On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Modular class primes in the Sundaram sieve

The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.     

The Conformation of Sterically Congested Seven-Membered Rings Containing Tetracoordinate Germanium(IV): A First X-Ray Crystallographic Structure Determination

The X-ray crystallographic analysis of 6,6-dimethyl-2,4,8,10-tetra-tert-octyl-dibenzo[d,f][1,3,2]dioxagermepin, 1 is reported. In the solid-state conformation of 1, the dihedral angle about the C─C sp²-sp ² σ bond connecting the two aryl rings is 50.1°. The observed C₂ symmetry in the solid-state conformation of 1 is consistent with the previously suggested solution conformation.     

Practical synthesis of bicyclic pyrazol-5-one derivatives

This communication describes a convenient synthesis of fused bicyclic pyrazolones in a one-pot reaction procedure. Modified protocols are also developed to access 5,5-bicyclic and bulky pyrazolones in good yields. The method reported herein represents a practical approach to structurally diversified bicyclic pyrazolones.     

Highly Efficient α‐Sialylation by Virtue of Fixed Dipole Effects of N‐Phthalyl Group: Application to Continuous Flow Synthesis of α(2‐3)‐and α(2‐6)‐Neu5Ac‐Gal Motifs by Microreactor

Highly α‐selective sialylation of sialic acid N‐phenyltrifluoroacetimidate with various galactose and lactose acceptors has been achieved by introducing the C‐5 N‐phthalyl group on the donor. The “fixed dipole effect” of the N‐phthalyl group was proposed to explain the high reactivity and α‐selectivity. The microfluidic system was applied to the present α‐sialylation, which is amenable to large‐scale synthesis. The N‐phthalyl group was removed by treatment with methylhydrazine acetate, for which protocol can be readily applied to the synthesis of a variety of sialic acid‐containing oligosaccharides.