相关论文: Graphical patterns in quadratic residues

We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.

We study topological properties of the graph topology.

We study cliques in graphs arising from quadratic forms where the vertices are the elements of the module of the quadratic form and two vertices are adjacent if their difference represents some fixed scalar. We determine structural…

We study functional graphs generated by quadratic polynomials over prime fields. We introduce efficient algorithms for methodical computations and provide the values of various direct and cumulative statistical parameters of interest. These…

Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.

Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…

This paper is a short survey of the recent results on examples of periodic two-dimensional continued fractions (in Klein's model). In the last part of this paper we formulate some questions, problems and conjectures on geometrical…

We obtain transformation formulas for quadratic character sums with quartic and cubic polynomial arguments.

It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

We describe convex quadric surfaces in n dimensions and characterize them as convex surfaces with quadric sections by a continuous family of hyperplanes.

In this work we deal with a symbolic approach to the general quadratic polynomial decomposition. By means of a symbolic implementation, we investigate some properties of the components sequences like orthogonality and symmetry. We present…

We determine the structure of linear maps on the tensor product of matrices which preserve the numerical range or numerical radius.

The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane…

We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. Nous proposons un tour d'horizon de propri\'et\'es math\'ematiques des…

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth.

Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…

The existence of conservative quasipolynomial (QP) maps is investigated. A classification is given for dimensions two and three, and the analytical solution of the former case is constructed. General properties of n-dimensional QP…

We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…