Related papers: A restricted version of the Hilbert's 16th problem…
We derive lower und upper bounds for the degree of regularity of an overdetermined, zero-dimensional and homogeneous quadratic semi-regular system of polynomial equations. The analysis is based on the interpretation of the associated…
We prove that the maximal number of limit cycles which bifurcate from an open period annulus under a given multi-parameter analytic deformation of a given analytic vector field is the same as in an appropriate one-parameter analytic…
The study of the dynamics of a continuous observable and non-controllable three-dimensional symmetric piecewise linear system with three zones can be reduced to the study of the existence of limit cycles for the piecewise differential…
In this short note, we show that cutting cycles of rods is fixed-parameter tractable by reducing the problem to computing a feedback vertex set in a mixed graph.
A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
The discovery of Standard-Model like Higgs at 125 GeV may raise more questions than the answers it provides. In particular, the hierarchy problem remains unsolved, and the Standard Model Higgs quartic self-coupling becomes negative below…
We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices for each $n\in\{16,\ldots,30\}$. When $n\leq 21$, our bounds match the best known lower bounds, and we fully enumerate the densest…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
A vector-like extension of the standard model for heavier quarks and leptons with $SU(2)\times U(1)$ gauge symmetry and only one Higgs doublet is examined. This scheme incorporates infinitely many fermions and avoids the appearance of a…
Let $\xi$ be a real analytic vector field with an elementary isolated singularity at $0\in \mathbb{R}^3$ and eigenvalues $\pm bi,c$ with $b,c\in \mathbb{R}$ and $b\neq 0$. We prove that all cycles of $\xi$ in a sufficiently small…
The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…
This paper is devoted to the study of the maximum number of limit cycles, $H(m,n)$, of a planar piecewise linear differential system with two zones separated by the curve $y^n-x^m=0$, with $n,m$ being positive integers. More precisely, we…
In this paper we show the finite cyclicity of the two graphics $(I_{12}^1)$ and $(I_{13}^1)$ through a triple nilpotent point of saddle type inside quadratic vector fields. These results contribute to the program launched in 1994 by…
This paper is concerned with a linear quadratic optimal control for a class of singular Volterra integral equations. Under proper convexity conditions, optimal control uniquely exists, and it could be characterized via Frechet derivative of…
Let K be an algebraic function field of characteristic 2 with constant field C_K. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u,x of K with u…
Extensions of the Standard Model that include vector-like quarks commonly also include additional particles that may mediate new production or decay modes. Using as example the minimal linear $\sigma$ model, that reduces to the minimal…
We analyze the complex dynamics dynamics of a family of $\mathbb{Z}_{12}-$equivariant planar systems, by using their reduction to an Abel equation. We derive conditions in the parameter space that allow uniqueness and hyperbolicity of a…
The feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…