Related papers: Mutually orthogonal frequency rectangles
A \emph{frequency square} is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only {\em binary} frequency squares of order $n$ with $n/2$ zeroes and $n/2$ ones in each row and column. Two…
Mutually orthogonal frequency squares (MOFS) of type $F(m\lambda;\lambda)$ generalize the structure of mutually orthogonal Latin squares: rather than each of $m$ symbols appearing exactly once in each row and in each column of each square,…
A frequency square is a square matrix in which each row and column is a permutation of the same multiset of symbols. A frequency square is of type $(n;\lambda)$ if it contains $n/\lambda$ symbols, each of which occurs $\lambda$ times per…
A \emph{frequency square} is a matrix in which each row and column is a permutation of the same multiset of symbols. Two frequency squares $F_1$ and $F_2$ with symbol multisets $M_1$ and $M_2$ are \emph{orthogonal} if the multiset of pairs…
A binary frequency square of type $(n;\lambda_0,\lambda_1)$ is a $(0,1)$-matrix of order $n$ with $\lambda_0$ zeros and $\lambda_1$ ones in each row and in each column. Two such squares are orthogonal if there are exactly $\lambda_1^2$…
An arrangement of s elements in s rows and s columns, such that no element repeats more than once in each row and each column is called a Latin square of order s. If two Latin squares of the same order superimposed one on the other and in…
We say that a diagonal in an array is {\em $\lambda$-balanced} if each entry occurs $\lambda$ times. Let $L$ be a frequency square of type $F(n;\lambda^m)$; that is, an $n\times n$ array in which each entry from $\{1,2,\dots ,m\}$ occurs…
The principle of orthogonal time-frequency-space (OTFS) signaling is firstly analyzed, followed by explaining that OTFS embeds another signaling scheme referred to as orthogonal short-time Fourier (OSTF). Then, the relationship among OTFS,…
Mixed (asymmetric) orthogonal arrays (MOAs) generalize classical orthogonal arrays by allowing columns over different alphabets. However, their study requires very different structural tools than those used for symmetric orthogonal arrays…
The optical wireless communication (OWC) with the intensity modulation (IM), requires the modulated radio frequency (RF) signal to be real and non-negative. To satisfy the requirements, this paper proposes two types of mixed orthogonal…
Orthogonal time frequency space (OTFS) is a promising waveform in high mobility scenarios for it fully exploits the time-frequency diversity using a discrete Fourier transform (DFT) based two dimensional spreading. However, it trades off…
Quantum oscillations (QO) describe the periodic variation of physical observables as a function of inverse magnetic field in metals. The Onsager relation connects the basic QO frequencies with the extremal areas of closed Fermi surface…
An Orthogonally resolvable Matching Design OMD$(n, k)$ is a partition of the edges the complete graph $K_n$ into matchings of size $k$, called blocks, such that the blocks can be resolved in two different ways. Such a design can be…
Let $q$ be an odd prime power. Let $f\in \mathbb{F}_q[x]$ be a polynomial having degree at least $2$, $a\in \mathbb{F}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $\chi$ be the quadratic character of $\mathbb{F}_q$, and…
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…
Two latin squares are orthogonal if, when they are superimposed, every ordered pair of symbols appears exactly once. This definition extends naturally to `incomplete' latin squares each having a hole on the same rows, columns, and symbols.…
For a field $\mathbb{F}$ and integers $d$ and $k$, a set ${\cal A} \subseteq \mathbb{F}^d$ is called $k$-nearly orthogonal if its members are non-self-orthogonal and every $k+1$ vectors of ${\cal A}$ include an orthogonal pair. We prove…
Array configuration is one of the effective ways to increase the output power of terahertz oscillators using resonant tunneling diodes. Mutual locking between the array elements results in coherent single-spectrum oscillation and a narrow…
An ${\ell}$-cycle system ${\mathcal F}$ of a graph $\Gamma$ is a set of ${\ell}$-cycles which partition the edge set of $\Gamma$. Two such cycle systems ${\mathcal F}$ and ${\mathcal F}'$ are said to be {\em orthogonal} if no two distinct…
We discuss the capabilities of spherical antenn\ae as single multifrequency detectors of gravitational waves. A first order theory allows us to evaluate the coupled spectrum and the resonators readouts when the first and the second…