$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 7 Issue 1

March 2009

Issue of Open Mathematics

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Contents
Journal Overview

Open Access January 10, 2009

Halphen pencils on weighted Fano threefold hypersurfaces

Ivan Cheltsov, Jihun Park

Page range: 1-45

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Abstract

On a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

Open Access January 10, 2009

Three-dimensional terminal toric flips

Osamu Fujino, Hiroshi Sato, Yukishige Takano, Hokuto Uehara

Page range: 46-53

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Abstract

We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.

Open Access January 10, 2009

Gonality for stable curves and their maps with a smooth curve as their target

Edoardo Ballico

Page range: 54-58

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Abstract

Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of with fixed topological type behaves like the stratification by gonality of M g.

Open Access January 10, 2009

SUX(r, L) is separably unirational

Georg Hein

Page range: 59-60

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Abstract

We show that the moduli space of SUX (r, L) of rank r bundles of fixed determinant L on a smooth projective curve X is separably unirational.

Open Access January 10, 2009

A version of Brauer’s theorem for integer central functions

Fedor Bogomolov, Jorge Maciel

Page range: 61-65

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Abstract

In this article we prove an effective version of the classical Brauer’s Theorem for integer class functions on finite groups.

Open Access January 10, 2009

Equational spectrum of Hilbert varieties

R. Padmanabhan, Sergiu Rudeanu

Page range: 66-72

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Abstract

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.

Open Access January 10, 2009

Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

Maria Joiţa

Page range: 73-83

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Abstract

We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].

Open Access January 10, 2009

Affine compact almost-homogeneous manifolds of cohomogeneity one

Daniel Guan

Page range: 84-123

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Abstract

This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.

Open Access January 10, 2009

On the Ricci operator of locally homogeneous Lorentzian 3-manifolds

Giovanni Calvaruso, Oldrich Kowalski

Page range: 124-139

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Abstract

We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.

Open Access January 10, 2009

On an inequality of Oprea for Lagrangian submanifolds

Franki Dillen, Johan Fastenakels

Page range: 140-144

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Abstract

We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.

Open Access January 10, 2009

On the solutions of Knizhnik-Zamolodchikov system

Lev Sakhnovich

Page range: 145-162

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Abstract

We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of the KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of the KZ system when the parameter ρ is an integer.

Open Access January 10, 2009

Erratum to “On homological classification of pomonoids by regular weak injectivity properties of S-posets”

Xia Zhang, Valdis Laan

Page range: 163-164

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Abstract

The original version of the article was published in Central European Journal of Mathematics, 2007, 5(1), 181–200, DOI: 10.2478/s11533-006-0036-3. Unfortunately, the original version of this article contains a mistake: in Theorem 5.2 only conditions (i) and (ii) (and not (iii)) are equivalent. We correct the theorem and its proof.

About this journal

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20 YEARS - 20 VOLUMES

Look back at the journal’s 20-year journey and browse its high-impact content. Visit the website

On this occasion seven papers of excellent and profound mathematics have been published to encourage reflection about further directions in the field.
See the content of the SPECIAL ISSUE ON "FUTURE DIRECTIONS OF FURTHER DEVELOPMENTS IN MATHEMATICS"　　　

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SPECIAL ISSUE PROPOSALS

If you have an idea for a prospective topical issue, please complete Special Issue proposal questionaire (in DOC), addressing your proposal to the Managing Editor (Dr. Justyna Zuk, Justyna.Zuk@degruyter.com).

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Open Mathematics is a fully peer-reviewed open access journal that publishes significant, original and relevant works on topics across the full span of mathematics. Coverage includes:

Algebra, Algebraic Geometry, Category Theory, Complex Analysis, Control Theory and Optimization, Differential Equations, Differential Geometry, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Functional Analysis, Geometry, Mathematical Logic and Foundations, Mathematical Physics, Number Theory, Numerical Analysis, Operator Theory, Probability Theory and Statistics, Real Analysis, Topology.

In order to sustain the publishing process, each article accepted for publication in Open Mathematics is subject to an Article Processing Charge of €1000. This fee is used to cover the costs of the peer-review process, professional typesetting and copyediting, as well as online hosting, long-term preservation, and extensive promotion to potential readers. There is no submission fee. Information regarding payment of the charge will be provided following acceptance for publication. Inquiries concerning Article Processing Charges should be addressed to the Managing Editor (Dr. Justyna Zuk, Justyna.Zuk@degruyter.com) before or just after submission of a manuscript.

Detailed information on　Article Processing Charges, Editorial Policy, Instructions for Authors etc. can be found as documents (in PDF) in the Supplementary Materials below. Publishing Ethics, Open Access Services at DG, FAQ for Authors and Editors etc. can be directed from External Links.