The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.

We study the Robin Laplacian in a domain with two corners of the same opening, and we calculate the asymptotics of the two lowest eigenvalues as the distance between the corners increases to infinity.

Let L(G) be the Laplacian matrix of G. In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than l; where l . = 3.2470 is the largest root of the equation μ3 − 5μ2 + 6μ − 1 = 0. Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three. © 2013 Elsevier Ltd. All rights rese...

We show the existence of simply-connected unbounded planar domains for which the second nodal line of the Dirichlet Laplacian does not touch the boundary.

Fuel cell is a promising choice for clean energy because of its eco-friendly system, high energy conversion efficiency and high power density. Recently, much of the research work is focused on the system of combining metal oxides to increase the durability and surface area and to reduce the cost. In this study, among the various fabrication methods, we used the precipitation method to synthesis...

In this paper, we investigate how the Laplacian coefficients changed after some graph transformations. So, I express some results about Laplacian coefficients ordering of graphs, focusing our attention to the bicyclic graphs. Finally, as an application of these results, we discuss the ordering of graphs based on their Laplacian like energy.

A graph is said to be Laplacian integral if the spectrum of its Laplacian matrix consists entirely of integers. Using combinatorial and matrix-theoretic techniques, we identify, up to isomorphism, the 21 connected Laplacian integral graphs of maximum degree 3 on at least 6 vertices.

We study the optimal sets Ω∗ ⊂ R for spectral functionals F ( λ1(Ω), . . . , λp(Ω) ) , which are bi-Lipschitz with respect to each of the eigenvalues λ1(Ω), . . . , λp(Ω) of the Dirichlet Laplacian on Ω, a prototype being the problem min { λ1(Ω) + · · ·+ λp(Ω) : Ω ⊂ R, |Ω| = 1 } . We prove the Lipschitz regularity of the eigenfunctions u1, . . . , up of the Dirichlet Laplacian on the optimal se...

We consider scattering by an obstacle in Rd, d ≥ 3 odd. We show that for the Neumann Laplacian if an obstacle has the same resonances as the ball of radius ρ does, then the obstacle is a ball of radius ρ. We give related results for obstacles which are disjoint unions of several balls of the same radius.