The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976, 12(4):747-756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear

Recent reaction measurements have been interpreted as evidence of a halo structure in the exotic neutron-rich isotopes 29,31 Ne. While theoretical studies of 31 Ne generally agree on its halo nature, they differ significantly in their predictions of its properties and underlying cause (e.g., that 31 Ne has an inverted ordering of p-f orbitals). We have made a systematic theoretical analysis of possible Neon halo signatures -the first using a fully microscopic, relativistic mean field approach that properly treats positive energy orbitals (such as the valence neutron in 31 Ne) self-consistently with bound levels, as well as the pairing effect that keeps the nucleus loosely bound with negative Fermi energy. Our model is the analytical continuation of the coupling constant (ACCC) method based on a relativistic mean field (RMF) theory with Bardeen-Cooper-Schrieffer (BCS) pairing approximation. We calculate neutron-and matter-radii, one-neutron separation energies, p-and f -orbital energies and occupation probabilities, and neutron densities for single-particle resonant orbitals in 27-31 Ne. We analyze these results for evidence of neutron halo formation in 29,31 Ne. Our model predicts a p-orbit 1n halo structure for 31 Ne, based on a radius increase from 30 Ne that is 7-8 times larger than the increase from 29 Ne to 30 Ne, as well as a decrease in the neutron separation energy by a factor of ∼ 10 compared to that of 27-30 Ne. In contrast to some other studies, our inclusion of resonances yields an inverted ordering of p and f orbitals for spherical and slightly deformed nuclei. Furthermore, we find no evidence of an s-orbit 1n halo in 29 Ne as recently claimed in the literature.

Background: Four strong single-particle bound levels with strikingly similar level spacings have recently been measured in 131 Sn and 133 Sn. This similarity has not yet been addressed by a theoretical nuclear structure model. Information on these single-particle bound levels, as well as on resonant levels above the neutron capture threshold, is also needed to determine neutron capture cross sections-and corresponding capture reaction rates-on 130,132 Sn. The 130 Sn(n, γ ) rate was shown in a recent sensitivity study to significantly impact the synthesis of heavy elements in the r-process in supernovae.Purpose: Understand the structure of bound and resonant levels in 131,133 Sn, and determine if the densities of unbound resonant levels are sufficiently high to warrant statistical model treatments of neutron capture on 130,132 Sn. Method: Single-particle bound and resonant levels for 131,133 Sn are self-consistently calculated by the analytical continuation of the coupling constant (ACCC) method based on a relativistic mean field (RMF) theory with BCS approximation.Results: We obtain four strong single-particle bound levels in both 131,133 Sn with an ordering that agrees with experiments and spacings that, while differing from experiment, are consistent between the Sn isotopes. We also find at most one single-particle level in the effective energy range for neutron captures in the r-process.Conclusions: Our RMF + ACCC + BCS model successfully reproduces observed single-particle bound levels in 131,133 Sn and self-consistently predicts single-particle resonant levels with densities too low for widely used traditional statistical model treatments of neutron capture cross sections on 130,132 Sn employing Fermi gas level density formulations.

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The purpose of this paper is to study the almost sure T -stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of φ-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T -stability and convergence for these two kinds of random iterative algorithms are proved.

We explore the effects of strangeness and ∆ resonance in baryonic matter and compact stars within the relativistic-mean-field (RMF) models. The covariant density functional PKDD is adopted for N -N interaction, parameters fixed based on finite hypernuclei and neutron stars are taken for the hyperon-meson couplings, and the universal baryon-meson coupling scheme is adopted for the ∆meson couplings. In light of the recent observations of GW170817 with the dimensionless combined tidal deformability 197 ≤Λ ≤ 720, we find it is essential to include the ∆ resonances in compact stars, and small ∆-ρ coupling gρ∆ is favored if the mass 2.27 +0.17 −0.15 M of PSR J2215+5135 is confirmed.

A particle number conserving BCS approach (FBCS) is formulated in the relativistic mean field (RMF) model. It is shown that the so-obtained RMF+FBCS model can describe the weak pairing limit. We calculate the ground-state properties of the calcium isotopes 32−74 Ca and compare the results with those obtained from the usual RMF+BCS model. Although the results are quite similar to each other, we observe an interesting phenomenon, i.e., for 54 Ca, the FBCS approach can enhance the occupation probability of the 2p 1/2 single particle level and slightly increases its radius, compared with the RMF+BCS model. This leads to an unusual scenario that although 54 Ca is more bound with a spherical configuration but the corresponding size is not the most compact one. We anticipate that such a phenomenon might happen for other neutron rich nuclei and should be checked by further more systematic studies. *