Time Eigenstates for Potential Functions without Extremal Points

Time Eigenstates for Potential Functions without Extremal Points

In a previous paper, we introduced a way to generate a time coordinate system for classical and quantum systems when the potential function has extremal points. In this paper, we deal with the case in which the potential function has no extremal points at all, and we illustrate the method with the harmonic and linear potentials.

Extremal points without compactness in L(μ)

We investigate the existence of extremal points and the KreinMIlman representation A = co ExtA of bounded convex subsets of L(μ) which are only closed with respect to the topology of μ -a.e. convergence.

Extremal functions for sequences

Davenport-Schinzel sequences DS(s) are finite sequences of some symbols with no immediate repetition and with no alternating subsequence (i.e. of the type ababab . . .) of the length s. This concept based on a geometrical motivation is due to Davenport and Schinzel in the middle of sixties. In the late eighties strong lower and upper (superlinear) bounds on the maximum length of the DS(s) seque...

Quasi-completeness and functions without fixed-points

Q-reducibility is a natural generalization of many-one reducibility (m-reducibility): if A ≤m B via a computable function f(x), then A ≤Q B via the computable function g(x) such that Wg(x) = {f(x)}. Also this reducibility is connected with enumeration reducibility (e-reducibility) as follows: if A ≤Q B via a computable function g(x), then ω −A ≤e ω −B via the c. e. set W = {〈x, 2y〉 | x ∈ ω, y ∈...

Image Surface Extremal Points, new feature points for Image Registration