaction, by changing the relative
position of the junctions, as well as by the size of the ring. We show that a
large class of unitary transformations can be attained with already one ring --
or a few rings in series -- including the important cases of the Z, X, and
Hadamard gates. By choosing appropriate parameters the spin transformations can
be made unitary, which corresponds to lossless gates.Comment: 4 pages, 4 figure
Enhanced hippocampal long-term potentiation and spatial learning in aged 11ß-hydroxysteroid dehydrogenase type 1 knock-out mice
Glucocorticoids are pivotal in the maintenance of memory and cognitive functions as well as other essential physiological processes including energy metabolism, stress responses, and cell proliferation. Normal aging in both rodents and humans is often characterized by elevated glucocorticoid levels that correlate with hippocampus-dependent memory impairments. 11ß-Hydroxysteroid dehydrogenase type 1 (11ß-HSD1) amplifies local intracellular ("intracrine") glucocorticoid action; in the brain it is highly expressed in the hippocampus. We investigated whether the impact of 11ß-HSD1 deficiency in knock-out mice (congenic on C57BL/6J strain) on cognitive function with aging reflects direct CNS or indirect effects of altered peripheral insulin-glucose metabolism. Spatial learning and memory was enhanced in 12 month "middle-aged" and 24 month "aged" 11ß-HSD1<sup>–/–</sup> mice compared with age-matched congenic controls. These effects were not caused by alterations in other cognitive (working memory in a spontaneous alternation task) or affective domains (anxiety-related behaviors), to changes in plasma corticosterone or glucose levels, or to altered age-related pathologies in 11ß-HSD1<sup>–/–</sup> mice. Young 11ß-HSD1<sup>–/–</sup> mice showed significantly increased newborn cell proliferation in the dentate gyrus, but this was not maintained into aging. Long-term potentiation was significantly enhanced in subfield CA1 of hippocampal slices from aged 11ß-HSD1<sup>–/–</sup> mice. These data suggest that 11ß-HSD1 deficiency enhances synaptic potentiation in the aged hippocampus and this may underlie the better maintenance of learning and memory with aging, which occurs in the absence of increased neurogenesis
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