Related papers: Prime tight frames
Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively - are useful for many applications. A…
We give explicit numerical estimates for the generalized Chebyshev functions. Explicit results of this kind are useful for estimating of computational complexity of algorithms which generates special primes. Such primes are needed to…
We prove that any tight frame in Hilbert space can be obtained by the Kaczmarz algorithm. An explicit way of constructing this correspondence is given. The uniqueness of the correspondence is determined.
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
In this paper we study the joint/generalized spectral radius of a finite set of matrices in terms of its rank-one approximation by singular value decomposition. In the first part of the paper, we show that any finite set of matrices with at…
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
A main goal in lattice theory is the construction of dense lattices. Most of the remarkable dense lattices in small dimensions have an additional symmetry, they are modular, i.e. similar to their dual lattice. Extremal lattices are densest…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
For a finite group $G$, the vertices of the prime graph $\Gamma(G)$ are the primes that divide $|G|$, and two vertices $p$ and $q$ are connected by an edge if and only if there is an element of order $pq$ in $G$. Prime graphs of solvable…
Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…
The most tight conformations of prime knots are found with the use of the SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry of the knots is analysed. Connections with the physics of polymers are discussed.
We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the…
Using the 4th and the 3rd degree spherical harmonics as the representations for volumetric frames, we describe a simple algebraic technique for combining multiple frame orientation constraints into a single quadratic penalty function. This…
Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…