Based on the analysis of stratification structure on random normed modules, we first present the notion of random smoothness in random normed modules. Then, we establish the relations between random smoothness and random strict convexity. Finally, a type of Gâteaux differentiability is defined for random norms, and its relation to random smoothness is given. The results are helpful in the furth...

We present a polynomial-time algorithm deciding bisimilarity between a normed BPA process and a normed BPP process. This improves the previously known exponential upper bound by Černá, Křet́ınský, Kučera (1999). The algorithm relies on a polynomial bound for the “finite-state core” of the transition system generated by the BPP process. The bound is derived from the “prime form” of the underlying...

In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate standard model elementary particles, and explore some applications cosmology. Remarkably, they permit interesting non-trivial realisations cosmological principle with an interplay between symmetry groups quaternions octonions. We also argue how these give rise potentially observational si...

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

The Khinchin–Kahane inequality is a fundamental result in the probability literature, with most general version to date holding Banach spaces. Motivated by modern settings and applications, we generalize this arbitrary metric groups which are abelian. If instead of abelian one assumes group's be norm (i.e., Z>0-homogeneous), then explain how improves same as This occurs via “transfer principle”...

Achievement and cognitive tests are used extensively in the diagnosis and educational placement of children with reading disabilities (RD). Moreover, research on scholastic interventions often requires repeat testing and information on practice effects. Little is known, however, about the test-retest and other psychometric properties of many commonly used measures within the beginning reader po...

Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of n points in strictly convex normed planes can be constructed in O(n log n) time. In addition, we confirm that, like in the Euclidean subcase, the 2-center problem with constrained circles can be solved also for strictly convex normed planes in O(n2) time. Some ideas for e...