Related papers: Optimal arithmetic structure in exponential Riesz …

Let $A$ be a unital separable simple ${\cal Z}$-stable C*-algebra which has rational tracial rank at most one and let $u\in U_0(A),$ the connected component of the unitary group of $A.$ We show that, for any $\epsilon>0,$ there exists a…

Using Rees index, the subsemigroup growth of free semigroups is investigated. Lower and upper bounds for the sequence are given and it is shown to have superexponential growth of strict type $n^n$ for finite free rank greater than 1. It is…

A set of complex numbers $\Lambda=\{\lambda_n,\mu_n\}_{n=1}^{\infty}$ with multiple terms \[ \{\lambda_n,\mu_n\}_{n=1}^{\infty}:= \{\underbrace{\lambda_1,\lambda_1,\dots,\lambda_1}_{\mu_1 - times},…

Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0,1}^N. By an application of the Chen-Stein method, we show that U(N)- 2 log(N)/log(2) converges in law to an extreme type (asymmetric)…

We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…

We discuss the growth of the singular values of symplectic transfer matrices associated with ergodic discrete Schr\"odinger operators in one dimension, with scalar and matrix-valued potentials. While for an individual value of the spectral…

We study the exponentiation of elements of the gauge Lie algebras ${\rm hs}(\lambda)$ of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of…

Let $G$ be the Lie group ${\Bbb{R}}^2\rtimes {\Bbb{R}}^+$ endowed with the Riemannian symmetric space structure. Take a distinguished basis $X_0,\, X_1,\,X_2$ of left-invariant vector fields of the Lie algebra of $G$, and consider the…

The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence $\mathbb{c}$ on a Riesz space. The first…

We bound an exponential sum that appears in the study of irregularities of distribution (the low-frequency Fourier energy of the sum of several Dirac measures) by geometric quantities: a special case is that for all $\left\{ x_1, \dots,…

Given a probability measure space $(X,\Sigma,\mu)$, it is well known that the Riesz space $L^0(\mu)$ of equivalence classes of measurable functions $f: X \to \mathbf{R}$ is universally complete and the constant function $\mathbf{1}$ is a…

For a sequence of sub-additive potentials, Dai [Optimal state points of the sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method of choosing state points with negative growth rates for an ergodic dynamical system.…

We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.

In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets…

Let $G$ be a multiplicative subgroup of the prime field $\mathbb F_p$ of size $|G|> p^{1-\kappa}$ and $r$ an arbitrarily fixed positive integer. Assuming $\kappa=\kappa(r)>0$ and $p$ large enough, it is shown that any proportional subset…

We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological…

A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the…

The classic Riesz representation theorem characterizes all linear and increasing functionals on the space $C_{c}(X)$ of continuous compactly supported functions. A geometric version of this result, which characterizes all linear increasing…

In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove…

Let $E$ be a module of projective dimension one over $R=k[x_1,\ldots,x_d]$. If $E$ is presented by a matrix $\varphi$ with linear entries and the number of generators of $E$ is bounded locally up to codimension $d-1$, the Rees ring…