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In this paper we introduce the notion of a quasi-modular and we prove that the respective Minkowski functional of the unit quasi-modular ball becomes a quasi-norm. In this way, we refer to and complete the well-known theory related to the…
We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semisimple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a…
We explore the topology of configuration spaces of hard disks experimentally, and show that several changes in the topology can already be observed with a small number of particles. The results illustrate a theorem of Baryshnikov, Bubenik,…
We experimentally observe lasing in a hexamer plasmonic lattice and find that when tuning the scale of the unit cell, the polarization winding of the emission changes. By a theoretical analysis we identify the lasing modes as quasi bound…
We develop the theory of invariant structure preserving and free functions on a general structured topological space. We show that an invariant structure preserving function is pointwise approximiable by the appropriate analog of…
We give a new formulation and proof of a theorem of Halmos and Wallen on the structure of power partial isometries on Hilbert space. We then use this theorem to give a structure theorem for a finite set of partial isometries which…
We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present certain corollaries of this result.
We study topological aspects of a compact lattice superconductor, and show that the characteristic energy splitting, $\Delta$, between almost degenerate ground states, is simply related to a novel order parameter $\tilde W$, which is…
In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact (or monotonically countably metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps.…
We consider the Zariski space of all places of an algebraic function field $F|K$ of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime…
Linkages are mechanical devices constructed from rigid bars and freely rotating joints studied both for their utility in engineering and as mathematical idealizations in a number of physical systems. Recently, there has been a resurgence of…
We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…
We initiate systematic study of EZ-structures (and associated boundaries) of groups acting on spaces that admit consistent and conical (equivalently, consistent and convex) geodesic bicombings. Such spaces recently drew a lot of attention…
In this paper we give two complete characterizations of the Poletsky- Stessin- Hardy spaces in the complex plane: First in terms of their boundary values as a weighted subclass of the usual $L^p$ class with respect to the arclength measure…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
In this paper, we study partitions of positive integers into distinct quasifibonacci numbers. A digraph and poset structure is constructed on the set of such partitions. Furthermore, we discuss the symmetric and recursive relations between…
We consider spaces of high-energy quasimodes for the Laplacian on a compact hyperbolic surface, and show that when the spaces are large enough, one can find quasimodes that exhibit strong localization phenomena. Namely, take any constant c,…