The Hildebrand solubility parameters have been calculated for eight ionic liquids. Retention data from the inverse gas chromatography measurements of the activity coefficients at infinite dilution were used for the calculation. From the solubility parameters, the enthalpies of vaporization of ionic liquids were estimated. Results are compared with solubility parameters estimated by different me...

Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we present a simple proof of Hildebrand’s result.

Hildebrand proved that the smooth approximation for number $\varPsi (x,y)$ of $y$-friable integers not exceeding $x$ holds $y \gt (\log x)^{2+\varepsilon }$ under Riemann hypothesis and he conjectured it fails when $y\leqslant x)^{2

The technique for order of preference by similarity to ideal solution (TOPSIS) is a method based on the ideal solutions in which the most desirable alternative should have the shortest distance from positive ideal solution and the longest distance from negative ideal solution. Depending on type of evaluations or method of ranking, different approaches have been proposing to calculate distances ...

Abstract: In recent decades, high profits of extended warranty have caused that third-party firms consider it as a lucrative after-sales service. However, customers division in terms of risk aversion and effect of offering extended warranty on manufacturers’ basic warranty should be investigated through adjusting such services. Since risk-averse customers welcome extended warranty, while the cu...