On Einstein four-manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-actions

We study closed Einstein 4-manifolds which admit S¹ actions of a certain type, i.e., warped products. In particular, we classify them up to isometry when the fixed point of the S¹ action satisfies certain natural geometric conditions. The proof uses the Bochner-Weitzenböck formula for 1-forms and the theory of minimal surfaces in 3-manifolds.in final form: 22 January 2003     

Multi-Item Scheduling by Benders' Decomposition

Scheduling the production of several items requires the determination of production quantities in different periods in the presence of resource constraints. Several approximate and heuristic algorithms have been proposed to solve this problem. However, no method for finding an optimal solution has as yet been developed. It is shown that the problem may be solved advantageously using Benders' decomposition. The subproblem in Benders' decomposition is shown to be a transportation problem, and some strategies for solving the master problem are indicated. The paper concludes with a sample problem demonstrating the application of the method.     

High temperature annealing effect on structural and magnetic properties of Ti/Ni multilayers

High temperature annealing effect on structural and magnetic properties of Ti/Ni multilayer (ML) up to 600 °C have been studied and reported in this paper. Ti/Ni multilayer samples having constant layer thicknesses of 50 Å each are deposited on float glass and Si(1 1 1) substrates using electron-beam evaporation technique under ultra-high vacuum (UHV) conditions at room temperatures. The micro-structural parameters and their evolution with temperature for as-deposited as well as annealed multilayer samples up to 600 °C in a step of 100 °C for 1 h are determined by using X-ray diffraction (XRD) and grazing incidence X-ray reflectivity techniques. The X-ray diffraction pattern recorded at 300 °C annealed multilayer sample shows interesting structural transformation (from crystalline to amorphous) because of the solid-state reaction (SSR) and subsequent re-crystallization at higher temperatures of annealing, particularly at ≥400 °C due to the formation of TiNi₃ and Ti₂Ni alloy phases. Sample quality and surface morphology are examined by using atomic force microscopy (AFM) technique for both as-deposited as well as annealed multilayer samples. In addition to this, a temperature dependent dc resistivity measurement is also used to study the structural transformation and subsequent alloy phase formation due to annealing treatment. The corresponding magnetization behavior of multilayer samples after each stage of annealing has been investigated by using Magneto-Optical Kerr Effect (MOKE) technique and results are interpreted in terms of observed micro-structural changes.     

An automated laboratory EXAFS spectrometer of Johansson type: indigenous development and testing

An automated linear laboratory EXAFS spectrometer of the Johansson type has been indigenously developed. Only two translational motions are required to achieve the necessary Rowland circle configuration for the (fixed) X-ray source, the dispersing and focusing bent crystal and the receiving slit. With the available crystals the spectral region from 5 to 25 keV can be scanned. The linear motions of the crystal and receiving slit including the detector assembly are achieved by employing software-controlled DC motors and utilizing optical encoders for position sensing. The appropriate rotation of the crystal is achieved by the geometry of the instrument. There is a facility to place the sample alternately in the path of the X-ray beam and out of the path to record both the incident X-ray intensityI ₀ and the transmitted intensityI employing the scintillation detector. An arrangement with a two-window proportional detector before the sample to measureI ₀ and the scintillation detector to recordI is also developed; in this case it is not necessary to oscillate the sample. Fast electronic circuits are employed to minimize counting errors. The instrument is user-friendly and it is operated through a menu-driven IBM compatible PC. EXAFS spectra of high resolution have been recorded using the spectrometer and employing the Si(111) reflecting planes; the X-ray source being a Rigaku 12 kW rotating anode with Cu target. We describe the spectrometer and discuss its performance with a few representative spectra.     

Reaction kinetics of the selective liquid phase hydrogenation of styrene oxide to β-phenethyl alcohol

Liquid phase hydrogenation of styrene oxide using 1% Pd/C and NaOH as a promoter was found to give selectively β-phenethyl alcohol (PEA) under very mild conditions (313–333 K; 0.68–5.5 MPa). The kinetics of this system was investigated by collecting initial rate data in a batch slurry reactor. Rate of hydrogenation was found to decrease beyond a certain concentration of both hydrogen (>3 MPa) and styrene oxide (>0.5 kmol/m³). A Langmuir–Hinshelwood type rate equation has been proposed based on the initial rate data in the kinetic regime. The model predictions agree very well with the experimentally observed concentration–time data indicating the applicability of the proposed rate model.     

Dielectric Studies of Glycine–Ethylene Glycol–Water Solutions Using Time Domain Reflectometry

Time domain reflectometry (TDR) has been used for dielectric relaxation measurements on the glycine–ethylene glycol–water ternary system (TDR) at 25, 30, 35, and 40°C in the frequency range from 10 MHz to 10 GHz. Glycine–ethylene glycol–water solutions are prepared with different concentrations of ethylene glycol (0, 5, 10, 15, 20, and 30%) and also for different glycine molar concentrations (0, 0.2, 0.4, 0.6, 0.8, and 1 M). The dielectric relaxation parameters are measured for aqueous glycine solutions also to compare the results with those for the glycine–ethylene glycol–water ternary system. For all the solutions considered, only one relaxation peak was observed in this frequency range. The complex permittivity spectra for the aqueous glycine solutions can be well described by the Cole–Davidson expression, whereas that for the ternary system can be well described by the Havriliak–Negami expression. The logarithm of the relaxation time log() shows a nonlinear relation with the glycine molar concentration that implies a change in the relaxation mechanism with glycine concentration. The dielectric strength increases with an increase in glycine molar concentration, whereas it decreases with an increase in ethylene glycol concentration.