Related papers: Some new periodic Golay pairs

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…

A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction.…

In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices. We give some basic properties and…

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. We study Ramsey-type problems in Gallai colorings. Given an integer $k\ge1$ and…

In \cite{Oz}, M. \"Ozdemir defined a new non-commutative number system called hybrid numbers. In this paper, we define the hybrid Fibonacci and Lucas numbers. This number system can be accepted as a generalization of the complex…

We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second order difference or differential operator. The most…

We consider a mirror symmetry between invertible weighted homogeneous polynomials in three variables. We define Dolgachev and Gabrielov numbers for them and show that we get a duality between these polynomials generalizing Arnold's strange…

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy conditions (i), (ii) below. (i) There exists a…

In this paper we consider periodic orbits of planar linear Filippov systems with a line of discontinuity. Unlike many publications researching only the maximum number of crossing periodic orbits, we investigate not only the number and…

First a formula for the number of zeros of the orthogonal polynomial in the intervals is presented. Then a criteria about the appearance of a zero in a gap is given. Finally a necessary and sufficient condition is derived such that the…

Classical Cepheid stars have been considered since more than a century as reliable tools to estimate distances in the universe thanks to their Period-Luminosity (P-L) relationship. Moreover, they are also powerful astrophysical…

We introduce mutually unbiased complex Hadamard (MUCH) matrices and show that the number of MUCH matrices of order 2n, n odd, is at most 2 and the bound is attained for n = 1,5,9. Furthermore, we prove that certain pairs of mutually…

To any graph we associate a sequence of integers called the gonality sequence of the graph, consisting of the minimum degrees of divisors of increasing rank on the graph. This is a tropical analogue of the gonality sequence of an algebraic…

In [J. Algebra 452 (2016), 372-389], we characterise when the sequence of free subgroup numbers of a finitely generated virtually free group $\Gamma$ is ultimately periodic modulo a given prime power. Here, we show that, in the remaining…

A graph is called homogeneously traceable if every vertex is an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for every integer $n\ge 9,$ there exists a homogeneously traceable nonhamiltonian graph of order…

Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.

The Collatz sequence for a given natural number $N$ is generated by repeatedly applying the map $N$ $\rightarrow$ $3N+1$ if $N$ is odd and $N$ $\rightarrow$ $N/2$ if $N$ is even. One elusive open problem in Mathematics is whether all such…

Characterizing existence or not of periodic orbit is a classical problem and it has both theoretical importance and many real applications. Here, several new criterions on nonexistence of periodic orbits of the planar dynamical system $\dot…

Explicit formulas are obtained for the number of periodic points and maximum tail length of split polynomial maps over finite fields for affine and projective space. This work includes a detailed analysis of the structure of the directed…

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display…