A famous lower bound for the bilinear complexity of the multiplication in associative algebras is the Alder–Strassen bound. Algebras for which this bound is tight are called algebras of minimal rank. After 25 years of research, these algebras are now well understood. We here start the investigation of the algebras for which the Alder–Strassen bound is off by one. As a first result, we completel...

The methyl ether derivatives 2, 4 and 6 of the mulberry Diels-Alder adducts chalcomoracin (1) and mulberrofuran C (3) and kuwanon J (5) respectively have been synthesized by a thermal [4 + 2]-cycloaddition reaction between a chalcone and dehydroprenyl diene. A H-bonded ortho OH substituent on the chalcone was found to be essential for Diels-Alder reactivity. Density functional theory calculatio...

Green alder (Alnus viridis ssp. fruticosa) is a dominant understory shrub during secondary successional development of upland forests throughout interior Alaska, where it contributes substantially to the nitrogen (N) economy through atmospheric N2 fixation. Across a replicated 200? year old vegetation chronosequence, we tested the hypotheses that green alder has strong effects on soil chemical ...

J. P. Rushton and A. R. Jensen (2005) ignore or misinterpret most of the evidence of greatest relevance to the question of heritability of the Black–White IQ gap. A dispassionate reading of the evidence on the association of IQ with degree of European ancestry for members of Black populations, convergence of Black and White IQ in recent years, alterability of Black IQ by intervention programs, ...

The first enantioselective total syntheses of prenylflavonoid Diels-Alder natural products (-)-kuwanon I, (+)-kuwanon J, (-)-brosimone A, and (-)-brosimone B have been accomplished from a common intermediate based on a concise synthetic strategy. Key elements of the synthesis include a biosynthesis-inspired asymmetric Diels-Alder cycloaddition mediated by a chiral ligand/boron Lewis acid, as we...

Unlike normal Diels-Alder reactions of acyclic alkadienes with alkenes, the vinylbicyclo[2.2.2]octene employed in the Baran total synthesis of vinigrol undergoes a quantitative Diels-Alder reaction with a tethered alkene at room temperature. Density functional theory calculations reveal that this unprecedented reactivity originates from a combination of preorganization, diene strain, and tether...