Compact elements in the lattice of radicals

Summary A radical R, in the sense of Kurosh--Amitsur, is said to be compact if, given any collection of radicals X such that R ≤;VX, we have R ≤;VX' for some finite subcollection X' of X. A ring A is said to be radical compact if the lower radical on the singleton {A} is compact. This paper explores the relationship between radical compact rings and rings satisfying certain finiteness conditions. Closure properties of the class of all radical compact rings are also investigated.     

A new characterization of <Emphasis Type="Italic">PSU</Emphasis>(<Emphasis Type="Italic">p,q</Emphasis>)

Summary Let G be a finite group. Order components of G were introduced in Chen [5]. Let OC(G) be the set of order components of G. Some finite groups are characterizable by their order components. This assertion was proved for the simple groups PSU(p,q), where p=3, 5, 7 and 11. In this paper, we prove that the simple groups PSU(p,q) can be uniquely determined by their order components, where p&ge;13 is a prime number. Main consequences of our results are the validity of a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.     

Large transversals to small families of unit disks

Summary It is proved that if the nonempty intersection of bounded closed convex sets AnB is contained in (A + F)U(B+F) and one of the following holds true: (i) the space X is less-than-three dimensional, (ii) AUB is convex, (iii) F is a one-point set, then AnBCA+F or AnBCB+F (Theorems 2 and 3). Moreover, under some hypotheses the characterization of A and B such that AnB is a summand of AUB is given (Theorem 3).     

A note on sequence-covering mappings

Summary Let f: X &rarr; Y be a mapping. f is called a sequence-covering mapping if in case S is a convergent sequence containing its limit point in Y then there is a compact subset K of X such that f(K) = S. It is shown that each quotient and compact mapping of a metric space is sequence-covering.     

Hypercyclic and chaotic convolution operators associated with the Dunkl operator on <Emphasis Type=”Bold”>C</Emphasis>

Summary We show that there exist infinitely many positive integers m not of the form n-&ohgr;(n) for any positive integer n. Here, &ohgr;(n) stands for the number of distinct prime factors of n. A similar result holds with &ohgr;(n) replaced by the total number of prime factors of n (counting multiplicities), or by the number of divisors of n.     

Heegaard spines of 3-manifolds

Summary We describe a procedure to construct a 4-coloured graph representing a closed, connected 3-manifold M starting from a Heegaard diagram of M. As a consequence, we prove that, to each Heegaard diagram of a (closed) 3-manifold M, canonically corresponds a spine (Heegaard spine) of M.     

On inclusion and summands of bounded closed convex sets

Summary This article introduces coset extensions and group coextensions of S-sets.     

Almost-all results on the <Emphasis Type=”Italic”>p</Emphasis><Superscript>&;#955;</Superscript> problem

Summary  We describe a procedure to construct a 4-coloured graph representing a closed, connected 3-manifold Italic>M starting from a Heegaard diagram of Italic>M. As a consequence, we prove that, to each Heegaard diagram of a (closed) 3-manifold Italic>M, canonically corresponds a spine (Italic>Heegaard spine) of Italic>M.     

Endoprime modules

Summary We study the harmonic analysis associated with the Dunkl operator on C and analyze the hypercyclicity and chaos of Dunkl convolution operators on the space of entire functions on C.     

Paracompact locally Lindelöf spaces and <Emphasis Type=”Italic”>L</Emphasis>-systems

Summary We establish relationships between paracompact locally Lindel&ouml;f spaces and all kinds of spaces with L-systems by means of closed mappings, weakly perfect mappings and quotient mappings. In particular, we obtain some characterizations of paracompact locally Lindel&ouml;f spaces. Interestingly, they are also characterized as weakly perfect inverse images of locally separable metric spaces.     

Polynomial extensions of quasi-Baer rings

Summary For a ring endomorphism &agr; and an &agr;-derivation &dgr;, we introduce &agr;-compatible rings which are a generalization of &agr;-rigid rings, and study on the relationship between the quasi Baerness and p.q.-Baer property of a ring R and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [6], [8] and [16].     

