Related papers: Helly's Theorem: New Variations and Applications
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
Given a map from a rectangle in the n-dimensional real Euclidean space into a metric semigroup, we introduce a concept of the total variation, which generalizes a similar concept due to T. H. Hildebrandt (1963) for real functions of two…
Brazitikos' results on quantititative Helly-type theorems (for the volume and for the diameter) rely on the work of Srivastava on sparsification of John's decompositions. We change this technique by a stronger recent result due to Friedland…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.
While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects
A separated $d$-interval is defined as a disjoint union of $d$ convex sets from the real line $\mathbb R$. In this paper, we establish a series of Helly-type theorems for convexity spaces derived from separated $d$-intervals. Our results…
Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i)…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving…
We develop a geometric invariant Littlewood-Paley theory for arbitrary tensors on a compact 2 dimensional manifold. We show that all the important features of the classical LP theory survive with estimates which depend only on very limited…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…