Volterra-Prabhakar derivative of distributed order and some applications

The paper studies the exact solution of two kinds of generalized Fokker-Planck equations in which the integral kernels are given either by the distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or the distributed order Prabhakar function $k_{2}(\alpha, \gamma; \lambda; t) = \int_{0}^{1} e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t) d\mu$, where the Prabhakar function is denoted as $e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t)$. Both of these integral kernels can be called the fading memory functions and are the Stieltjes functions. It is also shown that their Stieltjes character is enough to ensure the non-negativity of the mean square values and higher even moments. The odd moments vanish. Thus, the solution of generalized Fokker-Planck equations can be called the probability density functions. We introduce also the Volterra-Prabhakar function and its generalization which are involved in the definition of $k_{2}(\alpha, \gamma; \lambda; t)$ and generated by it the probability density function $p_2(x, t)$

Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

What inverted U can do for your country: A curvilinear relationship between confidence in the social system and political engagement

We examined the link between political engagement and the tendency to justify the sociopolitical system. On one hand, confidence in the system should be negatively related to political engagement, insofar as it entails reduced desire for social change; on the other hand, system confidence should also be positively related to political engagement to the extent that it carries an assumption that the system is responsive to citizens' political efforts. Because of the combination of these 2 opposing forces, the motivation for political engagement should be highest at intermediate levels of system confidence. Five studies revealed a negative quadratic relationship between system confidence and normative political engagement. In 2 representative surveys, Polish participants with moderate levels of system confidence were more likely to vote in political elections (Study 1) and to participate in solidarity-based collective action (Study 2). Two field studies demonstrated a negative quadratic relationship between system confidence and actual participation in political demonstrations (gender equality and teachers' protests in Poland; Studies 3 and 4). This pattern of results was further corroborated by analyses of data from 50 countries drawn from the World Value Survey: we observed negative quadratic relationships between system confidence and collective action as well as voting. These relationships were stronger in democratic (vs. nondemocratic) regimes (Study 5). Our results suggest that some degree of system confidence might be useful to stimulate political engagement within the norms of the system

Direct observation of long-lived isomers in 212^{212}Bi

Long-lived isomers in 212Bi have been studied following 238U projectile fragmentation at 670 MeV per nucleon. The fragmentation products were injected as highly charged ions into the GSI storage ring, giving access to masses and half-lives. While the excitation energy of the first isomer of 212Bi was confirmed, the second isomer was observed at 1478(30) keV, in contrast to the previously accepted value of >1910 keV. It was also found to have an extended Lorentz-corrected in-ring halflife >30 min, compared to 7.0(3) min for the neutral atom. Both the energy and half-life differences can be understood as being due a substantial, though previously unrecognised, internal decay branch for neutral atoms. Earlier shell-model calculations are now found to give good agreement with the isomer excitation energy. Furthermore, these and new calculations predict the existence of states at slightly higher energy that could facilitate isomer de-excitation studies.Comment: published in PRL 110, 12250

T-cell subpopulations αβ and γδ in cord blood of very preterm infants : The influence of intrauterine infection

Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are creditedPreterm infants are very susceptible to infections. Immune response mechanisms in this group of patients and factors that influence cord blood mononuclear cell populations remain poorly understood and are considered insufficient. However, competent immune functions of the cord blood mononuclear cells are also described. The aim of this work was to evaluate the T-cell population (CD3+) with its subpopulations bearing T-cell receptor (TCR) αβ or TCR γδ in the cord blood of preterm infants born before 32 weeks of gestation by mothers with or without an intrauterine infection. Being a pilot study, it also aimed at feasibility check and assessment of an expected effect size. The cord blood samples of 46 infants age were subjected to direct immunofluorescent staining with monoclonal antibodies and then analyzed by flow cytometry. The percentage of CD3+ cells in neonates born by mothers with diagnosis of intrauterine infection was significantly lower than in neonates born by mothers without infection (p = 0.005; Mann-Whitney U test). The number of cells did not differ between groups. Infection present in the mother did not have an influence on the TCR αβ or TCR γδ subpopulations. Our study contributes to a better understanding of preterm infants' immune mechanisms, and sets the stage for further investigations.Peer reviewedFinal Published versio