We consider examples Aλ = A + λ(φ, · )φ of rank one perturbations with φ a cyclic vector for A. We prove that for any bounded measurable set B ⊂ I, an interval, there exists A,φ so that {E ∈ I | some Aλ has E as an eigenvalue} agrees with B up to sets of Lebesgue measure zero. We also show that there exist examples where Aλ has a.c. spectrum [0,1] for all λ, and for sets of λ’s of positive Lebe...

Consider the family of Schrödinger operators (and also its Dirac version) on l(Z) or l(N) H W ω,S = ∆+ λF (S n ω) +W, ω ∈ Ω, where S is a transformation on (compact metric) Ω, F a real Lipschitz function and W a (sufficiently fast) power-decaying perturbation. Under certain conditions it is shown that H ω,S presents quasi-ballistic dynamics for ω in a dense Gδ set. Applications include potentia...

Let T ∈ B(H) be a bounded linear operator on a complex Hilbert space H. Let λ0 be an isolated point of σ(T ) and let E = 1 2 i ∫ |λ−λ0|=r (λ− T )−1 dλ be the Riesz idempotent for λ0. In this paper, we prove that if T is a p-quasihyponormal operator with 0 < p 1 and λ0 / = 0, then E is self-adjoint and EH = ker(T − λ0) = ker(T − λ0) ∗. © 2002 Elsevier Science Inc. All rights reserved. AMS classi...

SVM ( Support Vector Machine ) is a new method in the artificial neural network ( ANN ). In the steel making, how to use computer to predict the end point of BOF accuracy is a great problem. A lot of method and theory have been claimed, but most of the results is not satisfied. Now the hot topic in the BOF end point predicting is to use optical way the predict the end point in the BOF. And we f...

It is not immediate whether a self-adjoint operator H with purely point spectrum implies absence of transport under the time evolution U(t) = e−iHt; in fact, it is currently known examples of Schrödinger operators with such kind of spectrum and transport. In case of tight-binding models on l2(IN) the transport is usually probed by the moments of order m > 0 of the position operator Xek = kek, t...

We consider N = 2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges corresponding to two mutually non-local electro-magnetic charges vanish simultaneously, indicating the possibility of massless such states in the ...

We study the dynamics of metrics generated by measure-preserving transformations. We consider sequences of average metrics and entropies of the measure with respect to these metrics. The main result, which gives a criterion for checking that the spectrum of a transformation if purely point, is that the scaling sequence for the -entropies with respect to the averages of an admissible metric is b...

We prove that any n-dimensional Hamiltonian operator with pure point spectrum is completely integrable via self-adjoint first integrals. Furthermore, we establish that given any closed set Σ ⊂ R there exists an integrable n-dimensional Hamiltonian which realizes it as its spectrum. We develop several applications of these results and discuss their implications in the general framework of quantu...