Three limit cycles for a first‐order exothermic chemical reaction in a continuous stirred‐tank reactor

We study a first‐order exothermic chemical reaction in a continuous stirred‐tank reactor modelled by a 3‐parameter family of vector fields in . We prove that there exist regions in which contain points that depend on parameters such that the chemical reaction has 0, 1, 2, or 3 small amplitude limit cycles that surround the origin. We conclude that this model can reach two stable small amplitude limit cycles. Finally, we show that one of these regions contains the point in the parameter space considered by Gurel and Lapidus [6] who proved numerically the existence of one stable limit cycle. This revised version was published online in July 2006 with corrections to the Cover Date.     

The elimination kinetics and mechanisms of ethyl piperidine‐3‐carboxylate,ethyl 1‐methylpiperidine‐3‐carboxylate,and ethyl 3‐(piperidin‐1‐yl)propionate in the gas phase

The gas‐phase elimination kinetics of the above‐mentioned compounds were determined in a static reaction system over the temperature range of 369–450.3°C and pressure range of 29–103.5 Torr. The reactions are homogeneous, unimolecular, and obey a first‐order rate law. The rate coefficients are given by the following Arrhenius expressions: ethyl 3‐(piperidin‐1‐yl) propionate, log k₁(s^?1) = (12.79 ± 0.16) ? (199.7 ± 2.0) kJ mol^?1 (2.303 RT)^?1; ethyl 1‐methylpiperidine‐3‐carboxylate, log k₁(s^?1) = (13.07 ± 0.12)–(212.8 ± 1.6) kJ mol^?1 (2.303 RT)^?1; ethyl piperidine‐3‐carboxylate, log k₁(s^?1) = (13.12 ± 0.13) ? (210.4 ± 1.7) kJ mol^?1 (2.303 RT)^?1; and 3‐piperidine carboxylic acid, log k₁(s^?1) = (14.24 ± 0.17) ? (234.4 ± 2.2) kJ mol^?1 (2.303 RT)^?1. The first step of decomposition of these esters is the formation of the corresponding carboxylic acids and ethylene through a concerted six‐membered cyclic transition state type of mechanism. The intermediate β‐amino acids decarboxylate as the α‐amino acids but in terms of a semipolar six‐membered cyclic transition state mechanism. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 38: 106–114, 2006     

Radiation Damage and Racemic Protein Crystallography Reveal the Unique Structure of the GASA/Snakin Protein Superfamily

Proteins from the GASA/snakin superfamily are common in plant proteomes and have diverse functions, including hormonal crosstalk, development, and defense. One 63‐residue member of this family, snakin‐1, an antimicrobial protein from potatoes, has previously been chemically synthesized in a fully active form. Herein the 1.5 Å structure of snakin‐1, determined by a novel combination of racemic protein crystallization and radiation‐damage‐induced phasing (RIP), is reported. Racemic crystals of snakin‐1 and quasi‐racemic crystals incorporating an unnatural 4‐iodophenylalanine residue were prepared from chemically synthesized d ‐ and l ‐proteins. Breakage of the C?I bonds in the quasi‐racemic crystals facilitated structure determination by RIP. The crystal structure reveals a unique protein fold with six disulfide crosslinks, presenting a distinct electrostatic surface that may target the protein to microbial cell surfaces.     

Some characterizations of Riesz operators by means of invariant subspaces

In this paper we shall give several characterizations of Riesz operatorsT on Banach spaces by means of some closedT-invariant subspaces. Moreover we also give a characterization of these operators dual to that give by Dieudonné in [5].     

Synthesis, gastroprotective effect and cytotoxicity of new amino acid diterpene monoamides and diamides

Following our studies on the gastroprotective effect and cytotoxicity of terpene derivatives, new amides were prepared from the diterpene 8(17)-labden-15,19-dioic acid (junicedric acid) and its 8(9)-en isomer with C-protected amino acids (amino acid esters). The new compounds were evaluated for their gastroprotective effect in the ethanol/HCl-induced gastric lesions model in mice, as well as for cytotoxicity using the following human cell lines: normal lung fibroblasts (MRC-5), gastric adenocarcinoma cells (AGS) and liver hepatocellular carcinoma (Hep G2). A dose-response experiment showed that at 25 mg/kg the C-15 leucyl and C-15,19-dileucylester amides of junicedric acid reduced gastric lesions by about 65.6 and 49.6%, respectively, with an effect comparable to lansoprazole at 20 mg/kg (79.3% lesion reduction). The comparison of the gastroprotective effect of 18 new amino acid ester amides was carried out at a single oral dose of 25 mg/kg. Several compounds presented a strong gastroprotective effect, reducing gastric lesions in the 70.9-87.8% range. The diprolyl derivative of junicedric acid, the most active product of this study (87.8% lesion reduction at 25 mg/kg) presented a cytotoxicity value comparable with that of the reference compound lansoprazole. The structure-activity relationships are discussed.     

An efficient enzymatic preparation of 20-pregnane succinates: chemoenzymatic synthesis of 20β-hemisuccinyloxy-5αH-pregnan-3-one

Lipase-catalyzed transesterification of the 20 hydroxyl group in a series of pregnanes afforded novel 20-ethyl succinates that are not possible to prepare following the traditional synthetic methods. The reaction is stereoselective. The enzyme reacts selectively with the 20β epimers therefore only the 20β-succinyloxy derivatives are obtained. These compounds are obtained in variable yield, depending on the substitution in the ring A. The enzymatic approach allowed, for the first time, the synthesis of 20β-hemisuccinyloxy-5αH-pregnan-3-one, novel compound useful as a precursor of steroid-protein conjugates.     

FOAMING PROPERTIES OF SURFACTANT-OIL-VATER SYSTEMS IN THE NEIGHBOURHOOD OF OPTIMUM FORMULATION

The foaming properties of. surfactant-oil-water systems are found to be closely related to the phase behavior at equilibrium. In Winsor I systems both the surfactant-oil-water emulsion and its aqueous phase produce stable foams. The foaminess and the foam stability follow the same pattern of variation than the emulsion stability. In Winsor III (three phase microemulsion-oil-water) and Winsor II systems no foam can be formed. The changes are the same no matter the formulation variable used to scan the physico-chemical formulation or the method used to measure the foam stability.