We present a fast contour-integral eigensolver for finding selected or all the eigenpairs of a non-Hermitian matrix based on a series of analytical and computational techniques, such as the analysis of filter functions, quick and reliable eigenvalue count via low-accuracy matrix approximations, and fast shifted factorization update. The quality of some quadrature rules for approximating a relev...

In this paper we prove mean curvature comparisons and volume on a smooth metric measure space when the integral radial Bakry-Émery Ricci tensor potential function or its gradient are bounded. As applications, diameter estimates eigenvalue spaces. These results not only give supplement of author’s previous under bounds, but also generalizations Wei-Wylie’s pointwise results.

The path integral for the hydrogen atom, for example, is formulated as a onedimensional quantum gravity coupled to matter fields representing the electron coordinates. The (renormalized) cosmological constant, which corresponds to the energy eigenvalue, is thus quantized in this model. Possible implications of the quantized cosmological constant are briefly discussed. The problem of the cosmolo...

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.

The “drum problem”—finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition—has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed. Boundary integral equations are appealing for large-scale problems, yet certain difficulties have limited their use. We introduce two ideas to remedy this: 1) We solve t...

Davies’ version of the Hardy inequality gives a lower bound for Dirichlet integral function vanishing on boundary domain in terms squared with weight containing averaged distance to boundary. This is applied easily derive two classical results spectral theory, E. Lieb’s first eigenvalue Laplacian and G. Rozenblum’s estimate counting an unbounded number disjoint balls preset size whose intersect...

Abstract The present paper is devoted to the issue how critical load of some heterogeneous beams with three supports can be determined by using Green functions. stability problems these are equivalent three-point boundary value problems, paired homogeneous conditions. If functions known, eigenvalue that provide transformed into governed Fredholm integral equations. later reduced algebraic which...