Invarianz gewisser Operatorenklassen unter nichtkommutativen ergodischen Mitteln

Let be a group of *-automorphisms on the algebra of bounded linear operators on a complex Hilbert space H. Then the strongly closed convex hull of the orbit of any compact operator under consists of compact operators. The same is true if one replaces compact by nuclear, Hilbert-Schmidt or positive Fredholm. We further discuss these results in the framework of the noncommutative mean ergodic theorem of KOVACS and SZ#x00FC;CS and formulate an analogous theorem for the algebra of compact operators on a complex Hilbert space.

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Gefördert von der Deutschen Forschungsgemeinschaft im Rahmen des Forschungsvorhabens Ko 506/1.     

Descendants constructed from matter field in Landau-Ginzburg theories coupled to topological gravity

It is argued that gravitational descendants in the theory of topological gravity coupled to topological Landau-Ginzburg theory (not necessarily conformal) can be constructed from matter fields alone (without metric fields and ghosts). In this sense topological gravity is induced. We discuss the mechanism of this effect (that turns out to be connected with K. Saito's higher residue pairing: Kⁱ(_i(₁),₂)=K⁰(₁,₂)), and demonstrate how it works in a simplest nontrivial example: correlator on a sphere with four marked points. We also discuss some results on k-point correlators on a sphere. From the idea of induced topological gravity it follows that the theory of pure topological gravity (without topological matter) is equivalent to the trivial Landau-Ginzburg theory (with quadratic superpotential).Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 307–316, May, 1993.     

Stellare Abänderungen und Schälbarkeit von Komplexen und Polytopen

Brugesser and Mani proved that the boundary-complex of a convex polytope can be shelled. This result lead to McMullen's proof of the Upper-bound-conjecture. We show that the shellability of complexes has a close connection to the theory of stellar operations. Several results on special shelling procedures and on non-shellable complexes are obtained.     

On the Mechanism for Nonlinear Representations of the Lorentz Group Arising in Quantum Field Theory

A mechanism is identified that leads to the correct law for the relativistic Wigner function transformation with respect to the Lorentz group as long as the corresponding relativistic wave functions have special transformation properties.     

0-1-sequences of Toeplitz type

Summary 0-1-sequences are constructed by successive insertion of a periodic sequence of symbols 0, 1 and hole into the holes of the sequence already constructed. Assuming that finally all holes are filled with symbols 0, 1, an almost periodic point in shift space results. Under certain conditions, it is even strictly ergodic. It is proved that the attached invariant measure has pure point spectrum, and a rather explicit expression for eigenvectors is obtained.     

Applying a fuzzy relation to describe influence of flux behaviour in a printed coil

Summary Being a subject of expectedly fuzzy character, an attempt is made to apply fuzzy functions, more precisely fuzzy relations to investigate the problem of flux distortion in a printed coil.

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Zusammenfassung Da die Vorgänge in einer gedruckten Spule sich aus einer Vielzahl schwerer erfaßbarer Einzeleinflüsse zusammensetzen, die insbesondere den Magnetfluß verzerren, lag es nahe, den Versuch zu machen, die Fuzzy Functions (die logische Algebra, gemäß [1]) darauf anzuwenden. Die Fuzzy Functions sind gedacht für das Beschreiben von Vorgängen, oder Ereignissen, die im Ansatz ein breit gefächertes (fuzzy) Verhalten, ohne scharfe Grenzen aufweisen; siehe Fig. 4.Dieser gefächerten logischen Funktion entspricht eine reguläre mathematische Kurvenschar, die meßtechnisch nachgewiesen werden muß.Im vorliegenden Falle ergab sich eine Korrekturfunktion (5), die es gestattet, die Induktivität gedruckter Spulen, in einem weiten Bereich von Abmessungen und Windungen, mit einer Genauigkeit von –2% bis +5% zu bestimmen.