The wonderland of reflections

A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable ω-categorical relational structures have two algebraic counterparts for their polymorphism clones: a semantic one via the standard algebraic operators H, S, P, and a syntactic one via clone homomorphisms (capturing identities). We provide a similar characterization which incorporates all relational constructions relevant for CSPs, that is, homomorphic equivalence and adding singletons to cores in addition to ppinterpretations. For the semantic part we introduce a new construction, called reflection, and for the syntactic part we find an appropriate weakening of clone homomorphisms, called h1 clone homomorphisms (capturing identities of height 1).As a consequence, the complexity of the CSP of an at most countable ω-categorical structure depends only on the identities of height 1 satisfied in its polymorphism clone as well as the natural uniformity thereon. This allows us in turn to formulate a new elegant dichotomy conjecture for the CSPs of reducts of finitely bounded homogeneous structures.Finally, we reveal a close connection between h1 clone homomorphisms and the notion of compatibility with projections used in the study of the lattice of interpretability types of varieties.     

Quiescent double barrier regime in the DIII-D tokamak

A new sustained high-performance regime, combining discrete edge and core transport barriers, has been discovered in the DIII-D tokamak. Edge localized modes (ELMs) are replaced by a steady oscillation that increases edge particle transport, thereby allowing particle control with no ELM-induced pulsed divertor heat load. The core barrier resembles those usually seen with a low (L) mode edge, without the degradation often associated with ELMs. The barriers are separated by a narrow region of high transport associated with a zero crossing in the E x B shearing rate.     

Synthesis of racemic octaprenol ωtttcccsOH and nonaprenol ωtttccccsOH

Conclusions A ten-stage synthesis of the dolichol-related racemic octaprenol tttcccsOH and nonaprenol tttccccsOH was carried out using controlled aldol condensation at the key stage.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1546–1552, July, 1987.     

Stereoselective synthesis of a dolichol-like octaprenol (S)-WT3C3SOH

In accordance with the previously developed block method of constructing polyprenol molecules, a new stereospecific synthesis was carried out of their natural representative WT₃C₂OH, which was then converted in nine steps into the above chiral octaprenol. At the same time the synthesis of the racemate of the latter has been improved.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2325–2333, October, 1991.     

An alternative synthesis of a sex pheromone of the dry bean beetleCallosobruchus analis

A formal total synthesis of 3-methylhept-2(Z)-enoic acid, a sex pheromone of the dry bean beetleCallosobruchus analis, was performed on the basis of a highly stereoselective version of the Peterson olefination of ketones developed previously by the authors. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1389–1392, July, 1999.