6,876 research outputs found
The domestic dog: man's best friend in the genomic era
The domestic dog genome - shaped by domestication, adaptation to human-dominated environments and artificial selection - encodes tremendous phenotypic diversity. Recent developments have improved our understanding of the genetics underlying this diversity, unleashing the dog as an important model organism for complex-trait analysis
No news for Kerr-Schild fields
Algebraically special fields with no gravitational radiation are described.
Kerr-Schild fields, which include as a concrete case the Kinnersley photon
rocket, form an important subclass of them.Comment: 4 pages, Revtex
Invariants of Triangular Lie Algebras
Triangular Lie algebras are the Lie algebras which can be faithfully
represented by triangular matrices of any finite size over the real/complex
number field. In the paper invariants ('generalized Casimir operators') are
found for three classes of Lie algebras, namely those which are either strictly
or non-strictly triangular, and for so-called special upper triangular Lie
algebras. Algebraic algorithm of [J. Phys. A: Math. Gen., 2006, V.39, 5749;
math-ph/0602046], developed further in [J. Phys. A: Math. Theor., 2007, V.40,
113; math-ph/0606045], is used to determine the invariants. A conjecture of [J.
Phys. A: Math. Gen., 2001, V.34, 9085], concerning the number of independent
invariants and their form, is corroborated.Comment: LaTeX2e, 16 pages; misprints are corrected, some proofs are extende
The Confinement Property in SU(3) Gauge Theory
We study confinement property of pure SU(3) gauge theory, combining in this
effort the non-perturbative gluon and ghost propagators obtained as solutions
of Dyson--Schwinger equations with solutions of an integral ladder diagram
summation type equation for the Wilson loop. We obtain the string potential and
effective UV coupling.Comment: 7 pages, 7 figures, v2: references added, discussion reorganize
Computation of Invariants of Lie Algebras by Means of Moving Frames
A new purely algebraic algorithm is presented for computation of invariants
(generalized Casimir operators) of Lie algebras. It uses the Cartan's method of
moving frames and the knowledge of the group of inner automorphisms of each Lie
algebra. The algorithm is applied, in particular, to computation of invariants
of real low-dimensional Lie algebras. A number of examples are calculated to
illustrate its effectiveness and to make a comparison with the same cases in
the literature. Bases of invariants of the real solvable Lie algebras up to
dimension five, the real six-dimensional nilpotent Lie algebras and the real
six-dimensional solvable Lie algebras with four-dimensional nilradicals are
newly calculated and listed in tables.Comment: 17 pages, extended versio
Invariants of Lie Algebras with Fixed Structure of Nilradicals
An algebraic algorithm is developed for computation of invariants
('generalized Casimir operators') of general Lie algebras over the real or
complex number field. Its main tools are the Cartan's method of moving frames
and the knowledge of the group of inner automorphisms of each Lie algebra.
Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006,
V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras,
here the effectiveness of the algorithm is demonstrated by its application to
computation of invariants of solvable Lie algebras of general dimension
restricted only by a required structure of the nilradical.
Specifically, invariants are calculated here for families of real/complex
solvable Lie algebras. These families contain, with only a few exceptions, all
the solvable Lie algebras of specific dimensions, for whom the invariants are
found in the literature.Comment: LaTeX2e, 19 page
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional
maximal Abelian ideal). We find that for given n such a solvable algebra is
unique up to isomorphisms. Using the method of moving frames we construct a
basis for the Casimir invariants of the nilradical n_(n,2). We also construct a
basis for the generalized Casimir invariants of its solvable extension s_(n+1)
consisting entirely of rational functions of the chosen invariants of the
nilradical.Comment: 19 pages; added references, changes mainly in introduction and
conclusions, typos corrected; submitted to J. Phys. A, version to be
publishe
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