Related papers: Extensions of Steiner Triple Systems
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
We enumerate total cyclic orders on $\left\{1,\ldots,n\right\}$ where we prescribe the relative cyclic order of consecutive triples $(i,{i+1},{i+2})$, these integers being taken modulo $n$. In some cases, the problem reduces to the…
The derivation of a new family of magnetic fields inducing exactly solvable spin evolutions is presented. The conditions for which these fields generate the evolution loops (dynamical processes for which any spin state evolves cyclically)…
In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi-Koppinen structures and dual Doi-Koppinen modules introduced (in the infinite case over…
We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a…
We study $S(t-1,t,2t)$, which is a special class of Steiner systems. Explicit constructions for designing such systems are developed under a graph-theoretic platform where Steiner systems are represented in the form of uniform hypergraphs.…
Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper,…
We introduce the notion of poly-stable pairs of formal schemes over the valuation ring of a non-archimedean field. For such pairs we define and investigate the dual intersection complex. We proceed to develop the so called extended skeleton…
A Euclidean noncrossing Steiner $(1+\epsilon)$-spanner for a point set $P\subset\mathbb{R}^2$ is a planar straight-line graph that, for any two points $a, b \in P$, contains a path whose length is at most $1+\epsilon$ times the Euclidean…
The complexification of field variables is an elegant approach to attack the sign problem. In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays constant and can be factored out of the…
In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector…
In this work we intend to report on some results obtained by an analytical modelling of biomacromolecular structures as driven by the study of Steiner points and Steiner trees with an Euclidean definition of distance.
In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order $v$, where $v=3^k$, and $3$-rank $v-k$. We develop an…
We study a new class of vector solitons in trapped Nonlinear Schrodinger systems modelling the dynamics of coupled light beams in GRIN Kerr media and atomic mixtures in Bose-Einstein condensates. These solitons exist for different spatial…
On a basis of theory of Riemann extension of the space of constant affine connection associated with the R\"ossler system of equations relations between its parameters are investigated.
The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of…
Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…
In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.
Given a $2$-$(v,k,\lambda)$ design, $\cal{S}=(X,\cal{B})$, a {\it zero-sum $n$-flow} of $\cal{S}$ is a map $f: \cal{B} \longrightarrow \{\pm 1, \ldots ,\pm (n-1)\}$ such that for any point $x\in X$, the sum of $f$ around all the blocks…
In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of…