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We prove some properties of completely monotonic functions and apply them to obtain results on gamma and q-gamma functions.

The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites. We find the exact form of the stationary distribution of the number of incoming links of sites in the limit of long times, P(q), and the long-time limit of the average connectivity q(s,t) of a site s at time t (one site is added per unit of time). At long times,...

For $N\geq 3$, by the seminal paper of Brezis and V\'eron (Arch. Rational Mech. Anal. 75(1):1--6, 1980/81), no positive solutions $-\Delta u+u^q=0$ in $\mathbb R^N\setminus \{0\}$ exist if $q\geq N/(N-2)$; for $11$ $\theta\in \mathbb R$, we prove that nonlinear ell...

throughout the current study, the appropriate function for a description of egg production curve in a commercial broiler dam line was determined through fittings of a number of six mathematical models, namely: incomplete gamma function (wm): modified incomplete gamma function (mwm): compartmental function (cm): modified compartmental function )mcm): polynomial regression function of ali and sch...

X-ray flares are generally believed to be produced by the reactivation of central engine, and may have same energy dissipation mechanism as prompt emission gamma-ray bursts (GRBs). can therefore provide important clues understanding nature engines GRBs. In this work, we study for first time physical connection between differential size return distributions GRBs with known redshifts. We find tha...

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vignéras multiple gamma functions by considering the classical limit of the multiple q-gamma functions.

A novel analysis method named peak-to-charge ratio (V(p)/Q(total)) discrimination, aiming at background rejection especially for alpha decay self-activity in LaBr3: Ce scintillators has been developed. This method is based on a waveform analysis using the peak-to-charge ratio in the output waveform of a photomultiplier tube. The discrimination of alpha-induced events was achieved by using a thr...