Search results for "Abstract data type"

The norm of the characteristic function of a set in the John‐Nirenberg space of exponent p

2020

Geometric rigidity of a class of fractal sets

2017

We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally spread out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Derived length and character degrees of solvable groups

2003

We prove that the derived length of a solvable group is bounded in terms of certain invariants associated to the set of character degrees and improve some of the known bounds. We also bound the derived length of a Sylow p-subgroup of a solvable group by the number of different p-parts of the character degrees of the whole group.

A characterization of the line set of an odd-dimensional Baer subspace

1990

Generalizing a theorem of Beutelspacher and Seeger, we consider line sets\(\mathcal{L}\) inP=PG(2t + 1,q),t ∈ IN, with the following properties: (1) any (t + 1)-dimensional subspace ofP contains at least one line of\(\mathcal{L}\), (2) if a pointx ofP is incident with at least two lines of\(\mathcal{L}\) then the points in the factor geometryP/x which are induced by the lines of\(\mathcal{L}\) throughx form a blocking set of type (t, 1) inP/x, (3) any line of\(\mathcal{L}\) is coplanar with at least one further line of\(\mathcal{L}\). We will show that the examples of minimal cardinality are exactly the line sets of Baer subspaces ofP.

Degrees of characters in the principal block

2021

Abstract Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G / O p ′ ( G ) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.

On finite products of soluble groups

1998

Let the finite groupG =AB be the product of two soluble subgroupsA andB, and letπ be a set of primes. We investigate under which conditions for the maximal normalπ-subgroups ofA, B andG the following holds:Oπ(G) ∩Oπ(G) ⊆Oπ(G).

Forbidden Factors and Fragment Assembly

2002

In this paper we approach the fragment assembly problem by using the notion of minimal forbidden factors introduced in previous paper. Denoting by M(w) the set of minimal forbidden factors of a word w, we first focus on the evaluation of the size of elements in M(w) and on designing of an algorithm to recover the word w from M(w). Actually we prove that for a word w randomly generated by a memoryless source with identical symbol probabilities, the maximal length m(w) of words in M(w) is logarithmic and that the reconstruction algorithm runs in linear time. These results have an interesting application to the fragment assembly problem, i.e. reconstruct a word w from a given set I of substrin…

Kontsevich–Zagier Periods

2017

We compare the set of Kontsevich–Zagier periods defined by integrals over semi-algebraic subsets of \(\mathbb {R}^n\) with cohomological periods.

On the packing sums of pairs

1993

Abstract This paper is concerned with the determination of the length of the largest interval of consecutive integers of the set hA k , where A k is a sequence of integers which is a B h -sequence.

The OptQuest Callable Library

2005

In this chapter we discuss the development and application of a library of functions that is the optimization engine for the OptQuest system. OptQuest is commercial software designed for optimizing complex systems, such as those formulated as simulation models. OptQuest has been integrated with several simulation packages with the goal of adding optimization capabilities. The optimization technology within OptQuest is based on the metaheuristic framework known as scatter search. In addition to describing the functionality of the OptQuest Callable Library (OCL) with an illustrative example, we apply it to a set of unconstrained nonlinear optimization problems.