Related papers: Spiral Delone sets and three distance theorem

A uniform space $X$ is said to be proximally fine if every proximally continuous map on $X$ into a uniform is uniformly continuous. We supply a proof that every topological group which is functionnaly generated by its precompact subsets is…

We study the intermediate- and long-range forces between moving and spinning Skyrmions, employing two different methods. One uses a relativised product ansatz for the Skyrme fields, the other models Skyrmions as triplets of scalar dipoles.…

We study existence, asymptotics, and stability of spiral waves in a driven curvature approximation, supplemented with an anchoring condition on a circle of finite radius. We analyze the motion of curves written as graphs in polar…

In this paper we characterize all the linear $\mathbb{C}$-derivations of the Fermat ring. We show that the Fermat ring has linear $\mathbb{C}$-derivations with trivial ring of constants and construct some examples.

We prove an analogue of the Brauer-Siegel theorem for Fermat surfaces over a finite field. Namely, letting $F_d$ be the Fermat surface of degree $d$ over $\mathbb{F}_q$ and $p_g(F_d)$ be its geometric genus, we consider the product of the…

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We…

This paper presents the derivation of SPH from principles of continuum mechanics via a measure-based formu- lation. Additionally, it discusses a theoretical convergence result, the extensions achieved from previous works and the current…

Given a family of complex affine planes, we show that it is trivial over a Zariski open subset of the base. The proof relies upon a relative version of the contraction theorem.

We prove that the Neron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relatively prime to 6. The proof uses reduction modulo a…

Given a set of positive reals, we provide a necessary and sufficient condition for a free Borel flow to admit a cross section with all distances between adjacent points coming from this set.

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a H\"older space which is separable.

We consider the class of standard weighted Bergman spaces $A^2_{\alpha}(\mathbb{D})$ and the set $SF^N(\mathbb{T})$ of simple partial fractions of degree $N$ with poles on the unit circle. We prove that under certain conditions, the simple…

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in…

In the last years considerable attention has been paid for the orthogonal and non-linear projections of self-similar sets. In this paper we consider orthogonal transformation-free self-similar sets in $\mathbb{R}^3$, i.e. the generating IFS…

We propose the following conjecture extending Dirac's theorem: if $G$ is a graph with $n\ge 3$ vertices and minimum degree $\delta(G)\ge n/2$, then in every orientation of $G$ there is a Hamilton cycle with at least $\delta(G)$ edges…

We establish the $\varepsilon$-regularity theorem for $k$-dimensional, possibly forced, Brakke flows near a static, multiplicity-one triple junction. This result provides the parabolic analogue to L. Simon's foundational work on the…

We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function $f(x)$ which is bounded below by an integrable function, then the series is the Fourier series of $f(x)$ if the…

We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…

Let $Y$ be a smooth projective variety of dimension $n \geq 2$ endowed with a finite morphism $\phi:Y \to \mathbb P^n$ of degree $3$, and suppose that $Y$, polarized by some ample line bundle, is a scroll over a smooth variety $X$ of…