Learn More
In many practical applications, it is useful to represent a signal or an image by its average values on several fuzzy sets. The corresponding F-transform technique has many useful applications in signal and image processing. In principle, we can use different membership functions. Somewhat surprisingly, in many applications, the best results occur when we(More)
In many applications of interval computations, it turned out to be beneficial to represent polynomials on a given interval [x, x] as linear combinations of Bernstein polynomials (x − x) k · (x − x) n−k. In this paper, we provide a theoretical explanation for this empirical success: namely, we show that under reasonable optimality criteria, Bernstein(More)
One of the main problems with neural networks is that they are often very slow in learning the desired dependence. To speed up neural networks, Bruno Apolloni proposed to othogonalize neurons during training, i.e., to select neurons whose output functions are orthogonal to each other. In this paper, we use symmetries to provide a theoretical explanation for(More)
Several pyrimidine derivatives of ivalin acetate were synthesized as potential anti HIV agents. High stereoselective Michael addition to ivaline acetate was observed and a new C-C, C-N or C-S bond was formed. 2D NMR 1H and 13C as well as X-ray crystallographic studies were performed on the compounds herein described to establish the structure and(More)
In many applications, we have numerous molecules that are obtained from a " template " molecule like benzene C6H6 or cubane C8H8 by replacing some of its hydrogen atoms with other atoms or atom groups (called ligands). Depending on how many original atoms are replaced and which ones are replaced, we obtain a large number of different chemical substances. It(More)
The costunolide lactone, a sesquiterpene compound isolated from Zaluzania triiloba species, reacted with several dihalocarbene sources produced by trihaloform-NaOH under successive phase transfer reactions yielding mono-, bis- and tris-dihalocyclopropane adducts. The structures, as well as the configurational assignments of the different derivatives, were(More)
In fuzzy control, two approaches are mainly used: Mamdani's approach, in which we represent the knowledge base as a disjunction of statements A<inf>i</inf>(x) &amp; B<inf>i</inf>(u) corresponding to individual rules, and logical approach, in which the knowledge base is represented as a conjunction of the rules themselves A<inf>i</inf>(x) &#x2192;(More)