Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

Design of a new molecule that exhibits observable CD spectra under σ-σ* excitation: 2,6-Disilyl-2,6-disilaspiro[3.3]heptanes

Abstract

We previously designed and prepared the first molecules to exhibit observable CD spectra by n-σ* excitation, 2,6-dithiaspiro[3.3]heptane 2,6-dioxide. Spiro[3.3]heptane frameworks possess axial asymmetry due to puckering of 2 four-membered rings; the ring bonds are rich in p-character due to acute bond angles, which lowers the σ* energy levels. In contrast, the lone pairs are rich in s-character, which results in a good donor with conformational fixation. We expected that, instead of lone pairs as donating orbitals, the use of σ-electron-donating Si-Si bonds should result in UV absorption in the observable range (>180?nm), so that the Cotton effect could appear, at least partially, in that range. We designed 2,6-disilyl-2,6-disilaspiro[3.3]heptanes as models, and performed theoretical calculations to confirm our idea.     

UV-VIS and CD-spectroscopic investigations of intermolecular interactions of bile pigments with small proteins

Summary The intermolecular complex formation of bilirubin and biliverdin with two proteins (basic pancreatic trypsin inhibitor and lysozyme) were studied by optical and chiroptical methods. Evidence for specific intermolecular interactions of biliverdin with both proteins was found. Bilirubin forms a soluble complex only with lysozyme.

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UV-VIS und CD-spektroskopische Untersuchungen intermolekularer Wechselwirkungen von Gallenpigmenten mit kleinen Proteinen

Zusammenfassung Die intermolekulare Komplexbildung von Bilirubin und Biliverdin mit zwei Proteinen (basischer pankreatischer Trypsininhibitor und Lysozym) wurden mittels optischer und chiroptischer Spektroskopie untersucht. Für Biliverdin konnten intermolekulare Wechselwirkungen mit beiden Proteinen nachgewiesen werden. Bilirubin bildet nur mit Lysozym einen löslichen Komplex.

     

Enantiomerentrennung und chiroptische Eigenschaften eines 2,3-Dihydrobilatriens-abc

The enantiomers of the 2,3-dihydrobilatriene-abc1 have been separated by recycling chromatography on triacetylcellulose. Comparison of their chiroptical properties with those of amino acid substituted analogues, like3, reveals the chirality of center 3 to be of minor influence on the values. Stabilization of a definite helical conformation of these pigments seems to depend on this influence together with an appropriate dipole-dipole interaction.

     

Radiation: Waves or particles? A quantized approach to time

A fundamental difficulty in theoretical physics is the dual and apparently incompatible interpretations of radiation as showing both continuous and extensive wave properties but also those of discrete atomic or smaller individual particles. Some of these contradictions are outlined. The explanation offered is of a quantized nature of time; units t_o=h/m_oc² for a particle at rest, and of similar interval unit s_o when in relative motion, with conventional relativistic corrections.

For many purposes this form of quantization replaces the need for a wave concept which then appears as a mathematical approach, chosen to avoid the physical concept of an intrinsicc time for any particle, just as we have for its intrinsic mass, spin and electrical charge. t_o and s_o are directly related to its frequency, energy and mass. The uncertainty principle and interference relations follow directly from this model, without any physical wave concept.     

Synthesis and absolute configuration of (1S,8S)-as-hydrindacene-1,8-diol as determined by the circular dichroism exciton chirality method

2,3,6,7-Tetrahydro-as-indacene-1,8-dione 4 was prepared in 4 steps starting from 2-methyl-furan by modification of a literature procedure. Appliance of Noyori’s asymmetric transfer hydrogenation, resulted in (1S,8S)-1,2,3,6,7,8-hexahydro-as-indacene-1,8-diol 5 in high yield (81%) and excellent enantioselectivity (>99% ee) or (8S)-8-hydroxy-3,6,7,8-tetrahydro-2H-as-indacen-1-one 6 in moderate yield (58%) and equally high enantioselectivity (98.5% ee), depending on the conditions. The asymmetric reduction was expected to yield the (S)-alcohols using the (S,S)-Ts-DPEN ligand, which was confirmed by the appliance of the exciton chirality method on the corresponding bis(p-dimethylamino)benzoate 7.     

