Search results for "Filter"

The graded identities of upper triangular matrices of size two

2002

AbstractLet UT2 be the algebra of 2×2 upper triangular matrices over a field F. We first classify all possible gradings on UT2 by a group G. It turns out that, up to isomorphism, there is only one non-trivial grading and we study all the graded polynomial identities for such algebra. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally establish a result concerning the rate of growth of the identities for such algebra by proving that its sequence of graded codimensions has almost polynomial growth.

An extension of the algebra of sets

1973

We shall explain the aim which leads us in the construction of an extended system of the algebra of sets1. The symbol 1. {*:?(*)} denoting the set of these and only these elements of domain of the variable x which satisfy the propositional condition (propositional function or form) ?9 (x)" is in com? mon use nowadays, so that it is adopted in school courses of mathematics in many countries, and in Poland as well. This condition will be said to define the set 1. However, if we admit propositional conditions which are meaningless for some values of their variables then we encounter some difficulties connected with the ex? pression 1. The formulae 2. {x : 9 (*)} = {x : 9 (*)}' 3. {x : 9 (s) v …

POLYNOMIAL IDENTITIES ON SUPERALGEBRAS AND ALMOST POLYNOMIAL GROWTH

2001

Let A be a superalgebra over a field of characteristic zero. In this paper we investigate the graded polynomial identities of A through the asymptotic behavior of a numerical sequence called the sequence of graded codimensions of A. Our main result says that such sequence is polynomially bounded if and only if the variety of superalgebras generated by A does not contain a list of five superalgebras consisting of a 2-dimensional algebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and nontrivial gradings. Our main tool is the representation theory of the symmetric group.

Graded polynomial identities and Specht property of the Lie algebrasl2

2013

Abstract Let G be a group. The Lie algebra sl 2 of 2 × 2 traceless matrices over a field K can be endowed up to isomorphism, with three distinct non-trivial G-gradings induced by the groups Z 2 , Z 2 × Z 2 and Z . It has been recently shown (Koshlukov, 2008 [8] ) that for each grading the ideal of G-graded identities has a finite basis. In this paper we prove that when char ( K ) = 0 , the algebra sl 2 endowed with each of the above three gradings has an ideal of graded identities Id G ( sl 2 ) satisfying the Specht property, i.e., every ideal of graded identities containing Id G ( sl 2 ) is finitely based.

The Virasoro Algebra

1989

In this chapter we shall study the Lie algebra Vect S1 of vector fields on a circle and some of its generalizations. The Lie algebra Vect S1 has a central extension, the Virasoro algebra. The representation theory of the Virasoro algebra is closely related to the representation theory of affine Lie algebras. In fact, through the Sugawara construction, to be defined below, a highest weight representation of an affine Lie algebra carries always a highest weight representation of the Virasoro algebra. All the irreducible highest weight representations of the Virasoro algebra are known and they can be exponentiated to representations of associated infinite-dimensional Lie groups. The representa…

The Bohm-Aharonov effect: A seven-dimensional structural group

1996

We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys.1 (1976), 155–163.

The Representation Type of the Centre of a Group Algebra

1986

Sintonika un presbiopija

2017

Pēdējos gados sintonika kā metode ir kļuvusi pieejamāka un pielietojamāka redzes uztveres optometristu vidū. Metodi pielieto, lai sabalansētu simpātisko un parasimpātisko nervu sistēmu saskaņotu darbību, pielietojot dažādu krāsu filtrus. Darba mērķis bija novērtēt sintonikā pielietoto filtru iespējas sākotnējas presbiopijas ārstēšanai. Darbā tiek analizēti pacientu dati par sintonikas iedarbības efektivitāti sākotnējās presbiopijas gadījumos. Redzes asums, bet novērtējot to bez tuvuma aditīva, akomodācijas amplitūda un zīlītes α-ω mērījumi uzrāda statistiski nozīmīgi atšķirīgus rezultātus pirms un pēc sintonikas pielietošanas. Ietekme ir arī uz formas redzes funkcionālo lauku, kā arī uz fun…

Propriétés spectrales des filtres usuels en économie : désaisonnalisation par CENSUS XII, et différences d'ordre d

1985

This study concerns the efficiency of usual statistical filters in economics to reduce the tendencial and seasonal components : the moving average processes of CENSUS Xll seasonal adjustment method and the difference sof d order early proposed by BOX-JENKINS. We are herein using the spectral and cospectral analyses to know whether the other components keep stable in the filtering process and whether the leads and lags found on the basis of the initial original data are kept after these filtering processes. One application illustrates the problems by means of monthly indicators that are highly representative of French economic evolution from 1963 up to 1982.This theoretical and empirical res…

Foetal ECG recovery using dynamic neural networks

2002

Non-invasive electrocardiography has proven to be a very interesting method for obtaining information about the foetus state and thus to assure its well-being during pregnancy. One of the main applications in this field is foetal electrocardiogram (ECG) recovery by means of automatic methods. Evident problems found in the literature are the limited number of available registers, the lack of performance indicators, and the limited use of non-linear adaptive methods. In order to circumvent these problems, we first introduce the generation of synthetic registers and discuss the influence of different kinds of noise to the modelling. Second, a method which is based on numerical (correlation coe…