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If there arek
++ eventually functions fromk
+ intok or if there arek
++ eventually different functions fromk
+ then uniform ultrafilters onk
+ are (k, k
+)-regular.
The research of the first author was supported in part by NSF grant.
The second author is a Miller’s Fellow at the University of California in Berkeley. 相似文献
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Photodissociation of formyl fluoride (HCOF) is studied in Ar, Kr, and Xe matrixes at 248 and 193 nm excitation by following spectral changes in the infrared absorption spectra. In all matrixes, the main photodissociation products are CO/HF species, including CO-HF and OC-HF complexes and thermally unstable CO/HF species (a distorted CO/HF complex or a reaction intermediate), which indicate negligible cage exit of atoms produced via the C-F and C-H bond cleavage channels. However, the observation of traces of H, F, CO, CO(2), F(2)CO, FCO, and HRg(2)(+) (Rg = Kr or Xe) in Kr and Xe matrixes would imply some importance of other reaction channels too. The analysis of the decay curves of the precursor shows that dissociation efficiency of HCOF increases as Ar < Kr < Xe, the difference being the factor of 10 between Ar and Xe. Moreover, HCOF dissociates 20-50 times faster at 193 nm compared to 248 nm. Interestingly, whereas the CO/HF species are stable with respect to photolysis in Ar, they photobleach in Kr and Xe matrixes at 248 and 193 nm, even though the first excited states of CO and HF are not energetically accessible with 193 and 248 nm photons. In krypton matrix, the photodissociation of CO/HF species at 248 nm is observed to be a single photon process. Quantum chemical calculations of electronic excitation energies of CO-HF and OC-HF complexes show that the electronic states of HF and CO mostly retain their diatomic nature in the pair. This clearly demonstrates that photodissociation of CO/HF complexes is promoted by the surrounding rare gas lattice. 相似文献
25.
Jussi Behrndt Matthias Langer 《Journal of Mathematical Analysis and Applications》2010,371(2):750-758
In this note we investigate the asymptotic behavior of the s-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain Ω with smooth boundary ∂Ω. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on ∂Ω. It is shown that the resolvent difference of two generalized Robin Laplacians belongs to the Schatten-von Neumann class of any order p for which
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Jussi Laitila Pekka J. Nieminen Eero Saksman Hans-Olav Tylli 《Complex Analysis and Operator Theory》2013,7(1):163-181
Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C φ on VMOA implies compactness even from the Bloch space into VMOA. 相似文献
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Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity. 相似文献
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It is known since the early 20th century that regular indefinite Sturm-Liouville problems may possess non-real eigenvalues. However, finding bounds for this set in terms of the coefficients of the differential expression has remained an open problem until recently. In this note we prove a variant of a recent result in [1] on the bounds for the non-real eigenvalues of an indefinite Sturm-Liouville problem with Dirichlet boundary conditions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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