k-Blocks and ultrablocks in graphs

A k-block is a maximal k-vertex-connected subgraph, and a k-block which does not contain a (k + 1)-block is an ultrablock. It is shown that the maximum total number of k-blocks for all k ≥ 1 in any p-vertex graph is [$\text{(2p ? 1)}\text{3}$], and the maximum number of ultrablocks in any p-vertex graph having maximum subgraph connectivity κ? is $\text{[}\text{(p ?}\text{κ}\text{?}\text{+ 1)}\text{2}\text{]}$. In contrast to the linear growth rate of the maximum number of k-blocks in a p-vertex graph, it is shown that the maximum number of critical k-vertex-connected subgraphs of an ultrablock of connectivity k can grow exponentially with p.     

Ueber die Fällung von Serumeiweiß durch Kupfersalze

Ohne Zusammenfassung     

Defects induced by electron irradiation of p-type germanium†

The calculated shapes of blocking dips differ from the experimental ones since models for charged particle motion with in crystals assume a perfect lattice. In this paper we suggest that the difference between the transverse energy distribution π(E⊥) of the particles coming out from a real crystal and that calculated in a statistical equilibrum continuum model, corrected for thermal vibration effects by a diffusion equation, accounts for crystal defects and is approximately independent of the distribution of transverse energy before diffusion and of the energy of blocked particles. The extraction of π(E⊥) from experimental dips requires the inversion of an integral equation, that is analy = tically solved in a particular case of practical interest. This would provide a way of analysing nuclear reaction time measurements that makes use of the full shape of the blocking dips. An illustrative example of the method to a blocking lifetime measurement in ²⁷A1 (p,α) ²⁴Mg resonance reactions is presented.     

Automated microaxial tomography of cell nuclei after specific labelling by fluorescence in situ hybridisation

Microaxial tomography provides a good means for microscopic image acquisition of cells or sub-cellular components like cell nuclei with an improved resolution, because shortcomings of spatial resolution anisotropy in optical microscopy can be overcome. Thus, spatial information of the object can be obtained without the necessity of confocal imaging. Since the very early developments of microaxial tomography, a considerable drawback of this method was a complicated image acquisition and processing procedure that requires much operator time. In order to solve this problem the Heidelberg 2π-tilting device has been mounted on the Brno high-resolution cytometer as an attempt to bring together advanced microscopy and fast automated computer image acquisition and analysis. A special software module that drives all hardware components required for automated microaxial tomography and performs image acquisition and processing has been developed. First, a general image acquisition strategy is presented. Then the procedure for automation of axial tomography and the developed software module are described. The rotation precision has been experimentally proved followed by experiments with a specific biological example. For this application, also a method for the preparation of cell nuclei attached to glass fibres has been developed that allows for the first time imaging of three-dimensionally conserved, fluorescence in situ hybridisation-stained cell nuclei fixed to a glass fibre.     

Ramsey theory for graph connectivity

r_c(k) Denotes the smallest integer such that any c-edge-coloring of the r_c(k) vertex complete graph has a monochromatic k-connected subgraph. For any c, k ≧ 2, we show 2c(k – 1) + 1 ≦ r_c(k) < 10/3 c(k – 1) + 1, and further that 4(k – 1) + 1 ≧ r₂(k) < (3 + √ (k – 1) + 1. Some exact values for various Ramsey connectivity numbers are also computed.     

Bubble levitation and translation under single-bubble sonoluminescence conditions

Bubble levitation in an acoustic standing wave is re-examined for conditions relevant to single-bubble sonoluminescence. Unlike a previous examination [Matula et al., J. Acoust. Soc. Am. 102, 1522-1527 (1997)], the stable parameter space [Pa,R0] is accounted for in this realization. Forces such as the added mass force and drag are included, and the results are compared with a simple force balance that equates the Bjerknes force to the buoyancy force. Under normal sonoluminescence conditions, the comparison is quite favorable. A more complete accounting of the forces shows that a stably levitated bubble does undergo periodic translational motion. The asymmetries associated with translational motion are hypothesized to generate instabilities in the spherical shape of the bubble. A reduction in gravity results in reduced translational motion. It is hypothesized that such conditions may lead to increased light output from sonoluminescing bubbles.     

The effects of microgravity on nanoparticle size distributions generated by the ultrasonic reduction of an aqueous gold-chloride solution

A solution of gold chloride was reduced using ultrasound irradiation to prepare metallic gold nanoparticles under conditions of microgravity and normal gravity at sea level. Particle size distributions were measured using TEM analysis. A mean particle diameter of 10 nm was obtained in microgravity while a mean diameter of 80 nm was obtained in the laboratory. Absorbance measurements on the reacted solution found an enhanced reduction rate in the reduction of gold chloride in microgravity compared to that in the laboratory.