The initial size of a completely susceptible population in a group of individuals plays a key role in drawing inferences for epidemic models. However, this can be difficult to obtain in practice because, in any population, there might be individuals who may not transmit the disease during the epidemic. This short note describes how to improve the maximum likelihood estimators of the infection r...

An audio-visual (AV) speech presentation mode can significantly improve spoken word identification. Language comprehension and communication in patients with Alzheimer disease (AD) can be compromised; however, little is known about the extent to which patients might benefit from an AV mode. Patients with mild cognitive impairment (MCI) are at risk for developing AD and can demonstrate parallel ...

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...