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

On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N=3 are constructed

Metal Recovery and Preconcentration by Aminopolycarboxylic Acid modified Silica Surfaces

This study focuses on the adsorption and preconcentration of various metals by silica gel surfaces modified with aminopolycarboxylic acids namely ethylenediaminetetraacetic acid or diethylenetriamine-pentaacetic acid. The adsorption performance of the studied materials was determined in mixed metal solutions and the adsorption isotherm studies were conducted for cobalt, nickel, cadmium, and lead. The results were modeled using various theoretical isotherm equations, which suggested that two different adsorption sites were involved in metal removal although lead showed clearly different adsorption behavior attributed to its lowest hydration tendency. Efficient regeneration of the adsorbents and preconcentration of metals was conducted with nitric acid. Results indicated that the metals under study could be analyzed rather accurately after preconcentration from both pure, saline and ground water samples

A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation

An approach based on the spectral and Lie - algebraic techniques for constructing vertex operator representation for solutions to a Riemann type Gurevicz-Zybin hydrodynamical hierarchy is devised. A functional representation generating an infinite hirerachy of dispersive Lax type integrable flows is obtaned.Comment: 6 page

EFFECT OF LOW DOSES OF LOW-LET RADIATION ON THE INNATE ANTITUMOR REACTIONS IN RADIORESISTANT AND RADIOSENSITIVE MICE

BALB/c and C57BL/6 mice differ in their Th1/Th2 lymphocyte and M1/M2 macrophage phenotypes, radiosensitivity, and post-irradiation tumor incidence. In this study we evaluated the effects of repeated low-level exposures to X-rays on the development of artificial tumor colonies in the lungs of animals from the two strains and cytotoxic activities of natural killer (NK) cells and macrophages obtained from these mice. After ten daily irradiations of BALB/c or C57BL/6 mice with 0.01, 0.02, and 0.1 Gy X-rays NK cell-enriched splenocytes collected from the animals demonstrated significant and comparable up-regulation of their anti-tumor cytotoxic function. Likewise, peritoneal macrophages collected from the two irradiated strains of mice exhibited the similarly stimulated cytotoxicities against susceptible tumor cells and produced significantly more nitric oxide. These results were accompanied by the significantly reduced numbers of the neoplastic colonies induced in the lungs by intravenous injection of syngeneic tumor cells. The obtained results indicate that ten low-level irradiations with X-rays stimulate the generally similar anti-tumor reactions in BALB/c and C57BL/6 mice

Health Status of Afghan Refugees in Europe: Policy and Practice Implications for an Optimised Healthcare.

Four decades of civil war, violence, and destabilisation have forced millions of Afghans to flee their homes and to move to other countries worldwide. This increasing phenomenon may challenge physicians unfamiliar with the health status of this population, which may be markedly different from that of the host country. Moreover, several factors during their migration, such as transport in closed containers, accidental injuries, malnutrition, and accommodation in detention centres and refugee camps have a major influence on the health of refugees. By taking into account the variety of the specific diseases among migrant groups, the diversity of the origins of refugees and asylum seekers, and the increasing numbers of Afghan refugees, in this review we focus on the population of Afghans and describe their health status with the aim of optimising our medical approach and management. Our literature review shows that the most prevalent reported infections are tuberculosis and other respiratory tract infections and parasitic diseases, for example leishmaniasis, malaria, and intestinal parasitic infections. Anaemia, hyperlipidaemia, arterial hypertension, diabetes, smoking, overweight, malnutrition, low socioeconomic status, and poor access to healthcare facilities are additional risk factors for non-communicable diseases among Afghan refugees. With regards mental health issues, depression and post-traumatic stress disorder (PTSD) are the most common diagnoses and culture shock and the feeling of being uprooted modulate their persistence. Further research is needed in order to provide us with extensive, high-quality data about the health status of Afghan refugees. The main objective of this review is to identify protective factors which could ensure key health concepts and good clinical practice