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In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
Harmonic superspaces for spacetimes of dimension $d\leq 3$ are constructed. Some applications are given.
We use convergence theory as the framework for studying H-closed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space…
In this paper we suggest how the mathematical concept of hyperstructures may be a useful tool in the study of the higher, hierachical structure of languages.
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be…
The supersymmetric extensions of the Schr\"odinger algebra are reviewed.
Higher order anisotropic superspaces are constructed as generalized vector superbundles provided with compatible nonlinear connection, distinguished connection and metric structures.
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
It is shown that Nobeling spaces are uniquely determined by the universal extension and embedding properties.