Densities of the Raney distributions

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, $0<r\le p$, then $\mu(p,r)$ is absolutely continuous and its density $W_{p,r}(x)$ can be expressed in terms of the Meijer and the generalized hypergeometric functions. In some cases, including the multiplicative free square and the multiplicative free square root of the Marchenko-Pastur measure, $W_{p,r}(x)$ turns out to be an elementary function

ANALYSIS OF PROFITABILITY OF TRANSFORMATION OF THE PERPETUAL USUFRUCT RIGHT INTO THE RIGHT OF PROPERTY AT VARIOUS TIMES IN THE DURATION OF THE PERPETUAL USUFRUCT RIGHT

In view of the growing interest of foreign investors in investments in Poland, especially since Poland’s accession to the European Union, this article analyzes the profitability of the transformation of the perpetual usufruct law into the right of property at various times in the duration of this right, on the basis of the empirical formula presented in Polish law (the legal act) – The Ordinance of the Council of Ministers on the valuation of real estate and the estimated cadastre survey. It was analysed how the fee for the transformation of the perpetual usufruct law into the right of property changes depending on the assumed rate of capitalization, interest rate on the annual fee, the number of years in the unused period of usufruct.perpetual usufruct right, capitalization rate, Land Economics/Use,

Coherent States from Combinatorial Sequences

We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of the resolution of unity in a natural way. In each case the positive weight functions are given as solutions of associated Stieltjes or Hausdorff moment problems, where the moments are the combinatorial numbers.Comment: 4 pages, Latex; Conference 'Quantum Theory and Symmetries 2', Krakow, Poland, July 200

Resonance saturation in the odd-intrinsic parity sector of low-energy QCD

Using the large N_C approximation we have constructed the most general chiral resonance Lagrangian in the odd-intrinsic parity sector that can generate low energy chiral constants up to O(p^6). Integrating out the resonance fields these O(p^6) constants are expressed in terms of resonance couplings and masses. The role of eta' is discussed and its contribution is explicitly factorized. Using the resonance basis we have also calculated two QCD Green functions of currents: and and found, imposing high energy constraints, additional relations for resonance couplings. We have studied several phenomenological implications based on these correlators from which let us mention here our prediction for the pi0-pole contribution to the muon g-2 factor: $a_\mu^{\pi^0} = 65.8(1.2)\times 10^{-11}$.Comment: 42 pages, 3 figure

Average fidelity between random quantum states

We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by partial trace and the natural measure on the space of pure states. In certain cases explicit probability distributions for fidelity are derived. Results obtained may be used to gauge the quality of quantum information processing schemes.Comment: 15 revtex pages with 4 figures; Ver. 2: another distribution derived, an extra figure included, Ver. 3: comments in introduction and conclusion added ver 4. minor improvment