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Throughout this paper we consider smooth maps of positive codimensions, having only stable singularities (see [Ar2], §1.4 in Chapter 1). We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory for this type of singular maps.. These spaces are: 1) Kazarian’s space (generalising Vassiliev’s algebraic complex and)… (More)
In this talk we give a survey of older results and some new results about the following question: what type of polyhedra can be inscribed or circumscribed to convex bodies in Rn. 1991 Mathematics Subject Classification. Primary: 52A15; Secondary: 55Mxx.
We show that for a given planar convex set K of positive area there exist three pairwise internally disjoint convex sets whose union is K such that they have equal area and equal perimeter. © 2009 Elsevier Inc. All rights reserved.
The thesis consists of two parts. In the first part we study two graph transformations,<lb>namely the Kelmans transformation and the generalized tree shift. In the second part of this<lb>thesis we study an extremal graph theoretic problem and its relationship with algebraic graph<lb>theory. The main results of this thesis are the following. • We show that… (More)
A generic smooth map of a closed 2k-manifold into (3k− 1)-space has a finite number of cusps (Σ-singularities). We determine the possible numbers of cusps of such maps. A fold map is a map with singular set consisting of only fold singularities (Σsingularities). Two fold maps are fold bordant if there are cobordisms between their sourceand target manifolds… (More)
Autotransplantation is currently regarded as the optimal skin replacement method, sufficient donor site, however, is often not available in extensively burned patients. Intensive research and development of skin replacement products is conducted worldwide in order to decrease the size of the required donor site. Short- and long-term wound coverage is made… (More)
The thesis addresses problems from the field of geometric measure theory. It turns out<lb>that discrete methods can be used efficiently to solve these problems. Let us summarize<lb>the main results of the thesis.<lb>In Chapter 2 we investigate the following question proposed by Tamás Keleti. How<lb>large (in terms of Hausdorff dimension) can a compact set A… (More)