Orlicz capacities and Hausdorff measures on metric spaces

In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided thatwhere Θ⁻¹ is the inverse of the function Θ(t)=Φ(t)/t, and s is the “upper dimension” of the metric measure space. This condition is a generalization of a well known condition in Rⁿ. For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided.     

Hall effect on MHD free convection boundary layer flow past a vertical flat plate

Effects of Hall current on MHD free convection boundary layer flow of a viscous incompressible electrically conducting fluid past a heated vertical flat plate of finite dimension in the presence of a uniform transverse magnetic field have been studied. An exact solution of the governing equations describing the flow has been obtained. The velocity field, induced magnetic field and bulk temperature distributions in the boundary layer flow have been discussed. It is found that the velocity components increase with an increase in Hall parameter. It is noticed that the induced magnetic field components are radically influenced by the Hall parameter. It is also found that the magnitude of bulk temperature in the x-direction decreases with an increase in either Hall parameter or magnetic parameter. On the other hand, the magnitude of the bulk temperature in the z-direction increases with an increase in Hall parameter whereas it decreases with an increase in magnetic parameter.     

Prime ends for domains in metric spaces

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carathéodory and Näkki. Modulus ends and prime ends, defined by means of the p$p$-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.     

Which distance-hereditary graphs are cover–incomparability graphs?

In this paper we deal with cover–incomparability graphs of posets, or briefly C–I graphs. These are graphs derived from posets as the edge-union of their cover graph and their incomparability graph. We answer two recently posed open questions. Which distance-hereditary graphs are C–I graphs? Which Ptolemaic (i.e. chordal distance-hereditary) graphs are C–I graphs? It follows that C–I graphs can be recognized efficiently in the class of all distance-hereditary graph whereas recognizing C–I graphs in general is known to be NP-complete.     

Effect of annealing on structural and optical properties of diamond-like nanocomposite thin films

The annealing effect on structural and optical properties of the Diamond-like Nanocomposite (DLN) thin film deposited on glass substrate by Plasma Assisted Chemical Vapor Deposition (PACVD) method has been investigated. The films were annealed at temperature ranging from 300 to 600 °C, with 100 °C interval for 9 minutes by rapid thermal process (RTP) under vacuum. The structural changes of the annealed films have been studied using Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, Scanning Electron Microscope (SEM), and optical parameters have been determined using transmittance and reflectance spectra in UV-UIS-NIR range. The result shows that the refractive index increases gradually from 1.79 to 2.84 with annealing temperature due to out-diffusion of H by breaking Si–H and C–H bond leads to Si–C bond, i.e. more cross linking structure. In higher temperature range, graphitization also enhanced the refractive index. However, the optical band gap at up to 400 °C initially increases from 3.05 to 3.20 eV and then decreases due to graphitization. The film has a great potential to be used as anti-reflection coating (ARC) on silicon-based solar cell.     

2D water layer enclathrated between Mn(II)-Ni(CN)4 coordination frameworks

A [Ni(CN)₄]²⁻-based two-dimensional Mn(II) coordination polymer {Mn(H₂O)₂[NiCN]₄·4H₂O}, in which the coordination layers are stacked on top of each other sandwiching 2D water layer of boat-shaped hexagonal water clusters has been synthesized. The complex exhibits high thermal decomposition temperature and reversible water absorption, which were clearly demonstrated by thermal and PXRD studies on the parent and rehydrated complex after dehydration.     

The effect of polyethylene addition on the morphology of polystyrene/polyamide blends

The effect of a small admixture of high‐density polyethylene (HDPE) with a high or low viscosity to polystyrene/polyamide (PS/PA) blends of various compositions was studied. PS/PA blends with composition near 50/50 form sheet‐like or fiber‐like morphology at mixing that passes to the cocontinuous structure during compression molding. Ternary PS/PA/HDPE blends with PS/PA ratio about 50/50 show similar behavior. Generally, neither continuity nor shape of PS and PA phases was changed qualitatively by the addition of a small amount of HDPE. In agreement with existing rules for ternary blends, HDPE particles prefer a contact with PS phase to PA phase. On the other hand, none of these rules explains why a number of small HDPE subinclusions were dispersed into PS particles instead of HDPE‐PS core‐shell structure with a lower Gibbs free energy. Quantitative evaluation of the size of PA particles in blends with PS matrix showed that the previously proposed rule stating, that the addition of a small amount of a third immiscible component leads to a strong decrease in the size of dispersed particles, was not valid for the blends studied in this work. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2158–2170, 2009     

Near-infrared spectroscopy: A powerful tool in studies of acid-treated clay minerals

The benefit of near-infrared (NIR) spectroscopy in studies of acid-treated clay minerals is demonstrated. The effects of mineral type, composition and content of non-swelling interlayers on the dissolution rate are investigated. Detailed analysis of the NIR region is performed by comparing the first overtone (2ν_OH) and combination (ν + δ)_OH bands with the fundamental stretching (ν) and bending (ν) vibrations. Spectra of acid-treated samples show a gradual decrease in the intensities of the structural OH overtone (near 7100 cm^?1) and combination (4600–4300 cm^?1) bands reflecting a fewer number of octahedral atoms. The appearance of the 2ν_SiOH vibration for terminal (isolated) SiOH groups near 7315 cm^?1 indicates the formation of a protonated silica phase. The band near 7130 cm^?1 remaining in the spectra of acid-treated samples is assigned to 2ν_HOSiOH of geminal silanol groups. Thus the creation of geminal silanols, previously detected by ²⁹Si MAS-NMR spectroscopy in acid-treated hectorite, is confirmed also by NIR spectroscopy. The assignment of the 4555 cm^?1 band to the (ν + δ)_SiOH combination enabled calculation of the wavenumber for the SiO–H bending vibration (～810 cm^?1) that is not observable in the mid-IR region due to overlapping with the Si–O band of amorphous silica (～800 cm^?1). The NIR spectra confirm that trioctahedral hectorite is much more susceptible to dissolution in HCl than dioctahedral nontronite. The dissolution rate of kaolinite present in the Badin clay as an admixture is lower than that of the main mineral nontronite. The accessibility of the interlayers for protons significantly influences the stability of clay minerals in HCl. Mixed-layered mineral illite/smectite with only 30% of swelling interlayers dissolves more slowly than smectite of similar chemical composition containing mainly swelling interlayers.