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Displaying similar documents to “On the existence of positive solutions for certain difference equations and inequalities.”

On the weak non-defectivity of veronese embeddings of projective spaces

Edoardo Ballico (2005)

Open Mathematics

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Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(nn+x). Here we prove that the order x Veronese embedding ofP n is not weakly (k−1)-defective, i.e. for a general S⊃P n such that #(S) = k+1 the projective space | I 2S (x)| of all degree t hypersurfaces ofP n singular at each point of S has dimension (n/n+x )−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I 2S (x)| has an ordinary double point at each P∈ S and Sing (F)=S.

Support prices for weakly maximal programs of a growth model with uncertainty

Nikolaos S. Papageorgiou (1994)

Commentationes Mathematicae Universitatis Carolinae

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We consider an infinite dimensional, nonstationary growth model with uncertainty. Using techniques from functional analysis and the subdifferentiation theory of concave functions, we establish the existence of a supporting price system for a weakly maximal program.

The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm

Richard Laver, Sheila Miller (2013)

Open Mathematics

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The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the...