Topological spaces—such as classifying spaces, configuration spaces and spacetimes—often admit directionality. Qualitative invariants on such directed spaces often are more informative, yet more difficult, to calculate than classical homotopy invariants because directed spaces rarely decompose as homotopy colimits of simpler directed spaces. Directed spaces often arise as geometric realizations...

In this paper, we determine two families R and G of subsets of a hyperring R and sufficient conditions such that two geometric spaces (R,R) and (R,G) are strongly transitive. Moreover, we prove that the relations Γ and α are strongly regular equivalence relations on a hyperfield or a hyperring such that (R,+) has an identity element.

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalizes the Patterson conjecture. We also extend the range of zeta functions in con...

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of the “almost” independence of the quasi-symplectic structure with respect to the metric. Finally conditions to have contact structures on these s...

On the OrliczCesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.

We give a few simple methods to geometically describe some polygon and chain spaces in R. They are strong enough to give tables of m-gons and m-chains when m ≤ 6.

We summarize the results on the differential geometric structure of Alexandrov spaces developed in [Otsu and Shioya 1994; Otsu 1995; Otsu and Tanoue a]. We discuss Riemannian and second differentiable structure and Jacobi fields on Alexandrov spaces of curvature bounded below or above.

Geometric scale spaces are derived for observed geometric structures and its properties. By means of the scale space representation of the jet of the input image connections are deened for implicitly deened structures highly correlated to the induced geometric structures of an object in D-dimensional Euclidean space. The evolution of surfaces and space curves with their properties is derived in...

Words are not detached individuals but part of an interconnected web of related concepts, and to capture the full complexity of this web they need to be represented in a way that encapsulates all the semantic and syntactic facets of the language. Further, to enable computational processing they need to be expressed in a consistent manner so that common properties, e.g. plurality, are encoded in...