Determination of Water and Solute Transport in Polyacrylamide Gels

Summary: Water exchange between five polyacrylamide gels (Bulkamid®, Aquamid®, Rectamid®, HV-PAAG, Acuvue) with a physiological salt solution was determined by means of tritium-labeled water. Urea and chloride exchange was also determined in Acuvue. The method was a modified version to measure rapid transport processes in red blood cells. The study shows that water and solutes easily exchange between the hydrogel under study and the surrounding medium, independent of the solid polymer content (2.5–40 wt%) and an over ten-fold variation of the cross-linking density.     

Representations,decompositions and sample function continuity of random fields with independent increments

Standard fare in the study of representations and decompositions of processes with independent increments is pursued in the somewhat more complex setting of vector-valued random fields having independent increments over disjoint sets. Such processes are first constructed as almost surely uniformly convergent sums of Poisson type summands, that immediately yield information on sample function properties of versions. The constructions employed, which include a generalized version of the Ferguson-Klass construction with uniform convergence, are new even in the simpler setting of processes in one-dimensional time.Following these constructions, or representations, an analogue of the Lévy-Ito decomposition for Lévy processes is developed, which then enables a number of simple sample function properties of these processes to be read off from the Lévy measure in their characteristic functionals.The paper concludes with a study of general centred additive random fields and an appendix incorporating a brief survey of the theory of centred sums of independent random variables.     

Ruthenium-catalysed synthesis of 2- and 3-substituted quinolines from anilines and 1,3-diols

A straightforward synthesis of substituted quinolines is described by cyclocondensation of anilines with 1,3-diols. The reaction proceeds in mesitylene solution with catalytic amounts of RuCl(3)·xH(2)O, PBu(3) and MgBr(2)·OEt(2). The transformation does not require any stoichiometric additives and only produces water and dihydrogen as byproducts. Anilines containing methyl, methoxy and chloro substituents as well as naphthylamines were shown to participate in the heterocyclisation. In the 1,3-diol a substituent was allowed in the 1- or the 2-position giving rise to 2- and 3-substituted quinolines, respectively. The best results were obtained with 2-alkyl substituted 1,3-diols to afford 3-alkylquinolines. The mechanism is believed to involve dehydrogenation of the 1,3-diol to the 3-hydroxyaldehyde which eliminates water to the corresponding α,β-unsaturated aldehyde. The latter then reacts with anilines in a similar fashion as observed in the Doebner-von Miller quinoline synthesis.     

Binary diffusion coefficients of phenolic compounds in subcritical water using a chromatographic peak broadening technique

Infinite dilution diffusion coefficients of certain phenolic compounds were measured as a function of temperature in water slightly acidified with formic acid using the Taylor dispersion method. The diffusion coefficients calculated using the chromatographic peak broadening technique were found to increase exponentially with an increase in the temperature. The diffusion coefficients of the selected phenolic compounds did not vary as a function of their molecular weights and the diffusion coefficients of the phenolic compounds increased as a function of temperature (from 2.16 × 10⁻¹⁰ m² s⁻¹ at 298 K to 5.79 × 10⁻¹⁰ m² s⁻¹ at 413 K for malvidin-3,5-diglucoside). However, for some phenolic compounds such as gallic acid monohydrate, quercetin-3-β-d-glucoside, protocatechuic acid and (−)-epicatechin, there were difficulties in making measurements above temperatures of 352 K, 372 K, 392 K and 413 K, respectively, due to thermal degradation of the phenolic compounds in water above these temperatures. The experimentally measured diffusion coefficients of the phenolic compounds were correlated as a function of temperature and solvent viscosity and were compared with those predicted using theoretical models. The validity of the Stokes-Einstein diffusion model in predicting the diffusion coefficients of the phenolic compounds in hot pressurized water was also evaluated.     

Rhodium-catalyzed decarbonylation of aldoses

A catalytic procedure is described for decarbonylation of unprotected aldoses to afford alditols with one less carbon atom. The reaction is performed with the rhodium complex Rh(dppp)2Cl in a refluxing diglyme-DMA solution. A slightly improved catalyst turnover is observed when a catalytic amount of pyridine is added. Under these conditions most hexoses and pentoses undergo decarbonylation into the corresponding pentitols and tetrols in isolated yields around 70%. The reaction has been applied as the key transformation in a five-step synthesis of L-threose from D-glucose.     

Toward the synthesis of norzoanthamine: complete fragment assembly

The complex marine alkaloid norzoanthamine (2) was envisioned to be assembled from three key building blocks: the C1-C5 fragment A, the C6-C10 fragment B, and the C11-C24 fragment C. The synthesis of fragment A was achieved in 14 steps and 33% overall yield from (R)-gamma-hydroxymethyl-gamma-butyrolactone. Fragment B was made in two steps from PMB-protected 4-pentynol in 76% yield. The C11-C24 fragment C was made from (S)-carvone via (R)-isocarvone in 18 steps (6% overall yield). The convergent stereoselective synthesis of the entire carbon framework (C1-C24) of the target molecule was achieved via the following assemblage. Alkenyl iodide 20 derived from the C11-C24 fragment C was coupled to fragment B (C6-C10) through a high-yielding Stille coupling reaction of these two sterically very demanding coupling partners, affording the key Diels-Alder precursor 24. The intramolecular Diels-Alder reaction proceeded smoothly in excellent yield and diastereoselectivity, generating the tricyclic trans-anti-trans perhydrophenanthrene motif of norzoanthamine (C6-C24). The final fragment coupling between lithiated fragment A (C1-C5) and aldehyde 40 (C6-C24) has also been successfully accomplished affording the entire carbon framework of the natural product.     

Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales

Summary In this paper we focus on sequences of random vectors which do not admit a strong approximation of their partial sums by sums of independent random vectors. In the first part we prove conditional versions of the Strassen-Dudley theorem. We apply these in the second part of the paper to obtain strong invariance principles for vector-valued martingales which, when properly normalized, converge in law to a mixture of Gaussian distributions.Research partially supported by the Air Force Office of Scientific Research Contract NO. F49260 85 C 0144Part of this work was done while the second author was visiting the Department of Statistics and the Center for Stochastic Processes, University of North Carolina, Chapel Hill. He thanks the members of the Department of Statistics for their hospitality     

Gaussian quasimartingales

Summary Necessary and sufficient conditions in terms of the mean function and covariance are obtained for a separable Gaussian process to have paths of bounded variation, absolutely continuous or continuous singular. If almost all paths are of bounded variation, the L ² expansion of the Gaussian process is shown to converge in the total variation norm. One then obtains a decomposition of the paths of a Gaussian quasimartingale into a martingale and a predictable process of bounded variation paths such that these components are jointly Gaussian; the martingale component is decomposed into two processes, one consisting of (fixed) jumps and the other a continuous path martingale, and the bounded variation component is decomposed into three processes, one consisting of (fixed) jumps, another with absolutely continuous paths and the third with continuous singular paths. All components are jointly Gaussian. Uniqueness of the decompositions is also established.This work was partially supported by the National Science Foundation.