Related papers: On $(r,D,R)$-Blaschke-Santal\'o diagrams with regu…
Motivated by the barycenter problem in optimal transportation theory, Kolesnikov--Werner recently extended the notion of the Legendre duality relation for two functions to the case for multiple functions. We further generalize the duality…
The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$. First we study the basic properties of these maps such…
Bratteli--Vershik systems have been widely studied. In the context of general 0-dimensional systems, Bratteli--Vershik systems are homeomorphisms that have Kakutani--Rohlin refinements. Bratteli diagram has a strong power to analyze such…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
Motivated by the Blaschke-Santal\'o inequality, we define for a convex body K in ${\bf R}^n$ and for $t \in {\bf R}$ the Santal\'o-regions S(K,t) of K. We investigate properties of these sets and relate them to a concept of Affine…
We study the consistency of the non-Abelian Coulomb gauge. There are energy divergences in individual diagrams, which are known to cancel at 2-loop order when suitable sets of diagrams are summed. We investigate to 3-loop order the…
We investigate some properties of balayage of charges and measures for subclasses of subharmonic functions and their relationship to the geometry of domain or open set in finite-dimensional Euclidean space where this balayage is considered.
In view of future plans for accurate measurements of the theoretically clean branching ratios Br(K+ -> pi+ nu nu) and Br(KL -> pi0 nu nu), that should take place in the next decade, we collect the relevant formulae for quantities of…
In this paper our aim is to find the radii of $\gamma$-Spirallike of order $\alpha$ and convex $\gamma$-Spirallike of order $\alpha$ for three different kinds of normalizations of the function…
After many years of investigations, our understanding of the dynamics of strongly-coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly-coupled gauge theories, successfully applied to QCD, is…
We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…
This is a survey on recent developments on the Hausdorff dimension of projections and intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the Hausdorff dimension of exceptional sets and on restricted…
In this paper, we obtain new bounds for the Hausdorff dimension of planar elliptic measure via the application of quasiconformal mappings, with these bounds depending solely on the ellipticity constant of the matrix. In fact, in our case…
This paper addresses the challenge of spectral analysis and structural investigation for graphs that are not distance-regular, where computing the spectrum using standard methods based on equitable and orbit partitions can be complex. Our…
In this paper we introduce and study discrete analogues of Lebesgue and Hausdorff dimensions for graphs. It turned out that they are closely related to well-known graph characteristics such as rank dimension and Prague (or…
We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic…
We discuss the notions of circumradius, inradius, diameter, and minimum width in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the "size" of a given convex set in a finite-dimensional real vector space…
In this paper we present a novel approach in extremal set theory which may be viewed as an asymmetric version of Katona's permutation method. We use it to find more Tur\'an numbers of hypergraphs in the Erd\H{o}s--Ko--Rado range. An…
Recently, a large class of 3d $\mathcal{N} = 2$ gauge theories with mixed Chern-Simons levels, corresponding to plumbing 3-manifolds, has been identified. In this paper we generalize these theories by including in their content chiral…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…