Search results for "Mathematica"
showing 10 items of 7971 documents
Kollineationen und Schliessungssätze für Ebene Faserungen
1979
Every affine central collineation of a translation plane π induces a special collineation of the projective space π spanned by the spreadF belonging to π. Here the relations between these special collineations of π and certain incidence propositions inF are investigated; so new proofs are given for some characterisations of (A,B)-regular spreads included in [7].
Kontsevich formality and cohomologies for graphs
2004
A formality on a manifold M is a quasi isomorphism between the space of polyvector fields (Tpoly(M)) and the space of multidifferential operators (Dpoly(M)). In the case M=R d , such a mapping was explicitly built by Kontsevich, using graphs drawn in configuration spaces. Looking for such a construction step by step, we have to consider several cohomologies (Hochschild, Chevalley, and Harrison and Chevalley) for mappings defined on Tpoly. Restricting ourselves to the case of mappings defined with graphs, we determine the corresponding coboundary operators directly on the spaces of graphs. The last cohomology vanishes.
Nonlocalization Properties of Time Operators Transformations
2014
It is presented a general approach to the problem of extension of time operators and the associated Lambda transformations on singular measures. It is also shown that Lambda transformations defined on function spaces having the Urysohn property are non localized. Particular attention has been devoted to time and Lambda operators associated with the Walsh-Paley system and to a characterization of their domain and non locality.
Star-products and phase space realizations of quantum groups
1992
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
Some Problems on Homomorphisms and Real Function Algebras
2001
In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra.
Generalised Deformations, Koszul Resolutions, Moyal Products
1998
We generalise Gerstenhaber's theory of deformations, by dropping the assumption that the deformation parameter should commute with the elements of the original algebra. We give the associated cohomology and construct a Koszul resolution for the polynomial algebra [Formula: see text] in the "homogeneous" case. We then develop examples in the case of [Formula: see text] and find some Moyal-like products of a new type. Finally, we show that, for any field K, matrix algebras with coefficients in K and finite degree extensions of K are rigid, as in the commutative case.
Star representations of E(2)
1990
We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.
Arithmetic Problems Formulation and Working Memory Load
1987
First, third, and fifth graders (French children in American-numbered grades) were asked to solve arithmetic problems in which an initial state was modified by two successive transformations. Three independent variables were manipulated systematically. First, the unknown state was either the final state (Sl) or the initial state (S2). Second, either the known state (01) or the transformations (02) appeared in the first place in the problem wording. Third, the question was either located at the end (Ql) or at the beginning (42) of the problem text. As anticipated, these modifications strongly affected the performances at every age: S1 appears clearly easier than S2; 0 1 leads to a better per…