This derivation of (2) is not valid, because this duality applies to inferences and theorems only, not to definitions. In fact, (1) should be treated as an axiom. Accordingly, the duality of Lemma 3.3.1 would not be valid until the dual (2) of (1) is proved independently, as we do below. Our new proof will make use of Proposition 3.3.3, the original proof of which is based on duality. So, we mu...

Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

primary hepatic lymphoma is a rare malignancy usually presenting with symptoms of fever, hepatomegaly, jaundice and weight loss. this picture mimics infectious and inflammatory disorders and thus delays the diagnosis. here, we present a 47-year old man with prolonged fever who underwent several investigations and, in the meantime, developed fulminant hepatic failure before the diagnosis could b...

This book represents a delightful collection of essays on Welsh sport, in particular the Welsh sport of rugby union football and its place in Welsh society. Gareth Williams has provided sports historians with some of the best accounts of sport in the Principality over the years and 1905 And All That is no exception. Avid readers of sports history will recognise some of the articles, however, si...

In this state-of-the-art paper, important advances that have been made during the past five years for both general and interval type-2 fuzzy sets and systems are described. Interest in type-2 subjects is worldwide and touches on a broad range of applications and many interesting theoretical topics. The main focus of this paper is on the theoretical topics, with descriptions of what they are, wh...

After the boom of pharmacological research during the 1950s, mainly as a result of the screening technique, the identification of active molecules, their reshaping by means of pharmaco-chemical drug design, and the creation of extremely efficacious and successful medicines, the pharmaceutical world sought a new source of inspiration. Such biota as the tropical forest, a quantity of plants credi...

There are ideas about Bhuta found in Ancient Tamil Literatures. They Fall into Three categories. Among them, natural objects (five elements) associated with Religion, the worship god Sathukka is Sramana Religions like Jainism, Bhddhism, and protective Ganam or collective Bhutas Saivism. This Article examines these three types of detail.

al-ghallābī is rated as among the shī‘ī authors of the third/eighth century, through whom many historical traditions have been related in shī‘ī and sunnī sources. examining the status of al-ghallābī’s traditions in the two major sects (of shī‘a and sunnī), this writing is intended to find the reason for the permeation of his traditions into the sources belonging to the sunnīs – who are very cau...