Spherical T-Duality

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c ₂(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.     

Synthesis of nanoplate bismuth oxychloride—a visible light active material

We have synthesized bismuth oxychloride (BiOCl) by wet chemical route. Characterization of the synthesized samples has been carried out using XRD, SEM with EDAX, HRTEM, FT-IR, Raman Spectroscopy, PL and UV. XRD and SEM analysis confirms crystallite size varying from 20–40 nm. FTIR spectrum indicates that the prepared material is highly pure and there is no water molecule present. Raman and photoluminescence spectrum of the bismuth oxychloridenanoplate demonstrated strong blue light emission which brings them in a special class of materials which work under visible light exposure. UV-Vis spectroscopy shows very less charge carriers transit time under visible light thus confirming excellent photocatalytic properties of material.     

On cutting sequences of the <Emphasis Type="Italic">L</Emphasis>-shaped translation surface tiled by three squares

We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.     

Organically modified montmorillonite and chitosan–phosphotungstic acid complex nanocomposites as high performance membranes for fuel cell applications

Nanocomposite membranes based on polyelectrolyte complex (PEC) of chitosan/phosphotungstic acid (PWA) and different types of montmorillonite (MMT) were prepared as alternative membranes to Nafion for direct methanol fuel cell (DMFC) applications. Fourier transform infrared spectroscopy (FTIR) revealed an electrostatically fixed PWA within the PEC membranes, which avoids a decrease in proton conductivity at practical condition. Various amounts of pristine as well as organically modified MMT (OMMT) (MMT: Cloisite Na, OMMT: Cloisite 15A, and Cloisite 30B) were introduced to the PEC membranes to decrease in methanol permeability and, thus, enhance efficiency and power density of the cells. X-ray diffraction patterns of the nanocomposite membranes proved that MMT (or OMMT) layers were exfoliated in the membranes at loading weights of lower than 3 wt.%. Moreover, the proton conductivity and the methanol permeability as well as the water uptake behavior of the manufactured nanocomposite membranes were studied. According to the selectivity parameter, ratio of proton conductivity to methanol permeability, the PEC/2 wt.% MMT 30B was identified as the optimum composition. The DMFC performance tests were carried out at 70 °C and 5 M methanol feed and the optimum membrane showed higher maximum power density as well as acceptable durability compared to Nafion 117. The obtained results indicated that owing to the relatively high selectivity and power density, the optimum nanocomposite membrane could be considered as a promising polyelectrolyte membrane (PEM) for DMFC applications.     

Synthesis of Diaryl Ethers Through the Copper-Catalyzed Arylation of Phenols with Aryl Iodides Using KF/Al2O3

An efficient synthesis of diaryl ethers by the copper-catalyzed arylation of phenols with a variety of aryl iodide susing KF/Al₂O₃ as a suitable base and CuI and 1,3 diphenyl-1,3 propandione as the catalyst is described.     

Mode-I interlaminar fracture behaviour of nanoparticle modified epoxy/basalt fibre-reinforced laminates

The effect of nano-reinforcements on fracture behaviour of bulk epoxy nanocomposites and mode-I interlaminar fracture toughness of filament-wound basalt fibre-reinforced laminates was studied. Fracture energy of the bulk epoxy nanocomposites significantly increased with acrylic tri-block-copolymer addition but remained unchanged with incorporation of nanoclay. Delamination fracture toughness was not influenced by the presence of nanoparticles in the matrix. Decreasing fibre volume fraction, on the other hand, significantly improved interlaminar fracture energy. Rigid fibres in these composites constrict the stress field ahead of the crack-tip. Hence, increasing resin content enhanced composite delamination energy by increasing the capacity for matrix deformation. Interlaminar crack propagation through the composite was observed to occur mainly by interfacial failure and matrix cracking.     

