Towards EPC-syntheses of the structural class of cochleamycins and macquarimicins. Part 2: EPC-synthesis of the hydrindene subunit of the macquarimicins

The EPC-synthesis of the cis-hydrindene subunit of the macquarimicins, antibiotics with antitumour and anti-inflammatory activity, has been achieved. Desymmetrization of cis-1,4-cyclopent-2-enediol was succeeded by Diels-Alder reaction and functional group transformations to a tricyclic ketone. Regio- and stereoselective methylation via Claisen condensation and hydrogenation was followed by nucleophilic, intramolecular addition, reduction and acidic fragmentation. Further functional group transformations led to the target molecule.     

On a characterization of polynomials by divided differences

Summary We consider the functional equationf[x ₁,x ₂,, x _n ] =h(x ₁ + +x _n ) (x ₁,,x _n K, x _j x _k forj k), (D) wheref[x ₁,x ₂,,x _n ] denotes the (n – 1)-st divided difference off and prove Theorem. Let n be an integer, n 2, let K be a field, char(K) 2, with # K 8(n – 2) + 2. Let, furthermore, f, h: K K be functions. Then we have that f, h fulfil (D) if, and only if, there are constants a_j K, 0 j n (a := a_n, b := a_{n – 1}) such thatf = ax ⁿ +bx ^{n – 1} + +a ₀ and h = ax + b.     

Regulation of stearoyl-CoA desaturase-1 after central and peripheral nerve lesions

Background  

Interruption of mature axons activates a cascade of events in neuronal cell bodies which leads to various outcomes from functional regeneration in the PNS to the failure of any significant regeneration in the CNS. One factor which seems to play an important role in the molecular programs after axotomy is the stearoyl Coenzyme A-desaturase-1 (SCD-1). This enzyme is needed for the conversion of stearate into oleate. Beside its role in membrane synthesis, oleate could act as a neurotrophic factor, involved in signal transduction pathways via activation of protein kinases C.     

Tailoring of high-Q-factor surface plasmon modes on silver microtubes

We investigate the excitation of surface plasmon polaritons on silver tubes with finite-difference time-domain simulations. These surface plasmon polaritons exhibit azimuthal whispering gallery modes with quality factors in the hundreds. We show that the high quality factors arise from the coupling of the surface plasmon modes to photonic modes inside the tube. We examine the influence of a gain material on the quality factors and find that for material data of rhodamine 6G, the quality factors are enhanced significantly up to values of 3000.     

Associative formal power series in two indeterminates

Investigating the associativity equation for formal power series in two variables we show that the transcendental associative formal power series are of order one or two and that they can be represented by an invertible formal power series in one variable. We also discuss the convergence of associative formal power series.