arXiv research

Game of plates and olives counts Morse functions on a sphere.

Deep RNN predicts vehicle license plate auction prices with high accuracy.

Study examines forces between partially immersed plates and singular configurations.

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

Tensor variable elimination for plated factor graphs enables exact inference in models with repeated structure.

Estimates for plate eigenvalues with nonzero Poisson's ratio.

Bayesian method improves hit identification in compound screening.

The paper estimates the gap between eigenvalues of a clamped plate problem.

Extends plate problems to differential forms on manifolds.

Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.

In this paper, we study eigenvalues of a clamped plate problem. We obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter.

Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off a surface. Thi…

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

For a bounded domain $Ω$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.

PAVI speeds up Bayesian inference for large datasets.

New isoperimetric inequality for clamped plates in RCD(0,N) spaces, sharp and stable.

This research optimizes plate structures to reduce vibrations in vehicles and aircraft.

Flat systems of up to 2 dimensions have flat subsystems.

Study develops efficient algorithm for probabilistic penetration response of composite plates.

The study introduces a new stickiness parameter for stock prices using a non-linear model.

Study fundamental tones of clamped plates on curved spaces.

The paper studies eigenvalue inequalities for a clamped plate problem involving a generalized elliptic differential operator.

Solves the Poisson problem for elastic plates with specific boundary conditions.

Proves Payne conjecture for buckling and membrane eigenvalues.

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The…

We study the conformal plate buckling equation (Laplace--Beltrami)^2 u =1, where the L-B operator is for the metric g = e^{2u}g_0, with $g_0$ the standard Euclidean metric on R^2. This conformal elliptic PDE of fourth order is equivalent to the nonlinear system of elliptic PDEs of second order, Delta u +K_g e^(2u)=0, D…

Paper studies eigenvalues of a specific operator on Riemannian manifolds.

Develops control and observer methods for complex systems.

PAVI speeds up VI for large-scale studies by sharing parameterization across i.i.d. variables.

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a …

Paper tackles vehicle make & model classification with improved accuracy.

This research uses Siamese networks to identify partial mouse brain images from the Allen atlas.

Sophie Germain's mean curvature deserves recognition as a surface shape measure.

This work develops a high precision fault diagnosis classifier using XAI insights.

Shells resist three out of six possible loads if simply connected.

Six AI solutions accurately detect growth plate planes in mice bone scans.

Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.

In the first part of this article we revisit the theory of weighted spinors on conformal manifolds. In the second part we introduce the notions of asymptotically flat Weyl structures and of associated mass, and we prove a conformal version of the positive mass theorem on conformal spin manifolds.

We derive a new model for pre-strained thin films, which consists of minimizing a biharmonic energy of deformations $v\in W^{2,2}$ satisfying the Monge-Ampère constraint $\det\nabla^2v = f$. We further discuss multiplicity properties of the minimizers of this model, in some special cases.

Novel defects in hyperbolic sheets explain complex wrinkling patterns in nature.

We investigate isometric immersions of disks with constant negative curvature into $\mathbb{R}^3$, and the minimizers for the bending energy, i.e. the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls i…

In this paper, we establish sharp inequalities for four kinds of classical eigenvalues on a bounded domain of a Riemannian manifold. We also establish asymptotic formulas for the eigenvalues of the buckling and clamped plate problems. In addition, we give a negative answer to the Payne conjecture for the one-dimensiona…

Physics-informed neural network identifies and characterizes surface cracks in metals.

The private car license plates issued in Shanghai are bestowed the title of "the most expensive sheet iron all over the world", more expensive than gold. A citizen has to bid in an monthly auction to obtain a license plate for his new private car. We perform statistical analysis to investigate the influence of the mini…

In this paper, we establish universal inequalities for eigenvalues of the clamped plate problem on compact submanifolds of Euclidean spaces, of spheres and of real, complex and quaternionic projective spaces. We also prove similar results for the biharmonic operator on domains of Riemannian manifolds admitting spherica…

We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume…

New solutions found for bending of flat surfaces and origami structures.

This article is based on the lectures given at the ``Ecole thematique de theorie ergodique'', at the C.I.R.M. in Marseille, in April 2006. We give a complete proof of a theorem of Kerckhoff, Masur and Smillie on the unique ergodicity of the directional flow on a translation surface in almost every direction. The proof …