Jürg Schmid

Quasiorders and Sublattices of Distributive Lattices

We study the lattice of all (0,1)-sublattices of a distributive lattice L, using certain compatible quasiorders on the Priestley space of L as our principal tool. Special emphasis is put on the case of finite L, where epic sublattices, Frattini sublattices and covers are considered in some detail. We hope to demonstrate that quasiorders may serve as a concept suitable to unify the many different representations of sublattices of L which are found in the literature.

Maximal sublattices of finite distributive lattices

Algebraic properties of lattices of quotients of finite posets are considered. Using the known duality between the category of all finite posets together with all order-preserving maps and the category of all finite distributive (0, 1)-lattices together with all (0, 1)-lattice homomorphisms, algebraic and arithmetic properties of maximal proper sublattices and, in particular, Frattini sublattices of finite distributive (0, 1)-lattices are thereby obtained.

Deciding Frattini is NP-complete

We show that it is a NP-complete problem to decide whether a finite poset arises as the (Birkhoff) dual of the Frattini sublattice of some finite distributive lattice.

Identität im Hochleistungssport

Zusammenfassung. Die Athletic Identity Measurement Scale (Brewer, Van Raalte & Linder, 1993) ist ein Fragebogen zur Erfassung der athletischen Identitat. In diesem Artikel wird die psychometrische Qualitat einer deutschsprachigen Adaptation der AIMS (AIMS-D) an einer Stichprobe von Hochleistungssportlern (N = 610) untersucht. In konfirmatorischen Faktorenanalysen zeigt sich Evidenz fur eine Struktur mit drei korrelierten Faktoren erster Ordnung und einem Faktor zweiter Ordnung (Athletische Identitat). In Einklang mit der Literatur korrespondiert ein hohes Mas an athletischer Identitat mit den Merkmalen Trainingsaufwand, gesellschaftliche Bedeutung einer Sportart und Diversitat der Rollenstruktur. AIMS-D-Scores variieren uber die Laufbahnphasen, und Beziehungen zu den funf grosen Personlichkeitsfaktoren und dem Selbstwert sind kaum zu finden. Es wird gefolgert, dass die AIMS-D ein brauchbares Forschungsinstrument zur Messung der athletischen Identitat ist.

Die Bedeutung von Wohlbefinden im Zusammenhang zwischen Sportengagement und Gewaltverhalten bei Jugendlichen

Zusammenfassung. Obschon normative Erwartungen an Sport als Freizeitbeschaftigung mit gewaltpraventiver Wirkung immer wieder postuliert werden, sind empirische Befunde zum Zusammenhang zwischen Sport und Gewalt inkonsistent. Einhellig werden jedoch positive Auswirkungen des Sporttreibens auf das Wohlbefinden berichtet, ebenso wie negative Assoziationen zwischen Wohlbefinden und Gewaltverhalten. Vor einem sozialisations- und stresstheoretischen Hintergrund wird in der vorliegenden querschnittlichen Befragung von 1664 Schweizer Jugendlichen im Alter von 12 bis 18 Jahren die Annahme gepruft, ob ein indirekter Zusammenhang zwischen Sportengagement und Gewaltverhalten besteht, der durch das Wohlbefinden vermittelt wird. Die mit Strukturgleichungsmodellen gewonnenen Ergebnisse liefern schwache Unterstutzung fur diese Annahme. Allerdings sind die Pfadkoeffizienten klein (Sport – Wohlbefinden: β = .39; Wohlbefinden – Gewaltverhalten: β = −.13) und der indirekte Effekt entsprechend gering (−.05). Es wird gefolgert...

Formal concept analysis : 4th international conference, ICFCA 2006, Dresden, Germany, February 13-17, 2006 : proceedings

ThisvolumecontainsselectedpapersofICFCA2006,the4thInternationalC- ference on Formal Concept Analysis. The ICFCA conference series aims to be the prime forum for the publication of advances in applied lattice and order theory and in particular scienti?c advances related to formal concept analysis. Formalconceptanalysisis a?eldofappliedmathematics withitsmathema- calrootinordertheory,inparticularthetheoryofcompletelattices.Researchers had long been aware of the fact that these ?elds have many potential appli- tions. Formal concept analysis emerged in the 1980s from e?orts to restructure lattice theory to promote better communication between lattice theorists and potential users of lattice theory. The key theme was the mathematical form- ization of concept and conceptual hierarchy. Since then, the ?eld has developed into a growing research area in its own right with a thriving theoretical com- nity and an increasing number of applications in data and knowledge processing including data visualization, information retrieval, machine learning, data an- ysis and knowledge management. ICFCA2006re?ectedbothpracticalbene?tsandprogressinthefoundational theory of formal concept analysis. This volume contains four lecture notes from invited speakers and 17 regular papers, among them one position paper. All regular papers appearing in these proceedings were refereed by at least two, in most cases three independent reviewers. The ?nal decision to accept the papers was arbitrated by the Program Chairs based on the referee reports

Bialgebraic contexts for distributive lattices – revisited

In [8], Vogt used so-called bialgebraic contexts to represent the lattice Sub(L) of all sublattices of a finite distributive lattice L as the substructure lattice of an appropriately defined finite (universal) algebra, based on Rivals description (see [4] and [5]) by means of deleting suitable intervals from L. We show how to extend Vogts context in order to obtain a conceptually simpler description of Sub01(L) – the lattice of all 0-1-preserving sublattices of L – by means of quasiorders and an associated total binary operation on J (L)2, the set of all pairs of non-zero join-irreducibles of L. Our approach is based on Birkhoff- resp. Priestley-duality, a standard reference is [1].

The countable homogeneous universal model of B 2

We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B2 of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B2. The axioms of Schmid [7], [8] for the AC and EC members of B2 are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of Clark and Davey [3] for B2 and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B2, this method transfers the entire discussion into an equivalent dual category X2 of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X2 prove to be much more readily constructed and analyzed than the corresponding algebras in B2.

Amalgamation in Pseudocomplemented Semilattices

In this paper, we compare amalgamation properties of certain natural subclasses of the variety PCS of all pseudocomplemented semilattices (PCS’s, for short) with those of analogous subclasses of the variety DPCL of distributive pseudocomplemented lattices (DPCL’s, for short).