The connection between self‐associated two‐dimensional vector functionals and third degree forms

We deal with the 2‐orthogonal, 2‐symmetric self‐associated sequence (2‐orthogonal Tchebychev polynomials) and its cubic components. We prove that all the forms (linear functionals) arising are third degree forms. Therefore, an introduction to third degree forms is provided. We look for the connection between these components which are 2‐orthogonal with respect to the functional vector ^t(w₀{^μ},w₁ ^μ) and orthogonal sequences with respect to w₀ ^μ, μ=0,1,2. Associated forms w₀ ^μ)¹) and their inverse w₀ ^μ)^-1 are also studied through the symmetrized w₀}₀ ^μ, μ=0,1,2. Further, we give integral representations for some of these forms. This revised version was published online in June 2006 with corrections to the Cover Date.     

Thermoluminescence of nanocrystalline LiF:Mg, Cu, P

Nanocrystalline LiF:Mg, Cu, P of rod shape (about 30-40 nm in diameter and 0.3-0.5 μm in length) has been prepared by the chemical co-precipitation method. Thermoluminescence (TL) and dosimetric characteristics of the nanocrystalline phosphor are studied and presented here. The formation of the material was confirmed by the X-ray diffraction (XRD). Its shape and size were also observed by transmission electron microscope (TEM). The TL glow curve of the nanocrystalline powder shows a single peak at 410 K along with four overlapping peaks of lesser intensities at around 570, 609, 638 and 663 K. The observed TL sensitivity of the prepared nanocrystalline powder is less than that of the commercially available “Harshaw TLD-700H hot-pressed chips” at low doses but it still around three times more than that of LiF:Mg, Ti (TLD-100) phosphor. The 410 K peak of the nanomaterial phosphor shows a very linear response with exposures increasing up to very high values (as high as 10 kGy), where all the other thermoluminesent dosimeters (TLD) phosphors show saturation. This linear response over a large span of exposures (0.1 Gy-10 kGy) along with negligible fading and its insensitivity to heating treatments makes the nanocrystalline phosphor useful for its application to estimate high exposures of γ-rays. The ‘tissue equivalence’ property of this material also makes it useful over a wide range of high-energy radiation.     

Solutions of Kramer's Equations for Perfect Fluid Cylinders

Kramer's formulation of Einstein's fieldequations for static perfect fluid cylinders isconsidered. Three approaches are followed in seekingsolutions of Kramer's equations. First, a particularintegral is found which reproduces a previously knownclass of four solutions. Second, a fairly general ansatzis suggested, whereby a class of six new solutions isderived. Finally, the problem for an incompressible perfect fluid, with constant energy density, isreduced to a single second order equation. All solutionsare regular everywhere. Constraints are imposed on thesolutions parameters such that energy conditions are satisfied and hence the solutions arephysically reasonable.     

Blends of carbon blacks and multiwall carbon nanotubes as reinforcing fillers for hydrocarbon rubbers

The reinforcement of a styrene‐butadiene rubber (SBR) by single fillers—carbon black (CB) or multiwall carbon nanotubes (MWNTs)—or by mixtures of CB and MWNTs, is investigated. The morphologies, mechanical and electrical properties of the composites, are analyzed. A significant improvement in the tensile properties is observed for samples containing a dual phase. Using atomic force (AFM) and transmission electron (TEM) microscopies, we demonstrate that the double loading improves the dispersion of the nanotubes in SBR. Electrical measurements show lower resistivity and a lower percolation threshhold for composites containing blends of fillers, which provides further evidence of better dispersion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 46: 1939–1951, 2008     

Mossbauer, infrared and magnetic susceptibility studies of iron sodium borate glasses doped by sulphur

The affect of sulphur on the structural properties of iron sodium diborate glasses having the composition {(100−x)Na₂B₄O₇+xFe₂O₃}+yS, where x=0.05, 0.15 and 0.25 mol% and Y=0, 2.5 and 5 wt% was studied by infrared, Mossbauer spectroscopy and magnetic susceptibility measurements. It was found that, for samples having 5 mol% Fe₂O₃ and free from sulphur, the iron ions are present in both Fe²⁺ and Fe³⁺ states and also 92% of the total iron enters the glass network as a glass former. The ratio of Fe³⁺/Fe²⁺ increases with increasing the iron content for sulphur-free samples and others containing sulphur. This ratio also decreases with increasing the sulphur content. The magnetic susceptibility was found to decrease with increasing the sulphur content. Also, the increase of Fe₂O₃ content led to a less symmetrical environment of Fe³⁺ ions and vice versa for the Fe²⁺ environment.     

Design of donor–acceptor–donor (D–A–D) type small molecule donor materials with efficient photovoltaic parameters

Four Donor–Acceptor–Donor (D–A–D) type of donor molecules (M1‐M4) with triphenylamine (TPA) as donor moiety, thiophene as bridge, and thiazolothiazole as acceptor unit were designed and its photovoltaic parameters were equated with reference molecule “R.” DFT functional CAM‐B3LYP/6‐31G (d,p) was found best for geometry optimization and TD‐CAM‐B3LYP/6‐31G (d,p) was found suitable for excited state calculations. Among designed donor molecules, M4 manifests suitable lowest band gap of 4.73 eV, frontier molecular orbital energy levels as well as distinctive broad absorption of 455.3 nm due to the stronger electron withdrawing group. The electron‐withdrawing substituents contribute to red shifts of absorption spectra and better stabilities for designed molecules. The theoretically determined reorganization energies of designed donor molecules suggested excellent charge mobility property. The lower λ_e values in comparison with λ_h illustrated that these four donor materials would be ideal for electron transfer and M4 would be best amongst the investigated molecules with lowest λ_e of 0.0177. Furthermore, the calculated Voc of M4 is 2.04 V with respect to PC₆₀BM (phenyl‐C61‐butyric acid methyl ester). This study revealed that the designed donor materials are suitable and recommended for high performance organic solar cell devices.     

Equivalent contributing depth investigated by a lateral wave with axial transmission in viscoelastic cortical bone

Cortical bone is a viscoelastic heterogeneous medium which may be assessed with axial transmission. This work aims at evaluating the average depth investigated by the lateral wave for radial variations of material properties in relatively thick cortical bone. The equivalent contributing depth (ECD) is derived from the finite element simulation results for spatial variations of a viscoelastic coefficient (η(11)) and of porosity. A value of ECD equal to around 1.6 mm is obtained for a spatial variation of η(11). The method fails to predict accurate values of the ECD for a spatial variation of porosity, because all parameters vary simultaneously.