Ψ(x, y) denotes the number of positive integers ≤ x and free of prime factors > y. Hildebrand and Tenenbaum provided a good approximation of Ψ(x, y). However, their method requires the solution α = α(x, y) to the equation ∑ p≤y log p/(p α−1) = log x, and therefore it needs a large amount of time for the numerical solution of the above equation for large y. Hildebrand also showed 1 − ξu/ log y a...

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

The sketch deals w ith the problems of poetic letter. During exemplification issue, poems by Julian Przyboś, Cyprian Norwid and Ignacy Krasicki are used. It turns out that important issues can be seen from perspective selected, but also deep anthropological problems, arising interpretative process. tools for understanding them provided thinkers post-Husserlian phenomenology, in this case Dietri...

Schiffbase was obtained by condensation of camphor with 4-amino-phenol .The charge transfer complex of the Schiff base as a donor molecule with picric acid as acceptor molecule in methanol were estimated. Schiff-base compound and charge transfer complex were identified by elemental analysis, infrared spectra and UV-visible spectra.The physical parameters of the CT complex were calculated by app...

We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory–Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. This anomalous behavior results from combining features of Hildebrand’s two-sided discontinuous extreme functions and Basu–Hildebrand–Köppe’s piecewise linear extreme funct...

Tilman Laubert ([email protected]) Jens K Habermann ([email protected]) Claudia Hemmelmann ([email protected]) Markus Kleemann ([email protected]) Elisabeth Oevervmann ([email protected]) Ralf Bouchard ([email protected]) Philipp Hildebrand ([email protected]) Thomas Jungluth ([email protected]) Conny Bürk (Conny.Buerk...