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1
Content available remote

A simple proof of a result of Abramovich and Wickstead

100%
Ercan Z.
Open Mathematics
|
2005
|
tom 3
|
nr 2
242-244
EN
The paper presents a simple proof of Proposition 8 of [2], based on a new and simple description of isometries between CD 0-spaces.
2
Content available remote

Rigidity and flexibility of virtual polytopes

86%
Panina G.
Open Mathematics
|
2003
|
tom 1
|
nr 2
157-168
EN
All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.
3
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Quasilinearization for the periodic boundary value problem for hybrid differential equation

72%
Hall L., Hristova S.
Open Mathematics
|
2004
|
tom 2
|
nr 2
250-259
EN
The method of quasilinearization for a periodic boundary value problem for nonlinear hybrid differential equations is studied. It is shown that the convergence is quadratic.
4
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Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold

58%
Toda M.
Open Mathematics
|
2004
|
tom 2
|
nr 2
218-249
EN
The paper studies the first homology of finite regular branched coverings of a universal Borromean orbifold called B 4,4,4ℍ3. We investigate the irreducible components of the first homology as a representation space of the finite covering transformation group G. This gives information on the first betti number of finite coverings of general 3-manifolds by the universality of B 4,4,4. The main result of the paper is a criterion in terms of the irreducible character whether a given irreducible representation of G is an irreducible component of the first homology when G admits certain symmetries. As a special case of the motivating argument the criterion is applied to principal congruence subgroups of B 4,4,4. The group theoretic computation shows that most of the, possibly nonprincipal, congruence subgroups are of positive first Betti number.
5
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On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms

58%
Tyszkowska E.
Open Mathematics
|
2003
|
tom 1
|
nr 2
208-220
EN
The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain result of Macbeath, that such surfaces admit a symmetry which we shall call in this paper the Macbeath-Singerman symmetry. A classical theorem by Harnack states that the set of fixed points of a symmetry of a Riemann surface X of genus g consists of k disjoint Jordan curves called ovals for some k ranging between 0 and g+1. In this paper we show that given an odd prime p, a Macbetah-Singerman symmetry of Belyi surface with PSL(2,p) as a group of automorphisms has at most
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