Spring-block approach for crack patterns in glass

Fracture patterns resulting from point-like impact acting perpendicularly on the plane of a commercial sodalime glass plate is modelled by a spring-block system. The characteristic patterns consist of crack lines that are spreading radially from the impact point and concentric arcs intersecting these radial lines. Experimental results suggest that the number of radial crack lines is scaling linearly with the energy dissipated during the crack formation process. The elaborated spring-block model reproduces with success the observed fracture patterns and scaling law.     

UVB radiation induces changes in the ultra-structure of Iridaea cordata

Iridaea cordata cultivated in the presence of UVB radiation (UVBR) was studied using transmission electron microscopy. Apical segments were cultivated in 0.97 Wm^?2 of UVBR for 40 days, 3 h a day, and compared to a negative control (UVBR absent). UVBR caused modifications, mainly in the cortical cells, including an increased number of cell wall-producing vesicles, in addition to thicker and denser cellular walls, compared to the control. Additionally, cells were observed with an irregular contour and without defined organelles. The increase of cell-wall thickness could be interpreted as an acclimation to UVBR, which could lead to protection from this radiation.     

The Central Curve in Linear Programming

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answering a question of Bayer and Lagarias. These invariants, along with the degree of the Gauss image of the curve, are expressed in terms of the matroid of the input matrix. Extending work of Dedieu, Malajovich and Shub, this yields an instance-specific bound on the total curvature of the central path, a quantity relevant for interior-point methods. The global geometry of central curves is studied in detail.     

Optical characterization of sol gel TiO<Subscript>2</Subscript> monoliths doped with Brilliant Green

Amorphous titanium dioxide monoliths doped with brilliant green (BG) were synthesized by the sol-gel process. The optical properties of the monoliths were characterized by Photoacoustic Spectroscopy and Photoluminescence Spectroscopy. The absorption spectra for the BG-doped TiO₂ monoliths exhibited two well defined absorption regions: a band below 400 nm corresponding to TiO₂ absorption and three absorption bands centered at 424 nm, 588 nm, and 632 nm due to brilliant green. While the undoped TiO₂ monoliths showed no luminescence, the doped samples showed a strong luminescence band at 673 nm, which increased its intensity for increasing organic dye doping.     

Large Cliques in -Free Graphs

Dedicated to the memory of Paul Erdős A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs. Received October 25, 1999 RID="*" ID="*" Supported by OTKA grant T029074. RID="**" ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203.     

The Ex-Post Evaluation of the Minimum Local Reliability Level: An Enhanced Probabilistic Location Set Covering Model

In order to evaluate the behavior of three probabilistic location set covering models we propose a new method that allows the ex-post measurement of the so called minimum local reliability level, both under the independence and under the dependence assumption. We show experimentally, by means of a set of test problems, that the proposed loss-system version of Ball and Lin's model (1993) does almost always achieve the required reliability level. Moreover, if we compare this new version with the other two already known probabilistic models and consider as a second additional criteria the least number of required vehicles, we show that the new version has a better behavior both under the independence and the dependence assumption. In this paper we further propose a new model with the aim of reducing the number of required vehicles while satisfying the fixed reliability level. Our new model is formulated like Ball and Lin's model incorporating the servers workload estimate of the Binomial PLSCP of ReVelle and Hogan (1988). Finally, we check the precision of our ex-post evaluation method over the four considered models through a simulation study.     

Hyperbolicity of linear partial differential equations with delay

Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.The author thanks W. Desch (Graz), I. Gyri (Veszprém) and R. Schnaubelt (Halle) for helpful discussions.