Normann proved that the domains of the game model of PCF (the domains of sequential functionals) need not be dcpos. Sazonov has defined natural domains for a theory of such incomplete domains. This paper further develops that theory. It defines lub-rules that infer natural lubs from existing natural lubs, and lub-rule classes that describe axiom systems like that of natural domains. There is a ...

In this paper, I would like to propose an idea of semantics for discourse and pictorial representations. The central notion of this paper is function. A representation is a representation of something. A function determines the connection between representation and what is represented. This is true for both discourse and pictorial representations. To properly interpret a representation system m...

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...