Let H̃r ∞,β denote those 2π-periodic, real-valued functions f on R, which are analytic in the strip Sβ := {z ∈ C : |Im z| < β}, β > 0 and satisfy the restriction |f (r)(z)| ≤ 1, z ∈ Sβ . Denote by [x] the integral part of x. We prove that the rectangular formula QN (f) = 2π N N−1 ∑

In this paper definitions of many sorted closure system and many sorted closure operator are introduced. These notations are also introduced in [9], but in another meaning. In this article closure system is absolutely multiplicative subset family of many sorted sets and in [9] is many sorted absolutely multiplicative subset family of many sorted sets. Analogously, closure operator is function b...

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This book investigates the central role of reason in Islamic intellectual life. Despite widespread characterization of Islam as a system of belief based only on revelation, JohnWalbridge argues that rational methods, not fundamentalism, have characterized Islamic law, philosophy, theology, and education since the medieval period. His research demonstrates that this medieval Islamic rational tra...

For any fixed positive integer n, the Smarandache ceil function of order k is denoted by N∗ → N and has the following definition: Sk(n) = min{x ∈ N : n | x}, ∀n ∈ N∗. In this paper, we study the mean value properties of the Smarandache ceil function, and give a sharp asymptotic formula for it.

Similar as to how films are accompanied with bonus features and extras on their dvd release, digital games too are sometimes released with supplemental materials which provide insight in the creative development process. Examples of these are behind-the-scenes documentaries, concept art, audio commentaries, and so on. In the study of digital games this material could easily be overlooked or pri...

As long as technological and social innovation and change continue at the current rapid pace, the profile of the ideal IS graduate and perfect undergraduate IS curriculum will remain open for debate. What is, however, gaining more general acceptance across many professions and disciplines including IS, is the need for university graduates who are ready and able to embrace and succeed in self-di...

Probabilistic methods involving maximum-likelihood parameter estimation have become a powerful tool in computational crystallography. At the centre of these methods are the relevant probability distributions. Here, equations are developed based on the complex multivariate normal distribution that generalize the distributions currently used in maximum-likelihood model and heavy-atom refinement. ...