In this article, improved bounds for (kn)! and the factorial polynomial are obtained using Kober’s inequality and Lagrange’s identity.

The lattice Boltzmann method (LBM) was used to analyze two-dimensional (2D) non-Fourier heat conduction with temperature-dependent thermal conductivity. To this end, the evolution of wave-like temperature distributions in a 2D plate was obtained. The temperature distributions along certain parts of the plate, which was subjected to heat generation and constant thermal conductivity condit...

harkey & Sharkey (2010) have written a most interesting paper, raising interesting ethical and practical issues regarding robots as sole and parttime carers. What competencies can robots achieve in the near term? Can we experience social relatedness with them (and they with us)? Can robots care (in the sense of nurture) for us? Are their risks in deploying robots as carers for the young? Can we...

Let n, p, k be three positive integers. We prove that the numbers n k 3 F 2 (1 − k, −p, p−n ; 1, 1−n ; 1) are positive integers which generalize the classical binomial coefficients. We give two generating functions for these integers, and a straightforward application. z k k! , where for an indeterminate a and some positive integer k, the raising factorial is defined by (a) k = a(a + 1). .. (a ...