arXiv research

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

Extends plate problems to differential forms on manifolds.

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.

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.

This paper studies eigenvalues of the clamped plate problem on a bounded domain in an $n$-dimensional Euclidean space. We give an estimate for the gap between $\sqrt {Γ_{k+1}-Γ_{1}}$ and $\sqrt {Γ_{k}-Γ_{1}}$, for any positive integer $k$. According to the asymptotic formula of Agmon and Pleijel, we know, the gap betwe…

In Chinese societies, superstition is of paramount importance, and vehicle license plates with desirable numbers can fetch very high prices in auctions. Unlike other valuable items, license plates are not allocated an estimated price before auction. I propose that the task of predicting plate prices can be viewed as a …

The game of plates and olives, introduced by Nicolaescu, begins with an empty table. At each step either an empty plate is put down, an olive is put down on a plate, an olive is removed, an empty plate is removed, or the olives on two plates that both have olives on them are combined on one of the two plates, with the …

High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross…

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

Estimates for plate eigenvalues with nonzero Poisson's ratio.

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

A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…

PAVI speeds up Bayesian inference for large datasets.

In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine som…

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

Proves Payne conjecture for buckling and membrane eigenvalues.

Paper studies eigenvalues of a specific operator on Riemannian manifolds.

Un sous-système de dimension différentielle au plus 2 d'une extension plate est plate. Si un tel système plat est stationnaire, il admet des sorties plates indépendantes du temps. A subsystem of a flat system of differential dimension at most 2 is flat. Furthermore, if such a flat system is stationary, we show that the…

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…

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

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

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

We study Lord Rayleigh's problem for clamped plates on an arbitrary $n$-dimensional $(n\geq 2)$ Cartan-Hadamard manifold $(M,g)$ with sectional curvature $\textbf{K}\leq -κ^2$ for some $κ\geq 0.$ We first prove a McKean-type spectral gap estimate, i.e. the fundamental tone of any domain in $(M,g)$ is universally bounde…

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

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…

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 Poisson problem consists in finding an immersed surface $Σ\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a non-linear model for the equilibrium state of thin, clamped elastic plates originating f…

Develops control and observer methods for complex systems.

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

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…

This paper studies the problems of vehicle make & model classification. Some of the main challenges are reaching high classification accuracy and reducing the annotation time of the images. To address these problems, we have created a fine-grained database using online vehicle marketplaces of Turkey. A pipeline is prop…

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 …

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

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…

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.

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

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…

Study proves inequalities for eigenvalues of fourth-order elliptic operators on Riemannian manifolds.

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…