C18 tetraynoic fatty acids and essential oil composition of Mkilua fragrans

The fatty acids 17,18-dihydroxyoctadeca-9,11,13,15-tetraynoic acid (mkiluaynoic acid A) and 18-hydroxyoctadeca-9,11,13,15-tetraynoic acid (mkiluaynoic acid B), 5,7,3',4'-tetrahydroxyflavanol, 3,4-dihydroxybenzoic acid and a mixture of stearic and oleic acids were isolated from fruits and stem barks of Mkilua fragrans (Annonaceae). Mkiluaynoic acid A exhibited antifungal activity against Candida albicans comparable with that of the standard antifungal agent Ketoconazole. Structural determination was achieved by analysis of spectroscopic data. The flower stalks yielded essential oils that mainly consisted of sesquiterpenoids as revealed by GC-MS analysis, whereby 14 sesquiterpenes and four other compounds were identified.     

Asymmetric [3 + 2] annulations catalyzed by a planar-chiral derivative of DMAP

A planar-chiral DMAP derivative catalyzes an intriguing [3 + 2] annulation reaction of silylated indenes to produce diquinanes that bear three contiguous stereocenters (one quaternary and two tertiary).     

Temperature dependence of the hyperfine fields of 111In in sapphire (Al2O3) single crystals

Cr has been added to FeCo substituting 10 at.% of Co or Fe in the alloy. The alloys Fe₅₀Co₄₀Cr₁₀, Fe₄₀Co₅₀Cr₁₀ and Fe₅₀Co₅₀ were prepared by mechanical alloying for 2, 5, 10, 20, 40 and 60 h. The formation of the alloy and the incorporation of the elements have been followed by X-Ray Diffraction (XRD) and Mössbauer Spectroscopy. The kinetics of mixing occurs by incorporation of Co and Cr into the Fe structure. After prolonged milling it seems that Cr incorporates itself into both $\upalpha $ -Fe and $\upalpha $ -FeCo structures and a mixture of FeCoCr rich in Cr and FeCoCr rich in Co solid solutions is obtained.     

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.     

Estimation of the conformal factor under bounded Willmore energy

We prove for closed, orientable surfaces in $\ \mathbb{R }^3\ $ with Willmore energy less that $\ 8 \pi - \delta \ $ and whose conformal structures are compactly contained in moduli space that after applying appropriate Möbius transformations the conformal factors between the induced metrics and conformal metrics of constant curvature are uniformly bounded by constants depending only on $\ \delta > 0,$ the genus of the surfaces and the compact subset of the moduli space. Secondly, for a given sequence of closed, orientable surfaces as above, we prove that the conformal factor remains bounded without applying Möbius transformations if and only if no topology is lost. Similar estimates hold in higher codimension.