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

Why Consultations? The public participation in water management and local spatial planning in two Polish cases

Despite many novelties in participation: participatory budgeting, citizens jury, deliberatice poll etc. the engagement of different stakeholders’ groups in the decision making processes concerning detailed planning issues (local spatial management plans, water management plans, the preservation management plans of the Natura 2000 sites) is usually based on the organization of open discussion meetings. The study looks at the social consultations regarding acceptance of local spatial management plans managed by Poznań City Hall and consultations concerning the preparation of water management plans managed by Regional Water Management Board in Poznań. The comparative analysis served to exhibit similarities and differences between the processes in terms of legal conditions, the organization of meetings, the length and the scale of the process and the actors engaged

Patrioci krytyczni kontra mitomani. Walka o politykę historyczną w obliczu Grossa

Patriotism is one of the concepts that cannot be easily interpreted. It can be seen at least two models of patriotism - „critical”, which draws attention also to the shameful experience and „conservative”, associated with the myth of proud and suffering of the Polish nation, connected also with a specific historical policy. Visible manifestation of these extreme camps are public debates on the publications of J. T. Gross, showing the Poles as perpetrators of suffering and death of many Jews

The Influence of Changes in Personal Income Tax Regulations on Donating Non-Profit Organization

Each entity paying taxes would like to have real influence on the way of their allocation. Since 2004 in Poland payers of personal income tax were able to decide about donating 1 percent of personal income tax to a chosen public benefit organization for the first time. Since the introduction of the possibility of donating non-profit organization (NPO) tax regulations were repeatedly modified. Did tax-payers willingly use the ability to decide who they should donate their 1 percent of personal income tax to? In what way did changes of tax regulations influence taxpayers’ decision? In order to answer those questions soft modelling was used, which allowed to examine the influence of changes in regulations relating to 1 percent of personal income tax on taxpayers’ [email protected]żbieta Izabela Misiewicz, Ph.D. – Faculty of Economics and Management, University of Bialystok5(65)647

Internal Stresses and Formation of Switchable Nanowires at Thin Silica Film Edge

At vertical edges, thin films of silicon oxide (SiO_{2-x}) contain semiconductive c-Si layered nanocrystals (Si NC) embedded in and supported by an insulating g-SiO2 matrix. Tour et al. have shown that a trenched thin film geometry enables the NC to form switchable nanowires (SNW) when trained by an applied field. The field required to form SNW decreases rapidly within a few cycles, or by annealing at 600 C in even fewer cycles, and is stable to 700C. Here we describe the intrinsic evolution of Si NC and SNW in terms of the competition between internal stresses and electro-osmosis. The analysis relies heavily on experimental data from a wide range of thin film studies, and it explains why a vertical edge across the planar Si-SiOx interface is necessary to form SNW. The discussion also shows that the formation mechanisms of Si NC and Si/SiO_{2-x} SNW are intrinsic and result from optimization of nanowire conductivity in the presence of residual host misfit stresses