Preparation of rhodium–phyllosilicate catalysts without leaching in liquid-phase 1-hexene hydrogenation

Rhodium catalysts have been prepared on palygorskite and montmorillonite (clay) supports by reduction with hydrogen (1 atmosphere) at room temperature of a cationic organometallic rhodium compound anchored to the support. The activity of these catalysts for the hydrogenation of liquid-phase 1-hexene remains constant with increase of prehydrogenation time and with re-use for several runs. No rhodium leaching is observed.     

1H and 13C NMR spectroscopic study of oxidation of D,L‐cystine and 3,3′‐dithiobis(propionic acid) with hydrogen peroxide in aqueous solution

The oxidation of symmetrical disulfides [D ,L ‐cystine ( 1 ) and 3,3′‐dithiobis(propionic acid) ( 2 )] with hydrogen peroxide in D₂O–NaOH solution (pH 10–11) was studied by NMR spectroscopy. Assignments of the proton and carbon NMR signals of starting materials ( 1 and 2 ) and products of oxidation are based on conventional 1D NMR methods (DEPT, selective spin decoupling). Formation of C—S bond cleavage products or, in case of 2 , partially oxidized intermediates was not detected. The accelerating effect of Cu²⁺ cations, but not Fe³⁺ cations, on the oxidation rate of 1 in basic medium was demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

On a Question of Phillips

In [5] Phillips proved that one can obtain the additive group of any nonstandard model *? of the ring ? of integers by using a linear mod 1 function h : F ?, where F is the α-dimensional vector space over ? when α is the cardinality of *?. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

1H and 13C NMR assignments of abietane diterpenes from Aegiphila lhotzkyana

An NMR study of one new and several known abietane diterpenes isolated from the roots of Aegiphila lhotzkyana is described. In addition to 1D NMR, several 2D shift‐correlated NMR pulse sequences (¹H–¹H‐COSY, NOESY, HMQC and HMBC) were used to establish all the structures, and unambiguously perform the ¹H and ¹³C chemical shift assignments of the new natural diterpene and three derivatives, the NMR data for which have not been reported previously. Revision of current data assignment for teuvincenone H is also suggested. Copyright © 2003 John Wiley & Sons, Ltd.     

Characterization of reduced iso‐α‐acids derived from hops (Humulus lupulus) by NMR

Reduced forms of iso‐α‐acids (isohumulones), used in modern beer brewing were separated and characterized by ¹H and ¹³C NMR spectroscopy. Components from mixtures of rho‐iso‐α‐acids, tetrahydro‐iso‐α‐acids, and hexahydro‐iso‐α‐acids were isolated using high‐performance liquid chromatography (HPLC) and analyzed by use of one‐ and two‐dimensional NMR experiments. The data presented assign the identities of the main peaks in the HPLC traces for the reduced iso‐α‐acids. Previous tentative assignments regarding the cis and trans configurations and the structures of the acyl residues of the reduced iso‐α‐acids were confirmed and extensive NMR assignments were made. Furthermore, the previously unknown stereochemistry in the C‐4 side‐chain of the rho‐ and hexahydro‐iso‐α‐acids was assigned. Copyright © 2003 John Wiley & Sons, Ltd.     

A Simple Chaotic Circuit with Impulsive Switch Depending on Time and State

This paper presents a simple chaotic circuit consisting of two capacitors, one linear two-port VCCS and one time-state-controlled impulsive switch. The impulsive switch causes rich chaotic and periodic behavior. The circuit dynamics can be simplified into a one-dimensional return map that is piecewise linear and piecewise monotone. Using the return map, we clarify parameter conditions for existence of chaotic and periodic attractors and coexistence state of attractors.     

Solution 1H and 13C NMR of new chiral 1,4‐oxazepinium heterocycles and their intermediates from the reaction of 2,4‐pentanedione with α‐L‐amino acids and (R)‐(—)‐2‐phenylglycinol

The reaction of 2,4‐pentanedione ( 1 ) with (R)‐(—)‐2‐phenylglycine methyl ester ( 2 ), (R)‐(—)‐2‐phenylglycinol ( 3 ) and the proteinogenic amino acids (2S,3R)‐(—)‐2‐amino‐3‐hydroxybutyric acid (L ‐threonine) ( 4 ) and (R)‐(—)‐2‐amino‐3‐mercaptopropionic acid (L ‐cysteine) ( 5 ) methyl esters was investigated. The corresponding enamines 6 , 7 and 8 were isolated and characterized spectroscopically whereas 9 , which is unstable, was transformed in situ into 13 . Treatment of 7 , 8 and 9 with boron trifluoride etherate afforded the new [1,4]oxazepines 10 , 11 and [1,4]thiazepine ( 12 ) as their BF₃O^? salts. The structures of the enamines and their corresponding seven‐membered heterocycles were assessed by 1D and 2D NMR spectroscopy. Variable‐temperature experiments revealed different molecular mobility behavior among these heterocycles. Copyright © 2003 John Wiley & Sons, Ltd.     

A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.