Twistor spinors and gravitational instantons

We construct a complete Riemannian metric on the four-dimensional vector space ⁴ which carries a two-dimensional space of twistor spinor with common zero point. This metric is half-conformally flat but not conformally flat. The construction uses a conformal completion at infinity of theEguchi-Hanson metric on the exterior of a closed ball in ⁴.     

Zur additiven Primzahltheorie algebraischer Zahlkörper. III.

Ohne Zusammenfassung     

Druggable Allosteric Sites in β-Propeller Lectins

Carbohydrate-binding proteins (lectins) are auspicious targets in drug discovery to combat antimicrobial resistance; however, their non-carbohydrate drug-like inhibitors are still unavailable. Here, we present a druggable pocket in a β-propeller lectin BambL from Burkholderia ambifaria as a potential target for allosteric inhibitors. This site was identified employing ¹⁹F NMR fragment screening and a computational pocket prediction algorithm SiteMap. The structure–activity relationship study revealed the most promising fragment with a dissociation constant of 0.3±0.1 mM and a ligand efficiency of 0.3 kcal mol^?1 HA^?1 that affected the orthosteric site. This effect was substantiated by site-directed mutagenesis in the orthosteric and secondary pockets. Future drug-discovery campaigns that aim to develop small molecule inhibitors can benefit from allosteric sites in lectins as a new therapeutic approach against antibiotic-resistant pathogens.     

Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies

This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are allowed. The main result is a reduction to algebraic equations of the problem to find all solutions that are close to the heteroclinic network for all time, and their parameter values. A leading order expansion is given in terms of the time spent near vertices and, if applicable, the location on the non-trivial tangent directions. The only difference between a periodic orbit and an equilibrium is that the time parameter is discrete for a periodic orbit. The essential assumptions are hyperbolicity of the vertices and transversality of parameters. Using the result, conjugacy to shift dynamics for a generic homoclinic orbit to a periodic orbit is proven. Finally, equilibrium-to-periodic orbit heteroclinic cycles of various types are considered.     

Electronic and geometrical structures of cyclopropanes, part 51. fluorocyclopropanes. linear correlation of orbital energies with C–C bond lengths. further improvement of the two-orbitals model

The electronic and geometrical structures of fluorocyclopropanes (1–12) have been analysed using DFT B3LYP calculations. A linear relationship, Δɛ_ω=−0.172 Δr−0.171 (n=12, R=0.931), between Δɛ_ω (in eV), the difference of the energies of the Walsh orbitals ω_S and ω_A, and Δr (in pm), the difference of vicinal and distal C–C bond lengths, is established. Correcting the orbital splitting by the basic value at Δr=0.00 pm, an even better linear correlation Δɛ_ω ^eff=0.0720 Δr (n=12, R=0.984) is obtained. The results confirm the general applicability of the two-orbitals model for the relationship between geometrical and electronic structures for substituted cyclopropanes. ¹For Part 4 see Ref. [17].     

Molekülstruktur von gasförmigem 1,5-diazabicyclo-[3.3.0] octan(DABCO)

The molecular structure of DABCO was studied by vibrational spectroscopy and by gas phase electron diffraction. The infrared and Raman spectra indicate C₂ symmetry for DABCO, excluding conformational models of higher or lower symmetry. According to the diffraction data the most reasonable conformation is a twisted cis-exo-exo-form. Experimental bond distances (r_a) and bond angles (∠_a) are listed above. The dihedral angle ψ between the C₂N-groups was fo und to be 37.9 ± 3.3°.