Related papers: On a necessary and sufficient cyclicity condition …

Given a finite abelian group $G$ and cyclic subgroups $A$, $B$, $C$ of $G$ of the same order, we find necessary and sufficient conditions for $A$, $B$, $C$ to admit a common transversal for the cosets they afford. For an arbitrary number of…

We show that a necessary and sufficient condition for a cyclic code C over Z4 of odd length to be an LCD code is that C=(f(x)) where f is a self-reciprocal polynomial in Z4[X].

We prove that if the associated fourth order tensor of a quadratic form has a linear elastic cubic symmetry then it is quasiconvex if and only if it is polyconvex, i.e. a sum of convex and null-Lagrangian quadratic forms. We prove that…

Let $D$ be an directed graph on $p\geq 10$ vertices with minimum degree at least $p-1$ and minimum semi-degree at least $ p/2 -1$. We present a detailed proof of the following result [13]: The digraph $D$ is pancyclic, unless some extremal…

A convex quadrilateral, $Q$, is called a midpoint diagonal quadrilateral if the intersection point of the diagonals of $Q$ coincides with the midpoint of at least one of the diagonals of $Q$. A parallelogram, P, is a special case of a…

We present a necessary and sufficient condition for a cubic polynomial to be positive for all positive reals. We identify the set where the cubic polynomial is nonnegative but not all positive for all positive reals, and explicitly give the…

A Heron quadrilateral is a cyclic quadrilateral whose area and side lengths are rational. In this work, we establish a correspondence between Heron quadrilaterals and a family of elliptic curves of the form $y^2 = x3+/alpha x^2-n^2x.$ This…

This note is about an old conjecture of Voisin, which concerns zero--cycles on the self-product of surfaces of geometric genus one. We prove this conjecture for surfaces with $p_g=1$ and $q=2$.

Motivated by some questions in Euclidean Ramsey theory, our aim in this note is to show that there exists a cyclic quadrilateral that does not embed into any transitive set (in any dimension). We show that in fact this holds for almost all…

We prove that a strongly connected balanced bipartite digraph $D$ of order $2a$, $a\geq3$, satisfying $d(u)+d(v)\geq 3a$ for every pair of vertices $u,v$ with a common in-neighbour or a common out-neighbour, is either bipancyclic or a…

Let ${\mathbf P}^2$ denote the projective plane over a finite field ${\mathbb F}_q$. A pair of nonsingular conics $({\mathcal A}, {\mathcal B})$ in the plane is said to satisfy the Poncelet triangle condition if, considered as conics in…

We study algebras $A,$ over a field of characteristic zero, satisfying $(x^p, x^q, x^r)=0$ for $p, q, r$ in ${1, 2}.$ The existence of a unit element in such algebras leads to the third power-associativity. If, in addition, $A$ has degree…

It is shown that for a bounded weighted bilateral shift $T$ acting on $\ell_p(\Z)$ for $1\leq p\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient…

Let $\cD$ be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We establish a new sufficient condition for a function $f\in\cD$ to be {\em cyclic}, i.e. for $\{pf:…

In this paper we study some properties of quadrilaterals concerning concurrence of lines under few to none restrictive conditions, and obtain an extension of a transversal theorem from triangles to quadrilaterals.

With the $[0,1,2]$-family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic $q$-equivelar triangulations of orientable and non-orientable…

We apply the specialization technique based on the decomposition of the diagonal to find an explicit example over $\mathbb{Q}$ of a quadric and cubic hypersurface in $\mathbb{P}^6$ such that their intersection is a smooth stably irrational…

We give a complete proof of Thurston's Orbifold Theorem for very good 3-orbifolds of cyclic type. An orbifold is said to be very good when it has a finite cover which is a manifold. A 3-orbifold is of cyclic type if the singular set is a…

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…

Let $R=\mathbb{Z}_q+u\mathbb{Z}_q$, where $q=p^s$ and $u^2=0$. In this paper, some structural properties of cyclic codes over the ring $R$ are considered. A necessary and sufficient condition for cyclic codes over the ring $R$ to be free is…