Tom 51

2013

Data publikacji: 09.2014

Licencja: Żadna

Redakcja

Redaktor naczelny Sławomir Kołodziej

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On the rational real Jacobian conjecture

Andrew Campbell

Universitatis Iagellonicae Acta Mathematica, Tom 51, 2013, s. 7-15

Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of Rn to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational case is proved and the Galois case clarified. Two known special cases of the Strong Real Jacobian Conjecture (SRJC) are generalized to the rational map context. For an invertible map, the associated extension of rational function fields must be of odd degree and must have no nontrivial automorphisms. That disqualifies the Pinchuk counterexamples to the SRJC as candidates for invertibility.

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Remarks on the Yang:Mills flow on a compact Kahler manifolds

Tristan C. Collins, Adam Jacob

Universitatis Iagellonicae Acta Mathematica, Tom 51, 2013, s. 14-43

We study the Yang{Mills ow on a holomorphic vector bundle E over a compact Kahler manifold X. We construct a natural barrier function along the ow, and introduce some techniques to study the blow- up of the curvature along the ow. Making some technical assumptions, we show how our techniques can be used to prove that the curvature of the evolved connection is uniformly bounded away from an analytic subvariety determined by the Harder-Narasimhan-Seshadri ltration of E. We also discuss how our assumptions are related to stability in some simple cases.

2010 Mathematics Subject Classification - 53C07, 53C44

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Finitely based monoids obtained from non-finitely based semigroups

Edmond W. H. Lee

Universitatis Iagellonicae Acta Mathematica, Tom 51, 2013, s. 45-49

Presently, no example of non-finitely based finite semigroup S is known for which the monoid S¹is finitely based. Based on a general result of M. V. Volkov, two methods are established from which examples of such semigroups can be constructed.

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Asymptotic estimate of absolute projection constants

Grzegorz Lewicki

Universitatis Iagellonicae Acta Mathematica, Tom 51, 2013, s. 51-60

In this note we construct a sequence of real, k-dimensional symmetric spaces Y k satisfying lim inf k Sk = p k lim inf k (Y k; l1)= p k > max w2[0;a2] h(w) > 1=(2 p 2= ); where Sk is de ned by (4) and h(w) = a21 p 2= + 2a1 q a22 w2 + w q a22 w2 with a1 = 1=(2 p 2= ) and a2 = 1 a1. This improves the lower bound obtained in [3], Th. 5.3 by maxw2[0;a2] h(w)

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The topology on the space deltamathcal δ ε x

Hoang Nhat Quy

Universitatis Iagellonicae Acta Mathematica, Tom 51, 2013, s. 61-73

In this paper, we construct a locally convex topology on the vector space E_x. We also prove that with this topology it is a non-separable and non-re exive Frechet space.

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Słowa kluczowe: Real rational map, Jacobian conjecture, Semigroup, monoid, finitely based, Absolute projection constant, minimal projection, symmetric spaces, δ-plurisubharmonic functions, locally convex topological vector space, Frechet space

Tom 51

2013 Następne

Zawartość numeru

2013