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Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors…

In this note, we investigate some topological properties of probabilistic modular spaces.

The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set. We see, in particular, that some topological conditions are sufficient to guarantee that these sets…

This paper presents a new version of boundary on coarse spaces. The space of ends functor maps coarse metric spaces to uniform topological spaces and coarse maps to uniformly continuous maps.

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…

We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained…

We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of…

We describe all possible topological structures of codimension one gradient vector fields on the shpere with at most ten singular points. To describe structures, we use a graph whose edges are one-dimensional stable manifolds. The…

A direct saddle-point analysis (without relying on any modular forms, identities or functional equations) is developed to establish the asymptotics of Fishburn matrices and a large number of other variants with a similar sum…

Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…

We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.

A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in…

This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…

This paper develops the necessary ingredients for the variational approach of initial boundary-value problems of parabolic partial differential equations on a fixed spatial domain containing evolving subdomains. In particular, we introduce…

In this paper we classify all topological vector spaces with linear topology with the property that all algebraic automorphisms are continuous. Moreover, we prove some properties of these spaces.

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…

Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…

We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.

Kendall's Similarity Shape Theory for constellations of points in the carrier space $\mathbb{R}^n$ was developed for use in Probability and Statistics. It was subsequently shown to reside within (Classical and Quantum) Mechanics'…