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.     

An efficient, rapid and regioselective nuclear bromination of aromatics and heteroaromatics with NBS using sulfonic-acid-functionalized silica as a heterogeneous recyclable catalyst

A simple, efficient and rapid method has been developed for high-yielding regioselective nuclear monobromination of aromatic and heteroaromatic compounds using NBS in the presence of sulfonic-acid-functionalized silica at room temperature. The catalyst works under heterogeneous conditions and can be recycled.     

Transition metal chemistry of oxime-containing ligands,VI: magnetic and structural properties of mono (pyridine-2-aldoxime) dithiocyanato iron (II) and mono (6-methylpyridine-2-aldoxime) dithiocyanato iron (II) complexes

The complexes of pyridine-2-aldoxime (HPOX) and 6-methylpyridine-2-aldoxime (HMPX) with iron (II) thiocyanate of the type [Fe(L)(NCS)₂] (L=HPOX and HMPX) have been prepared and characterized. A study of X-ray, magnetic, vibrational spectra (conventional and far-infrared), electronic spectra andMössbauer spectra has indicated that these complexes have polymeric, pseudo octahedral, coordination geometry with linear bridging thiocyanate ligands. The electronic spectra of mono complexes show a larger, low symmetry, ligand field than that present in [Fe(L)₂(NCS)₂] complexes. UnperturbedMössbauer spectra show a large quadrupole splitting, E _Q, and smaller isomer shift values in these iron (II) thiocyanate complexes. The magnetically perturbedMössbauer spectra of these iron(II) thiocyanate complexes at room temperature show that the principal component of the electric field gradient tensor is positive and corresponds to ad _xy (⁵B₂) ground state.With 2 Figures     

Temperature Dependent Dielectric Relaxation in Solvent Mixtures at Microwave Frequencies

By the use of time domain reflectometry method, dielectric measurements were carried out on dimethylformamide‐2‐nitrotoluene solvent mixtures in the frequency range 10 MHz‐20 GHz, at various temperatures from 15 °C to 45 °C. These solvent mixtures as well as pure solvents display a Debye type dispersion. Their frequency dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters for these solvent mixtures at various concentrations and temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The excess permittivity is found to be positive for all concentrations and temperatures whereas the excess inverse relaxation time is negative.     

A Sensitive HPTLC Method for Estimation of Amentoflavone,a Bioactive Principle from Biophytum sensitivum (Linn.) DC. and Putranjiva roxburghii Wall.

JPC – Journal of Planar Chromatography – Modern TLC - A sensitive high-performance thin-layer chromatographic (HPTLC) method has been developed for estimation of amentoflavone, an...     

Computer modelling of the director configuration in a supertwist nematic liquid crystal cell

Abstract

The director distribution in a supertwist nematic cell, containing La-Roche liquid crystal mixture 3010, has been studied extensively using Berreman's computer simulation approach. It is seen that the director distribution in the cell depends critically on the total twist angle θ_t, the surface tilt angle θ_o and the ratio of the cell thickness to the pitch d/p. The values of θ_o and φ_t have been optimized to yield a small bistability (ΔV = 0.06 V) and a relatively large change in the midplane tilt angle (Δθ_m = 51°) in an unstrained cell with ?_t = (d/p) × 360°. The optimum values of θ_o and Ø_t were found to be 15° and 240°, respectively. The effect of varying d/p on the director distribution has also been studied in great detail in supertwist cells with θ_o = 30° and Ø_t = 270°. Some interesting features in understrained and overstrained cells have been observed.