Related papers: Shifted lattices and asymptotically optimal ellips…
We analyze the limit of the p-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the p-form Laplacian has small positive eigenvalues in a…
We defined exponential maps with one parameter, associated with geodesics on the parameter surface. By group theory we proposed a formula of the critical points, which is a direct sum of the Lie subalgebras at the critical temperature. We…
Consider the elliptic curves given by $ E_{n,\theta}:\quad y^2=x^3+2s n x^2-(r^2-s^2) n^2 x $ where $0 < \theta< \pi$, $\cos(\theta)=s/r$ is rational with $0\leq |s| <r$ and $\gcd (r,s)=1$. These elliptic curves are related to the…
Given any full rank lattice and a natural number N , we regard the point set given by the scaled lattice intersected with the unit square under the Lambert map to the unit sphere, and show that its spherical cap discrepancy is at most of…
We give an asymptotic formula for the number of elliptic curves over $\mathbb{Q}$ with bounded Faltings height. Silverman has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of modular…
The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers,…
The underlying motivation of the present work lies on a cornerstone question in spectral optimization that consists of determining sharp lower and upper uniform estimates for fundamental frequencies of a set of uniformly elliptic operators…
In this paper we study a perturbative approach to the problem of quantization of measures in the plane. Motivated by the fact that, as the number of points tends to infinity, hexagonal lattices are asymptotically optimal from an energetic…
We analyze the problem of approximating a smooth quantum waveguide with a quantum graph. We consider a planar curve with compactly supported curvature and a strip of constant width around the curve. We rescale the curvature and the width in…
We study minimizing cones in the Alt-Phillips problem when the exponent {\gamma} is close to 1. When {\gamma} converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise,…
We study lattice points on hyperbolic circles centred at Heegner points of class number one. Our main result is that, on a density one subset of radii tending to infinity, the angles of such points equidistribute on the unit circle. To…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
This paper investigates limit points of the deformed Laplacian matrix, which merges the Laplacian and signless Laplacian matrices of a graph through a quadractic one-parameter family of matrices. First, we show that any value greater or…
The breaking of rotational symmetry on the lattice for bound eigenstates of the two lightest alpha conjugate nuclei is explored. Moreover, a macroscopic alpha-cluster model is used for investigating the general problems associated with the…
Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…
We consider the problem of maximizing the first eigenvalue of the $p$-laplacian (possibly with non-constant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$,…
We clarify the lore that anomaly-free symmetries are either on-site or can be transformed into on-site symmetries. We prove that any finite, internal, anomaly-free symmetry in a 1+1d lattice Hamiltonian system can be disentangled into an…
This paper generalizes the result of Elmachtoub et al to any weighted barycenter, where a transformation is considered which takes an arbitrary point of division $\xi \in (0,1)$ of the segments of a polygon with $n$ vertices. We then…
We denote by Conc(L) the semilattice of all finitely generated congruences of a lattice L. For varieties (i.e., equational classes) V and W of lattices such that V is contained neither in W nor its dual, and such that every simple member of…
A lattice model of critical dense polymers is solved exactly on a cylinder with finite circumference. The model is the first member LM(1,2) of the Yang-Baxter integrable series of logarithmic minimal models. The cylinder topology allows for…