Results 11 to 20 of about 203 (65)

Efficiency and localisation for the first Dirichlet eigenfunction [PDF]

, 2019
Bounds are obtained for the efficiency or mean to peak ratio $E(\Omega)$ for the first Dirichlet eigenfunction (positive) for open, connected sets $\Omega$ with finite measure in Euclidean space $\R^m$. It is shown that (i) localisation implies vanishing
Berg, Michiel van den, Della Pietra, Francesco, Di Blasio, Giuseppina, Gavitone, Nunzia   +3 more
core   +2 more sources

Analysis of the divide-and-conquer method for electronic structure calculations [PDF]

, 2015
We study the accuracy of the divide-and-conquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method.
Chen, Jingrun, Lu, Jianfeng
core   +1 more source

Laplacian eigenvalues functionals and metric deformations on compact manifolds [PDF]

, 2007
In this paper, we investigate critical points of the Laplacian's eigenvalues considered as functionals on the space of Riemmannian metrics or a conformal class of metrics on a compact manifold.
Agricola, Ahmad El Soufi, Bando, Berger, Bérard-Bergery, Colbois, Colbois, Colin de Verdière, Eells, Eells, El Soufi, El Soufi, El Soufi, El Soufi, El Soufi, Ferus, Friedlander, Girouard, Grigoryan, Hersch, Hsiang, Jakobson, Korevaar, Li, Mutô, Mutō, Nadirashvili, Park, Saïd Ilias, Takahashi, Tanno, Toth, Urakawa, Yang   +33 more
core   +4 more sources

A Spectral Gap Estimate and Applications

, 2017
We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in terms of ...
Georgiev, Bogdan, Mukherjee, Mayukh, Steinerberger, Stefan   +2 more
core   +1 more source

Mathematical analysis of some new adequate broad-ranging soliton solutions of nonlinear models through the recent technique

Partial Differential Equations in Applied Mathematics
The Bogoyavlenskii and the simplified modified Camassa-Holm (SMCH) models are studied through the recent technique namely auxiliary equation method in this paper.
M. Ashikur Rahman, M. Al-Amin, Mst. Kamrunnaher, M. Abul Kawser, Rajaul Haque, M. Ali Akbar, M. Nurul Islam   +6 more
doaj   +1 more source

Computational analysis and wave propagation behavior of hyper-geometric soliton waves in plasma physics via the auxiliary equation method

Partial Differential Equations in Applied Mathematics
This study investigate the widely used nonlinear fractional Kairat-II (K-II) model, which is used to explain the differential geometry of curves and equivalence aspects.
M. Al-Amin, M. Nurul Islam, M. Ali Akbar
doaj   +1 more source

On the location of spectral edges in $\mathbb{Z}$-periodic media

, 2010
Periodic $2$nd order ordinary differential operators on $\R$ are known to have the edges of their spectra to occur only at the spectra of periodic and antiperiodic boundary value problems.
Exner, Pavel, Kuchment, Peter, Winn, Brian   +2 more
core   +1 more source

Isoperimetric inequalities for some integral operators arising in potential theory [PDF]

, 2017
In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a ...
EM Harrell, G Pólya, G Rozenblum, J Arazy, J Delgado, JL Troutman, JL Troutman, JM Luttinger, M Kac, M Kac, M Kac, M Ruzhansky, M Ruzhansky, M Ruzhansky, M Ruzhansky, M Ruzhansky, MR Dostanic, MR Dostanic, N Saito, R Banuelos, RD Benguria, S Zoalroshd   +21 more
core   +2 more sources

Carleson Measures and Logvinenko-Sereda sets on compact manifolds [PDF]

, 2010
Given a compact Riemannian manifold $M$ of dimension $m\geq 2$, we study the space of functions of $L^2(M)$ generated by eigenfunctions of eigenvalues less than $L\geq 1$ associated to the Laplace-Beltrami operator on $M$.
Ortega-Cerdà, Joaquim, Pridhnani, Bharti   +1 more
core   +2 more sources

Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk

, 2018
It is known that the first eigenvalue for Aharonov--Bohm operators with half-integer circulation in the unit disk is double if the potential's pole is located at the origin. We prove that in fact it is simple as the pole $a\neq 0$
Abatangelo, Laura
core   +1 more source