In the first part we study general properties of the metrics obtained by isometrically identifying a generic metric space with a subset of a Banach space; we obtain a rigidity result. We then discuss the Hausdorff distance, proposing some less–known but important results: a closed–form formula for geodesics; generically two compact sets are connected by a continuum of geodesics. In the second p...

It is the objective of this paper to introduce a new class of generalizations of continuous functions via λ-open sets called weakly λcontinuous functions. Moreover, we study some of its fundamental properties. It turns out that weak λ-continuity is weaker than λ-continuity [1]. AMS Mathematics Subject Classification (2000): 54C10, 54D10

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new notions of ellipticity and hypoellipticity, study their interrelation, and give a number of new examples and counterexamples. Using the concept of G∞-regularity of...

Let X be a discrete subset of Euclidean d-space. We allow subsequently continuous movements of single elements, whenever the minimum distance to other elements does not decrease. We discuss the question, if it is possible to move all elements of X in this way, for example after removing a finite subset Y from X . Although it is not possible in general, we show the existence of such finite subse...

We extend classical results from the Colombeau algebra, concerning point-value characterizations of generalized functions, to the more general case of multi-parameter (C,E,P)–algebras. Our investigations include considerations of the different definitions of subspaces related to tempered generalized functions. AMS Mathematics Subject Classification (2010): 46F30, 46T30, 46A19, 46H10

In this paper, we consider the problem of farthest poinst for bounded sets in a real 2-normed spaces. We investigate some properties of farthest points in the setting of 2-normalised spaces and present various characterizations of b-farthest point of elements by bounded sets in terms of b-linear functional. We also provide some applications of farthest points in the setting of 2inner product sp...

In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Lévy processes. AMS 2010 Mathematics Subject Classification: Primary 60J45, Secondary 60J25, 60J50.

Goryunov proved that the space of local invariants of Vassiliev type for generic maps from surfaces to three-space is three-dimensional. The basic invariants were the number of pinch points, the number of triple points and one linked to a Rokhlin type invariant. In this paper we show that, by colouring the complement of the image of the map with a chess board pattern, we can produce a six-dimen...

This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras. AMS Mathematics Subject Classification: 06F35, 13A15, 8A...

As is well-known, the real quaternion division algebra H is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra O can not be algebraically isomorphic to any matrix algebras over the real number field R, because O is a non-associative algebra over R. However since O is an extension of H by the Cayley-Dickson process and is also finite-dimensional, som...