Projection methods for computing Moore-Penrose inverses of unbounded operators

In this article we give a characterization of the convergence of projection methods which are useful for approximating the Moore-Penrose inverse of a closed densely defined operator between Hilbert spaces. We illustrate the main theorem with an example. Also a procedure for constructing the admissible sequence of projections is discussed.     

Synthesis of 48 disaccharide building blocks for the assembly of a heparin and heparan sulfate oligosaccharide library

[Structure: see text] An efficient synthesis of the entire set of suitably protected 48 disaccharide building blocks for the assembly of a heparin and heparan sulfate oligosaccharide library is described here.     

Efficient synthesis of a C-analogue of the immunogenic bacterial glycolipid BbGL2

Synthesis of a C-analogue of bacterial glycolipid BbGL2 is reported using Grignard reaction of in situ generated beta-galactosyl iodide and subsequent olefin cross metathesis reaction of C-vinyl galactoside as key steps. [reaction: see text]     

Novel phase transformation in ZnO nanowires under tensile loading

We predict a previously unknown phase transformation from wurtzite to a graphitelike (P6(3)/mmc) hexagonal structure in [0110]-oriented ZnO nanowires under uniaxial tensile loading. Molecular dynamics simulations and first principles calculations show that this structure corresponds to a distinct minimum on the enthalpy surfaces of ZnO for such loading conditions. This transformation is reversible with a low level of hysteretic dissipation of 0.16 J/m3 and, along with elastic stretching, endows the nanowires with the ability to recover pseudoelastic strains up to 15%.     

PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.     

On the structural properties of small-world networks with range-limited shortcut links

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter (r$r$) sets the length scale over which shortcuts are uniformly distributed. When r=0$r=0$ we have an ordered network, whereas r=1$r=1$ corresponds to the original Watts–Strogatz SWN model. These limited range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for r?1$r?1$, indicating that global shortcuts are not necessary for the small-world effect. For limited range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. We propose an expression for the average path length for limited range SWNs based on numerical simulations and analytical approximations.     

Energy dependence of ion beam mixing at Fe-Al and Fe-Cu interface: A conversion electron Mössbauer spectroscopic study

The energy dependence of ion beam mixing in the Fe-Al and Fe-Cu bilayer configuration on the energy of bombarding Kr⁺ ions has been investigated by using the technique of conversion electron Mössbauer spectroscopy. The ion energy has been varied over a range between 30 keV and 120 keV by keeping the dose value fixed at 10¹⁶ ions/cm². In both the cases the extent of mixing shows an interesting variation with increase in the value of ion energy. This behaviour is discussed in the light of the calculated energy deposition distributions for the case of the given bilayer systems. The variations in the microstructural details of the mixed region with change in the incident ion energy have also been brought out via determination of hyperfine interaction parameters.     

An optimal greedy routing algorithm for triangulated polygons

In this paper, we prove that a triangulated polygon G admits a greedy embedding into an appropriate semi-metric space such that using an appropriate distance definition, for any two vertices u and w in G, a most virtual distance decreasing path is always a minimum-edge path between u and w. Therefore, our greedy routing algorithm is optimal. The greedy embedding of G can be obtained in linear time. To the best of our knowledge, this is the first optimal greedy routing algorithm for a nontrivial subcategory of graphs.     

X-ray absorption spectroscopy study of the electronic structure and local coordination of 1st row transition metal-promoted Chevrel-phase sulfides

Abstract

The electronic structures of S and Mo as well as the local coordination of Mo are investigated as a function of metal promotion Chevrel-phase (CP) sulfides. We observe the effect of metal promoter-induced electron donation into the stoichiometric range M_xMo₆S₈ (M?=?Fe, Ni, Cu; x?=?0–2) through analysis of X-ray absorption near-edge structure regions. We further observe the effect of this promotion on the bonding environment of Mo₆ metal centers through extended X-ray absorption fine structure analysis. We monitor expansion and contraction of Mo₆ octahedra with and without metal promotion, as has been predicted by Hückel molecular orbital theory. We further observe a marked tunability in the electronic structure of sulfur upon charge transfer between promoting species and Mo₆S₈ units. Average Mo₆ octahedron Mo–Mo bond contraction from 2.76 Å to as short as 2.69 Å was observed upon incorporation of metal promoters, while intercluster separation displays a pronounced increase for promoter-host lattices compared to un-promoted Mo₆S₈. To corroborate spectroscopically observed phenomena, we performed computational analyses of spin-polarized densities of state for the CP materials investigated herein, where a detectable increase in sulfur-based frontier orbital population is observed in accordance with experimentally validated orbital filling.