Related papers: Explicit rank-one constructions for irrational rot…
For a unital ring R, a Sylvester rank function is a numerical invariant which can be described in 3 equivalent ways: on finitely presented left R-modules, or on rectangular matrices over R, or on maps between finitely generated projective…
We determine the twistor deformation of rank one local systems on compact Kaehler manifolds which correspond to smooth twistor modules of rank one in the sense of C. Sabbah. Our proof is rather elementary, and uses a natural description of…
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal…
Bruns and Roddy constructed a $3$-generated modular ortholattice $L$ which cannot be embedded into any complete modular ortholattice. Motivated by their approach, we use shift operators to construct a $*$-regular $*$-ring $R$ of…
False theta functions form a family of functions with intriguing modular properties and connections to mock modular forms. In this paper, we take the first step towards investigating modular transformations of higher rank false theta…
Kronecker sequences $(k \alpha \mod 1)_{k=1}^{\infty}$ for some irrational $\alpha > 0$ have played an important role in many areas of mathematics. It is possible to associate to each finite segment $(k \alpha \mod 1)_{k=1}^{n}$ a…
The goal of this paper is to show there is a single orbit of the c.e. sets with inclusion, $\mathcal{E}$, such that the question of membership in this orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice corollaries:…
We extend rotation theory of circle maps to tiling spaces. Specifically, we consider a 1-dimensional tiling space $\Omega$ with finite local complexity and study self-maps $F$ that are homotopic to the identity and whose displacements are…
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We show that the set of occupied sites for this model on an infinite regular tree is a…
Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…
This paper aims at the following results: \begin{enumerate} \item The class of all $*$-regular rings forms a variety. \item A subdirectly irreducible $*$-regular ring $R$ is faithfully representable (i.e. isomorphic to a subring of an…
We classify stably/retract rational norm one tori in dimension $p-1$ where $p$ is a prime number and in dimension up to ten with some minor exceptions.
We prove that there exists a rank one perturbation of a unitary operator on a complex separable infinite dimensional Hilbert space which is hypercyclic.
We determine the ring structure of the torus-equivariant cohomology of rank-one juggling varieties with rational coefficients. By realizing these varieties as cyclic quiver Grassmannians, we construct a Knutson--Tao type basis for their…
We consider closed manifolds that possess a so called rank one ray structure. That is a (flat) affine structure such that the linear part is given by the products of a diagonal transformation and a commuting rotation. We show that closed…
Let $k\geq 1$ be a small fixed integer. The rational approximations $\left |p/q-\pi^{k} \right |>1/q^{\mu(\pi^k)}$ of the irrational number $\pi^{k}$ are bounded away from zero. A general result for the irrationality exponent $\mu(\pi^k)$…
We give necessary and sufficient conditions to specify vector bundles of conformal blocks for $\mathfrak{sl}_{2m}$ with rectangular weights which have ranks zero, one, and larger than one. First Chern classes of rank one bundles are shown…
Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''Tyurin parameters'' for the stable framed holomorphic vector…
For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the…
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $\zeta(2)$ and $\zeta(3)$, as well as to explain…