Oxidation-Induced Structural Alterations and Its Effect on Chaperone Function of Rat Lens α-Crystallin

An ascorbate-FeCl₃-EDTA-H₂O₂ system was used to oxidize rat lens α-crystallins. Under this oxidative insult, the chaperone activity of α-crystallin toward γ-crystallin was shown to decrease significantly, which is quite different from the result reported by Wang and Spector. (Invest. Ophthalmol. Vis. Sci. 1995 , 36, 311-321.) Fluorescence spectroscopy and circular dichroism were employed to characterize the structural changes of oxidized α-crystallin. It was found that fluorescence intensity of l-anilinonaphthalene-8-sul-phonate (ANS) bound to oxidized α-crystallin increased comparing to that bound to normal α-crystallin, suggesting oxidation causes the exposure of more hydrophobic regions. Further, α-crystallin's fluorescence intensity in response to tryptophan residues showed a pseudo first order decline. Amino acid analysis of normal versus oxidized α-crystallin confirmed actual decline in tryptophan levels, showing about 80% of tryptophan being modified after 10-hour oxidation. Circular dichroism showed both changes in the secondary and tertiary structures of oxidized α-crystallin, characterized by a large loss of aromatic-type amino acid interactions and a large loss of β-sheet structure. In conclusion, modified tryptophan, secondary and tertiary structural changes of α-crystallin correlate best with the reduction of chaperone function, the curves all showing a linear slope for 10 hours, then plateauing. These results indicate that the decrease of α-crystallin chaperone activity is attributed to the structural changes.     

Stereochemistry of planarchiral compounds,part X

2,7-Dibromo-1,6-methano[10]anulene (3) and 2,9-Dibromo-syn-1,6:8,13-diimino[14]anulene (9) were quantitatively separated into their enantiomers by chromatography on triacetylcellulose (TAC) in ethanol. X-ray structure analysis (Bijvoet technique) established the chiralities (+)(R)-3 and (+)(S)-9 for the dextrorotatory enantiomers.Comparison of the CD spectra allowed the configurational assignment to further optically active [10] and [14] anulenes which were also accessible by chromatography onTAC. Conversion of (+)(R)-2-bromo-1,6-methano[10]anulene (2) into the corresponding methylester (–)-4 confirmed its previously proposed chirality (–)(R).2,7-Dibromo-1,6-oxido[10]anulene (7) and 2,9-dibromo-syn-diimino[14]anulene (9) are in contrast to the 2,9-dibromo-syn-dioxido[14]anulene (10) optically stable until 250°C. Consequently their inversion barriers are higher than 42 kcal (176 kJ) mol^–1.The CD spectra of mono and disubstituted anulenes (with C₁ and C₂ symmetry, resp.) are compared: For the [10]anulenes theCotton effect around 330 nm seems to be specific for their configuration with a positive effect indicating (S)-chirality and vice versa. Some regularities concerning the chromatographic resolutions are discussed.

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Stereochemie planar chialer Verbindungen, 10. Mitt.: Röntgenkristallstruktur und absolute Chiralität überbrückter [10]- und [14] Anulene

