Related papers: On some points-and-lines problems and configuratio…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…

This paper presents a family of new methods for locating/fitting hyperplanes with respect to a given set of points. We introduce a general framework for a family of aggregation criteria of different distance-based errors. The most popular…

We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.

This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We…

We establish some new theorems on pentagon and pentagram.

In this paper we construct several arrangements of lines and/or conics that are derived from the geometry of the Klein arrangement of $21$ lines in the complex projective plane.

We study three covering problems in the plane. Our original motivation for these problems come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up to four unit-sized, axis-parallel…

Singularities of plane into plane mappings described by parabolic two-component systems of quasi-liner partial differential equations of the first order are studied. Impediments arising in the application of the original Whitney's approach…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…

The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…

This study presents novel methods for computing fixed points of positive concave mappings and for characterizing the existence of fixed points. These methods are particularly important in planning and optimization tasks in wireless…

For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.

We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…

We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…

On objects of a triangulated category with a stability condition, we construct a topology.

It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.