The Cigler simple derivation of the q-Carlitz-Dobinski formula is recalled and it is noticed that the formula may be interpreted as the average of powers of random variable X q with the q-Poisson distribution. In parallel new q-Cigler-Dobinski and psi-Carlitz-Dobinski formulas are introduced. At first let us anticipate with ψ-remark. ψ denotes an extension of 1 n! n≥0 sequence to quite arbitrar...

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

A simple Rouse-type model, generalized to incorporate the effects of chemical cross-links, is used to obtain a theoretical prediction for the critical behavior of the normal-stress coefficients Psi(1) and Psi(2) in polymeric liquids when approaching the gelation transition from the sol side. While the exact calculation shows Psi(2) identical with 0, a typical result for these types of models, a...

This article is based on a pilot study that investigated the Swedish people’s awareness of Public Sector Information (PSI) directive, their understanding difference between PSI-directive and Access Act whether they had prerequisite skills required for use (PSI). Sweden has long tradition readily access to official documents which could have delayed implementation European was enacted in 2003. i...

Every word $w$ in a free group naturally induces probability measure on every compact $G$. For example, if $w=\left[x,y\right]$ is the commutator word, random element sampled by $w$-measure given $\left[g,h\right]$ of two independent, Haar-random elements Back 1896, Frobenius showed that $G$ finite and $\psi$ an irreducible character, then expected value $\psi\left(\left[g,h\right]\right)$ $\fr...

Abstract In this paper, we establish the Kobayashi–Hitchin correspondence, that is, equivalence of existence an Einstein–Hermitian metric and $\psi $-polystability a generalized holomorphic vector bundle over compact Kähler manifold symplectic type. Poisson modules provide intriguing bundles, obtain $-stable complex surfaces are not stable in ordinary sense.

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s doubl...

We study the transverse single-spin asymmetry (TSSA) in $p^{\uparrow}p \to J/\psi X$ reaction, incorporating both transverse-momentum and spin effects. To predict production cross section of prompt $J/\psi$ we use two different approaches, non-relativistic QCD (NRQCD) factorization approach Improved Color Evaporation Model (ICEM), show how predicted results for TSSAs depend on choice hadronizat...

Closed integral form expressions are derived for the Mathieu-type a-series and for the associated alternating series whose terms contain Fox’s H -function. In the final section, two similar results on Mathieu-type series with the Fox–Wright Psi-function pΨq and the generalized hypergeometric function pFq which can be expressed in terms of Fox’s H -functions are deduced respectively. c © 2006 El...

Results: Mean scores were 3.96 4.3 for the MGC and 7.66 4.6 for the QMGS. Neither scale fit the Rasch model (Xp<0.05). The MGC had lower PSI (0.14) than the QMGS (0.7). There was evidence of local dependency in both scales, as well as DIF for ocular and generalized disease. Disordered thresholds were found in 6(60%) items of the MGC and in 4(31%) of the QMGS. Collapsing response options did not...