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...

merization of dental composite materials during lightcuring is a leading cause of adhesive restoration failure, resulting in postoperative sensitivity, marginal staining, and recurrent caries.1 This polymerization contraction shrinkage creates stresses as high as 13 MPa between the composite material and tooth interface2 (1 MPa = 145 psi). This stress can exceed the tensile strength of the enam...

The existence, uniqueness, and various forms of Ulam–Hyers (UH)-type stability results for nonlocal pantograph equations are developed extended in this study within the frame novel psi-piecewise Caputo fractional derivatives, which generalize piecewise operators recently presented literature. required proven using Banach’s contraction mapping Krasnoselskii’s fixed-point theorem. Additionally, p...

We provide an overview of the design of PSI (“a Private data Sharing Interface”), a system we are developing to enable researchers in the social sciences and other fields to share and explore privacy-sensitive datasets with the strong privacy protections of differential privacy. ∗This work is part of the “Privacy Tools for Sharing Research Data” project at Harvard, supported by NSF grant CNS-12...

let $g$ be a finite group‎. ‎we denote by $psi(g)$ the integer $sum_{gin g}o(g)$‎, ‎where $o(g)$ denotes the order of $g in g$‎. ‎here we show that‎ ‎$psi(a_5)< psi(g)$ for every non-simple group $g$ of order $60$‎, ‎where $a_5$ is the alternating group of degree $5$‎. ‎also we prove that $psi(psl(2,7))

The ability to assess the importance of secretin in various physiological processes is limited by the lack of specific potent antagonists. Recently, reduced peptide bond (psi) analogues of bombesin or substance P in which the -CONH- bond is replaced by -CH2NH- are reported to be receptor antagonists. To attempt to develop a new class of secretin receptor antagonists, we have adopted a similar s...