Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Scaling of decay lengths for surface states in the gaps of one-dimensional semi-infinite superlattices

We look at some one-dimensional semi-infinite superlattices with an underlying Hamiltonian that is of the nearest neighbour, tight binding type. A real space rescaling procedure which is exact in one dimension is applied to obtain the location of the subbands. It has been found that these subbands never overlap in 1D, and we interpret this as a band repulsion effect. Relevance in the case of a disordered system where this band repulsion crosses over to the well-known level repulsion is discussed. Then with a proper matching at the boundary we solve for the sets of denumerably infinite number of decaying solutions (the surface states) in the gaps. These types of states have been proposed quite some time ago. We look at detail theirexact analytical solutions in 1D and find that their decay lengths near the band edges diverge as |E–E _b|^–v, wherev=1/2 andE _b is the nearest band edge. The decay lengths and their divergence exponent match extremely well with those obtained from transfer matrix method. Some recent experiments on quantum well structures seem to have observed such states.     

Validation of LC/MS electrospray ionisation method for the estimation of ursodiol in human plasma and its application in bioequivalence study

A novel High Performance Liquid Chromatography-electrospray mass spectrometric method has been developed for the estimation of Ursodiol (Ursodeoxycholic acid)--a bile acid, in human plasma using Ornidazole as internal standard. The methodology involved solid phase extraction of the analyte from human plasma matrix. The chromatographic separation was achieved within seven minutes by an isocratic mobile phase containing 1.0 mM ammonium acetate and Acetonitrile (65:35, v/v), flowing through XTerra MS C18, 100 x 2.1, 3.5 microm analytical column, at a flow rate of 0.2 ml/min. Ion signals were measured in negative mode for Ursodiol and internal standard at m/z 391.3 and 278.1, respectively. A detailed validation of the method was performed as per USFDA guidelines and the standard curves were found to be linear in the range 50.0 ng/ml to 3000.0 ng/ml with the mean correlation coefficient more than 0.99. The absolute recovery was more than 54.90% for Ursodiol and 76.51% for internal standard. Ursodiol was stable for sixty-nine days at -70 degrees C and for eight hours at ambient temperature. After extraction from plasma, the reconstituted samples of Ursodiol were stable in autosampler at 10 degrees C for forty-eight hours. Upon subjecting to three freeze thaw cycles, there was no change in the recovery of the analyte. The integrity of the plasma samples remained unaffected even upon four-fold dilution with drug free human plasma. The method was simple, specific, sensitive, precise, accurate and suitable for bioequivalence and pharmacokinetic studies. It was successfully applied to the pilot bioequivalence study of Ursodiol in male human subjects.     

Trace Spectrophotometric Determination of Dichlorvos using Diphenyl Semicarbazide (DPC) in Environmental and Agricultural Samples

A new and highly sensitive spectrophotometric method is developed for the determination of sub ppm levels of the widely used organophosphorus insecticide dichlorvos. The method is based on alkaline hydrolysis of dichlorvos to dichloroacetaldehyde followed by coupling with diphenyl semicarbazide (DPC) in alkaline medium. The absorption maxima of the wine red dye compound formed is measured at 490 nm. Beer's law is obeyed over the concentration range of 4.3 to 34 μg in a final solution volume of 25 mL (0.18–1.36 ppm). The molar absorptivity, Sandell's sensitivity and correlation coefficient were found to be 2.9 × 10⁵ l mole^?1 cm^?1, 0.013 μg cm^?2 and 0.9999, respectively. The standard deviation and relative standard deviation were found to be ± 0.007 and 1.90%, respectively. The lower limit of detection is 0.04 μg. The method is simple, sensitive and free from interferences of other pesticides and diverse ions. Other organophosphorous pesticides do not interfere with the proposed method. The method has been satisfactorily applied to the determination of dichlorvos in environmental and agricultural samples.     

Simultaneous densitometric determination of artemisinin, artemisinic acid and arteannuin-B in Artemisia annua using reversed-phase thin layer chromatography

A rapid and simple RP-TLC method for simultaneous quantification of pharmacologically important sesquiterpene artemisinin (AM) together with its precursors arteannuin-B (AB) and artemisinic acid (AA) in the inflorescence part of Artemisia annua plant has been developed. The RP-TLC of sesquiterpenes was performed on RP-18 F254 S thin-layer chromatographic plates by developing in mobile phase, containing 0.2% TFA in water/ACN (35:65, v/v). The densitometric determination of AM, AB and AA was carried out after derivatization with anisaldehyde reagent at 426 nm in absorption-reflectance mode.     

Laser spectroscopy of Si3C

The C 1B1<--X 1A1 band system of the potential interstellar species Si3C has been recorded in a silane/acetylene discharge by resonant two-color two-photon ionization spectroscopy. The origin band is located near 24,925 cm-1 (3.09 eV). Several other features in the spectrum are assigned to progressions in the Si-Si stretching modes as well as to sequence and hot band transitions. The assignment was facilitated by ab initio calculations, which also indicate that this is the strongest electronic transition of Si3C in the visible region of the spectrum. Features in the spectrum are broadened considerably (ca. 10 cm-1), and suggest an excited state lifetime of a few picoseconds. Possible reasons for the short-lived nature of the excited state are discussed.