66 research outputs found
Optical measurement methods in thermogasdynamics
A review is presented of a number of optical methods of flow measurements. Consideration is given to such spectroscopic methods as emission and absorption techniques, electron beam-stimulated fluorescence, and light scattering - Rayleigh, Raman and Mie - methods. The following visualization methods are also discussed: shadow photography, schlieren photography, interferometry, holographic interferometry, laser anemometry, particle holography, and electron-excitation imaging. A large bibliography is presented and the work is copiously illustrated with figures and photographs
Non-solvable contractions of semisimple Lie algebras in low dimension
The problem of non-solvable contractions of Lie algebras is analyzed. By
means of a stability theorem, the problem is shown to be deeply related to the
embeddings among semisimple Lie algebras and the resulting branching rules for
representations. With this procedure, we determine all deformations of
indecomposable Lie algebras having a nontrivial Levi decomposition onto
semisimple Lie algebras of dimension , and obtain the non-solvable
contractions of the latter class of algebras.Comment: 21 pages. 2 Tables, 2 figure
Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras
We show that the In\"on\"u-Wigner contraction naturally associated to a
reduction chain of semisimple Lie algebras
induces a decomposition of the Casimir operators into homogeneous polynomials,
the terms of which can be used to obtain additional mutually commuting missing
label operators for this reduction. The adjunction of these scalars that are no
more invariants of the contraction allow to solve the missing label problem for
those reductions where the contraction provides an insufficient number of
labelling operators
On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras
We establish an improved upper estimate on dimension of any solvable algebra
s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we
consider Levi decomposable algebras with a given nilradical n and investigate
restrictions on possible Levi factors originating from the structure of
characteristic ideals of n. We present a new perspective on Turkowski's
classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased;
author's version of the published pape
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
The partially alternating ternary sum in an associative dialgebra
The alternating ternary sum in an associative algebra, , gives rise to the partially alternating ternary sum in an
associative dialgebra with products and by making the
argument the center of each term: . We use computer algebra to determine the polynomial identities in
degree satisfied by this new trilinear operation. In degrees 3 and 5 we
obtain and ; these identities define a new variety of partially alternating ternary
algebras. We show that there is a 49-dimensional space of multilinear
identities in degree 7, and we find equivalent nonlinear identities. We use the
representation theory of the symmetric group to show that there are no new
identities in degree 9.Comment: 14 page
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