Some observations on the connection between Stirling numbers and Bessel numbers

We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular recurrence relation in two different ways and comparing the coefficients in the resulting polynomial expressions. We also briefly discuss a probabilistic setting where this recurrence relation occurs.Comment: 10 page

On occupation times of one-dimensional diffusions

In this paper we study the moment generating function and the moments of occupation time functionals of one-dimensional diffusions. Assuming, specifically, that the process lives on $\mathbb{R}$ and starts at~0, we apply Kac's moment formula and the strong Markov property to derive an expression for the moment generating function in terms of the Green kernel of the underlying diffusion. Moreover, the approach allows us to derive a recursive equation for the Laplace transforms of the moments of the occupation time on $\mathbb{R}_+$. If the diffusion has a scaling property, the recursive equation simplifies to an equation for the moments of the occupation time up to time 1. As examples of diffusions with scaling property we study in detail skew two-sided Bessel processes and, as a special case, skew Brownian motion. It is seen that for these processes our approach leads to simple explicit formulas. The recursive equation for a sticky Brownian motion is also discussed.Comment: 32 page

Longitudinal stability and interrelations between health behavior and subjective well-being in a follow-up of nine years

Background The bidirectional relationship between health behavior and subjective well-being has previously been studied sparsely, and mainly for individual health behaviors and regression models. In the present study, we deepen this knowledge focusing on the four principal health behaviors and using structural equation modeling with selected covariates. Methods The follow-up data (n = 11,804) was derived from a population-based random sample of working-age Finns from two waves (2003 and 2012) of the Health and Social Support (HeSSup) postal survey. Structural equation modeling was used to study the cross-sectional, cross-lagged, and longitudinal relationships between the four principal health behaviors and subjective well-being at baseline and after the nine-year follow-up adjusted for age, gender, education, and self-reported diseases. The included health behaviors were physical activity, dietary habits, alcohol consumption, and smoking status. Subjective well-being was measured through four items comprising happiness, interest, and ease in life, and perceived loneliness. Results Bidirectionally, only health behavior in 2003 predicted subjective well-being in 2012, whereas subjective well-being in 2003 did not predict health behavior in 2012. In addition, the cross-sectional interactions in 2003 and in 2012 between health behavior and subjective well-being were statistically significant. The baseline levels predicted their respective followup levels, the effect being stronger in health behavior than in subjective well-being. Conclusion The four principal health behaviors together predict subsequent subjective well-being after an extensive follow-up. Although not particularly strong, the results could still be used for motivation for health behavior change, because of the beneficial effects of health behavior on subjective well-being.Peer reviewe

Neutral Pion Distributions in PHENIX at RHIC

Transverse momentum spectra for identified $\pi^0$'s in the range 1 GeV/c $< p_T <$ 4 GeV/c have been measured by the PHENIX experiment in Au-Au collisions at $\sqrt{s}=130$ GeV. The spectra from peripheral nuclear collisions are consistent with the simple expectation of scaling the spectra from p+p collisions by the average number of nucleon-nucleon binary collisions. The spectra from central collisions and the ratio of central/peripheral spectra are significantly suppressed when compared to point-like scaling.Comment: 6 pages, 3 figure

PHENIX measurement of jet properties and their modification in heavy-ion collisions

The properties of jets produced in p+p, d+Au and Au+Au collisions at sqrt{s_NN}=200 GeV are studied using the method of two particle correlations. The trigger particle is assumed to be a leading particle from a high p_T jet while the associated particle is assumed to come from either the same jet or the away jet. From the angular width and yield of the same and away side correlation peaks, the parameters characterizing the jet properties are extracted.Comment: 4 pages, 3 figures, contribution to the proceedings of the 17th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter, Oakland, January 11-17, 2004). To appear in the proceedings (Journal of Physics G

Hadron production in the forward and backward rapidities in dAu collisions at RHIC

We have developed new techniques to detect hadrons with the PHENIX muon spectrometers. This allows us to study the centrality dependent nuclear modification factor $R_{CP}$ with high $p_{T}$ hadrons in both forward (d direction) and backward (Au direction) rapidities, $1 < |\eta| < 2$, in dAu collisions at $\sqrt{s_{NN}} = 200 GeV$. Preliminary results show a suppression (enhancement) of high $p_{T}$ hadron production in central $0-20$ dAu collisions relative to the peripheral one ($60-88$ in centrality) at forward (backward) rapidity.Comment: 4 pages, 4 figures, Quark Matter 2004 tal

Two Particle Azimuthal Correlation Measurements in PHENIX

Two particle azimuthal correlation functions are presented for charged hadrons produced in Au-Au collisions at RHIC sqrt(s_NN)=200 GeV.The correlation functions indicate sizeable asymmetries and anisotropies. The trend of the asymmetries is compatible with the presence of emission patterns associated with mini-jets. The magnitude and the trend of the differential anisotropies v_2(p_T) and v_2(N_Part), provide important model constraints.Comment: 4 pages 3 fig

Results on Photon Production in Au+Au Collisions at RHIC

The status of the search for direct photons in Au+Au collisions at sqrt{s_NN} = 130 GeV and sqrt{s_NN} = 200 GeV with the PHENIX experiment is presented. Within errors, no excess of direct photons was found in a first analysis pass done on a limited data set. Significantly reduced systematic and statistical uncertainties are expected in future analyses.Comment: 4 pages, 3 figures. Talk presented at the Quark Matter 2002 conference, Nantes, France, July 18-24, 2002. To appear in the proceedings (Nucl. Phys. A