Related papers: On the parameter space of B\"or\"oczky configurati…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
Planar point sets with many triple lines (which contain at least three distinct points of the set) have been studied for 180 years, started with Jackson and followed by Sylvester. Green and Tao has shown recently that the maximum possible…
Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of…
This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a planar 4-bar linkage. Building upon the previous work from Izmestiev (2015), this library expands on the…
The purpose of this note is to provide an overview of the containment problem for symbolic and ordinary powers of homogeneous ideals, related conjectures and examples. We focus here on ideals with zero dimensional support. This is an area…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
We construct a strongly regular graph with the parameters (65; 32; 15; 16). The idea is to search for an adjacency matrix that consists of circulant blocks. Equations with such matrices can be reduced to congruences with polynomials…
The purpose of this note is to find an elemenary explanation of a surprising result of Ein--Lazarsfeld--Smith \cite{ELS} and Hochster--Huneke \cite{HH} on the containment between symbolic and ordinary powers of ideals in simple cases. This…
We review a new formalism based on Orlicz spaces for the description of large regular statistical systems. Our presentation includes both classical and quantum systems. The presented approach has the advantage that statistical mechanics is…
I introduce the problem of finding maximal sets of equiangular lines, in both its real and complex versions, attempting to write the treatment that I would have wanted when I first encountered the subject. Equiangular lines intersect in the…
We analyze the parameter space of harmonic trinomial equations of the form $z^{n+m}+b\overline{z}^m+c$, where $n,m\in\mathbb{Z}^+$ are coprime and $b,c\in\mathbb{C}$. Using versions of the Bohl and Egerv\'ary theorems for harmonic…
In this paper, we investigate the numerous parameters choices for linear lattice Boltzmann schemes according to the definition of the isotropic order given in \cite{ADG11}. This property---written in a general framework including all of the…
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type…
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…
In this paper we consider metrics determined by hierarchical posets and give explicit formulae for the main parameters of a linear code: the minimum distance and the packing, covering and Chebyshev radii of a code. We also present ten…
Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+\epsilon}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description…
We consider the finiteness problem for central configurations of the $n-$body problem. We prove that, for $n\geq4$, there exists a (Zariski) closed subset $B$ in the mass space $\mathbb{R}^{n}$, such that if $(m_1,...,m_n) \in…