In this paper, we study arithmetic properties of weighted Catalan numbers. Previously, Postnikov and Sagan found conditions under which the 2-adic valuations numbers are equal to We obtain same result weaker by considering a map from class functions integers. These methods also extended q-weighted numbers, strengthening previous Konvalinka. Finally, prove some results on periodicity modulo an i...

We examine oscillations in a number of sums arithmetic functions involving [Formula: see text], the total prime factors and distinct text]. In particular, we text] for show example that each inequalities is true infinitely often, disproving some hypotheses Sun.

A fundamental task in reputation systems is to aggregate multiple feedback ratings into a single value that can be used to compare the reputation of different entities. Feedback is most commonly aggregated using the arithmetic mean. However, the mean is quite susceptible to outliers and biases, and thus may not be the most informative aggregate of the reports. We consider three criteria to asse...

A phenetic analysis of the 12 taxa or operational taxonomic units (OTUs) belonging to the three sections; Genea, Neobromus, and Nevskiella of the genus Bromus was performed. Unweighted pair-group method using arithmetic averages (UPGMA) and weighted pair-group method using arithmetic averages (WPGMA) clustering and factoriel method analyses were used to set the taxa apart. Forty-four characters...

In this paper, we have proved two main theorems under more weaker conditions dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series. We also obtained certain new results on the different methods.