We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

We adapt and modify the eigenfunction method of computing the powerlaw spectrum of particles accelerated at a relativistic shock front via the first-order Fermi process [6] to apply to shocks of arbitrarily high Lorentz factor. The power-law index of accelerated particles undergoing isotropic small-angle scattering at an ultrarelativistic, unmagnetized shock is found to be s = 4.23± 0.2 (where ...

An analytic method originated by Y. H. Chin was extended to calculate the electromagnetic fields and the longitudinal impedance due to coherent wiggler radiation (CWR) in a rectangular chamber. The method used dyadic Green functions based on eigenfunction expansion method in electromagnetic theory and was rigorous for the case of straight chamber. We re-derived the theory and did find the full ...

A method for simultaneously approximating to high accuracy the corresponding eigenvalue and zeros of the (n + l)st eigenfunction of a regular Sturm-Liouville eigenvalue problem is presented. It is based upon equilibrating the minimum eigenvalues of several problems on subintervals that form a partition of the orginal interval. The method is easily derived from classical mini-max variational pri...

A method using eigenfunction expansions has been implemented to determine the diffusion coefficients of electroactive species. The method has been successfully applied to the process of single-electron oxidation of N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD). The results obtained by the method agree very well with those from the well established finite difference algorithm and are more reli...

The goal of this paper is to estimate the size of the first eigenfunction u uniformly for all convex domains. In particular, we will locate the place where u achieves its maximum to within a distance comparable to the inradius, uniformly for arbitrarily large diameter. In addition, we will estimate the location of other level sets of u by showing that u is well-approximated by the first eigenfu...