Boundary Techniques for the Multistep Formulation of the Optimized Lax-Wendroff Method for Non-linear Hyperbolic Systems in Two Space Dimensions

Gourlay & Morris (1970) presented a multistep formulationof a scheme proposed by Strang (1968) for the numerical solutionof non-linear hyperbolic systems. This formulation did not takeaccount of given boundary data and led to instability in certainproblems. This note presents boundary techniques for the incorporationof the given boundary data and in numerical experiments, itis shown that the instabilities, which arose in the problemsof Gourlay & Morris, are prohibited.     

Ring Homomorphisms and Finite Gorenstein Dimension

The local structure of homomorphisms of commutative noetherianrings is investigated from the point of view of dualizing complexes.A concept of finite Gorenstein dimension, which substantiallyweakens the notion of finite flat dimension, is introduced forhomomorphisms. It is shown to impose structural constraints,due to a remarkable equivalence of subcategories of the derivedcategory of all modules. An essential part of this study is the development of relativenotions of dualizing complexes and Bass numbers. It is provedthat the Bass numbers of local homomorphisms are rigid, extendinga known result for local rings. Quasi-Gorenstein homomorphismsare introduced as local homomorphisms that base-change a dualizingcomplex for the source ring into one for the target. They areshown to have the stability properties of the Gorenstein homomorphismthat they generalize. 1991 Mathematics Subject Classification:primary 13H10, 13D23, 14E40; secondary 13C15.     

Seasonal erythemal UV doses in Belo Horizonte, Brazil

The ultraviolet radiation (UVR) emitted by the Sun causes many effects on the biosphere. On human beings they vary from the benefit of vitamin D synthesis to the harm of skin cancer induction. The biological dose depends on the effect, the exposure time to the Sun and the amount of UVR received. In this work we show that the measured incidence of erythemal dose (ED) in Belo Horizonte (19.92 degrees S, 43.94 degrees W, 858 m a.s.l., Brazil) for a cloudless day can vary from 7503 to 2926 J m(-2) in the summer-winter seasonal variation. In addition, supposing a linear relationship between the ED and the geophysical parameters of solar zenith angle cosine (cos(SZA)), column ozone and reflectivity from the ozone monitoring instrument overpass measurements, a model for the forecast of UVR incidence on a monthly-based period is developed. From this an annual ED of 1,451,099 J m(-2) is obtained.     

Plant delta(15)N associated with arbuscular mycorrhization, drought and nitrogen deficiency

It has long been evident that plant (15)N chiefly reflects the processes which fractionate (15)N/(14)N rather than the (15)N of plant N source(s). It has emerged recently that one of the most important fractionating processes contributing to the whole plant (15)N is the presence/absence, type or species of mycorrhiza, especially when interacting with nutrient deficiency. Ecto- and ericoid mycorrhizas are frequently associated with (15)N-depleted foliar (15)N, commonly as low as -12 per thousand. As shown by the present study, plants having no mycorrhiza, or those infected with various species of arbuscular mycorrhiza (AM)-forming fungi, interact with varying concentrations of soil nitrogen [N] and moisture to enrich plant (15)N by as much as 3.5 per thousand. Hence the lack of a mycorrhiza, or variation in the species of AM-forming fungal associations, can account for about 25% of the usually reported variations of foliar (15)N found in field situations and do so by (15)N enrichment rather than depletion. Copyright 1999 John Wiley & Sons, Ltd.     

Shakedown and limit analysis of periodic composites

The optimization of fiber distribution is analyzed in order to improve the strength performance of metal-matrix composite material, which is submitted to two variable independent loads by coupling homogenization and shakedown theories. Numerical Direct Methods are applied to acquire the shakedown domain of three-dimensional heterogeneous elastic-perfectly plastic fiber-reinforced composite for optimal design. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Einfaches Gerät zur Messung sehr kleiner Druckdifferenzen

A quadratic plate moves with very small clearance in an annular duct with a width of 1 cm². This plate is connected to a turnable spindle in the axis of the duct and can move with it against a thin spiral spring. On both sides of this plate pressures are applied, the difference of which is to be measured. Its amount can be read with a pointer on a scale. In measuring a small loss of gas will occur through the narrow slit between plate and annular duct. If this loss is not admissable, it can be avoided by using two equal instruments, of which one works as zero-instrument in a kind of compensation method. The loss of the second instrument is supplied from an additional source of gas. The instrument permits measurements with an accuracy of fractions of thousandth of a mm water column.

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Einfaches Gerät zur Messung sehr kleiner Druckdifferenzen

Zusammenfassung Eine quadratische Platte bewegt sich mit seht geringem Spiel in einem ringförmigen Kanal von l cm² Querschnitt, sie ist mit einer drehbaren Welle verbunden, die in der Achse des Kanals liegt und kann sich mit dieser gegen eine dünne Spiralfeder bewegen. Auf die beiden Seiten dieser Platte wirkt die zu messende Druckdifferenz und ihre Größe kann mit Hilfe eines Zeigers abgelesen werden. Die Messung ist mit einer geringen Menge überströmenden Gases durch den Spalt zwischen Platte und Ringkanal verbunden. Ist diese Überströmung nicht zulässig, so kann man sie durch Verwenden von zwei Geräten gleicher Art vermeiden, von denen das eine als Nullinstrument nach einer Art von Kompensationsverfahren arbeitet und der Gasverlust des anderen von einer zusätzlichen Gasquelle geliefert wird. Das Gerät erlaubt Messungen mit einer Genauigkeit von Bruchteilen eines Tausendstel mm Wassersäule.

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Prof. Dr.-Ing. U. Grigull zum 60. Geburtstag.