Abstract:
We study the probability measure $\mu_{0}$ for which the moment sequence is $\binom{3n}{n}\frac{1}{n+1}$. We prove that $\mu_{0}$ is absolutely continuous, find the density function and prove that $\mu_{0}$ is infinitely divisible with respect to the additive free convolution.

Abstract:
We prove that if $p\geq 1$ and $-1\leq r\leq p-1$ then the binomial sequence $\binom{np+r}{n}$, $n=0,1,...$, is positive definite and is the moment sequence of a probability measure $\nu(p,r)$, whose support is contained in $\left[0,p^p(p-1)^{1-p}\right]$. If $p>1$ is a rational number and $-11$ the measures $\nu(p,-1)$ and $\nu(p,0)$ are certain free convolution powers of the Bernoulli distribution. Finally we prove that the binomial sequence $\binom{np+r}{n}$ is positive definite if and only if either $p\geq 1$, $-1\leq r\leq p-1$ or $p\leq 0$, $p-1\leq r \leq 0$. The measures corresponding to the latter case are reflections of the former ones.

Abstract:
In this paper we obtain some properties of orthogonal polynomials given by a weight function which is a limit density of a rescaled discrete-time quantum walk on the line.

Abstract:
We prove that if $p\ge 1$ and $0< r\le p$ then the sequence $\binom{mp+r}{m}\frac{r}{mp+r}$, $m=0,1,2,...$, is positive definite, more precisely, is the moment sequence of a probability measure $\mu(p,r)$ with compact support contained in $[0,+\infty)$. This family of measures encompasses the multiplicative free powers of the Marchenko-Pastur distribution as well as the Wigner's semicircle distribution centered at $x=2$. We show that if $p>1$ is a rational number, $0

Abstract:
We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we study free multiplicative powers of the Marchenko-Pastur (MP) distribution, ${\rm MP}^{\boxtimes s}$, which for an integer $s$ yield Fuss-Catalan distributions corresponding to a product of $s$ independent square random matrices, $X=X_1\cdots X_s$. New formulae for the level densities are derived for $s=3$ and $s=1/3$. Moreover, the level density corresponding to the generalized Bures distribution, given by the free convolution of arcsine and MP distributions is obtained. We also explain the reason of such a curious convolution. The technique proposed here allows for the derivation of the level densities for several other cases.

Abstract:
Consciousness attracts the attention of researchers representing various disciplines. Hence, there is a demand for a theoretical tool that could integrate data and theoretical concepts originating from distinct fields. The paper proposes to use the framework of the theory of integrative levels. The development and the definitions of the concept of levels are briefly discussed. The final part of the paper presents a proposal for incorporating the levels of consciousness into the framework of the integrative levels theory.

Abstract:
Reclaimed mine soils (RMS) which develop on post-mining sites play significant role in Carbon sequestration in new ecosystems, especially in local range on areas disturbed by human activity. This study presents the potential for Carbon sequestration in RMS developing on 3 post sur- face mining areas in Poland (Central Europe) reforested with Scots pine (Pinus sylvestris L). Research was conducted on waste heaps and quarry which accompany open cast lignite, sul- fur, and sand mining. Control plots were arrang- ed in managed pine forests on natural sites in the surrounding area. The results shows high Carbon accumulation in RMS, estimated on 16.77 Mg?ha-1 in poor (oligotrofic) soils on Quaternary sands on sand quarry and up to 65.03 Mg?ha-1 on external waste heap after Sulfur sur- face mining exploitation on Quaternary sands mixed with Tertiary clays. These results were very similar to natural forest soils on control plots. Potential rate of Carbon sequestration in RMS was estimated on 0.73 (on the poorest sa- ndy soils on quarry) to 2.17 Mg?ha-1?yr-1 (on potentially abundant sandy-clayish soils on Sulfur waste heap), and 5.26 Mg?ha-1?yr-1 (on Tertiary sands substrate soils on lignite mining waste heap). In conslusion the average Carbon accu- mulation in RMS was estimated on 41 Mg?ha-1 and Carbon sequestration rate was 1.45 Mg? ha-1?yr-1. According to the result of this study and range of post-mining areas reclaimed to forestry in Poland (ca 15000 ha) total Carbon accumulation in RMS was estimated on 615 × 103 Mg and potential Carbon sequestration rate in new ecosystems on 21.75 × 103 Mg?ha-1?yr-1. However, the main factors affecting Carbon sequestration and protection in RMS under tree stand were substrate, percentage of clay and silt sized fraction, in order to formulate guidelines for sustainable management of post-mining ec- osystem, further study must be continue for be- tter understanding.

Abstract:
The principal testing ground for general relativity is the observable Universe. Gravitational lensing is the leading observational technique that gives insight into the distribution of baryonic matter in the stellar, galactic and cosmological scale, as well as the distribution of dark matter and dark energy, due to their gravitational interaction. Interpretation of ever more precise observational data requires increasingly subtle analytical techniques. In this paper, I discuss a formalism that can handle a nonlinear superposition of gravitational and refractive lensing by a grouping of baryonic matter, dark matter and dark energy for a given distribution of those entities (i.e. for a given spacetime metric) and their refractive properties. The role of refraction in gravitational lensing is exemplified in the case of a microlensing event and a signature of such an effect is discussed.

Abstract:
Reclaimed mine soils (RMS) which develop on post-mining sites play significant role in Carbon sequestration in new ecosystems, especially in local range on areas disturbed by human activity. This study presents the potential for Carbon sequestration in RMS developing on 3 post sur- face mining areas in Poland (Central Europe) reforested with Scots pine (Pinus sylvestris L). Research was conducted on waste heaps and quarry which accompany open cast lignite, sul- fur, and sand mining. Control plots were arrang- ed in managed pine forests on natural sites in the surrounding area. The results shows high Carbon accumulation in RMS, estimated on 16.77 Mg?ha-1 in poor (oligotrofic) soils on Quaternary sands on sand quarry and up to 65.03 Mg?ha-1 on external waste heap after Sulfur sur- face mining exploitation on Quaternary sands mixed with Tertiary clays. These results were very similar to natural forest soils on control plots. Potential rate of Carbon sequestration in RMS was estimated on 0.73 (on the poorest sa- ndy soils on quarry) to 2.17 Mg?ha-1?yr-1 (on potentially abundant sandy-clayish soils on Sulfur waste heap), and 5.26 Mg?ha-1?yr-1 (on Tertiary sands substrate soils on lignite mining waste heap). In conslusion the average Carbon accu- mulation in RMS was estimated on 41 Mg?ha-1 and Carbon sequestration rate was 1.45 Mg? ha-1?yr-1. According to the result of this study and range of post-mining areas reclaimed to forestry in Poland (ca 15000 ha) total Carbon accumulation in RMS was estimated on 615 × 103 Mg and potential Carbon sequestration rate in new ecosystems on 21.75 × 103 Mg?ha-1?yr-1. However, the main factors affecting Carbon sequestration and protection in RMS under tree stand were substrate, percentage of clay and silt sized fraction, in order to formulate guidelines for sustainable management of post-mining ec- osystem, further study must be continue for be- tter understanding.

Abstract:
We show that even moderate excess of neutrons over protons in nuclear matter, such as in ${}^{208} Pb$, can lead to large $\rho$-$\omega$ mixing at densities of the order of twice the nuclear saturation density and higher. The typical mixing angle is of the order of $10^o$. The mixing may result in noticeable shifts of the positions and widths of resonances. We also analyze temperature effects and find that temperatures up to 50 MeV have practically no effect on the mixing.