On the explicit determination of the polar decomposition in n-dimensional vector spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.

A determination of the structure of the intramolecular charge transfer state of 4-dimethylaminobenzonitrile (DMABN) by time-resolved resonance Raman spectroscopy

Picosecond time-resolved resonance Raman spectra of the A (intramolecular charge transfer, ICT) state of DMABN, DMABN-d(6) and DMABN-N-15 have been obtained. The isotopic shifts identify the nu (s)(ph-N) mode as a band at 1281 cm(-1). The similar to 96 cm(-1) downshift of this mode from its ground state frequency rules out the electronic coupling PICT model and unequivocally supports the electronic decoupling TICT model. However, our results suggest some pyramidal character of the A state amino conformation.

High contrast imaging and thickness determination of graphene with in-column secondary electron microscopy

We report a new method for quantitative estimation of graphene layer thicknesses using high contrast imaging of graphene films on insulating substrates with a scanning electron microscope. By detecting the attenuation of secondary electrons emitted from the substrate with an in-column low-energy electron detector, we have achieved very high thickness-dependent contrast that allows quantitative estimation of thickness up to several graphene layers. The nanometer scale spatial resolution of the electron micrographs also allows a simple structural characterization scheme for graphene, which has been applied to identify faults, wrinkles, voids, and patches of multilayer growth in large-area chemical vapor deposited graphene. We have discussed the factors, such as differential surface charging and electron beam induced current, that affect the contrast of graphene images in detail. (C) 2011 American Institute of Physics. doi:10.1063/1.3608062]

Calcium ruthenates: Determination of Gibbs energies of formation using electrochemical cells

Metallic Ru has been found to coexist separately with CaO, RuO2, and the interoxide phases, Ca2RuO4, Ca3Ru2O7, and CaRuO3, present along the pseudobinary system CaO-RuO2. The standard Gibbs energies of formation (Df((ox))G(o)) of the three calcium ruthenates from their component oxides have been measured in the temperature range 925-1350 K using solid-state cells with yttria-stabilized zirconia as the electrolyte and Ru+RuO2 as the reference electrode. The standard Gibbs energies of formation (Deltaf((ox))G(o)) of the compounds can be represented by Ca2RuO4:Deltaf((ox))G(o)/J mol(-1)=-38,340-6.611 T (+/-120), Ca3Ru2O7 : Df((ox))G(o)/J mol(-1)=-75,910-11.26 T (+/-180), and CaRuO3 : Deltaf((ox))G(o)/J mol(-1)=-35,480-3.844 T(+/-70). The data for Ca2RuO4 corresponds to the stoichiometric composition, which has an orthorhombic structure, space group Pbca, with short c axis ("S'' form). The structural features of the ternary oxides responsible for their mild entropy stabilization are discussed. A three-dimensional oxygen potential diagram for the system Ca-Ru-O is developed as a function of composition and temperature from the results obtained. Using the Neumann-Kopp rule to estimate the heat capacity of the ternary oxides relative to their constituent binary oxides, the standard enthalpies of formation of the three calcium ruthenates from the elements and their standard entropies at 298.15 K are evaluated. (C) 2003 The Electrochemical Society.

Determination of critical micelle concentration by hyper-Rayleigh scattering

The critical micelle concentration (CMC) of several surfactants that contain an NLO chromophore, either at the hydrocarbon tail, or at the hydrophilic headgroup, or even as a counterion, was determined by hyper-Rayleigh scattering (HRS). In all cases, the HRS signal exhibited a similar variation with surfactant concentration, wherein the CMC is inferred from a rather unprecedented drop in the signal intensity. This drop is attributed to the formation of small pre-micellar aggregates, whose concentrations become negligible above CMC. In addition, a probe molecule, which upon protonation yielded a species with significantly enhanced HRS intensity, was developed and its utility for the determination of the CIVIC of simple fatty acids was demonstrated.

