On certain classes of exact solutions of Einstein equations for rotating fields in conventional and nonconventional form

Using the symmetry reduction approach we have herein examined, under continuous groups of transformations, the invariance of Einstein exterior equations for stationary axisymmetric and rotating case, in conventional and nonconventional forms, that is a coupled system of nonlinear partial differential equations of second order. More specifically, the said technique yields the invariant transformation that reduces the given system of partial differential equations to a system of nonlinear ordinary differential equations (nlodes) which, in the case of conventional form, is reduced to a single nlode of second order. The first integral of the resulting nlode has been obtained via invariant-variational principle and Noether’s theorem and involves an integration constant. Depending upon the choice of the arbitrary constant two different forms of the exact solutions are indicated. The generalized forms of Weyl and Schwarzschild solutions for the case of no spin have also been deduced as particular cases. Investigation of nonconventional form of Einstein exterior equations has not only led to the recovery of solutions obtained through conventional form but it also yields physically important asymptotically flat solutions. In a particular case, a single third order nlode has been derived which evidently opens up the possibility of finding many further interesting solutions of the exterior field equations.     

Analysis of posterior availability distributions of series and parallel systems

The lifetime distribution of an engineering system is a powerful tool for analysing the system in respect of its reliability characteristics. The analysis can be improved if the experimenter has, and is able to combine, the prior belief about the system with the operational or experimental data. Moreover, in many situations, the operational data with the complete system may either be costlier or non-existent. The problem can still be tackled by making use of such information available on the subunits or components of the system. Pursuing these concepts, the present study deals with the analysis of posterior availability distributions for a series and a parallel system. Time truncated failure and repair information and prior beliefs about the failure and repair rates of the compoents of the systems have been employed in the analysis.     

Studies on the Reduction of Coefficient of Variation: A Case Study

In a spinning mill, yarn is the final product. Linear density expressed in terms of count is one of the important characteristics of yarn. Because variability of textile strands increases as the linear density increases, the variability in the count is often measured in terms of coefficient of variation (CV)%. The yarn with a high CV% of count leads to a higher end breakage rate during the spinning and subsequent weaving/knitting operations, and consequently, results in lesser productivity and poorer appearance quality of the woven/knitted fabric. When this woven/knitted fabric is dyed, uneven shades are generated. Because the production of yarn involves processing of raw cotton in multimachines at multistages, possible sources that lead to a high CV% of count are many. Enrick's (1960) analysis procedure, which is based on the modification of the range method for analysis of variance, is used conventionally for detecting the stages where excessive “between-machine” differences are present. When the CV% of count is inflated due to the generation of systematic variation in any machine or introduction of high variability by any machine, this inflation remains undetected when using Enrick's procedure. The case study presented here demonstrates that a step-by-step analysis of linear densities of different stage-outputs starting from yarn to card sliver, using appropriate nested design models along with Duncan's multiple range test, is very useful in detecting all possible sources of a high CV% of count of yarn.     

Retailers' tagging practices: a potential liability?

This study investigates the coverage of federally mandated information on over‐the‐counter (OTC) drug labels by electronic article surveillance (EAS) tags applied to the exterior of cartons. Using adult‐strength analgesics containing acetaminophen as a case study, researchers investigated the issue in Houston, Texas (24 stores) and Lansing, Michigan (33 stores). The information obscured by EAS tags was identified and classified for a total of 849 packages using a standardized data collection instrument. The results indicated that 293 packages examined, or 34.5%, had information mandated by the US Food and Drug Administration (US FDA) fully or partially obscured by the EAS tags. Retailers and manufacturers should be aware of such practices to reduce potential liability. Recommendations for improving EAS tag usage on OTC products are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of indoor particles and gases and their evolution with natural ventilation

The air composition and reactivity from outdoor and indoor mixing field campaign was conducted to investigate the impacts of natural ventilation (ie, window opening and closing) on indoor air quality. In this study, a thermal desorption aerosol gas chromatograph (TAG) obtained measurements of indoor particle‐ and gas‐phase semi‐ and intermediately volatile organic compounds both inside and outside a single‐family test home. Together with measurements from a suite of instruments, we use TAG data to evaluate changes in indoor particles and gases at three natural ventilation periods. Positive matrix factorization was performed on TAG and adsorbent tube data to explore five distinct chemical and physical processes occurring in the indoor environment. Outdoor‐to‐indoor transport is observed for sulfate, isoprene epoxydiols, polycyclic aromatic hydrocarbons, and heavy alkanes. Dilution of indoor species is observed for volatile, non‐reactive species including methylcyclohexane and decamethylcyclopentasiloxane. Window opening drives enhanced emissions of semi‐ and intermediately volatile species including TXIB, DEET, diethyl phthalate, and carvone from indoor surfaces. Formation via enhanced oxidation was observed for nonanal and 2‐decanone when outdoor oxidants entered the home. Finally, oxidative depletion of gas‐phase terpenes (eg, limonene and α‐pinene) was anticipated but not observed due to limited measurement resolution and dynamically changing conditions.     

