Assembly of Carbohydrates on a Nickel(II) Center by Utilizing N-Glycosidic Bond Formation with Tris(2-aminoethyl)amine (tren). Syntheses and Characterization of [Ni{N-(aldosyl)-tren}(H(2)O)](2+), [Ni{N,N'-bis(aldosyl)-tren}](2+) and [Ni{N,N',N"-tris(aldosyl)-tren}](2+)

Reactions of [Ni(tren)(H(2)O)(2)]X(2) (tren = tris(2-aminoethyl)amine; X = Cl (1a), Br (1b); X(2) = SO(4) (1c)) with mannose-type aldoses, having a 2,3-cis configuration (D-mannose and L-rhamnose), afforded {bis(N-aldosyl-2-aminoethyl)(2-aminoethyl)amine}nickel(II) complexes, [Ni(N,N'-(aldosyl)(2)-tren)]X(2) (aldosyl = D-mannosyl, X = Cl (2a), Br (2b), X(2) = SO(4) (2c); aldosyl = L-rhamnosyl, X(2) = SO(4) (3c)). The structure of 1c was confirmed by X-ray crystallography to be a mononuclear [Ni(II)N(4)O(2)] complex with the tren acting as a tetradentate ligand (1c.2H(2)O: orthorhombic, Pbca, a = 15.988(2) ?, b = 18.826(4) ?, c = 10.359(4) ?, V = 3118 ?(3), Z = 8, R = 0.047, and R(w) = 0.042). Complexes 2a,c and 3c were characterized by X-ray analyses to have a mononuclear octahedral Ni(II) structure ligated by a hexadentate N-glycoside ligand, bis(N-aldosyl-2-aminoethyl)(2-aminoethyl)amine (2a.CH(3)OH: orthorhombic, P2(1)2(1)2(1), a = 16.005(3) ?, b = 20.095(4) ?, c = 8.361(1) ?, V = 2689 ?(3), Z = 4, R = 0.040, and R(w) = 0.027. 2c.3CH(3)OH: orthorhombic, P2(1)2(1)2(1), a = 14.93(2) ?, b = 21.823(8) ?, c = 9.746(2) ?, V = 3176 ?(3), Z = 4, R = 0.075, and R(w) = 0.080. 3c.3CH(3)OH: orthorhombic, P2(1)2(1)2(1), a = 14.560(4) ?, b = 21.694(5) ?, c = 9.786(2) ?, V = 3091 ?(3), Z = 4, R = 0.072, and R(w) = 0.079). The sugar part of the complex involves novel intramolecular sugar-sugar hydrogen bondings around the metal center. The similar reaction with D-glucose, D-glucosamine, and D-galactosamine, having a 2,3-trans configuration, resulted in the formation of a mono(sugar) complex, [Ni(N-(aldosyl)-tren)(H(2)O)(2)]Cl(2) (aldosyl = D-glucosyl (4b), 2-amino-2-deoxy-D-glucosyl (5a), and 2-amino-2-deoxy-D-galactosyl (5b)), instead of a bis(sugar) complex. The hydrogen bondings between the sugar moieties as observed in 2 and 3 should be responsible for the assembly of two sugar molecules on the metal center. Reactions of tris(N-aldosyl-2-aminoethyl)amine with nickel(II) salts gave the tris(sugar) complexes, [Ni(N,N',N"-(aldosyl)(3)-tren)]X(2) (aldosyl = D-mannosyl, X = Cl (6a), Br (6b); L-rhamnosyl, X = Cl (7a), Br (7b); D-glucosyl, X = Cl (9); maltosyl, X = Br (10); and melibiosyl, X = Br (11)), which were assumed to have a shuttle-type C(3) symmetrical structure with Delta helical configuration for D-type aldoses on the basis of circular dichroism and (13)C NMR spectra. When tris(N-rhamnosyl)-tren was reacted with NiSO(4).6H(2)O at low temperature, a labile neutral complex, [Ni(N,N',N"-(L-rhamnosyl)(3)-tren)(SO(4))] (8), was successfully isolated and characterized by X-ray crystallography, in which three sugar moieties are anchored only at the N atom of the C-1 position (8.3CH(3)OH.H(2)O: orthorhombic, P2(1)2(1)2(1), a = 16.035(4) ?, b = 16.670(7) ?, c = 15.38(1) ?, V = 4111 ?(3), Z = 4, R = 0.084, and R(w) = 0.068). Complex 8 could be regarded as an intermediate species toward the C(3) symmetrical tris(sugar) complexes 7, and in fact, it was readily transformed to 7b by an action of BaBr(2).     

On the Korteweg-de Vries equation

Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s= being included For the proper KdV equation, existence of global solutions follows if s2. The proof is based on the theory of abstract quasilinear evolution equations developed elsewhere.Dedicated to Hans Lewy and Charles B. Morrey Jr.Partially supported by NSF Grant MCS76-04655.     

X-ray structure analysis of trans-1,4-polybutadiene

The crystal structure of trans-1,4-polybutadiene has been reported by Natta et al. to be pseudo-hexagonal below its solid-phase transition temperature. In the present X-ray structure analysis, it is revealed that the crystal belongs to the monoclinic system with the space group P2¹/a. The unit cell, with the lattice constants a = 8.63 Å, b = 9.11 Å, c = 4.83 Å, and β = 114°, includes four molecular segments.     

Biow-up of solutions of some nonlinear hyperbolic equations

We prove that any nontrivial solution of certain nonlinear hyperbolic partial differential equations of second order blows up in a finite time if the initial data are localized, the initial velocity being on the average non-negative.