Related papers: On the existence of cyclic difference sets with sm…
In this paper we deal with the problem of finding the smallest and the largest elements of a totally ordered set of size $n$ using pairwise comparisons if $k$ of the comparisons might be erroneous where $k$ is a fixed constant. We prove…
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…
We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually…
We settle 22 conjectures of Cohen about cyclic numbers (positive integers $n$ with $\gcd(n,\varphi(n))=1$), proving 16 and disproving 6, and we completely resolve a related OEIS problem about sequences whose running averages are Fibonacci…
In this note we show that there are no real configurations of $d\geq 4$ lines in the projective plane such that the associated Kummer covers of order $3^{d-1}$ are ball-quotients and there are no configurations of $d\geq 4$ lines such that…
Let $p$ be a large odd prime, let $x=\log p)(\log\log p)^{3+\varepsilon}$ and let $q\ll\log\log p$ be an integer, where $\varepsilon>0$ is a small number. This note proves the existence of small prime quadratic residues and small prime…
We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters…
We consider the quotient variety associated to a linear representation of the cyclic group of order p in characteristic p>0. We estimate the minimal discrepancy of exceptional divisors over the singular locus. In particular, we give…
We say that a linear space is harmonious if it is resolvable and admits an automorphism group acting sharply transitively on the points and transitively on the parallel classes. Generalizing old results by the first author et al. we present…
A theorem on the existence of exactly $N$ limit cycles around a critical point for the Lienard system $\ddot{x}+f(x) \dot{x}+g(x) =0$ is proved. An alogrithm on the determination of a desired number of limit cycles for this system has been…
Motivated by the controllability/reachability problems for switched linear control systems and some classes of nonlinear (mechanical) control systems we address a related problem of existence of a cyclic vector for an associative (matrix)…
We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but…
We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices…
We prove a variety of results concerning singular sets of reals. Our results concern: Kysiak and Laver-null sets, Kocinac and gamma-k-sets, Fleissner and square Q-sets, Alikhani-Koopaei and minimal Q-like-sets, Rubin and sigma-sets, and…
New criteria are established for upper bounds on the number of limit cycles of periodic Abel differential equations having two periodic invariant curves, one of them bounded. The criteria are applied to obtain upper bounds of either zero or…
The aim of this paper is to extend and generalise some work of Katona on the existence of perfect matchings or Hamilton cycles in graphs subject to certain constraints. The most general form of these constraints is that we are given a…
Piecewise linear differential systems separated by two parallel straight lines of the type of center-center-Hamiltonian saddle and the center-Hamiltonian saddle-Hamiltonian saddle can have at most one limit cycle and there are systems in…
In this paper it was shown that all prime numbers lie on 96 half-lines. At the same time, it was shown that if a given number does not lie on any of the above half-lines, then it is a composite number. A corresponding linear mathematical…
In this paper we completely classify infinite cyclic projective skew translation quadrangles through a new approach first partially introduced in [17], and in the present paper (unexpectedly) adapted to the infinite case. Very surprisingly,…