Related papers: On the Pappus arrangement of lines, forth and back…
The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, this type of…
We consider finite configurations of particles and holes sampled according to Bernoulli product measure and with a second class particle added to a random position. The stabilization time is the number of steps needed to reach an ordered…
In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes…
This is a short note on various results about the combinatorial properties of line arrangements in terms of the Chern numbers of the corresponding log surfaces. This resembles the study of the geography of surfaces of general type. We prove…
The ICH E9(R1) addendum (2019) proposed principal stratification (PS) as one of five strategies for dealing with intercurrent events. Therefore, understanding the strengths, limitations, and assumptions of PS is important for the broad…
The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical theorems. This idea leads to a new result generalizing…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
An efficient way to get implicit equations of conics on five points and quadrics on nine, using pencils of conics and quadrics, is revealed. Parallel axis right cones intersect on a conic. An example, to show how to place five coplanar…
We consider arrangements of $n$ pseudo-lines in the Euclidean plane where each pseudo-line $\ell_i$ is represented by a bi-infinite connected $x$-monotone curve $f_i(x)$, $x \in \mathbb{R}$, s.t.\ for any two pseudo-lines $\ell_i$ and…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
An analysis using a composition of currently-accepted theories is given. Starting with a synthesis of what may be generically termed ``paths'', analysis of representations for these ``paths'' is developed. Foreground and background…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
In this article we obtain the classification of the congruences of lines with one-dimensional focal locus. It turns out that one can restrict to study the case of $\mathbb{P}^3$.
The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…
We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…
In this paper we study polycubes: orthogonal polyhedra with axis-aligned quadrilateral faces. We present a complete characterization of polycubes of any genus based on their dual structure: a collection of oriented loops which run in each…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…