The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...

W is the category of archimedean l-groups with distinguished weak order unit, with l-group homomorphisms which preserve unit. This category includes all rings of continuous functions C(X) and all rings of measurable functions modulo null functions, with ring homomorphisms. The authors, and others, have studied previously the epimorphisms (right-cancellable morphisms) in W. There is a rich theor...

It is well known that a commutative ring R is complemented (that is, given a ∈ R there exists b ∈ R such that ab = 0 and a + b is a regular element) if an only if the total ring of quotients of R is von Neumann regular. We consider generalizations of the notion of a complemented ring and their implications for the total ring of quotients. We then look at the specific case when the ring is a rin...

This paper gives a characterization of the branch set of a finite covering X → S of a topological space S, by means of finite C(S)-subalgebras A of C(X) that separate points in X and the module ΩA/C(S) of its Kähler differentials.

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-inputsingle-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearlyparameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learnin...