The existence of symmetric designs with parameters (105, 40, 15)

The existence of symmetric designs with parameters (105, 40, 15) was shown. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 17–19, 1999     

Modeling snow crystal growth II: A mesoscopic lattice map with plausible dynamics

We present a local lattice model for the evolution of snow crystals that combines diffusion-limited aggregation with anisotropic attachment kinetics and an idealized quasi-liquid layer. Despite a voluminous modeling literature, this is apparently the first approach that successfully captures the essential form of core and tip instabilities, branch faceting, and other aspects of real snow crystal growth. As parameters are varied, our nearest neighbor system reproduces the basic features of most of the observed varieties of planar snowflakes and offers new insights into their genesis.     

Reflexivity of the commutant and local commutants of an algebraic operator

We show that an algebraic operator on a complex Banach space has reflexive commutant if and only if each zero of the minimal polynomial of the operator is simple. Further, for any operator, the local commutant at an eigenvector is reflexive. On the other hand, for an algebraic operator whose minimal polynomial has at least one zero that is not simple, the local commutant of the operator at a given vector is reflexive precisely when the vector is an eigenvector.     

Verallgemeinerung eines Satzes von B. Huppert und J. G. Thompson

Ohne Zusammenfassung     

Endliche Gruppen mit lauter nilpotenten zweitmaximalen Untergruppen

Ohne ZusammenfassungHerrnReinhold Baer zum 60. Geburtstag am 22. Juli 1962 gewidmet     

Operators in pre-Riesz spaces: moduli and homomorphisms

We focus on two topics that are related to moduli of elements in partially ordered vector spaces. First, we relate operators that preserve moduli to generalized notions of lattice homomorphisms, such as Riesz homomorphisms, Riesz* homomorphisms, and positive disjointness preserving operators. We also consider complete Riesz homomorphisms, which generalize order continuous lattice homomorphisms. Second, we characterize elements with a modulus by means of disjoint elements and apply this result to obtain moduli of functionals and operators in various settings. On spaces of continuous functions, we identify those differences of Riesz* homomorphisms that have a modulus. Many of our results for pre-Riesz spaces of continuous functions lead to results on order unit spaces, where the functional representation is used.

     

Towards Massively Parallel Computations in Algebraic Geometry

Foundations of Computational Mathematics - Introducing parallelism and exploring its use is still a fundamental challenge for the computer algebra community. In high-performance numerical...