Zusammenfassung 2,7-Dibrom-1,6-methano[10]anulen (3) und 2,9-Dibrom-syn-1,6:8,13-diimino[14]anulen (9) wurden durch Chromatographie an Triacetylcellulose (TAC) in Ethanol quantitativ in ihre Enantiomeren getrennt. Röntgenstruktur-analyse (Bijvoet-Technik) bewies für die rechtsdrehenden Enantiomeren die Chiralität (+)(R)-3 bzw. (+)(S)-9.Ein Vergleich der CD-Spektren ermöglichte die Konfigurationszuordnung weiterer optisch aktiver [10]- und [14]Anulene, die gleichfalls durch Chromato-graphie anTAC erhalten worden waren. Umwandlung von (+)(R)-2-Brom-1,6-methano[10]anulen (2) in den entsprechenden Methylester (–)-4 bestätigte dessen schon früher vorgeschlagene Chiralität (–)(R).Dibrom-1,6-oxido[10]anulen (7) und Dibrom-diimino[14]anulen (9) sind im Gegensatz zum Dioxido[14]anulen (10) bis 250°C optisch stabil. Ihre Inver-sionsbarrieren liegen somit über 42 kcal (176kJ) mol^–1.Die CD-Spektren von mono- und disubstituierten Anulenen (mit C₁ bzw. C₂-Symmetrie) werden verglichen: Für die [10]Anulene scheint derCottoneffekt um 330 nm konfigurationsspezifisch zu sein, wobei ein positiver Effekt (S)-Chiralität anzeigt — und vice versa. Einige Regelmäßigkeiten bezüglich der chromatographischen Enantiomerentrennung werden diskutiert.

     

Chirality due to deuterium substitution: synthesis and circular dichroism of (+)(R) p -2,7-dideuterio-1,6-methano[10]annulene

Summary The title compound was prepared from (–)(S) _p -2,7-dibromo-1,6-methano[10]annulene by treatment withn-Bu-Li and subsequent quenching with D₂O. The optical rotations at four wavelengths and the circular dichroism spectrum are reported.

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Chiralität durch Deuterium-Substitution: Synthese und Circulardichroismus von (+)(R) _p -2,7-Dideuterio-1,6-methano[10]annulen (Kurze Mitt.)

Zusammenfassung Die Titelverbindung wurde aus (–)(S) _p -2,7-Dibrom-1,6-methano[10]annulen durch Umsetzung mitn-Bu-Li und nachfolgende Reaktion mit D₂O dargestellt. Optische Rotationen bei vier Wellenlängen und das Circulardichroismus-Spektrum wurden bestimmt.

     

On the synthesis and chiroptical properties of the tri- and tetragalloylquinic acids

Summary A synthesis of the potential pharmaceutical agents 3,4,5-trigalloylquinic acid and 1,3,4,5-tetragalloylquinic acid is described. It involves three steps starting from commercially available quinic acid and provides overall yields of about 15%. The acylation of benzyl or 4-nitrobenzyl quinate with tribenzylgalloyl chloride is the key step. It leads selectively to the triacyl product in the case of benzyl quinate and can be either stopped at the triacyl stage or driven to the tetraacyl derivative in the case of the 4-nitrobenzyl quinate. From the chiroptical properties of the two compounds their stereochemistry was derived by means of the benzoate rule.

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Zu Synthese und chiroptischen Eigenschaften der Tri- und Tetragalloylchinasäuren

Zusammenfassung Eine Synthese von 3,4,5-Trigalloylchinasäure und 1,3,4,5-Tetragalloylchinasäure. die potentielle Pharmaka darstellen, wird beschrieben. Sie umfaßt drei Stufen, welche ausgehend von kommerziell erhältlicher Chinasäure Gesamtausbeuten um 15% ergeben. Die entscheidende Stufe dabei ist die Acylierung von Benzyl- oder 4-Nitrobenzylchinat mit Tribenzylgalloylchlorid. Sie führt im Falle des Benzylchinats selektiv zum Triacylprodukt und kann im Fall des 4-Nitrobenzylchinats entweder auf der Stufe des Triacylderivates abgebrochen oder bis zum Tetraacylprodukt durchgezogen werden. Aus den chiroptischen Eigenschaften der beiden Verbindungen wurde ihre Stereochemie abgeleitet.