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.     

Fejér summability of multi-parameter bounded Ciesielski systems

We investigate the Kronecker product of bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system from the Haar system. It is shown that the maximal operator of the Fejér means of the d-dimensional Ciesielski-Fourier series is bounded from the Hardy space H _p([0,1)^d ₁ × ¨ × [0,1)^d _l) to L _p([0,1)^d) if 1/2 < p < &infin; and m _j &ge; 0, |k _j| &le; m _j + 1. By an interpolation theorem, we get that the maximal operator is also of weak type (H ₁ ^#i,L ₁) (I=1,¨,l), where the Hardy space H ₁ ^#i is defined by a hybrid maximal function and H ₁ ^#i L(logL)^l-1. As a consequence, we obtain that the Fejér means of the Ciesielski-Fourier series of a function f converge to f a.e. if f H ₁ ^#i and converge in a cone if f &isin; L ₁.     

Synthesis of 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylic acid derivatives, doubly constrained ACC derivatives, by a remarkable cyclopropanation process

Reaction of N-benzoyl-1,2,3,4-tetrahydroquinoline-2-carboxylic acid with acetic anhydride resulted in 1H,3H,5H-oxazolo[3,4-a]quinolin-3-one derivative 13. Different cyclopropanation processes were applied to 13, but only diazomethane in the presence of water furnished the hitherto unknown methyl 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylate 14, which can be considered as a doubly constrained 1-aminocyclopropane-1-carboxylic acid system. The mechanism of the cyclopropanation was studied in detail. The new ACC ester 14 was transformed into fused tetracyclic hydantoin derivatives, which comprised a new type of heterocyclic system.     

The Densest Packing of 19 Congruent Circles in a Circle

Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n = 2,..., 16. In 1969 Pirl found the optimal packings for n 10, he also conjectured the dense configurations for 11 n 19. In 1994, Melissen provided a proof for n = 11. In this paper we exhibit the densest packing of 19 congruent circles in a circle with the help of a technique developed by Bateman and Erdös.     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.     

Polarographisches Verhalten von 1,2,3-Cyclohexantrion-trioxim in sauren Lösungen

The deoximation kinetics of 1,2,3-cyclohexanetrione trioxime was studied polarographically in 0.5 and 1.0M-HClO₄ solutions. From the three vicinal oxime groups, that in position 2 is hydrolysed by protonisation, followed by water uptake and hydroxylamine loss. The probable mechanism of the deoximation was proved by the study of the polarographic behaviour of 1,2,3-cyclohexanetrione-1,3-dioxime and by means of amperometric determination of the unchanged trioxime with Ni(II)-salt.     

ESR spectrometer with a loop-gap resonator for cw and time resolved studies in a superconducting magnet

The design and performance of an electron spin resonance spectrometer operating at 3 and 9 GHz microwave frequencies combined with a 9-T superconducting magnet are described. The probehead contains a compact two-loop, one gap resonator, and is inside the variable temperature insert of the magnet enabling measurements in the 0-9T magnetic field and 1.5-400 K temperature range. The spectrometer allows studies on systems where resonance occurs at fields far above the g approximately 2 paramagnetic condition such as in antiferromagnets. The low quality factor of the resonator allows time resolved experiments such as, e.g., longitudinally detected ESR. We demonstrate the performance of the spectrometer on the NaNiO2 antiferromagnet, the MgB2 superconductor, and the RbC60 conducting alkaline fulleride polymer.     

Nica’s <Emphasis Type="Italic">q</Emphasis>-Convolution is Not Positivity Preserving

It is shown that the q-convolution of Nica is not positivity preserving unless q=0 or q=1, i.e. the q-convolution of two probability measures with finite moments of all orders is not necessarily a probability measure.Supported by Grant-in-Aid for JSPS Fellows