Synthesis and nucleophilic substitutions of 3-alkyl-5-chloroisoxazoles

A 3-alkyl-5-chloroisoxazole synthesis is described based on the cycloaddition of nitrile oxides to 1,1-dichloroethylene, an inexpensive dipolarophile. Substitution of the chloride in these adducts by various nucleophiles is also described.     

Reactions of 2,5-diphenyl-1,4 dithin sulfones with sodium azide

A number of unanticipated transformations were observed when various 2,5-diphenyl-1,4-dithiin sulfones were treated with sodium azide. These include a fragmentation to give 1,2-dicyano-1,2-diphenylethen, the formation of 2,5-dipehnyl-1,4-thiazine-1,1-dioxide, and the rearrangement of 3-bromo-2,5-diphenyl-1,4-dithiin-1,1-dioxide to its 2-bromo- isomer. Possible mechanism for these unusual reactions are discussed.     

Further studies on the utility of sodium hypochlorite in organic synthesis. Selective oxidation of diols and direct conversion of aldehydes to esters

Sodium hypochlorite in acetic acid solution selectively oxidizes secondary alcohols to ketones in the presence of primary alcohols and converts aldehydes to methyl esters in the added presence of methanol.     

Tests for specific nonparametric relations between two distribution functions with applications

Let (X,Y) be a random vector and let G and H be the marginal distributions of X and Y, respectively. In this paper, we propose two tests, one of Kolmogorov‐Smirnov type and the other of Wilcoxon type, for the null hypothesis Ψ(G) = H against the alternative Ψ(G) < H, where Ψ() is a function such that Ψ(G) is a distribution function. The tests are based on the empirical distribution functions of the observations on X and Y, which are dependent. We obtain their asymptotic null distributions. A suspected relationship between the distribution functions of two dependent outcomes can be specified as a hypothesis to be tested in examples like the load sharing models, record values, and auction bidding models. As an application, we consider in detail the problem of testing the effect of load sharing in two component parallel systems.