Related papers: A Multi-Dimensional Block-Circulant Perfect Array …
We present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one-, two- and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families…
Jaeger's directed cycle double cover conjecture can be formulated as a problem of existence of special perfect matchings in a class of graphs that we call hexagon graphs. In this work, we explore the structure of hexagon graphs. We show…
The main focus of this thesis is a generalization of covering arrays, covering arrays on graphs. Two vectors v,w in Z_k^n are qualitatively independent if for all ordered pairs (a,b) in Z_k x Z_k there is a position i in the vectors where…
For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant…
We prove that reiteratively hypercyclic operators have perfect spectrum. Consequently, it follows that there exist separable infinite dimensional Banach spaces that do not support any reiteratively hypercyclic operator. For this, we study…
Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single $H$-ary Golay sequence and $4^q$-QAM…
Without using Gabber's theorem, the finite-dimensionality of the space of conformal blocks in the WZNW-models is proved.
Let $X$ be a separated scheme of dimension $d$ of finite type over a perfect field $k$ of positive characteristic $p$. In this work, we show that Bloch's cycle complex $\mathbb{Z}^c_X$ of zero cycles mod $p^n$ is quasi-isomorphic to the…
We propose a procedure of constructing new block designs starting from a given one by looking at the intersections of its blocks with various sets and grouping those sets according to the structure of the intersections. We introduce a…
The Cayley-Dickson Construction is a generalization of the familiar construction of the complex numbers from pairs of real numbers. The complex numbers can be viewed as two-dimensional vectors equipped with a multiplication. The…
We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or, equivalently, completely regular $\{14;2\}$-codes in the $14$-cube ($30848$ equivalence classes). In particular, we find that there is exactly one…
We introduce near triple arrays as binary row-column designs with at most two consecutive values for the replication numbers of symbols, for the intersection sizes of pairs of rows, pairs of columns and pairs of a row and a column. Near…
Constant amplitude zero auto-correlation (CAZAC) sequences are widely applied in waveforms for radar and communication systems. Motivated by a recent work [Berggren and Popovi\'c, IEEE Trans. Inf. Theory 70(8), 6068-6075 (2024)], this paper…
In this study a phenomenological three-dimensional coupled (3DC) mixed-mode cohesive zone model (CZM) is proposed. This is done by extending an improved version of the well established exponential CZM of Xu and Needleman (XN) to 3D contact…
A de Bruijn array code is a set of $r \times s$ binary doubly-periodic arrays such that each binary $n \times m$ matrix is contained exactly once as a window in one of the arrays. Such a set of arrays can be viewed as a two-dimensional…
We wish to renew the discussion over recent combinatorial structures that are 3-uniform hypergraph expanders, viewing them in a more general perspective, shedding light on a previously unknown relation to the zig-zag product. We do so by…
Large arrays of individually controlled atoms trapped in optical tweezers are a very promising platform for quantum engineering applications. However, to date, only disordered arrays have been demonstrated, due to the non-deterministic…
Inspired by protein folding, we explored the construction of three-dimensional structures and machines from one-dimensional chains of simple building blocks. This approach not only allows us to recreate the self-replication mechanism…
Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common…
Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasi-asynchronous environments. In this letter, we propose three new…