The state space of a model for the Bray-Liebhafsky oscillating reaction

It has been known for a long time that the decomposition of hydrogen peroxide catalyzed by hydrogen and iodate ions, the Bray-Liebhafsky reaction, can generate oscillations in a batch reactor. Recently, mixed-mode oscillations and chaos have also been observed in a CSTR. The model we had previously proposed to explain the kinetics in a batch reactor can also simulate these new complex behaviors. Time series give only a limited view of the features of the calculated behaviors and more information is obtained studying the properties of the state space. We use projections of the trajectories, calculation of the correlation dimension of the attractor, Poincaré sections, and return maps. As the state space of the model is six-dimensional, we try to answer the questions of whether the projections into a 3D subspace give correct pictures of the real trajectories and whether we have reasons to prefer a special subspace. The text was submitted by the authors in English.     

Regularisierte Faltung von Distributionen. Teil 1: Zur Berechnung von Fundamentallösungen

Zusammenfassung Für 2 Distributionen, deren Faltung nicht existiert, wird—mehrdeutig—eine bezüglich eines Differentialoperators regularisierte Faltung definiert.An 4 Beispielen wird die Anwendbarkeit der regularisierten Faltung bei der Berechnung von Fundamentallösungen faktorisierbarer Differentialoperatoren gezeigt. Dabei wurde die Fundamentallösung in Beispiel 3.2. erstmalig ohne Überlegungen physikalischer Art hergeleitet. Beispiel 3.3. verallgemeinert bekannte Ergebnisse, wobei diese als Spezialfälle erscheinen (Bemerkung 3) oder als fehlerhaft nachgewiesen werden (Bemerkung 4). Die Fundamentallösungen der Beispiele 3.1 und 3.4 scheinen in dieser Form neu zu sein.Schließlich folgen einige einfache Sätze, mittels derer Fundamentallösungen von iterierten Differentialoperatoren angegeben werden können. Sie werden im 2. Teil der Arbeit (Eine Tabelle von Fundamentallösungen) angewendet. Literaturhinweise finden sich am Ende von Teil 2.

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Summary For two distributions (whose convolution does not necessarily exist) we define a (manyvalued) convolution regularized with respect to a differential operator.We illustrate by four examples the usefulness of the concept of a regularized convolution for computing fundamental solutions of factorisable differential operators. The fundamental solution of example 3.2 is derived for the first time without considerations from physics. Example 3.3 generalizes well-known results, which either appear as special cases (remark 3) or are proved to contain errors (remark 4). The fundamental solutions of examples 3.1 and 3.4 seem to be new in this form.Finally we give some simple propositions concerning fundamental solutions of iterated differential operators. They will be used in part 2 of this paper (a table of fundamental solutions)The references are given at the end of part 2.

     

Optimization of an electrolytic conductivity detector for determination of toxic nitrogen-containing food contaminants separated by open tubular column gas chromatography

The combination of open tubular column gas chromatography with electrolytic conductivity detection has been evaluated for the determination of nitrogen-containing pesticide residues in food extracts. Optimization of the column position at the column-detector interface was crucial to the successful operation of the detector. The signal-to-noise ratio and response stability of the detector are greatly influenced by the composition of the electrolyte solvent. Large volume splitless injections using retention gaps and optimized detector operating conditions enabled pesticide residues in food extracts to be determined at sub parts-per-million levels. Although the electrolytic conductivity detector is less sensitive than the thermionic ionization detector, its greater nitrogen selectivity can he crucial to the determination of nitrogen-containing contaminants in food extracts, particularly in complex mixtures where phosphorus-containing contaminants or matrix compounds are also present.     

Identification de stérols à chaîne latérale oxygénée dans une éponge de l'espèce Hyrtios

Thirty-two sterols are identified in the sponge Hyrtios sp. In addition to fourteen monohydroxylated compounds, the sterol fraction contains eight functionalized sidechain sterols, three of them new: 3 β-hydroxy-24-norchol-5-en-23-al (19) , (22-trans)-3 β-hydroxycholest-5, 22-dien-24-one (20) and (22R, 23R, 24S) or (22S, 23S, 24S)- 22,23-epoxy-24-methylchoest-5-en-3 β-ol (24). The probable biological origin, rather than artifact production, of these undescribed components is discussed.     

Structures and cytotoxicities of fascaplysin and related alkaloids from two marine phyla—Fascaplysinopsis sponges and Didemnum tunicates

The structural variations and bioactivity properties of the alkaloids in the fascaplysin (1) and the reticulatine (3) families were examined. Four organisms were analyzed consisting of two collections of the sponge Fascaplysinopsis reticulata and two collections of the tunicate Didemnum sp. Reported are the isolation of three new compounds: 3-bromofascaplysin (2), 14-bromoreticulatine (4), and 14-bromoreticulatate (6) along with reticulatate (5) previously known as a semi-synthetic product of 1. Compounds 1 and 5 showed selectivity in a cell based cytotoxicity assay.     

Hydrogen‐bonding patterns in rac‐1‐acetyl‐5‐methyl‐2‐thioxoimidazolidin‐4‐one

In the title compound, C₆H₈N₂O₂S, also known as N‐acetyl‐2‐thiohydantoin–alanine, the molecules are joined by N—H...O hydrogen bonds, forming centrosymmetric R₂²(8) dimers; these dimers are linked by C—H...O interactions to form R₂²(10) rings, thus forming C₂²(10) chains that run along the [101] direction.     

The reaction of aromatic α,β-unsaturated ketones with 4,5-diamino-1,6-dihydropyrimidin-6-ones

The reaction of 4,5-diamino-1,6-dihydropyrimidin-6-ones 1 with one equivalent of the chalcones 2 leads in an acidic medium to the formation of the 2,4-diaryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]diazepin-6-ones 3a-m . The structure elucidation of the products is based on detailed nmr investigations including selective ¹³C[¹H] decoupling experiments.     

A New Strategy for the Synthesis of alpha-Difluoromethyl-Substituted alpha-Hydroxy and alpha-Amino Acids

A new method for the preparation of alpha-chlorodifluoromethyl-, alpha-bromodifluoromethyl-, and alpha-difluoromethyl-substituted alpha-hydroxy and alpha-amino acid esters 11, 19-21 is described. The key step of the synthesis is the regioselective alkylation of ketones 5, 7-9 and imines 16-18 with C-nucleophiles. The ketones 7-9 are readily available from 3,3,3-trifluorolactate 1 by a five-step procedure. Subsequent removal of the protecting groups from 19-21 provides the corresponding free amino acids 25, 26, 28.     

Photochemical reactions. 146th communication. Photochemistry of conjugated methano-epoxydienes: Participation of the neighboring cyclopropane ring in product formation via carbonyl ylide and carbene intermediates

On singlet excitation (λ = 254 nm, THF, pentane or hexane), the diastereoisomeric methano-epoxydienes (E)- 6 and (E)- 7 undergo interconversion and yield the products 8 – 11 . The main process is the cleavage of the oxirane ring to the vinyl carbene intermediate e which undergoes addition to the adjacent double bond furnishing the cyclopropene 8 . The alternative carbene intermediate f is evidenced by the formation of the cyclobutene 10 . For the fragmentation leading to 11 , the carbene f as well as the dipolar species h are considered as possible intermediates. On triplet sensitization (acetone, λ > 280 nm), (E)- 7 shows behavior typical of epoxydienes, undergoing fission of the C? O bond of the oxirane ring and isomerization to the compounds 13 , 14 and (E/Z)- 15 .