Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Skin-friction measurements in high-enthalpy hypersonic boundary layers

Skin-friction measurements are reported for high-enthalpy and high-Mach-number laminar, transitional and turbulent boundary layers. The measurements were performed in a free-piston shock tunnel with air-flow Mach number, stagnation enthalpy and Reynolds numbers in the ranges of 4.4-6.7, 3-13 MJ kg(-1) and 0.16 x 10(6)-21 x 10(6), respectively. Wall temperatures were near 300 K and this resulted in ratios of wall enthalpy to flow-stagnation enthalpy in the range of 0.1-0.02. The experiments were performed using rectangular ducts. The measurements were accomplished using a new skin-friction gauge that was developed for impulse facility testing. The gauge was an acceleration compensated piezoelectric transducer and had a lowest natural frequency near 40 kHz. Turbulent skin-friction levels were measured to within a typical uncertainty of +/-7%. The systematic uncertainty in measured skin-friction coefficient was high for the tested laminar conditions; however, to within experimental uncertainty, the skin-friction and heat-transfer measurements were in agreement with the laminar theory of van Driest (1952). For predicting turbulent skin-friction coefficient, it was established that, for the range of Mach numbers and Reynolds numbers of the experiments, with cold walls and boundary layers approaching the turbulent equilibrium state, the Spalding & Chi (1964) method was the most suitable of the theories tested. It was also established that if the heat transfer rate to the wall is to be predicted, then the Spalding & Chi (1964) method should be used in conjunction with a Reynolds analogy factor near unity. If more accurate results are required, then an experimentally observed relationship between the Reynolds analogy factor and the skin-friction coefficient may be applied.

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

Climate of fear in organisational settings: Construct definition, measurement and a test of theory

This paper reports a study that explored a new construct: climate of fear. We hypothesised that climate of fear would vary across work sites within organisations, but not across organisations. This is in contrast a to measures of organisational culture, which were expected to vary both within and across organisations. To test our hypotheses, we developed a new 13-item measure of perceived fear in organisations and tested it in 20 sites across two organisations (N = 209). Culture variables measured were innovative leadership culture, and communication culture. Results were that climate of fear did vary across sites in both organisations, while differences across organisations were not significant, as we anticipated. Organisational culture, however, varied between the organisations, and within one of the organisations. The climate of fear scale exhibited acceptable psychometric properties.

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

Opening windows into the mind: mothers' preferences for mental state explanations and children's theory of mind

A new questionnaire, the Maternal Mental State Input Inventory (MMSII) was created to measure mothers' preferences for introducing and elaborating on mental states in conversation with their young children. In two studies, the questionnaire was given to mothers of young children, and the children's theory of mind (ToM) development was assessed with standard tasks. In both studies, the questionnaire exhibited good internal reliability, and significant correlations emerged between mothers' self-reported preferences for elaborated, explanatory talk about the mental states and children's theory of mind performance. Further, mothers' conversational preferences, as measured by the MMSII, were the best predictors of children's theory of mind development when relevant control variables were included in the analyses. These results converge with naturalistic observational research that has demonstrated links between mothers' conversational styles and their children's theory of mind. They go further in suggesting that mothers' tendencies toward elaborated, explanatory talk about a range of mental states is particularly beneficial to children's theory of mind development. (C) 2003 Elsevier Inc. All rights reserved.

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump pump, Stokes signal, and Raman coherence idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Wall mediated transport in confined spaces: Exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory.

Effect of pore-network connectivity on multicomponent adsorption of large molecules

The effect of pore-network connectivity on binary liquid-phase adsorption equilibria using the ideal adsorbed solution theory (LAST) was studied. The liquid-phase binary adsorption experiments used ethyl propionate, ethyl butyrate, and ethyl isovalerate as the adsorbates and commercial activated carbons Filtrasorb-400 and Norit ROW 0.8 as adsorbents. As the single-component isotherm, a modified Dubinin-Radushkevich equation was used. A comparison with experimental data shows that incorporating the connectivity of the pore network and considering percolation processes associated with different molecular sizes of the adsorptives in the mixture, as well as their different corresponding accessibility, can improve the prediction of binary adsorption equilibria using the LAST Selectivity of adsorption for the larger molecule in binary systems increases with an increase in the pore-network coordination number, as well with an increase in the mean pore width and in the spread of the pore-size distribution.