Related papers: On multiple null-series in the Walsh system, M- an…
In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and…
We review the basic theory of More Sums Than Differences (MSTD) sets, specifically their existence, simple constructions of infinite families, the proof that a positive percentage of sets under the uniform binomial model are MSTD but not if…
We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…
We address a linear control system under geometric constraints on control and study its reachable sets starting at zero time from the origin. The main result is the existence of a limit shape of the reachable sets as the terminal time tends…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
The erosion of a set in Euclidean space by a radius r>0 is the subset of X consisting of points at distance >/-r from the complement of X. A set is resilient to erosion if it is similar to its erosion by some positive radius. We give a…
An $m$-distance set is a collection of points such that the distances between any two points have $m$ possible values. We use two different methods to construct large $m$-distance sets on the triangular lattices. One is to use the first m…
This paper discusses the question of how many non-empty subsets of the set $[n] = \{ 1, 2, ..., n\}$ we can choose so that no chosen subset is the union of some other chosen subsets. Let $M(n)$ be the maximum number of subsets we can…
A family of degenerate domain wall configurations, partially preserving supersymmetry, is discussed in a generalized Wess-Zumino model with two scalar superfields. We establish some general features inherent to the models with continuously…
It is well known that in $n$-dimensional Euclidean space ($n\geq 2$) the classes of (diametrically) complete sets and of bodies of constant width coincide. Due to this, they both form a proper subfamily of the class of reduced bodies. For…
The cross-ratios do not uniquely fix the class of conformally equivalent configurations of null polygons. In view of applications to Wilson loops and scattering amplitudes we characterise all conformal classes of null hexagon configurations…
This work creates two categories of "array-weighted sets" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps…
In this article, we investigate meandric systems having one shallow side: the arch configuration on that side has depth at most two. This class of meandric systems was introduced and extensively examined by I. P. Goulden, A. Nica, and D.…
This paper presents an algebraic construction of families of unitary matrices that achieve full diversity. They are obtained as subsets of cyclic division algebras.
Additional remarks and questions for transseries. In particular: properties of composition for transseries; the recursive nature of the construction of R[[[ x ]]]; modes of convergence for transseries. There are, at this stage, questions…
We show that certain families of sets in $\mathbb{R}^2$ (or $\mathbb{R}^n$) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately definable in the real field, an o-minimal structure.
We consider the question of determining the structure of the set of all $d$-dimensional vectors of the form $N^{-1}(1_A*1_{-A}(x_1), ..., 1_A*1_{-A}(x_d))$ for $A \subseteq \{1,...,N\}$, and also the set of all $(2N+1)^{-1}(1_B*1_B(x_1),…
We introduce a transformation for converting a series in a parameter, \lambda, to a series in the inverse of the parameter \lambda^{-1}. By applying the transform on simple examples, it becomes apparent that there exist relations between…
A 1965 result of Crapo shows that every elementary lift of a matroid $M$ can be constructed from a linear class of circuits of $M$. In a recent paper, Walsh generalized this construction by defining a rank-$k$ lift of a matroid $M$ given a…
Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a…