The orthorhombic polymorph of diammonium trichromate(VI) decaoxide, <Emphasis Type="Italic">α</Emphasis>–(NH<Subscript>4</Subscript>)<Subscript>2</Subscript>Cr<Subscript>3</Subscript>O<Subscript>10</Subscript>

Synthesis and crystal structure of a trichromium(VI) decaoxide compound, α–(NH₄)₂Cr₃O₁₀, is reported. The crystal structure has been determined from three dimensional X-ray data collected at low temperature, 173 K. The structure is isomorphous with its Rb and Cs trichromate analogues, orthorhombic, space group Pbca, with a = 11.2558(3), b = 9.3193(3), c = 18.9819(5) ? and Z = 8. The title compound is composed of discrete [Cr₃O₁₀]^2– chains held together by the counter ion charge and a hydrogen bonding network. The different conformations adopted by trichromate anion within its ammonium, alkali and organic salts are discussed.     

Instabilities in viscoelastic flow past a square cavity

Elastic flow transitions in viscoelastic flow past a square cavity adjacent to a channel are reported. The critical conditions for the onset of flow transitions and the qualitative and quantitative characterization of the secondary flows generated by the instability have been examined using streakline photography and instantaneous pressure measurements. Cellular type of instabilities inside the cavity is observed for flow rates beyond a critical value. Small and large scale eddies are observed at high flow rates. The flow inside the cavity and in the channel upstream and downstream of the cavity becomes weakly time-dependent for high flow rates.     

On unsteady unidirectional flows of a second grade fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows produced by the sudden application of a constant pressure gradient or by the impulsive motion of one or two boundaries. Exact analytical solutions for these flows are obtained and the results are compared with those of a Newtonian fluid. It is found that the stress at the initial time on the stationary boundary for flows generated by the impulsive motion of a boundary is infinite for a Newtonian fluid and is finite for a second grade fluid. Furthermore, it is shown that initially the stress on the stationary boundary, for flows started from rest by sudden application of a constant pressure gradient is zero for a Newtonian fluid and is not zero for a fluid of second grade. The required time to attain the asymptotic value of a second grade fluid is longer than that for a Newtonian fluid. It should be mentioned that the expressions for the flow properties, such as velocity, obtained by the Laplace transform method are exactly the same as the ones obtained for the Couette and Poiseuille flows and those which are constructed by the Fourier method. The solution of the governing equation for flows such as the flow over a plane wall and the Couette flow is in a series form which is slowly convergent for small values of time. To overcome the difficulty in the calculation of the value of the velocity for small values of time, a practical method is given. The other property of unsteady flows of a second grade fluid is that the no-slip boundary condition is sufficient for unsteady flows, but it is not sufficient for steady flows so that an additional condition is needed. In order to discuss the properties of unsteady unidirectional flows of a second grade fluid, some illustrative examples are given.     

On unsteady motions of a second-order fluid over a plane wall

In this paper, three types of unsteady flows of second-order fluids are considered, namely, flow caused by impulsive motion of a flat plate, flow induced by a constantly accelerating plane and flow imposed by a flat plate that applies a constant tangential stress to the fluid. The previous attempts made regarding these problems, by using the Laplace transform, have failed. In this paper, the sine and the cosine transforms are used to solve these problems and exact solutions for the velocity distributions are found in terms of definite integrals. It is shown that these exact solutions satisfy the initial and the boundary conditions and the governing equation.     

On γ-semi-open sets

Summary We introduce the concepts of γ-semi-open set, γ_s-set, γ^s-set, generalized γ_s-set, generalized γ^s-set, semi-T₁^γspace and semi-R₀^γspace by using γ-open-sets.     

Heat transfer due to the flow through a conical tube

Résumé On étudie la distribution de la température dans un fluide visqueux incompressible s'écoulant dans un tube conique. On fait également la comparaison de la distribution de température entre deux parois inclinées non-parallèles à celle du tube conique précédemment étudiée.     

Component testing of repairable systems in multistage missions

We consider the component testing problem of a device that is designed to perform a mission consisting of a sequence of stages. Once a stage is over, the device is overhauled to replace all failed components before the next stage starts to improve mission reliability. The components fail exponentially where the failure rate depends on the stage of the mission. The reliability structure of the device involves a series connection of redundant subsystems. The optimal component testing problem is formulated as a semi-infinite linear programme. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical results.     

Boundary-layer flow about a vertical spinning cone under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar boundary-layer flow in the presence of a transverse magnetic field over a down-pointing and spinning cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic and spin parameters and the Prandtl number. The spin of the cone compresses the velocity profiles towards the surface by inducing an upward flow and decreases the surface temperature. The magnetic field suppresses the velocity profiles and increases the surface temperature. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.     

Influence measures in ridge regression when the error terms follow an Ar(1) process

Influence concepts have an important place in linear regression models and case deletion is a useful method for assessing the influence of single case. The influence measures in the presence of multicollinearity were discussed under the linear regression models when the errors structure is uncorrelated and homoscedastic. In contrast to other article on this subject, we consider the influence measures in ridge regression with autocorrelated errors. Theoretical results are illustrated with a numerical example and a Monte Carlo simulation is conducted to see the effect autocorrelation coefficient, strength of multicollinearity and sample size on leverage points and influential observations.     

Broad band metamaterial absorber based on wheel resonators with lumped elements for microwave energy harvesting

A new metamaterial absorber structure is designed and characterized both numerically and experimentally for microwave energy harvesting applications. The proposed structure includes four wheel resonators with different dimensions, from which the overall response of the structure can then be obtained by summing all the overlapping frequency responses corresponding to each dimension. The essential operation frequency range of the wheels is selected in such a way that the energy used in wireless communications and found within the environment that we live is absorbed. The dimensions are obtained using parametric study and genetic algorithm to realize wideband absorption response. When the simulation and measurement results are taken into account, it is observed that the metamaterial absorber based harvester has potential to absorb and convert microwave energy with an absorption ratio lying within the range of 80 and 99% for the frequency band of 3–5.9 and 7.3–8 GHz. The conversion efficiency of the structure as a harvester is found to be greater than 0.8 in the interval of 2–5 GHz. Furthermore, the incident angle and polarization dependence of the wheel resonator based metamaterial absorber and harvester is also investigated and it is observed that the structure has both polarization and incident angle independent frequency response with good absorption characteristics in the entire working frequency band. Hence, the suggested design having good absorption, polarization and angle independent characteristics with wide bandwidth is a potential candidate for future energy harvester using wireless communication frequency band.