Optimal design of elastic columns subject to the general conservative behaviour of loading

Zusammenfassung Optimale Formen eines gedrückten elastischen Stabes werden bei allgemeinem Verhalten der Druckkraft nach dem Stabilitätsverlust untersucht. Als Zielfunktion wird das minimale Volumen angenommen unter der Nebenbedingung einer konstanten kritischen Belastung. Das konservative Verhalten der Kraft ist mit einer Beziehung verbunden, welche die allgemeine Euler-Lagrangesche Gleichung vereinfacht. Es werden räumlich sowie eben verjüngte Stäbe untersucht und die Resultate bei einigen Beispielen diskutiert.     

Synthesis of heavily substituted 1,2-amino alcohols in enantiomerically pure form

[reaction: see text] A simple and convenient methodology for the preparation of optically pure 2-amino-2-aryl-1,1-diphenylethanols is presented. Allylamine was found to produce the ring-opening of triaryloxiranes in a regioselective and a stereospecific fashion. Removal of the allyl protecting group provided the free 1,2-amino alcohols in enantiomerically pure form.     

General approach to glycosidase inhibitors. Enantioselective synthesis of deoxymannojirimycin and swainsonine

[reaction: see text] Deoxymannojirimycin (2) and swainsonine (4) have been synthesized from each enantiomer of the same bicyclic carbamate precursor 7. The key intermediate was prepared by a simple and efficient three-step synthesis involving RCM of the diene 8, which in turn is easily accessible in any configuration from enantiomerically enriched 2,3-epoxy-4-penten-1-ol 9.     

Interpolation by type I factors and the flip automorphism

Given two von Neumann algebras $\text{A}$ ?$\text{B}$ we study the relation between the existence of an interpolating type I factor $\text{F}$, namely $\text{A}$ ?$\text{F}$ ?$\text{B}$, the implementability of the flip automorphism of $\text{A}$ ? $\text{A}$ by a unitary in $\text{B}$ ? $\text{B}$, and the statistical independence of $\text{A}$ and $\text{B}$′ ($\text{A}$ and $\text{B}$′ generate a $\text{W}$¹-tensor product). As an application in Q.F.T. we derive in a natural way a structure theorem of Buchholz for the von Neumann algebras of local observables associated to free fields.     

Physico-chemical properties and possible photocatalytic applications of titanate nanotubes synthesized via hydrothermal method

Titanate nanotubes (TNTs) were prepared from TiO₂ P25 via hydrothermal method. The reaction temperature was 130 or 140 °C and the reaction time was 24 or 48 h. The samples were characterized by transmission electron microscopy, X-ray diffraction, thermogravimetry and N₂ adsorption as well as Raman, FTIR-DRS and UV-vis/DR spectroscopy. The obtained samples exhibited similar properties, regardless of the preparation temperature and time. The most notable difference between properties of TNTs prepared under different conditions was observed in case of BET surface area, which was increasing from 386 to 478 m²/g along with increasing the reaction time and temperature. Based on TEM, XRD and TG measurements we have suggested that the structure of TNTs was H₂Ti₂O₄(OH)₂. The TEM and Raman spectroscopy measurements showed that the obtained products contained also low amount of anatase phase. The TNTs exhibited no photoactivity towards degradation of model azo dye Acid Red 18. However, TNTs were successfully applied for photocatalytic generation of CH₄ and H₂ in a solution of acetic acid. The amount of methane produced with application of TNTs synthesized at 140 °C was about 2.5 times higher than that generated with use of TiO₂ P25. To the best of our knowledge this is a first report on the photocatalytic generation of hydrocarbons using TNTs in the current state of the art.     

Stereodivergent syntheses of conduramines and aminocyclitols

[reaction: see text] The diastereomers of 6-amino-cyclohex-3-ene-1,2-diols 1 (4-deoxy-3-conduramines), key building blocks for the syntheses of a large range of natural products, have been enantioselectively prepared. Diastereoselective dihydroxylation of the compounds provided a new family of aminocyclitols 2 (deoxyinosamines). The key reactions of our syntheses are Sharpless catalytic asymmetric epoxidation, diastereoselective addition of vinylmetal reagents to the aldehydes, and ring-closing metathesis (RCM).     

Ultra‐Tough Inverse Artificial Nacre Based on Epoxy‐Graphene by Freeze‐Casting

Epoxy nanocomposites combining high toughness with advantageous functional properties are needed in many fields. However, fabricating high‐performance homogeneous epoxy nanocomposites with traditional methods remains a great challenge. Nacre with outstanding fracture toughness presents an ideal blueprint for the development of future epoxy nanocomposites. Now, high‐performance epoxy‐graphene layered nanocomposites were demonstrated with ultrahigh toughness and temperature‐sensing properties. These nanocomposites are composed of ca. 99 wt % organic epoxy, which is in contrast to the composition of natural nacre (ca. 96 wt % inorganic aragonite). These nanocomposites are named an inverse artificial nacre. The fracture toughness reaches about 4.2 times higher than that of pure epoxy. The electrical resistance is temperature‐sensitive and stable under various humidity conditions. This strategy opens an avenue for fabricating high‐performance epoxy nanocomposites with functional properties.