Note on ordering and complexity of Platonic and Archimedean polyhedra based on solid angles

The missing values for the solid angles of the two snub semiregular polyhedra have been calculated, and integrated into the whole series of Platonic and Archimedean polyhedra. This is the only criterion which so far gives an unambiguous answer (without any degeneracy leading to posets) on how to order these polyhedra according to their increasing complexity.     

Tietze extension theorem for Hilbert -modules

We prove the following generalization of the noncommutative Tietze extension theorem: if is a countably generated Hilbert -module over a -unital -algebra, then the canonical extension of a surjective morphism of Hilbert -modules to extended (multiplier) modules, , is also surjective.

     

Techno-Economic Analysis of FiWi Access Networks Based on 802.11ac WLAN and NG-PON2 Networks

In this article, techno-economic analysis of a fiber-wireless access network is presented. With high bandwidth capacity of the gigabit passive optical network and with cost-effectiveness of very high throughput 802.11ac wireless local area networks that enable user mobility in the wireless segment, fiber-wireless access networks can be considered as an alternative to the fiber-to-the-home architecture for next generation access networks. Analysis based on the proposed scenario here, shows that a fiber-wireless access network is a more cost-effective solution in densely populated areas, but with some introduced improvements, even other geotypes can be considered as a commercially-viable solution.     

Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges

Research on the topological indices based on end-vertex degrees of edges has been intensively rising recently. Randić index, one of the best-known topological indices in chemical graph theory, is belonging to this class of indices. In this paper, we introduce a novel topological index based on the end-vertex degrees of edges and its basic features are presented here. We named it as geometrical-arithmetic index (GA).     

Interaction of a deformable solid with two-phase flows: An Eulerian-based numerical model for fluid-structure interaction using the level contour reconstruction method

We describe the formulation of a method for fluid-structure interaction involving the coupling of moving and/or flexible solid structures with multiphase flows in the framework of the Level Contour Reconstruction Method. We present an Eulerian-based numerical procedure for tracking the motion and interaction of a liquid-gas interface with a fluid-solid interface in the Lagrangian frame together with the evaluation of the fluid transport equations coupled to those for the solid transport, namely the left Cauchy-Green strain tensor field, in the Eulerian frame. To prevent excessive dissipation due to the convective nature of the solid transport equation, a simple incompressibility constraint for the strain field is enforced. A single grid structure is used for both the fluid and solid phases which allows for a simple and natural coupling of the fluid and solid dynamics. Several benchmark tests are performed to show the accuracy of the numerical method and which demonstrate accurate results compared to several of those in the existing literature. In particular we show that surface tension effects including contact line dynamics on the deforming solid phase can be properly simulated. The three-phase interaction of a droplet impacting on a flexible cantilever is investigated in detail. The simulations follow the detailed motion of the droplet impact (and subsequent deformation, breakup, and fall trajectory) along with the motion of the deformable solid cantilever due to its own weight as well as due to the force of the droplet impact.     

Structural Changes in a Protein Fragment from Abalone Shell during the Precipitation of Calcium Carbonate

Mineralized tissues grow through biologically controlled processes in which specific macromolecules are involved. Some of these molecules, which are present in very low concentrations and are difficult to localize and characterize, become entrapped inside the mineralized tissue. Herein, a protein fragment, GP, which was obtained by the alkaline digestion of the green sheet of the abalone shell, is used as a probe to study the changes in molecular structure that occur during the precipitation of calcium carbonate. This important goal was achieved by exploiting a fluorescent tag in GP. The experimental results that were obtained by using spectroscopic‐, chromatographic‐, and microscopic techniques indicate that GP controls the precipitation kinetics and morphology of calcium carbonate crystals, and that it only undergoes structural reorganization when entrapped inside calcium carbonate crystals. To the best of our knowledge, this report represents one of the first studies on the conformational changes of a protein fragment that is involved in biomineralization processes on moving from the solution phase into the mineral phase.     

Augmented Zagreb index

Inspired by recent work on the atom-bond connectivity (ABC) index we propose here a new topological index, augmented Zagreb index (AZI). The tight upper and lower bounds for chemical trees are obtained. Moreover, it has been shown that among all trees the star has the minimum AZI value. Characterizing trees with maximal augmented Zagreb index remains an open problem for future research.     

Surface hydration and nanoindentation of silicate glasses

The near-surface mechanical properties of glasses and differences in mechanical behaviour between high and low durability silicate glasses are investigated. Nanoindentation is used to examine the effect of hydration on the near-surface mechanical properties of silicate glasses with varying degrees of chemical durability. It is shown that hydration has little if any effect on high durability glasses even at long immersion times, whereas in low durable glasses hydration reduces the near-surface mechanical properties significantly and the thickness of hydrated layer may exceed the indentation depth. In addition an attempt is made to measure the thickness and mechanical properties of hydrated layer in low durability glasses where influence of the substrate is negligible.     

Halogen anion-induced formation of[(PdLX)2] (X = Cl-, Br-, I-) vs. [PdL2] (L = [6-MeO(O)CC6H4NHC(S)NP(S)(OiPr)2]-): reversible photoinduced cis/trans isomerization of [PdL2

Reaction of the potassium salt of N-thiophosphorylated thiourea 6-MeO(O)CC(6)H(4)NHC(S)NHP(S)(OiPr)(2) (HL) with PdX(2) (X = Cl(-), Br(-), I(-)) leads to the dark red binuclear complexes [(PdLX)(2)], while the same reaction with PdY(2) (Y = NO(3)(-), CN(-), CH(3)COO(-)) leads to the light red mononuclear complex [PdL(2)]. [PdL(2)] exhibits reversible photoinduced cis-isomerization upon irradiation at 365 or 450 nm, reverting back to the trans-isomer in darkness or upon irradiation at 546 nm.