Remarks on Asymptotic Centers and Fixed Points

We introduce a class of nonlinear continuous mappings defined on a bounded closed convex subset of a Banach space X. We characterize the Banach spaces in which every asymptotic center of each bounded sequence in any weakly compact convex subset is compact as those spaces having the weak fixed point property for this type of mappings

The Jordan–von Neumann constants and fixed points for multivalued nonexpansive mappings

AbstractThe purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of Banach spaces. Furthermore, we demonstrate a relationship between the weakly convergent sequence coefficient WCS(X) and the Jordan–von Neumann constant CNJ(X) of a Banach space X. Using this fact, we prove that if CNJ(X) is less than an appropriate positive number, then every multivalued nonexpansive mapping T:E→KC(E) has a fixed point where E is a nonempty weakly compact convex subset of a Banach space X, and KC(E) is the class of all nonempty compact convex subsets of E

The Effect of Heat Treatment on Crystal Structure in Zircon Monitored by ESR and XRD

AbstractX-band ESR spectra of zircon before and after heat treatment under oxygen rich atmosphere were measured with directions of the magnetic field applied in parallel and perpendicular to c-axis [001]. Seven peaks of Zeeman interaction were generated from the microwave energy absorptions due to the transitions between the spin states of natural impurity, gadolinium ions (Gd3+, S = 7/2). Angular variation of peak positions reflects that the symmetry surrounding of Gd3+ is D2d, signifying the replacement of Zr4+ by Gd3+ in the lattice. From XRD patterns, the unheated and after heated zircon are the same phase i.e. tetragonal phase of the space group I41/amd. The Rietveld refinement method was employed for derivation of the bond distance and bond angles of zirconium, silicon and oxygen atoms

First Results from the AMoRE-Pilot neutrinoless double beta decay experiment

The Advanced Molybdenum-based Rare process Experiment (AMoRE) aims to search for neutrinoless double beta decay (0$\nu\beta\beta$) of $^{100}$Mo with $\sim$100 kg of $^{100}$Mo-enriched molybdenum embedded in cryogenic detectors with a dual heat and light readout. At the current, pilot stage of the AMoRE project we employ six calcium molybdate crystals with a total mass of 1.9 kg, produced from $^{48}$Ca-depleted calcium and $^{100}$Mo-enriched molybdenum ($^{48\textrm{depl}}$Ca$^{100}$MoO$_4$). The simultaneous detection of heat(phonon) and scintillation (photon) signals is realized with high resolution metallic magnetic calorimeter sensors that operate at milli-Kelvin temperatures. This stage of the project is carried out in the Yangyang underground laboratory at a depth of 700 m. We report first results from the AMoRE-Pilot $0\nu\beta\beta$ search with a 111 kg$\cdot$d live exposure of $^{48\textrm{depl}}$Ca$^{100}$MoO$_4$ crystals. No evidence for $0\nu\beta\beta$ decay of $^{100}$Mo is found, and a upper limit is set for the half-life of 0$\nu\beta\beta$ of $^{100}$Mo of $T^{0\nu}_{1/2} > 9.5\times10^{22}$ y at 90% C.L.. This limit corresponds to an effective Majorana neutrino mass limit in the range $\langle m_{\beta\beta}\rangle\le(1.2-2.1)$ eV

On stationary points of nonexpansive set-valued mappings

In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of such points under certain conditions follows as a consequence of the existence of approximate stationary sequences. In particular we provide abstract extensions of well-known fixed point theorems.Dirección General de Enseñanza SuperiorJunta de Andalucí