The effect of ethanol on the phase behaviour and micro-rheology of liquid crystals

The effect of ethanol on the phase behaviour and micro-rheology of lyotropic liquid crystals (LC) has been studied using a binary mixture of monoglyceride (MG) and aqueous ethanol. The phase behaviour study reveals the structural modulation of surfactant aggregates with increasing ethanol concentration, namely a bicontinuous cubic phase (Ia3d) transitions to the lamellar phase (L_α), at a fixed MG concentration. This behaviour is explained by considering the critical packing parameter (CPP) of the surfactant molecule. Because ethanol dehydrates the surfactant head group (a _s), the CPP values increase (decreasing a _s) and thus the formation of larger CPP aggregates is favoured (i.e., the Ia3d–L_α transition occurs). Cross-polarised images and X-ray scattering data support this conclusion. The structural modulation of the LC has further been investigated using a diffusing wave spectroscopy technique. The correlation and relaxation times, determined from the intersection point at short and long time scales of the mean square displacement (MSD), decrease with increasing concentrations of ethanol, indicating structural modulation of the LC. The micro-viscoelastic moduli (G′ and G′′) derived from the Laplace transformation of the MSD decrease with increasing ethanol concentrations, due to the LC modulation. The thermal effects on the micro-rheology of the LC have also been studied.     

Nanosized sulfated zirconia as solid acid catalyst for the synthesis of 2-substituted benzimidazoles

The condensation reaction of o-phenylenediamine and arylaldehydes was investigated in the presence of nanosized sulfated zirconia (SO ₄ ^2? -ZrO₂) as the solid acid catalyst. Nanosized SO ₄ ^2? -ZrO₂ was prepared and characterized by the XRD, FT-IR, and SEM techniques. The results confirm good stabilization of the tetragonal phase of zirconia in the presence of sulfate. Reusability experiments showed partial deactivation of the catalyst after each run; good reusability can be achieved after calcinations of the recovered catalyst before its reuse.     

Pertraction of methylene blue using a mixture of D2EHPA/M2EHPA and sesame oil as a liquid membrane

An experimental study on the pertraction of methylene blue (MB) through a supported liquid membrane (SLM) using a mixture of mono-(2-etylhexyl) ester of phosphoric acid (M2EHPA) and bis-(2-etylhexyl) ester of phosphoric acid (D2EHPA) and sesame oil as the liquid membrane (LM) was performed. Parameters affecting the pertraction of MB such as initial MB concentration, carrier concentration, feed phase pH, and stripping phase concentration were analyzed. Optimal experimental conditions for MB pertraction (permeability of 5.63 × 10^?6) were obtained after a 7 h separation with the MB concentration in the feed phase of 80 mg L^?1, D2EHPA/M2EHPA concentration in membrane phase of 40 vol. %, feed pH of 6, and acetic acid concentration in the stripping phase of 0.4 mol L^?1. Kinetics of transport and stability of the SLM system were also studied and the mass transfer coefficient for this system was evaluated. Scanning electron microscopy (SEM) was used to morphologically characterize the membrane surface.     

Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, \({f \in \mathcal{A}(\bar{\mathbb{C}} \setminus A)}\), \({\# A< \infty}\). J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Padé approximants for f. The Padé approximants, which are rational functions and thus single-valued, approximate a holomorphic branch of f in the domain of their convergence. At the same time most of their poles tend to the boundary of the domain of convergence and the support of their limiting distribution models the system of cuts that makes the function f single-valued. Nuttall has conjectured (and proved for many important special cases) that this system of cuts has minimal logarithmic capacity among all other systems converting the function f to a single-valued branch. Thus the domain of convergence corresponds to the maximal (in the sense of minimal boundary) domain of single-valued holomorphy for the analytic function \({f\in\mathcal{A}(\bar{\mathbb{C}} \setminus A)}\). The complete proof of Nuttall’s conjecture (even in a more general setting where the set A has logarithmic capacity 0) was obtained by H. Stahl. In this work, we derive strong asymptotics for the denominators of the diagonal Padé approximants for this problem in a rather general setting. We assume that A is a finite set of branch points of f which have the algebro-logarithmic character and which are placed in a generic position. The last restriction means that we exclude from our consideration some degenerated “constellations” of the branch points.