Chemical Signals of Synthetic Disaccharide Derivatives Dominate Rhamnolipids at Controlling Multiple Bacterial Activities

Microbes secrete molecules that modify their environment. Here, we demonstrate a class of synthetic disaccharide derivatives (DSDs) that mimics and dominates the activity of naturally secreted rhamnolipids by Pseudomonas aeruginosa. The DSDs exhibit the dual function of activating and inhibiting the swarming motility through a concentration‐dependent activity reversal that is characteristic of signaling molecules. Whereas DSDs tethered with a saturated farnesyl group exhibit inhibition of both biofilm formation and swarming motility, with higher activities than rhamnolipids, a saturated farnesyl tethered with a sulfonate group only inhibits swarming motility but promote biofilm formation. These results identified important structural elements for controlling swarming motility, biofilm formation, and bacterial adhesion and suggest an effective chemical approach to control intertwined signaling processes that are important for biofilm formation and motilities.     

Comparison of performances of five prospective approaches for the multi-response optimization

The Taguchi method of experimental design is widely used for optimization of process performance. However, this method has been developed to optimize single-response processes. But, in many situations, the engineers are required to determine the process settings that can simultaneously optimize multiple responses. In the recent past, researchers have proposed several systematic procedures for multi-response optimization. Most of these methods use complicated statistical/mathematical models and are, therefore, not easily comprehendible to the engineers who do not have a strong background in mathematics. Only a few methods, e.g. weighted signal-to-noise (WSN) ratio, Grey relational analysis, multiple-response signal-to-noise ratio, VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian), and weighted principal component methods, use relatively simpler procedures. In this paper, the computational procedures for these five methods are standardized. Three sets of experimental data are analyzed using these standardized procedures and the predicted optimization performances of the five methods are compared. The results show that no method can give better optimization than the WSN method.     

Directional solidification of aluminum-nickel eutectic alloys using electroslag remelting

Attempts were made to produce directionally solidified, specifically grain aligned Al-6 wt pct Ni eutectic alloy using a laboratory scale ESR unit. For this purpose sand cast alloy electrodes were electroslag remelted under different mold conditions. The grain structure of the ingots obtained from these meltings showed that insulated silica molds gave the best vertical alignment of grains along the length of the ingot. The NiAl₃ fibers within the grains tended to fan out and there was only a preferred alignment of fibers along the growth direction under the conditions of our experiments. The ESR parameters most suitable for vertical alignment of eutectic grains have been identified. In some electroslag remelting trials ingots were grown on a seed ingot. This resulted in a fewer vertical grains compared to the case when no seed ingot was used. The sand cast specimen of the eutectic exhibited a maximum tensile strength of around 88.2 MN/m² (9.0 kg/mm²) whereas conventional ESR using water cooled mold gave strength value of 98.0 MN/m² (10 kg/mm²). The directionally solidified ESR material showed longitudinal tensile strength as high as 213.7 MN/m² (21.8 kg/mm²) which could be further increased to 220.6 MN/m² (22.5 kg/mm²) by using the seed ingot. The average growth rate was varied between 5 to 25 mm/min during electroslag remelting in this study. The flow stresses, tangent modulus and ultimate tensile strength of directionally solidified eutectic increased with increasing growth rates. Formerly Research Fellow, Indian Institute of Science, Bangalore 560012 is now     

CSCC for the mean and standard deviation of non-normally distributed life test data

In this paper Cumulative Sum Control Charts (CSCC) have been constructed for the mean and standard deviation of non-normally distributed life test data. The parameters of the V-mask have been determined and finally the expression for the Average Run Length is derived.     

Physicochemical,thermal and pasting properties of starch separated from γ-irradiated and stored potatoes

The morphological, thermal and pasting properties of starch separated from potatoes of three varieties (Kufri Chandramukhi, Kufri Jyoti and Kufri Chipsona-2), treated either with CIPC (isopropyl N-(3 chlorophenyl) carbamate) or γ-irradiation (Co⁶⁰, 0.1 and 0.5 kGy) and subsequently stored at 8, 12 and 16 °C for 90 days, were studied. Scanning electron microscopy (SEM) showed the presence of oval and irregular shaped starch granules with a diameter range of 15–16 μm. Mean granule size of starch separated from potatoes stored at 12 °C ranged from 18–25 μm and irradiation treatment resulted in an increase in the proportion of small size granules. The irradiation of potatoes with 0.5 kGy resulted in starch with significantly lower peak-, trough- and breakdown-viscosity as compared to starch from potatoes treated with either CIPC or 0.1 kGy irradiation. The irradiation of potatoes with 0.5 kGy caused a significant increase in setback and pasting temperature. Pasting temperature of starch was observed to vary with the storage temperature. Starch separated from potatoes stored at higher temperature showed lower pasting temperature and vice versa. The starch from potatoes stored at 8 °C showed higher peak-, trough- and breakdown-viscosity and lower setback. Peak viscosity increased and swelling volume decreased with increase in storage temperature. FTIR spectra showed that the starch from irradiated potatoes displayed a significant decrease in the intensity of the C–H stretch region between 2800 and 3000 cm⁻¹, which was observed to be irradiation dose-dependent, and higher with 0.5 than 0.1 kGy. However, a slight broadening of O–H stretch (3000–3600 cm⁻¹) in starches from irradiated potatoes was observed. The spectral changes caused by γ-irradiation were apparent in the O–H stretch (3000–3600 cm⁻¹), C–H stretch (2800–3000 cm⁻¹) and bending mode of water (1600–1800 cm⁻¹).