We investigate non-homogeneous linear differential equations of the form x′′(t) + x′(t) − x (t) = p (t) where p (t) is either a polynomial or a factorial polynomial in t. We express the solution of these differential equations in terms of the coefficients of p (t), in the initial conditions, and in the solution of the corresponding homogeneous differential equation y′′(t) + y′(t) − y (t) = 0 wi...

It is reported that every year hundreds of bridges were collapsed due to the dynamic forces acting on piers particularly during floods and scour around foundations. Since determination velocity distribution upstream pier directly related with this force, it important predict effect a presence diameter bridge turbulence parameters. In study, time variation point velocities in stream-wise vertica...

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

Older adults are more likely than young to fall upon a loss of balance, yet the factors responsible for this difference are not well understood. This study investigated whether age-related differences in movement stability, limb support, and protective stepping contribute to the greater likelihood of falling among older adults. Sixty young and 41 older, safety-harnessed, healthy adults were exp...

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 ...

A combined PLL/DLL algorithm is developed for tracking GNSS carrier phase and code phase using the output from a large number of correlators. This approach has advantages for limb-scanning applications, in which useful meteorological information, available only at the initial rising time of a GPS satellite, is desired. The technique uses the bank of correlators to span wide ranges of uncertaint...