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A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new construction of the Berkovich analytic space associated to an affinoid algebra as the completion of a canonical uniform structure on the associated rigid-an...

The governing equation is ut= a x ux x, 0 x 1, t 0, u x ,0 =0, u 0, t =0, a 1 u 1, t = f t . The extra data are u 1, t =g t . It is assumed that a x is a piecewise-constant function and f 0. It is proved that the function a x is uniquely defined by the above data. No restrictions on the number of discontinuity points of a x and on their locations are made. The number of discontinuity points is ...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...