Czech project in history of mathematics

The paper describes the Czech project in the history of mathematics which was initiated at the Faculty of Mathematics and Physics of Charles University in Prague at the end of the eighties of the 20th century. Its main aim is to map the development of mathematical research in the Czech lands in the second half of the nineteenth and the first half of the twentieth century. The main result of this project is the production of monographs. These chart out the life and work of some prominent Czech personalities-mathematicians who have had substantial influence on the development of Czech mathematics. The aim of the project, the structure of the monographs and the general method are discussed in the paper.     

The PIBETA spectrometer for studying rare and forbidden decays of muons and pions

The construction and characteristics of the PIBETA spectrometer are described. This spectrometer is designed to implement a program of precise measurement of pion decay ^{+ 0} + e ⁺ + _e at the Paul Scherrer Institute (Switzerland). A spherical calorimeter, consisting of 240 crystals of pure CsI scintillator and embracing a solid angle of 3, is the main detector of the setup. In addition, the spectrometer is composed of an active collimator (which also acts as a beam degrader), a segmented active plastic target, two multiwire cylindrical proportional chambers, a 20-element cylindrical plastic hodoscope, and veto counters of cosmic muons.__________Translated from Pribory i Tekhnika Eksperimenta, No. 2, 2005, pp. 39–48.Original Russian Text Copyright © 2005 by Baranov, Kalinnikov, Karpukhin, Khomutov, A. Korenchenko, S. Korenchenko, Kravchuk, Kuchinskii, Mzhaviya, Rozhdestvenskii, Sidorkin, Tsamalaidze, Sakhelashvili, Frlez, Poanic, Li, Minehart, Smith, Stephens, Ziock, Bertl, Horisberger, Ritt, Schnyder, Wirtz, Ritchie, Supek, Kozlowski.     

Use of the Roughness Parameters Ssk and Sku to Control Friction—A Method for Designing Surface Texturing

The aim of this work was to show that with the use of the surface roughness parameters S_sk and S_ku we can predict tribological behavior of contact surfaces and use these parameters to plan surface texturing. This article presents a continuation of our research on virtual texturing and experimental work on surface textures in the form of channels. For this investigation, steel samples were laser surface textured in the shape of dimples with different spacings between the dimples and different dimple depths. The experimental results confirmed that the parameters S_sk and S_ku can be used to design the surface texturing, where a higher value of S_ku and more negative S_sk lead to lower friction.     

Influence of Field Effects on the Performance of InGaAs-Based Terahertz Radiation Detectors

A detailed electrical characterization of high-performance bow-tie InGaAs-based terahertz detectors is presented along with simulation results. The local surface potential and tunnelling current were scanned over the surfaces of the detectors by means of Kelvin probe force microscopy (KPFM) and scanning tunnelling microscopy (STM), which also enabled the determination of the Fermi level. Current-voltage curves were measured and modelled using the Synopsys Sentaurus TCAD package to gain deeper insight into the processes involved in detector operation. In addition, we performed finite-difference time-domain (FDTD) simulations to reveal features related to changes in the electric field due to the metal detector contacts. The investigation revealed that field-effect-induced conductivity modulation is a possible mechanism contributing to the high sensitivity of the studied detectors.     

Stereometric analysis of nanostructured boehmite coatings synthesized by aluminum nitride powder hydrolysis

We studied the morphological properties of precipitated, nanostructured, boehmite coatings on a polished alumina surface by exploiting the aluminum nitride (AlN) powder hydrolysis at elevated temperatures. The hydrolysis tests of the 3 wt% AlN powder suspensions in the temperature range 50–90 °C were performed in order to estimate the time needed for the synthesis of the coatings. They consisted of interlocked boehmite lamellas, positioned perpendicularly to the ceramic surface, and they exhibited a strong temperature-dependent size and surface density. The aim of this research was a quantitative assessment of the as-formed boehmite coatings. Based on electron microscopy micrographs, a stereometric analysis of the as-prepared coatings was performed in order to estimate the relevant geometric parameters of the lamellas. In spite of the temperature-dependent lamellas’ size and surface density, the specific volume of the coatings was similar for all the synthesis temperatures.     

Discrete (n + 1)-valued states and n-perfect pseudo-effect algebras

We give sufficient and necessary conditions to guarantee that a pseudo-effect algebra admits an (n + 1)-valued discrete state. We introduce n-perfect pseudo-effect algebras as algebras which can be split into n + 1 comparable slices. We prove that the category of strong n-perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups of a special type.     

Signal shaper with a distributed delay: Spectral analysis and design

Input shapers with time delays have proved useful in many applications related to controls for various oscillatory devices, for example flexible manipulators and cranes. In the paper, a novel approach for designing a zero-vibration signal shaper based on equally distributed delay is proposed. The parameter assessment of the shaper is based on the spectral approach. Various characteristics of the shaper are analyzed and compared with the classical zero-vibration shaper with a lumped delay. The analysis shows that the novel shaper is a slower, but more robust alternative to the classical shaper. Besides, the discrete implementation of the shaper is proposed and tested. It includes zero placement based parameter adjustment with the objective to preserve full compensation of the oscillatory mode by the discrete algorithm.