We present a McShane-Whitney extension theorem for real-valued fuzzy Lipschitz maps defined between metric spaces. Motivated by the potential applications of obtained results, we generalize mathematical theory extensions to context. develop problem in its full generality, explaining similarities and differences with classical case on

We introduce the notion of a Whitney dual graded poset. Two posets are duals to each other if (the absolute value of) their numbers first and second kind interchanged between two posets. define new types edge labelings which we call labelings. prove that every poset with labeling has dual. Moreover, show how explicitly construct using technique involving quotient As applications our main theore...

The Wilcoxon-Mann-Whitney statistic is commonly used for a distribution-free comparison of two groups. One requirement for its use is that the sample sizes of the two groups are fixed. This is violated in some of the applications such as medical imaging studies and diagnostic marker studies; in the former, the violation occurs since the number of correctly localized abnormal images is random, w...

In this paper we show Whitney’s fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivial...