3,358 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
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
An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
We consider the scalar wave equation in the Kerr geometry for Cauchy data
which is smooth and compactly supported outside the event horizon. We derive an
integral representation which expresses the solution as a superposition of
solutions of the radial and angular ODEs which arise in the separation of
variables. In particular, we prove completeness of the solutions of the
separated ODEs.
This integral representation is a suitable starting point for a detailed
analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction
Elevated temperature crack growth
The objective of the Elevated Temperature Crack Growth Project is to evaluate proposed nonlinear fracture mechanics methods for application to combustor liners of aircraft gas turbine engines. During the first year of this program, proposed path-independent (P-I) integrals were reviewed for such applications. Several P-I integrals were implemented into a finite-element postprocessor which was developed and verified as part of the work. Alloy 718 was selected as the analog material for use in the forthcoming experimental work. A buttonhead, single-edge notch specimen was designed and verified for use in elevated-temperature strain control testing with significant inelastic strains. A crack mouth opening displacement measurement device was developed for further use
Special Lagrangian cones with higher genus links
For every odd natural number g=2d+1 we prove the existence of a countably
infinite family of special Lagrangian cones in C^3 over a closed Riemann
surface of genus g, using a geometric PDE gluing method.Comment: 48 page
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
Problematic Internet use, mental health and impulse control in an online survey of adults
Background and aims:
Internet use has become a popular entertainment source and has become highly integrated into daily life. However, some people display problematic or addictive usage of the Internet. The present study attempts to fill current knowledge gaps regarding at-risk/problematic Internet use (ARPIU) and its relation to various health and functioning measures.
Methods:
Online survey data from 755 adults in the United States were analyzed using chi-square and ANOVAs.
Results:
The ARPIU group did not differ from the non-ARPIU group with respect to substance use. Individuals with ARPIU were, however, more likely to report at-risk/problematic engagement in video-game playing and gambling. Compared to the non-ARPIU group, the ARPIU group reported poorer self-control and higher levels of impulsivity and depression.
Conclusions:
ARPIU appears associated with other risk behaviors, particularly those that might be performed on the Internet. Future studies should examine the extent to which the Internet may promote engagement in these risk behaviors and the extent to which preventative interventions targeting better self-control or negative mood states might help a range of non-substance-related addictive behaviors
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