Related papers: New gaps on the Lagrange and Markov spectra

Although it is well recognized that waves propagating in periodic media have forbidden gaps in the continuous spectrum, it is still yet unknown about the minimum number and depth of periodic modulations for clear spectral formation. This…

We present JHKs photometry, far red spectra, and spectral classifications for an additional 67 L dwarfs discovered by the Two Micron All Sky Survey. One of the goals of this new search was to locate more examples of the latest L dwarfs. Of…

We exhibit a Lavrentiev gap phenomenon for the neo-Hookean energy in three-dimensional nonlinear elasticity. More precisely, we construct boundary data for which the infimum of the neo-Hookean energy over deformations satisfying a natural…

Following recent work by Koll\'{a}r and Sarnak, we study gaps in the spectra of large connected cubic and quartic graphs with minimum spectral gap. We focus on two sequences of graphs, denoted $\Delta_n$ and $\Gamma_n$ which are more…

Let $X$ be a closed, connected, oriented surface of genus $g$, with a hyperbolic metric chosen at random according to the Weil--Petersson measure on the moduli space of Riemannian metrics. Let $\lambda_1=\lambda_1(X)$ bethe first non-zero…

We show that $1+3/\sqrt{2}$ is a point of the Lagrange spectrum $L$ which is accumulated by a sequence of elements of the complement $M\setminus L$ of the Lagrange spectrum in the Markov spectrum $M$. In particular, $M\setminus L$ is not a…

LHC experiments have placed strong bounds on the production of supersymmetric colored particles (squarks and gluinos), under the assumption that all flavors of squarks are nearly degenerate. However, the current experimental constraints on…

The Lagrange and Markov spectra have been studied since late 19th century, concerning badly approximable real numbers. The Mordell-Gruber spectrum has been studied since 1936, concerning the supremum of the area of a rectangle centered at…

The Lagrange spectrum $L$ is the set of finite values of the best approximation constants $k(\alpha)=\limsup_{|p|,|q|\to \infty}|q(q\alpha-p)|^{-1}$, where $\alpha\in \mathbb{R}\setminus \mathbb{Q}$. It is a classical result that the pairs…

It is shown that if a Markov map $T$ on a noncommutative probability space $\mathcal{M}$ has a spectral gap on $L_2(\mathcal{M})$, then it also has one on $L_p(\mathcal{M})$ for $1<p<\infty$. For fixed $p$, the converse also holds if $T$ is…

The (classical) Lagrange spectrum is a closed subset of the positive real numbers defined in terms of diophantine approximation. Its structure is quite involved. This article describes a polynomial time algorithm to approximate it in…

In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…

Let $G = (V,E)$ be an undirected graph with maximum degree $\Delta$ and vertex conductance $\Psi^*(G)$. We show that there exists a symmetric, stochastic matrix $P$, with off-diagonal entries supported on $E$, whose spectral gap…

We propose a new extension of the Standard Model by a $U(1)_{B-L}$ gauge symmetry in which the anomalies are canceled by two right-handed neutrinos plus four chiral fermions with fractional B-L charges. Two scalar fields that break the B-L…

Let $(M,g)$ be a closed Riemannian surface with Anosov geodesic flow. We prove the existence of a spectral gap for Pollicott--Ruelle resonances on random finite coverings of $M$ in the limit of large degree, which is expected to be optimal.…

We present a 0.6-4.1 micron spectroscopic sequence of M, L, and T dwarfs. The spectra have R~2000 from 0.9 to 2.4 microns and R=2500-200 from 2.9 to 4.1 microns. These new data nearly double the number of L and T dwarfs that have reported…

Using McMullen's Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the…

We present near-infrared spectra for a sample of T dwarfs, including eleven new discoveries made using the Two Micron All Sky Survey. These objects are distinguished from warmer (L-type) brown dwarfs by the presence of methane absorption…

We study the spectral gap of subgraphs of the hypercube induced by monotone subsets of vertices. For a monotone subset $A\subseteq\{0,1\}^{n}$ of density $\mu(A)$, the previous best lower bound on the spectral gap, due to Cohen, was…

The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap of finite dimensional systems is given by Theorem 1.1, in terms…