Riemann's hypothesis as an eigenvalue problem. III

The Choptuik spacetime as an eigenvalue problem

By fine-tuning generic Cauchy data, critical phenomena have recently been discovered in the black hole/no black hole “phase transition” of various gravitating systems. For the spherisymmetric real scalar field system, we find the “critical” spacetime separating the two phases by demanding discrete scale-invariance, analyticity, and an additional reflection-type symmetry. The resulting nonlinear...

An unusual eigenvalue problem

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires special methods to solve it. One of such methods based on continued fractions is presented in detail and applied to determine the eigenvalues.

Automatic focal length estimation as an eigenvalue problem

This paper focuses on automatic focal length estimation. In several vision applications one can assume that the utilized cameras are semi-calibrated, which means that all the intrinsic camera parameters but the focal length (aspect ratio, principal point, and skew) are known. In this case the camera calibration procedure reduces to the computation of the focal length(s). The main contribution o...

The cumulative reaction probability as eigenvalue problem

It is shown that the cumulative reaction probability for a chemical reaction can be expressed (absolutely rigorously) as N(E) =Xkp#>, where {pk} are the eigenvalues of a certain Hermitian matrix (or operator). The eigenvalues {pk} all he between 0 and 1 and thus have the interpretation as probabilities, eigenreaction probabilities which may be thought of as the rigorous generalization of the tr...

Quantization as Selection Rather than Eigenvalue Problem