$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 4 Issue 3

September 2006

Issue of Open Mathematics

Submit manuscript

Contents
Journal Overview

Open Access September 1, 2006

Left-symmetric algebras, or pre-Lie algebras in geometry and physics

Dietrich Burde

Page range: 323-357

More Download PDF

Abstract

In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs play an important role. Furthermore we study the algebraic theory of LSAs such as structure theory, radical theory, cohomology theory and the classification of simple LSAs. We also discuss applications to faithful Lie algebra representations.

Open Access September 1, 2006

The set of toric minimal log discrepancies

Florin Ambro

Page range: 358-370

More Download PDF

Abstract

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points.

Open Access September 1, 2006

Generalized Alexandroff Duplicates and CD 0(K) spaces

Mert Çaglar, Zafer Ercan, Faruk Polat

Page range: 371-375

More Download PDF

Abstract

We define and investigateCD Σ,Γ(K, E)-type spaces, which generalizeCD 0-type Banach lattices introduced in [1]. We state that the space CD Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].

Open Access September 1, 2006

Non functorial cylinders in a model category

J. García-Calcines, P. García-Díaz, S. Rodríguez-Machín

Page range: 376-394

More Download PDF

Abstract

Taking cylinder objects, as defined in a model category, we consider a cylinder construction in a cofibration category, which provides a reformulation of relative homotopy in the sense of Baues. Although this cylinder is not a functor we show that it verifies a list of properties which are very closed to those of an I-category (or category with a natural cylinder functor). Considering these new properties, we also give an alternative description of Baues’ relative homotopy groupoids.

Open Access September 1, 2006

On the periodicity of trigonometric functions generalized to quotient rings of R[x]

Claude Gauthier

Page range: 395-412

More Download PDF

Abstract

We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.

Open Access September 1, 2006

On presentations of Brauer-type monoids

Ganna Kudryavtseva, Volodymyr Mazorchuk

Page range: 413-434

More Download PDF

Abstract

We obtain presentations for the Brauer monoid, the partial analogue of the Brauer monoid, and for the greatest factorizable inverse submonoid of the dual symmetric inverse monoid. In all three cases we apply the same approach, based on the realization of all these monoids as Brauer-type monoids.

Open Access September 1, 2006

Accelerating the convergence of trigonometric series

Anry Nersessian, Arnak Poghosyan

Page range: 435-448

More Download PDF

Abstract

A nonlinear method of accelerating both the convergence of Fourier series and trigonometric interpolation is investigated. Asymptotic estimates of errors are derived for smooth functions. Numerical results are represented and discussed.

Open Access September 1, 2006

Local geometry of orbits for an ordinary classical lie supergroup

Tomasz Przebinda

Page range: 449-506

More Download PDF

Abstract

In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.

Open Access September 1, 2006

Duality triads of higher rank: Further properties and some examples

Matthias Schork

Page range: 507-524

More Download PDF

Abstract

It is shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line. Furthermore, some examples of duality triads of higher rank are discussed. In particular, it is shown that the generalized Stirling numbers of rank r give rise to a duality triad of rank r.

Open Access September 1, 2006

Remarks on affine complete distributive lattices

Dominic Zypen

Page range: 525-530

More Download PDF

Abstract

We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.

Open Access September 1, 2006

Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

Roman Wituła, Damian Słota

Page range: 531-546

More Download PDF

Abstract

In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.

About this journal

Open Mathematics is a fully peer-reviewed open access journal that publishes original and relevant works on topics across the full span of mathematics. The journal's primary goal is to maintain the high quality of its published content and to provide free, instant, and continued access to all content worldwide.

AIMS AND SCOPE
Open Mathematics aims to promote knowledge directly relevant to all fields of mathematics. Subject areas suitable for publication include, but are not limited to, the following:

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, and Topology.

The journal accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before its submission.