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Smooth Stable Maps of Discriminant Varieties
Proceedings of the London Mathematical Society, 1985In this series of papers (see also the two following reviews) we classify certain smooth stable maps and then give a number of applications of the classification. Let \(\Delta\), \(O\subset R^ k\), O denote the germ of the discriminant variety of a singularity of type \(A_ k\) at the origin 0. In Commun. Pure Appl. Math.
Bruce, J.W., Giblin, P.J.
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Imperfect Price Discrimination and Variety
The Journal of Business, 1983In many environments a monopolist can price discriminate even though consumers can select any option offered by the firm. Though consumers seem indistinguishable to the firm, the monopolist can discriminate by exploiting its knowledge of the joint distribution of agents' characteristics (in this paper, locations and reservation prices) to offer the ...
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Discriminator polynomials and arithmetical varieties
Algebra Universalis, 1985The author proves the following theorem: Given a locally finite semisimple arithmetical variety. For each natural number n there exists a term \(t_ n(x,y,z,u_ 1,...,u_ n)\) such that in any n-generated simple algebra, with generators \(s_ 1,...,s_ n\) the polynomial \(t_ n(x,y,z,s_ 1,...,s_ n)\) is a discriminator polynomial. A corollary of this is the
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Compact algebras in discriminator varieties
Algebra Universalis, 1993It is proved that the compact members of a discriminator variety of topological algebras are precisely the products of finite simple algebras.
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Stable mappings of discriminant varieties
Mathematical Proceedings of the Cambridge Philosophical Society, 1988Smooth mappings defined on discriminant varieties of -versal unfoldings of isolated singularities arise in many interesting geometrical contexts, for example when classifying outlines of smooth surfaces in ℝ3 and their duals, or wave-front evolution [1, 2, 5]. In three previous papers we have classified various stable mappings on discriminants.
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Free algebras in discriminator varieties
Algebra Universalis, 1995The main result of this paper is the representation of the free algebras of a certain class of discriminator varieties, called \({\mathcal M}\)-spectral varieties by the author, as certain Boolean products. \({\mathcal M}\)-spectral varieties are defined as follows: If \({\mathcal L}\) is a language of algebras, \({\mathcal M}\) a class of \({\mathcal ...
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Vector Fields on Discriminants and Bifurcation Varieties
Bulletin of the London Mathematical Society, 1985Let f: (\({\mathbb{C}}^ n,0)\to ({\mathbb{C}},0)\) be a holomorphic map germ and B the associated full bifurcation variety. One knows that B is a hypersurface germ, and a result of \textit{H. Terao} in Math. Ann. 263, 313- 321 (1983; Zbl 0497.32016) states that the module of logarithmic vector fields tangent to B is free over the ring of holomorphic ...
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The word problem for discriminator varieties
Siberian Mathematical Journal, 1992See the review in Zbl 0756.08004.
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Dual discriminator subvarieties of a variety
Algebra Universalis, 1995The dual discriminator function \(d(x,y,z)\) on a set \(A\) is defined as \(d (a, b, c) = a\) if \(a = b\) and \(d(a,b,c) = c\) if \(a \neq b\). Let \(q(x,y,z)\) be a term of a variety \({\mathcal V}\) of algebras. Then the subvariety \({\mathcal X}\) of \({\mathcal V}\) generated by all algebras in \({\mathcal V}\) where \(q(x,y,z)\) yields the dual ...
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Children’s emerging ability to discriminate L1-varieties
First Language, 2018Children in Austria are exposed to a large amount of variation within the German language. Most children grow up with a local dialect, German standard language and ‘intermediate’ varieties summarized as ‘Umgangssprache’. Using an ABX design, this study analyses when Austrian children are able to discriminate native varieties of their L1 German ...
Irmtraud Kaiser, Gudrun Kasberger
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