Circularly Symmetric Static Metric in Three Dimensions and Its Killing Symmetry

In this note we consider a general three-dimensional circularly symmetric static metric and investigate possible Killing symmetries it possesses.We then summarize the work by addressing Einstein equations and briefly discuss their implications on the energy momentum content of some of the metrics that arise in the process.     

Constrained adaptive lifting and the CAL4 metric for helicopter transmission diagnostics

This paper presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting (CAL) algorithm, an adaptive manifestation of the lifting scheme. Lifting is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Adaptivity is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation synchronous signal-averaging algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have approximately the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local waveform changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. A diagnostic metric based on the lifting prediction error vector termed CAL4 is developed. The CAL diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the CAL4 metric is compared with the classic metric FM4.     

Diastereomeric Xe chemical shifts in tethered cryptophane cages

Cryptophane cages serve as host molecules to a Xe atom. Functionalization of cryptophane-A has permitted the development of Xe as a biosensor. Synthetic routes used to prepare cryptophanes result in racemic mixtures of the chiral cages. In the preparation of a tethered cryptophane-A cage for biosensor applications, some achiral and chiral substituents such as left-handed amino acids have been used. When the substituent is achiral, the NMR signal of the Xe atom in the functionalized cage in solution is a single isotropic peak, since the Xe shielding tensor components in the R and L cages differ by no more than the signs of the off-diagonal elements. Chiral substituents can split the cage-encapsulated Xe NMR signal into one or more sets of doublets, depending on the number of asymmetric centers in the substituent. We carry out quantum mechanical calculations of Xe nuclear magnetic shielding for the Xe atom at the same strategic position within an L cryptophane-A cage, under the influence of chiral potentials that represent r or l substituents outside the cage. Calculations of the Xe shielding response in the Lr and Ll diastereomeric pairs permit the prediction of the relative order of the Xe chemical shifts in solutions containing the Rl and Ll diastereomers. Where the substituent itself possesses two chiral centers, comparison of the calculated isotropic shielding responses in the Llr, Lrl, Rll, and Lrr systems, respectively, permits the prediction of the Xe spectrum of diastereomeric systems in solutions containing Llr, Rlr, Lll, and Rll systems. Assignment of the peaks observed in the experimental Xe NMR spectra is therefore possible, without having to undertake the difficult synthetic route that produces a single optically pure enantiomer.     

Sensitivity enhancement in multiple-quantum NMR experiments with CPMG detection

We present a modified multiple-quantum (MQ) experiment, which implements the Carr-Purcell-Meiboom-Gill (CPMG) detection scheme in the static MQ NMR experiment proposed by W. S. Warren et al. (1980, J. Chem. Phys.73, 2084-2099) and exploited further by O. N. Antzutkin and R. Tycko (1999, J. Chem. Phys.110, 2749-2752). It is demonstrated that a significant enhancement in the sensitivity can be achieved by acquiring echo trains in the MQ experiments for static powder samples. The modified scheme employing the CPMG detection was superior to the original MQ experiment, in particular for the carbonyl carbon with a very large chemical shift anisotropy.     

Simultaneous Determination of Ritodrine and Isoxsuprine Using Coupling Technique of Synchronous Fluorimetry and H-Point Standard Addition Method

Simultaneous determination of two structurally related ß₂ adrenergic receptor agonists namely, Ritodrine HCl (RTH) and Isoxsuprine HCl (ISP) was performed using coupling technique of synchronous fluorimetry and H-point standard addition method. Under optimum conditions, linear determination ranges were 1.48 – 14.80?×?10^?6 mol L^?1 and 1.54 – 15.44?×?10^?6 mol L^?1 for ISP and RTH respectively. RTH and ISP could be determined simultaneously without interference from each other when their concentration ratio varies from 5:1 to 1:5 in the mixed sample. The proposed method was applied to the determination of RTH and ISP in synthetic mixture of pharmaceutical samples, the accuracy and precision of the results were satisfactory.