Effect of a low magnetic field on crystallinity and magnetic susceptibility of molecular magnet {NBu4[FeCr(ox)3]}x (NBu4=tetra( n-butyl) ammonium ion; ox=oxalate ion)

Molecular magnet {NBu₄[Fe Cr(ox)₃]}_x (NBu₄⁺=tetra(n-buty1) ammonium ion; ox²⁻=oxalate ion) was synthesized under an applied low magnetic field of 0.3 T in comparison to that synthesized without a field. Their crystallinities, morphologies and magnetic properties were characterized by using the X-ray diffractionmeter, the transmission electron microscope, and a superconducting quantum interference device. It is found that the average size of particles synthesized under the applied field appears larger than that synthesized without a field. Moreover, its crystallinity, morphology and magnetic susceptibility have also been improved. However, its chemical structure and ferromagnetic phase transition temperature T_c do not change. Possible reasons to explain this effect are also discussed.     

Synthesis and 1H, 19F NMR spectroscopic characterization of (pentafluorophenyl)3-n (pyrazol-1-yl-tetrafluorophenyl)n=1,2 porphyrins

Three new porphyrins bearing in the meso positions 4-(pyrazol-1-yl)-2,3,5,6-tetrafluorophenyl substituents have been prepared and characterized by nmr spectroscopy.     

Porous surfaces

In fractal modeling, porous surfaces in the plane are usually described as the residual setE of a packing by connected open domains \(C_n\) . In the case whereE is nonempty, we investigate the relationships between the dimensionality ofE and the geometry of the complementary sets \(C_n\) . If they satisfy suitable regularity conditions, then the Bouligand dimension ofE is equal to the exponent of convergence of the series ∑(diam \(C_n\) ) ^α . We give here general conditions to obtain this equality, together with numerous examples and possible ways of developing this theory.     

Gelfand numbers of operators with values in a Hilbert space

In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol ₂ ⁿ with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml ₁ ^N into a Hilbert space satisfy the inequality