Hexaaquacobalt(II) bis(hypophosphite) and hexaaquacobalt(II)/nickel(II) bis(hypophosphite)

The title compounds, hexa­aqua­cobalt(II) bis­(hypophosphite), [Co(H₂O)₆](H₂­PO₂)₂, and hexa­aqua­cobalt(II)/nickel(II) bis(hypophosphite), [Co_0.5Ni_0.5(H₂O)₆](H₂PO₂)₂, are shown to adopt the same structure as hexa­aqua­magnesium(II) bis­(hypophosphite). The packing of the Co(Ni) and P atoms is the same as in the structure of CaF₂. The Co^II(Ni^II) atoms have a pseudo‐face‐centred cubic cell, with a = b～ 10.3 Å, and the P atoms occupy the tetrahedral cavities. The central metal cation has a slightly distorted octahedral coordination sphere. The geometry of the hypophosphite anion in the structure is very close to ideal, with point symmetry mm2. Each O atom of the hypophosphite anion is hydrogen bonded to three water mol­ecules from different cation complexes, and each H atom of the hypophosphite anion is surrounded by three water mol­ecules from further different cation complexes.     

Efficient algorithms for the recognition of topologically conjugate gradient-like diffeomorhisms

It is well known that the topological classification of structurally stable flows on surfaces as well as the topological classification of some multidimensional gradient-like systems can be reduced to a combinatorial problem of distinguishing graphs up to isomorphism. The isomorphism problem of general graphs obviously can be solved by a standard enumeration algorithm. However, an efficient algorithm (i. e., polynomial in the number of vertices) has not yet been developed for it, and the problem has not been proved to be intractable (i. e., NPcomplete). We give polynomial-time algorithms for recognition of the corresponding graphs for two gradient-like systems. Moreover, we present efficient algorithms for determining the orientability and the genus of the ambient surface. This result, in particular, sheds light on the classification of configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field.     

Reverse fragment based drug discovery approach via simple estimation of fragment contributions

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N-Pyrrolidine-2-ylmethyl)-2-hydroxy-3-aminopinanes as novel organocatalysts for asymmetric conjugate additions of ketones to α-nitroalkenes

Novel stereoisomeric natural pinane-derived bifunctional catalysts 3a–d bearing a pyrrolidine unit have been synthesized and examined in the asymmetric conjugate additions of carbonyl compounds to α-nitroalkenes. Six-membered cyclic ketones react with β-nitrostyrene derivatives in the presence of (1R,2R,3R,5R)-2-hydroxy-3-((S)-pyrrolidin-2-ylmethylamino) pinane 3b (10 mol %) with high conversion to afford with diastereoselectivity (dr (syn/anti) up to 97/3), the corresponding Michael adducts with enantiomeric purities of up to 88% ee.     

Rearrangement of O,O’-bis(2-benzylideneaminophenyl) phenylphosphonite into 1,6,7-triphenyl-3,4:9,10-dibenzo-2,11-dioxa-5,8-diaza-1-phosphatricyclo[6.3.0.01,5]undeca-3,9-diene

Keeping of O,O’-bis(2-benzylideneaminophenyl) phenylphosphonite in a CCl4 solution for 50 days resulted in its spontaneous rearrangement into 1,6,7-triphenyl-3,4:9,10-dibenzo-2,11-dioxa-5,8-diaza-1-phosphatricyclo[6.3.0.01,5]undeca-3,9-diene, a representative of spirophosphoranes with P–N bonds.     

Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.