相关论文: Three-phase Golay sequence and array triads
For over three decades, the pursuit of perfect periodic autocorrelation sequences has been constrained by Mow's conjecture, which posits that no perfect sequence over an $n$-phase alphabet can exist with a length greater than $n^2$. While a…
A Barker sequence is a binary sequence for which all nontrivial aperiodic autocorrelations are either 0, 1 or -1. The only known Barker sequences have length 2, 3, 4, 5, 7, 11 or 13. It is an old conjecture that no longer Barker sequences…
A major drawback of orthogonal frequency division multiplexing (OFDM) systems is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by adopting large codebooks consisting of complementary sequences with…
An Agol cycle is a complete invariant of the conjugacy class of a pseudo-Anosov mapping class. We study necessary and sufficient conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
The Tribonacci sequence is a well-known example of third order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized Tribonacci sequence is introduced and defined by…
Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological…
The Erd\H{o}s--Gallai criteria for recognizing degree sequences of simple graphs involve a system of inequalities. Given a fixed degree sequence, we consider the list of differences of the two sides of these inequalities. These differences…
The periods of the three-form on a Calabi-Yau manifold are found as solutions of the Picard-Fuchs equations; however, the toric varietal method leads to a generalized hypergeometric system of equations which has more solutions than just the…
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional…
This paper is devoted to sequences and focuses on designing new two-dimensional (2-D) Z-complementary array pairs (ZCAPs) by exploring two promising approaches. A ZCAP is a pair of 2-D arrays, whose 2-D autocorrelation sum gives zero value…
We construct a set $H$ of orthogonal polynomial sequences that contains all the families in the Askey scheme and the $q$-Askey scheme. The polynomial sequences in $H$ are solutions of a generalized first-order difference equation which is…
In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces.…
This paper studies the iterates of the third order Lyness' recurrence $x_{k+3}=(a+x_{k+1}+x_{k+2})/x_k,$ with positive initial conditions, being $a$ also a positive parameter. It is known that for $a=1$ all the sequences generated by this…
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the…
In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on…
The design of sub-arrayed phased arrays (PAs) with sub-array-only amplitude and phase controls that afford arbitrary-shaped power patterns matching reference ones is addressed. Such a synthesis problem is formulated in the power pattern…
The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…
Recurrences of the form \begin{equation*} T(n,k) = (\alpha n+\beta k +\gamma) \ T(n-1,k) + (\alpha'n+\beta'k+\gamma')\ T(n-1,k-1)+\delta_{n,0}\delta_{k,0}. \end{equation*} show up as the recurrence for many well-studied combinatorial…
The trinomial transform of a sequence is a generalization of the well-known binomial transform, replacing binomial coefficients with trinomial coefficients. We examine Pascal-like triangles under trinomial transform, focusing on the ternary…