Determination of solid fraction evolution during solidification of aluminum alloy in presence of linear electromagnetic stirring

In many industrial casting processes, knowledge of the solid fraction evolution during the solidification process is a key factor in determining the process parameters such as cooling rate, stirring intensity and in estimating the total solidification time. In the present work, a new method of estimating solid fraction is presented, which is based on calorimetric principles. In this method, the cooling curve data at each point in the melt, along with the thermal boundary conditions, are used to perform energy balance in the mould, from which solid fraction generation during any time interval can be estimated. This method is applied to the case of a rheocasting process, in which Al-Si alloy (A356 alloy) is solidified by stirring in a cylindrical mould placed in the annulus of a linear electromagnetic stirrer. The metal in the mould is simultaneously cooled and stirred to produce a cylindrical billet with non-dendritic globular microstructure. Temperature is measured at key locations in the mould to assess the various heat exchange processes prevalent in the mould and to monitor the solidification rate. The results obtained by energy balance method are compared with those by the conventional procedure of calculating solid fraction using the Schiel equation.

Theoretical determination of HI vertical scale heights in the dwarf galaxies DDO 154, Ho II, IC 2574 and NGC 2366

In this paper, we model dwarf galaxies as a two-component system of gravitationally coupled stars and atomic hydrogen gas in the external force field of a pseudo-isothermal dark matter halo, and numerically obtain the radial distribution of HI vertical scale heights. This is done for a group of four dwarf galaxies (DDO 154, Ho II, IC 2574 and NGC 2366) for which most necessary input parameters are available from observations. The formulation of the equations takes into account the rising rotation curves generally observed in dwarf galaxies. The inclusion of self-gravity of the gas into the model at par with that of the stars results in scale heights that are smaller than what was obtained by previous authors. This is important as the gas scale height is often used for deriving other physical quantities. The inclusion of gas self-gravity is particularly relevant in the case of dwarf galaxies where the gas cannot be considered a minor perturbation to the mass distribution of the stars. We find that three out of four galaxies studied show a flaring of their HI discs with increasing radius, by a factor of a few within several disc scale lengths. The fourth galaxy has a thick HI disc throughout. This flaring arises as a result of the gas velocity dispersion remaining constant or decreasing only slightly while the disc mass distribution declines exponentially as a function of radius.

The determination of stem cell fate by 3D scaffold structures through the control of cell shape

Stem cell response to a library of scaffolds with varied 3D structures was investigated. Microarray screening revealed that each type of scaffold structure induced a unique gene expression signature in primary human bone marrow stromal cells (hBMSCs). Hierarchical cluster analysis showed that treatments sorted by scaffold structure and not by polymer chemistry suggesting that scaffold structure was more influential than scaffold composition. Further, the effects of scaffold structure on hBMSC function were mediated by cell shape. Of all the scaffolds tested, only scaffolds with a nanofibrous morphology were able to drive the hBMSCs down an osteogenic lineage in the absence of osteogenic supplements. Nanofiber scaffolds forced the hBMSCs to assume an elongated, highly branched morphology. This same morphology was seen in osteogenic controls where hBMSCs were cultured on flat polymer films in the presence of osteogenic supplements (OS). In contrast, hBMSCs cultured on flat polymer films in the absence of OS assumed a more rounded and less-branched morphology. These results indicate that cells are more sensitive to scaffold structure than previously appreciated and suggest that scaffold efficacy can be optimized by tailoring the scaffold structure to force cells into morphologies that direct them to differentiate down the desired lineage. Published by Elsevier Ltd.

