Related papers: New gaps on the Lagrange and Markov spectra

We calculate the likelihood map in the full 7 dimensional parameter space of the minimal supersymmetric standard model (MSSM) assuming universal boundary conditions on the supersymmetry breaking terms. Simultaneous variations of m_0, A_0,…

We present preliminary results of a radial-velocity search for companions to a volume limited sample of M dwarfs. Typical accuracy range between 10m/s for the brighter stars and 70m/s at our limiting magnitude. We complement the radial…

The ATLAS report in August 2016 provided an upper limit for the $pp\to$ diboson and $t\bar t$ cross sections. We consider a pseudoscalar-mediated fermionic dark matter together with gluon and photon effective operators interacting with the…

We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense…

We prove several results on (fractal) geometric properties of the classical Markov and Lagrange spectra. In particular, we prove that the Hausdorff dimensions of intersections of both spectra with half-lines always coincide, and may assume…

Discovery of supersymmetric (SUSY) particles at the Large Hadron Collider(LHC) has been studied for the models where squarks and gluino are much heavier than the lightest supersymetric particle (LSP). In this paper, we investigate the SUSY…

Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects…

We report the first detection of the dark matter distribution around Lyman break galaxies (LBGs) at high redshift through the Cosmic Microwave Background (CMB) lensing measurements with the public {\it Planck} PR3 $\kappa$ map. The LBG…

We establish a sub-convexity estimate for Rankin-Selberg $L$-functions in the combined level aspect, using the circle method. If $p$ and $q$ are distinct prime numbers, $f$ and $g$ are non-exceptional newforms (modular or Maass) for the…

We present the discovery of seven new T dwarfs identified in the Two Micron All Sky Survey. Low-resolution (R$\sim$150) 0.8--2.5 micron spectroscopy obtained with the IRTF SpeX instrument reveal the characteristic H$_2$O and CH$_4$ bands in…

In this work, we use publicly available data from ATLAS collaboration collected at LHC run 2 at a center-of-mass energy of $\sqrt{s}=13$TeV with an integrated luminosity of $139 fb^{-1}$ to derive lower mass limits on the $Z^\prime$ gauge…

We show that the solid lower bound of about 10^{-44} cm^2 is obtained for the cross section between the supersymmetric dark matter and nucleon in a theory in which the supersymmetric fine-tuning problem is solved without extending the Higgs…

This paper surveys the main results obtained during the period 1992-1999 on three aspects mentioned at the title. The first result is a new and general variational formula for the lower bound of spectral gap (i.e., the first non-trivial…

We consider the "Mandelbrot set" $M$ for pairs of complex linear maps, introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and others. It is defined as the set of parameters $\lambda$ in the unit disk such that the…

The fundamental gap is the difference between the first two Dirichlet eigenvalues of a Schr\"odinger operator (and the Laplacian, in particular). For horoconvex domains in hyperbolic space, Nguyen, Stancu and Wei conjectured that it is…

Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…

Let $f$ and $g$ be normalized Hecke-Maass cusp forms for the full modular group having spectral parameters $t_f$ and $t_g$ respectively with $t_f,t_g\asymp T\rightarrow \infty $. In this paper we show that the Rankin Selberg $L$-function…

Consider a random matrix $H:\mathbb{R}^n\longrightarrow\mathbb{R}^m$. Let $D\geq2$ and let $\{W_l\}_{l=1}^{p}$ be a set of $k$-dimensional affine subspaces of $\mathbb{R}^n$. We ask what is the probability that for all $1\leq l\leq p$ and…

Let $G$ be a simple connected graph of size $m$. Let $A$ be the adjacency matrix of $G$ and let $\rho(G)$ be the spectral radius of $G$. A graph is said to be $H$-free if it does not contain a subgraph isomorphic to $H$. Let $H(\ell,3)$ be…

Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field (MRF) with continuous state…