Benzene Induced 1H NMR Shifts of Chromeno-Compounds: An Aid to Differentiate Linear and Angular Chromenoflavones

Benzene-induced shifts (BIS) in the ¹H NMR spectra of nine chromeno-compounds have been studied. It provides a simple non-destructive technique for distinguishing linear isomers of chromenoflavones from their angular counterparts. BIS also assists in the assignment of chromene proton signals in chromeno-compounds.     

Convenient Preparation of α-Tert-Butyl N-Blocked Glutamates Through γ-Allyl Ester Protection

Utilisation of γ-allyl ester protection of glutamates provides a convenient route to the synthesis of Z-Glu-OBu^t, Tr-Glu-OBu^t and (Boc)2-Glu-OBu^t.     

A note on Srivastava and Hui’s tests of multivariate normality

The aim of the paper is to point out some imprecision in Srivastava and Hui’s tests for multivariate normality. A correction for their tests is proposed.     

Bivariate distributions characterized by one family of conditionals and conditional percentile or mode functions

It is well known that full knowledge of all conditional distributions will typically serve to completely characterize a bivariate distribution. Partial knowledge will often suffice. For example, knowledge of the conditional distribution of X given Y and the conditional mean of Y given X is often adequate to determine the joint distribution of X and Y. In this paper, we investigate the extent to which a conditional percentile function or a conditional mode function (of Y given X), together with knowledge of the conditional distribution of X given Y will determine the joint distribution. Finally, using this methodology a new characterization of the classical bivariate normal distribution is given.