Szlenk indices of convex hulls Lancien, G.; Procházka, A.; Raja, M.
Journal of functional analysis,
01/2017, Letnik:
272, Številka:
2
Journal Article
Recenzirano
Odprti dostop
We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their ω-iterates. We introduce the notions of convexifiable and sublinear ...measure of non-compactness and investigate the properties of its associated fragment and slice derivations. We apply our results to the Kuratowski measure of non-compactness and to the study of the Szlenk index of a Banach space. As a consequence, we obtain that the Szlenk index and the convex Szlenk index of a separable Banach space are always equal. We also give, for any countable ordinal α, a characterization of the Banach spaces with Szlenk index bounded by ωα+1 in terms of the existence of an equivalent renorming. This extends a result by Knaust, Odell and Schlumprecht on Banach spaces with Szlenk index equal to ω.
Taking benefit of the R3B/SOFIA setup to measure the mass and the nuclear charge of both fission fragments in coincidence with the total prompt-neutron multiplicity, the scission configurations are ...inferred along the thorium chain, from the asymmetric fission in the heavier isotopes to the symmetric fission in the neutron-deficient thorium. Against all expectations, the symmetric scission in the light thorium isotopes shows a compact configuration, which is in total contrast to what is known in the fission of the heavier thorium isotopes and heavier actinides. This new main symmetric scission mode is characterized by a significant drop in deformation energy of the fission fragments of about 19 MeV, compared to the well-known symmetric scission in the uranium-plutonium region.
We present the charge-changing cross sections (CCCS) of 11−15C, 13−17N, and 15,17−18O at around 300 MeV/nucleon on a carbon target, which extends to p-shell isotopes with N<Z for the first time. The ...Glauber model, which considers only the proton distribution of projectile nuclei, underestimates the cross sections by more than 10%. We show that this discrepancy can be resolved by considering the contribution from the charged-particle evaporation process (CPEP) following projectile neutron removal. Using nucleon densities from the deformed relativistic Hartree-Bogoliubov theory in continuum, we investigate the isospin-dependent CPEP contribution to the CCCS for a wide range of neutron-to-proton separation energy asymmetry. Our calculations, which include the CPEP contribution, agree well with existing systematic data and reveal an “evaporation peak” at the isospin symmetric region where the neutron-to-proton separation energy is close to zero. These results suggest that analysis beyond the Glauber model is crucial for accurately determining nuclear charge radii from CCCSs.
The refill records of computerized pharmacy systems are used increasingly as a source of compliance information. We reviewed the English-language literature to develop a typology of methods for ...assessing refill compliance (RC), to describe the epidemiology of compliance in obtaining medications, to identify studies that attempted to validate RC measures, to describe clinical features that predicted RC, and to describe the uses of RC measures in epidemiologic and health services research. In most of the 41 studies reviewed, patients obtained less medication than prescribed; gaps in treatment were common. Of the studies that assessed the validity of RC measures, most found significant associations between RC and other compliance measures, as well as measures of drug presence (e.g., serum drug levels) or physiologic drug effects. Refill compliance was generally not correlated with demographic characteristics of study populations, was higher among drugs with fewer daily doses, and was inconsistently associated with the total number of drugs prescribed. We conclude that, though some methodologic problems require further study, RC measures can be a useful source of compliance information in population-based studies when direct measurement of medication consumption is not feasible.
The β-delayed neutron emission probabilities of neutron rich Hg and Tl nuclei have been measured together with β-decay half-lives for 20 isotopes of Au, Hg, Tl, Pb, and Bi in the mass region N≳126. ...These are the heaviest species where neutron emission has been observed so far. These measurements provide key information to evaluate the performance of nuclear microscopic and phenomenological models in reproducing the high-energy part of the β-decay strength distribution. This provides important constraints on global theoretical models currently used in r-process nucleosynthesis.
Using the high-resolution performance of the fragment separator FRS at GSI we have discovered 60 new neutron-rich isotopes in the atomic number range of 60 <= Z <= 78 . The new isotopes were ...unambiguously identified in reactions with a U 238 beam impinging on a Be target at 1 GeV/nucleon. The production cross-section for the new isotopes have been measured down to the pico-barn level and compared with predictions of different model calculations. For elements above hafnium fragmentation is the dominant reaction mechanism which creates the new isotopes, whereas fission plays a dominant role for the production of the new isotopes up to thulium.
Isobaric single charge-exchange reactions, changing nuclear charges by one unit but leaving the mass partitions unaffected, have been for the first time investigated by peripheral collisions of 112Sn ...ions accelerated up to 1A GeV at the GSI facilities. The high-resolving power of the FRS spectrometer allows us to obtain (p,n)-type isobaric charge-exchange cross sections with an uncertainty of 3.5% and to separate quasi-elastic and inelastic components in the missing-energy spectra of the ejectiles. The inelastic component is associated to the excitation of the Δ(1232) isobar resonance and the emission of pions in s-wave both in the target and projectile nucleus, while the quasi-elastic contribution is associated to the nuclear spin-isospin response of nucleon-hole excitations. An apparent shift of the Δ-resonance peak of ∼63 MeV is observed when comparing the missing-energy spectra obtained from the measurements with proton and carbon targets. A detailed analysis, performed with a theoretical model for the reactions, indicates that this observation can be simply interpreted as a change in the relative magnitude between the contribution of the excitation of the resonance in the target and in the projectile.
The shell structure of atomic nuclei is associated with 'magic numbers' and originates in the nearly independent motion of neutrons and protons in a mean potential generated by all nucleons. During ...β(+)-decay, a proton transforms into a neutron in a previously not fully occupied orbital, emitting a positron-neutrino pair with either parallel or antiparallel spins, in a Gamow-Teller or Fermi transition, respectively. The transition probability, or strength, of a Gamow-Teller transition depends sensitively on the underlying shell structure and is usually distributed among many states in the neighbouring nucleus. Here we report measurements of the half-life and decay energy for the decay of (100)Sn, the heaviest doubly magic nucleus with equal numbers of protons and neutrons. In the β-decay of (100)Sn, a large fraction of the strength is observable because of the large decay energy. We determine the largest Gamow-Teller strength so far measured in allowed nuclear β-decay, establishing the 'superallowed' nature of this Gamow-Teller transition. The large strength and the low-energy states in the daughter nucleus, (100)In, are well reproduced by modern, large-scale shell model calculations.
The inverse kinematics technique, applied to radioactive beams and combined to the Coulomb excitation method, is a powerful tool to study low-energy fission. A novel experimental setup was developed ...within the R3B/SOFIA (Reactions with Relativistic Radioactive Beams/Studies On FIssion with Aladin) collaboration to identify in mass and atomic numbers both fission fragments in coincidence. These new data provide elemental, isobaric, and isotonic yields for the fission along the thorium isotopic chain. Results are also compared to previous measurements using either the same reaction mechanism or thermal-neutron induced fission. This latter comparison permits to probe the influence of the excitation energy in the fission process.
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