Deng, Quanling Ern, Alexandre

We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting to the standard stiffness bilinear form a least-squares penalty on the gradient jumps across the mesh interfaces. T...

Bérard, Pierre Helffer, Bernard Kiwan, Rola

The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, t...

Bérard, Pierre Helffer, Bernard Kiwan, Rola

The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, t...

Suhov, Yuri Kelbert, Mark Stuhl, Izabella

This paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in Rd. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a boundary condition at the border of a `box’). The particles interact with each other through a two-body finite-range potential depending on the distance between them a...

Bérard, Pierre Webb, David

The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other non-orientable. For this purpose, we apply Sunada's and Buser's methods in the framework of orbifolds. Choosing a symmetric...

Bérard, Pierre Helffer, Bernard

The purpose of this note is to prove an Euler-type formula for partitions of the Möbius strip. This formula was introduced in our joint paper with R. Kiwan, "Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip" (arXiv:2005.01175).

alluhaibi, nadia mofarreh, fatemah ali, akram mior othman, wan ainun

In the present paper, we prove that if Laplacian for the warping function of complete warped product submanifold M m = B p × / h F q in a unit sphere S m + k satisfies some extrinsic inequalities depending on the dimensions of the base B p and fiber F q such that the base B p is minimal, then M m must be diffeomorphic to a unit sphere S m . Mo...

Kassel, Adrien Lévy, Thierry

In this short note, we revisit Zeilberger's proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.

Wang, Junqi Xiao, Li Wilson, Tony W Stephen, Julia M Calhoun, Vince D Wang, Yu-Ping
Published in
Journal of neuroscience methods

Longitudinal neuroimaging studies have demonstrated that adolescence is a crucial developmental period of continued brain growth and change. Motivated by both achievements in graph signal processing and recent evidence that some brain areas act as hubs connecting functionally specialized systems, we propose an approach to detect these regions from ...

Bouin, Emeric Dolbeault, Jean Schmeiser, Christian

This paper is intended to give a characterization of the optimality case in Nash's inequality, based on methods of nonlinear analysis for elliptic equations and techniques of the calculus of variations. By embedding the problem into a family of Gagliardo-Nirenberg inequalities, this approach reveals why optimal functions have compact support and al...