Electrochemical Determination of the Stability of Mono- and Dicalcium Stannates

he thermodynamic properties of mono- and dicalcium stannates have been determined in the temperature range 973–-1423°K from the electromotive force measurements on solid oxide galvanic cells[dformula Pt, Ni + NiO//CaO - ZrO[sub 2]/Y[sub 2]0[sub 3] - ThO[sub 2]//SnO[sub 2] + Sn, W, Pt][dformula Pt, Ni + NiO//CaO - ZrO[sub 2]/Y[sub 2]O[sub 3] - ThO[sub 2]//CaSnO[sub 3] + SnO[sub 2] + Sn, W, Pt][dformula Pt, Ni + NiO//CaO - ZrO[sub 2]/Y[sub 2]O[sub 3] - ThO[sub 2]/Ca[sub 2]SnO[sub 4] + CaSnO[sub 3] + Sn, W, Pt]and [dformula Pt, Ni + NiO//CaO - ZrO[sub 2]sol;Y[sub 2]O[sub 3] - ThO[sub 2]//Ca[sub 2]SnO[sub 4] + CaO, W, Pt] The Gibbs free energy changes accompanying the formation of the stannates from component oxides may be represented by the equations[dformula 2CaO + SnO[sub 2] --> Ca[sub 2]SnO[sub 4]][dformula Delta G[degree] = - 17,040 + 0.85T ([plus-minus]300) cal][dformula CaO + SnO[sub 2] --> CaSnO[sub 3]][dformula Delta G[degree] = - 17,390 + 2.0T ([plus-minus]300) cal]The partial pressures of the tin bearing oxide species resulting from the decomposition of the stannates have been calculated as a function of the oxygen partial pressure by combining the results of this study with published information on the partial pressures and composition of oxide species over stannic oxide.

Potentiometric determination of the Gibbs free energy of formation of cadmium and magnesium chromites

The standard Gibbs free energy of formation of magnesium and cadmiumchromites have been determined by potentiometric measurements on reversiblesolid-state electrochemical cells [dformula (Au-5%Cd, , Au-5%Cd; Pt, + , CaO-ZrO[sub 2], + ,Pt; CdO, , CdCr[sub 2]O[sub 4] + Cr[sub 2]O[sub 3])] in the temperature range 500°–730°C, and [dformula Pt, Cr + Cr[sub 2]O[sub 3]/Y[sub 2]O[sub 3]-ThO[sub 2]/Cr + MgCr[sub 2]O[sub 4] + MgO, Pt] in the temperature range 800°–1200°C. The temperature dependence of the freeenergies of formation of the ternary compounds can be represented by theequations [dformula CdO(r.s.) + Cr[sub 2]O[sub 3](cor) --> CdCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 42,260 + 7.53T ([plus-minus]400) J] and [dformula MgO(r.s.) + Cr[sub 2]O[sub 3](cor) --> MgCr[sub 2]O[sub 4](sp)] [dformula Delta G[sup 0] = - 45,200 + 5.36T ([plus-minus]400) J] The entropies of formation of these spinels are discussed in terms of cationdisorder and extent of reduction of Cr3+ ions to Cr2+ ions. Thermodynamicdata on the chromates of cadmium and magnesium are derived by combiningthe results obtained in this study with information available in the literatureon high temperature, high pressure phase equilibria in the systems CdO-Cr2O3-O2 and MgO-Cr2O3-O2.

Electrochemical determination of activities in Cr2O3 Al2O3 solid solutions

The activity of Cr20~ in Cr20~-A12Oa solid solution has been determined in the temperature range 800~176 from electromotive force measurements on the solid oxide galvanic cell Pt,Cr + Cr2OJY~O~-ThO2/Cr + Cr~A12-xO~,Pt The activities of Cr203 and A120~ in the solid solution show both positive and negative deviations from Raoult's law. The heat and entropy of mixing of the solid Solution obtained from the temperature dependence of the emf can be expressed as AH = XCr203XA1203 [31,700Xcrzo3 -}- 37,470XA1203] J mole -I hS = -- 1.8R [Xcr2o3 In Xcr2o3 + XA12o3 In XAaos]The entropy of mixing is 10% lower than that predicted by the Temkin model.The large positive heat of mixing in the Cr2Os-A12Oa solid solution, however, suggests that this apparent: entropy discrepancy originates with the clustering of positive ions on the cation sublattice. The asymmetric miscibility gap exhibited in the CrzOa-A12Oa system below 900~ is consistent with the thermodynamic data trends recorded at the more elevated temperatures.