Weak stability and generalized weak convolution for random vectors and stochastic processes

A random vector ${\bf X}$ is weakly stable iff for all $a,b\in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X}+b{\bf X}'\stackrel{d}{=}{\bf X}\Theta$. This is equivalent (see \cite{MOU}) with the condition that for all random variables $Q_1,Q_2$ there exists a random variable $\Theta$ such that $$X Q_1 + X' Q_2 \stackrel{d}{=} X \Theta,$$ where ${\bf X},{\bf X}',Q_1,Q_2,\Theta$ are independent. In this paper we define generalized convolution of measures defined by the formula $$L(Q_1) \oplus_{\mu} L(Q_2) = L(\Theta),$$ if the equation $(*)$ holds for ${\bf X},Q_1,Q_2,\Theta$ and $\mu ={\cal L}(\Theta)$. We study here basic properties of this convolution, basic properties of $\oplus_{\mu}$-infinitely divisible distributions, $\oplus_{\mu}$-stable distributions and give a series of examples.Comment: Published at http://dx.doi.org/10.1214/074921706000000149 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Comparison of methods for estimating the carcass stiffness of agricultural tyres on hard surfaces

Loading soil via pneumatic tyres is a major cause of compaction of agricultural soils, which causes damage to the soil-water-air-plant system. The loads applied to the soil and the resulting pressure influences the degree of soil compaction. This study was conducted to determine an effective method to measure the pressure distribution under a selection of pneumatic agricultural tyres. This was conducted initially on a non-deformable surface; a later study will consider pressures within the subsoil. From this the tyre carcass stiffness was determined and methods to predict carcass stiffness were evaluated. Tyre carcass stiffness is defined as an equivalent pressure resulting from the stiffness of the tyre carcass. In order to estimate the carcass stiffness of tyres a number of approaches were considered including: (i) footprint area, (ii) tyre load – deflection, (iii) pressure mapping and (iv) tyre manufacturer's specification methods. Carcass stiffness values obtained from the footprint area method gave results significantly lower (30–40%) than those obtained using the pressure mapping system. The method based on the tyre load – deflection characteristics was found to give a better estimation of the tyre carcass stiffness of the smooth rather than the treaded tyre. The technique of using the tyre manufacturer's specification data, where the estimation of the tyre carcass stiffness was calculated using the theoretical load that the tyre could support at zero inflation pressure, produced estimates that were within ±20% of the mean carcass stiffness determined using the pressure mapping system

Verification of band offsets and electron effective masses in GaAsN/GaAs quantum wells : Spectroscopic experiment versus 10-band k.p modeling

Optical transitions in GaAs1-xNx/GaAs quantum wells (QWs) have been probed by two complementary techniques, modulation spectroscopy in a form of photoreflectance and surface photovoltage spectroscopy. Transition energies in QWs of various widths and N contents have been compared with the results of band structure calculations based on the 10-band k.p Hamiltonian. Due to the observation of higher order transitions in the measured spectra, the band gap discontinuities at the GaAsN/GaAs interface and the electron effective masses could be determined, both treated as semi-free parameters to get the best matching between the theoretical and experimental energies. We have obtained the chemical conduction band offset values of 86% for x = 1.2% and 83% for x = 2.2%, respectively. For these determined band offsets, the electron effective masses equal to about 0.09 m(o) in QWs with 1.2% N and 0.15 m(o) for the case of larger N content of 2.2%.Publisher PDFPeer reviewe

Exciton lifetime and emission polarization dispersion in strongly in-plane asymmetric nanostructures

We present experimental and theoretical investigation of exciton recombination dynamics and the related polarization of emission in highly in-plane asymmetric nanostructures. Considering general asymmetry- and size-driven effects, we illustrate them with a detailed analysis of InAs/AlGaInAs/InP elongated quantum dots. These offer a widely varied confinement characteristics tuned by size and geometry that are tailored during the growth process, which leads to emission in the application-relevant spectral range of 1.25-1.65 {\mu}m. By exploring the interplay of the very shallow hole confining potential and widely varying structural asymmetry, we show that a transition from the strong through intermediate to even weak confinement regime is possible in nanostructures of this kind. This has a significant impact on exciton recombination dynamics and the polarization of emission, which are shown to depend not only on details of the calculated excitonic states but also on excitation conditions in the photoluminescence experiments. We estimate the impact of the latter and propose a way to determine the intrinsic polarization-dependent exciton light-matter coupling based on kinetic characteristics.Comment: 11 pages, 8 figure