The Length-scale Effect in the Buckling of Thin Periodic Plates Resting on a Periodic Winkler Foundation

In this paper a new modelling method, called the tolerance averaging method, is presented and applied to analyse a buckling of thin periodic plates resting on a periodically heterogeneous Winkler foundation. The derived length-scale model makes it possible to take into account the effect of periodicity cell size (the length-scale effect) on the overall plate behaviour, on the contrary to the known homogenised models of periodic plates neglecting this effect. In order to evaluate obtained results the buckling problems of those plates are analysed using not only the proposed model but also a certain effective stiffnesses model. A comparison between obtained results leads to a conclusion that the length-scale effect could not be neglected in buckling of periodic plates resting on a Winkler foundation.     

Properties of β-sitostanol/DPPC monolayers studied with Grazing Incidence X-ray Diffraction (GIXD) and Brewster Angle Microscopy

Although the influence of structurally modified sterols on artificial membranes has been intensively investigated, studies on the properties of stanols, which are saturated analogs of sterols, are very rare. Therefore, we have performed Grazing Incidence X-ray Diffraction (GIXD) experiments aimed at studying in-plane organization of a plant stanol-β-sitostanol monolayer and its mixtures with 1,2-dipalmitoyl-sn-glycero-3-phosphocholine - DPPC at the air/water interface. The collected GIXD data, resulting in-plane parameters and BAM images provide information on molecular organization and in-plane ordering of the investigated films. It was found that the lateral organization of β-sitostanol/DPPC monolayers depends on their composition. The oblique structure of the in-plane lattice of tilted hydrophobic region of molecules, found for DPPC film, is maintained at 10 mol% of stanol in the system. However, at 30 and 90 mol% of stanol in the mixture, the arrangement of molecules is hexagonal and they are oriented perpendicularly to the interface. With the addition of stanol the extend of the in-plane order of the monolayers decreases. Moreover, in mixtures the ordered domains consist of both monolayer's components. Additionally, β-sitostanol film is of similar in-plane organization as the corresponding sterol monolayer (β-sitosterol) and stanol induces condensing effect on DPPC.     

An instrumented vehicle for offroad dynamics testing

The paper presents an instrumented vehicle that was equipped with measuring systems to perform complete dynamics tests, especially in off-road conditions. The equipment consists of four wheel dynamometers, a steering robot, and a differential GPS system together with an inertial platform, a non-contact vehicle speed sensor, and an on-board computer with software to control the devices and collect experimental data. The four wheel dynamometers measure six elements; based on strain gage force transducers, it measures three orthogonal forces and three moments. The steering robot can control the steering wheel of the vehicle at a variety of excitation modes; it can carry out typical vehicle dynamics tests (ISO 7401, ISO 4138, ISO/TR3888, etc.) as well as custom engineered tests at a wide range of setting parameters (steer angle rate up to 1600 deg/s). The differential GPS system gives true time vehicle kinematics data (velocities, accelerations, angles, etc.) at 10-ns sample rate and 20-mm accuracy. The base vehicle, a Suzuki Vitara 4 × 4, required no special modifications or changes to install the measuring equipment. The paper also describes typical tests performed with the use of the instrumented vehicle together with sample results.     

Equation of state of CaMnO3: a combined experimental and computational study

Elastic properties of CaMnO₃ are of primary importance in the science and technology of CaMnO₃-based perovskites. From X-ray diffraction experiments performed at pressures up to 100 kbar using a diamond-anvil cell to hydrostatically compress our sample, a bulk modulus, K ₀, of 1734(96) kbar was obtained after fitting parameters to the third-order Birch–Murnaghan equation of state. Mean field, semiclassical simulations predict, for the first time, the third-order equation-of-state parameters and show how the bulk modulus increases with pressure (the zero pressure value being 2062.1 kbar) and decreases with the extent of nonstoichiometry caused by the formation of oxygen vacancies. These trends are amplified for the shear modulus. A more accurate model that allows for the explicit reduction of Mn ions, or localization of excess electrons, yields qualitatively similar results. The experimental and calculated axial ratios show the same trends in their variation with rising pressure.     

New aspects of the electronic structure of the GaSb-InAs (001) superlattice

Relativistic pseudopotentials have been used to calculate the electronic structure of the GaSb-InAs (001) superlattice of period 36A.We present energy levels and charge densities of the states in the superlattice. In particular, new resonances and confined states with large amplitudes at interfaces are identified. We also show that scattering processes associated with wavelengths which are comparable with the width of the confining layers are not important in the formation of the confined states but are essential in the formation of the resonances.     

Some Results Connected with the Class Number Problem in Real Quadratic Fields

We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h（d） of the real quadratic field Q（√d）. In particular, we give a new proof of the result of Hasse, asserting that in this case h（d） = 1 is possible only if d is of the form p, 2q or qr. where p.q. r are primes and q≡r≡3（mod 4）.     

Indirect determination of mercury(ii) with an air-gap cyanide sensor

The method is based on the stability of the dicyanomercurate(II) complex at pH 0.5–1, where most other cyanide complexes decompose. The selectivity is much better than that in the direct application of mercury-selective electrodes. The method is useful in the range 5 × 10^-5–5 × 10^-3 M mercury(II).     

Arbiter as the Third Man in Classical and Quantum Games

We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.     

Time decay of the solution to the Cauchy problem for a three-dimensional model of nonsimple thermoelasticity

This paper is devoted to the investigation of the solution to the Cauchy problem for a system of partial differential equations describing thermoelasticity of nonsimple materials in a three-dimensional space. The model of linear dynamical thermoelasticity of nonsimple materials is considered as the system of partial differential equations of fourth order. In this paper, we proposed a convenient evolutionary method of approach to the system of equations of nonsimple thermoelasticity. We proved the L^p−L^q time decay estimates for the solution to the Cauchy problem for linear thermoelasticity of nonsimple materials.