On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models

It is shown, under fairly general conditions, that Efron′s bootstrap procedure captures the limit distribution of weighted empirical processes based on M-estimated residuals in multiple linear regression models. As an application, we construct bootstrap confidence bands for the error distribution function F. The main result can also be used to design distribution-free goodness-of-fit tests for F without any recourse to the split-sample estimation of the regression parameters.     

Robust Hierarchical Bayes Estimation of Small Area Characteristics in the Presence of Covariates and Outliers

A robust hierarchical Bayes method is developed to smooth small area means when a number of covariates are available. The method is particularly suited when one or more outliers are present in the data. It is well known that the regular Bayes estimators of small. area means, under normal prior distribution, perform poorly in presence of even one extreme observation. In this case the Bayes estimators collapse to the direct survey estimators. This paper introduces a general theory for robust hierarchical Bayes estimation procedure using a fairly rich class of scale mixtures of normal prior distributions. To retain maximum benefit from combining information from related sources, we suggest to use Cauchy prior distribution for the outlying areas and an appropriate scale mixture of normal prior whose tail is lighter than the Cauchy prior for the rest of the areas. It is shown that, unlike the hierarchical Bayes estimator under a normal prior, our estimator has more protection against outlying observations.     

Separation of carrier free65Zn and66,67,68Ga, the alpha-particle activation products of copper with HDEHP

A radiochemical charged particle activation procedure has been developed for the production and separation of the carrier free radioisotopes,⁶⁵Zn and^66,67,68Ga. The carrier free radioisotopes produced by the irradiation of a pure copper foil with 50 MeV -particle beam through the nuclear reactions, (, pxn), (,pxn) and (,xn), have been quantitatively separated from the activated copper matrix from an aqueous hydrochloric acid and an alkaline solution using the liquid cation exchanger HDEHP, as an extractant. Detection of different radionuclides in the activated copper target and verification of their purity at different stages of their LLX separation have been performed by -ray spectrometric studies.     

Importance of steric factors in face-selective cycloadditions: 1,6-annulated cyclohexa-1,3-dienes

Diastereotopically nonequivalent π-facial 1,6-annulated-1,3-cyclohexadienes have been explored as probe molecules to assess the face-selectivities in cycloadditions. Steric factors have been found to be important in controlling the face-selectivities with these dienes. Studies with the hitherto unexplored diene 5 were also consistent with the order C-H > C-C for hyperconjugative stabilization of the transition state.     

Thermal and electron-impact transformations of cis-1,2-dibbnzoylalkenes

Several cis-1,2-dibenzoylalkene derivatives have been prepared in yields ranging between 60–80%, through the Diels-Alder addition of the appropriate dienes to dibenzoylacetylene. These include, 2,3-dibenzoyl-bicyclo [2.2.1]hepta-2,5-diene (10), 2,3-dibenzoylbicyclo[2.2.2]octa-2,5-diene (11), 7-oxa-2,3-dibenzoyl-bicyclo [2.2.1]hepta-2,5-diene (12), 1,4-diphenyl-2,3-dibenzoyl-1,4-epoxynaphthalene (13) and 9,10-dihydro-11,12-dibenzoy1-9, 10-ethenoanthracene (15), formed from cyclopentadiene, cyclohexa-1,3-diene, furan, 1,3-diphenylisobenzofuran and anthracene, respectively.

Thermolysis of 2,3-dibenzoylbicyclo[2.2.1]hepta-2,5-diene gave chiefly cyclopentadiene, arising through a retro-Diels-Alder mode of fragmentation. Similar retro-Diels-Alder fragmentations have been observed in the cases of 7-oxa-2,3-dibenzoylbicyclo[2.2.1]hepta-2,5-diene and 9,10-dihydro-11,12-dibenzoyl-9,10-ethenoanthracene. The thermoylsis of 1,4-diphenyl-2,3-dibenzoyl-1,4-epoxynaphthalene, however, gave a mixture of 1,3-diphenylisobenzofuran and 1,2-dibenzoylbenzene. The formation of 1,2-dibenzoylbenzene in this case has been shown to be through the air-oxidation of 1,3-diphenylisobenzofuran. Thermolysis of 2,3-dibenzoylbicyclo[2.2.2]octa-2,5-diene, on the other hand, gave a nearly quantitative yield of 1,2-dibenzoylbenzene, which did not undergo further transformation even on heating around 260° for several hours. In none of these cases, the expected pericyclic transformation, analogous to the conversion of cis-1,2-dibenzoylstilbene (6) to the isomeric 2,2,3,4-tetraphenylbut-3-enolide (9), has been observed under thermal conditions. Treatment of 9,10-dihydro-11,12-dibenzoyl-9,10-ethenoanthracene (15) with phosphorous pentasulphide resulted in the formation of a mixture of 12,14-diphenyl-9, 10(3', 4')furanoanthracene (28) and 12,14-diphenyl-9,10(3',4')thiophenoanthracene (31), arising through the postulated intermediates, 9,10-dihydro-11-benzoyl-12-thiobenzoyl-9,10-ethenoanthracene (26) and 9,10-dihydro-11,12-dithiobenzoyl-9, 10-ethenoanthracene (29), respectively.

The electron-impact induced transformations of the cis-1,2-dibenzoylalkenes, 6, 10, 11, 12, 13 and 15 on the other hand, can be rationalized in terms of both retro-Diels-Alder type fragmentations and pericyclic transformations of the dibenzoylalkene components.