of “Rational Homotopy Calculus of Functors” by Ben C. Walter, Ph.D., Brown University, July 2005. We construct a homotopy calculus of functors in the sense of Goodwillie for the categories of rational homotopy theory. More precisely, given a homotopy functor between any of the categories of differential graded vector spaces (DG), reduced differential graded vector spaces, differential graded Li...

Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type ...

In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

In this research paper, the concepts of uniform fuzzy modules and semiuniform were studied. We discussed necessary sufficient conditions between (and modules) in set theory module theory.

One of basic principles in designing treatment environments is to design air conditioning/ventilation system proportionate to environment. Essentially, appropriate air conditioner in treatment spaces must bear the following capabilities: providing healthy and clean air, reducing the concentration of pollutants produced in the atmosphere, emission of pollutants and impeding their spread in exter...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

In this paper we prove convergence rates for the problem of approximating functions f by neural networks and similar constructions. We show that the rates are the better the smoother the activation functions are, provided that f satisses an integral representation. We give error bounds not only in Hilbert spaces but in general Sobolev spaces W m;r ((). Finally, we apply our results to a class o...