Generalized projection and approximation of fixed points of nonself maps

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.     

Optical transitions,XPS, electronic states in NiPS3

We have measured the optical absorption below the fundamental threshold, the normal-incidence reflectivity between 1.5 and 30 eV and the X-ray photoemission spectra of NiPS₃. Shake-up satellites present at the Ni 2p and 3p core levels are strong evidence for the ionicity of the NiS bonds. We have also derived a qualitative molecular orbital model of NiPS₃ in which the trigonal crystal field splits the P and S 3p_xp_y-3p_a states, and strong covalent hybridization between P and S p_xp_y orbitals leads to covalent electronic bonding. Ni is envisaged as a divalent ion which plays little role in the electronic bonding and its 3d levels are localized, lying near the top both of the valence states. This model accounts well for both the valence band XPS data and the low energy optical transitions. Our model should represent, at the center of the Brillouin zone but not at the boundaries, the energy level sequence in NiPS₃ and other related MPX₃ layer-type compounds where M Co²⁺, Mn²⁺, Fe²⁺, Zn²⁺ and X is sulfur or selenium.The XPS spectra and optical properties of NiPS₃ have been obtained and interpreted on a qualitative molecular orbital model in which the Ni is a divalent positive ion which plays little role in the bonding. Evidence for such ionicity appears in the optical properties and XPS satellite structures, as well as in the magnetic properties. The model should represent qualitatively the band structure at the center of the Brillouin zone, but not at the boundaries. It should also be valid for other compounds similar to NiPS₃, i.e. those with other metals in place of Ni and those with Se in place of S.     

The electronic structure of ZrSe32

The energy bands of the semiconductor ZrSe₃ have been evaluated using the KKR method. The general features of the electronic structure are expected to pertain to other transition metal trichalcogenides which have similar trigonal prismatic coordination. The calculated density of states agrees well with X-ray photoemission spectra for the valence band. The joint density of states has been evaluated and is discussed in terms of optical measurements.     

Characterization of amino acids in silk sericin protein from Gonometa rufobrunnae by MEKC with phenyl isothiocyanate derivatization

An MEKC method was developed for the separation and characterization of phenyl-isothiocyanate (PITC)-labeled amino acids derived from Gonometa rufobrunnae silkworm after microdialysis sample cleanup. The influence of the buffer and SDS concentration on the resolution of the amino acids was investigated. A buffer system consisting of 25 mM phosphate, 10 mM borate buffer at pH 9.00, and 70 mM SDS showed the best results, with 13 PITC-amino acid derivatives being resolved out of 15 possible amino acids that were under study. Microdialysis sampling demonstrated its efficiency as a sample cleanup technique. Sericin protein from G. rufobrunnae was found to be characterized by at least 11 positively identified amino acids. These included His, Tyr, Ser, Ala, Phe, Lys, Gly, Arg, Cys, Glu, and Asp. Leu/Met and Val/Thr were coeluting pairs and hence could not be positively confirmed.     

A new multistage spectral relaxation method for solving chaotic initial value systems

In this paper, we present a new pseudospectral method application for solving nonlinear initial value problems (IVPs) with chaotic properties. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a novel technique of extending Gauss–Siedel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudo-spectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous chaotic systems such as the such as Lorenz, Chen, Liu, Rikitake, Rössler, Genesio–Tesi, and Arneodo–Coullet chaotic systems. The accuracy and validity of the proposed method is tested against Runge–Kutta and Adams–Bashforth–Moulton based methods. The numerical results indicate that the MSRM is an accurate, efficient, and reliable method for solving very complex IVPs with chaotic behavior.     

Silver nanostructures embedding in polymethyl methacrylate patterns fabricated using proton beam writing

Proton beam writing (PBW) on polymethyl methacrylate (PMMA) followed by embedding of biosynthesized silver nanoparticles (AgNPs) was investigated. This is the first demonstration of the use of 3 MV Tandetron accelerator at iThemba LABS for fabricating patterns using PBW technique. The irradiation of PMMA was carried out using 3.0-MeV proton beam focused down to micrometer spot size. The fluence of protons was counted as electrical charge per unit monitored by exposure time, beam current, and irradiated area. As expected, the PMMA behaved as a positive resist because of chain scissioning induced from the interaction with proton beam. Morphological characterization using scanning electron microscope (SEM) revealed fabrication of square-like patterns, and atomic force microscopy (AFM) provided the possibility of observing the presence of AgNPs that stood out of the PMMA matrix.     

Positional and compositional disorder in a ruthenium(II) piano‐stool complex

In (η⁶‐p‐cymene)(difluorophosphinato‐κO){2‐[(1H‐pyrazol‐1‐yl)methyl‐κN²]pyridine‐κN}ruthenium(II) 0.85‐hexafluorophosphate 0.15‐tetrafluoroborate, [Ru(PO₂F₂)(C₁₀H₁₄)(C₉H₉N₃)](PF₆)_0.85(BF₄)_0.15, (I), the [PO₂F₂]⁻ ligand exhibits positional disorder due to one F atom and one O atom sharing the same two positions related by a mirror reflection across the O—P—F plane. The correct composition of this coordinated anion was successfully determined to be [PO₂F₂]⁻ by refining the complex with various tetrahedral anions in which terminal atoms have similar atomic form factors. The noncoordinated counter‐ion is compositionally disordered between [PF₆]⁻ and [BF₄]⁻. The difficulty in determining the correct composition of this anion illustrates the importance of a crystallographer remaining impartial and open to encountering unexpected moieties in the process of elucidating a structure.     

New collective structures in the 163Yb nucleus

The European Physical Journal A - Photon strength functions describing the average response of the nucleus to an electromagnetic probe are key input information in the theoretical modelling of...