Hydrolysis of carboxylate and phosphate esters using monopyridinium oximes in cationic micellar media

The reactions of p‐nitrophenyl acetate (PNPA) with a series of monopyridinium oximes, viz. 2‐PAM (2‐hydroxyiminomethyl‐1‐methylpyridinium iodide), 3‐PAM (3‐hydroxyiminomethyl‐1‐methylpyridinium iodide), and 4‐PAM (4‐hydroxyiminomethyl‐1‐methylpyridinium iodide) have been studied in the presence of cationic surfactants of same hydrophobic chain length (C₁₆) within the concentration range of 0.5–6.0 mM at pH 8.0 under the pseudo‐first‐order condition. The observed rate constant (k_obs) increases with increasing surfactant concentration culminating into a maximum, and this has been analyzed in detail following the concepts of micellar catalysis. The structure–activity relationship of the investigated oximes has been discussed, and 2‐PAM was found to be the most reactive among all the three investigated oximes for the cleavage of PNPA. Esterolytic decomposition of p‐nitrophenyldiphenyl phosphate with oximate ions (? CH?NO^?) was followed in cetyltrimethylammonium bromide micelles at pH 9.0, and 4‐PAM was the most reactive oxime for the micellar hydrolysis of phosphate ester. The apparent acid dissociation constants (pK_a) of the investigated oximes have been determined spectrophotometrically. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 569–578, 2011     

On Sets that Meet Every Hyperplane in n-Space in at Most n Points

A simple proof that no subset of the plane that meets everyline in precisely two points is an F-set in the plane is presented.It was claimed that this result can be generalized for setsthat meet every line in either one point or two points. No proofof this assertion is known, however. The main results in thispaper form a partial answer to the question of whether the claimis valid. In fact, it is shown that a set that meets every linein the plane in at least one but at most two points must bezero-dimensional, and that if it is -compact then it must bea nowhere dense G-set in the plane. Generalizations for similarsets in higher-dimensional Euclidean spaces are also presented.     

Error bounds for minimal energy bivariate polynomial splines

Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002 RID="*" ID="*" Supported by the National Science Foundation under grant DMS-9870187 RID="**" ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160     

Products of conjugacy classes in Chevalley groups I. Extended covering numbers

This paper is concerned with products of conjugacy classes in Chevalley groups. We prove that in any quasisimple Chevalley groupG proper or twisted, over any field, the extended covering number is bounded above linearly in terms of the rank ofG, that is, for some constante, for any Chevalley groupG, the product of anye · rank(G) non-central classes covers all ofG. We give estimates for the constante in different cases. The authors gratefully acknowledge the support of EPSRC through a Visiting Fellowship number GR/M58542 and a Research grant number GR/L92174.     

Topological equivalence of discontinuous norms

We show that for everyp>0 there is an autohomeomorphismh of the countable infinite product of linesR ^Nsuch that for everyr>0,h maps the Hilbert cube [−r, r] ^N precisely onto the “elliptic cube” . This means that the supremum norm and, for instance, the Hilbert norm (p=2) are topologically indistinguishable as functions onR ^N.The result is obtained by means of the Bing Shrinking Criterion. Research supported in part by a grant from NSF-EPSCoR Alabama.