Synthesis, crystal structure, magnetic behavior and thermal property of three polynuclear complexes: [M(dca)(2)(H2O)2](n)center dot(hmt)(n) [M = Mn(II), Co(II)] and [Co(dca)(2)(bpds)](n) [dca, dicyanamide; hint, hexamethylenetetramine; bpds, 4,4 '-bipyridyl disulfide]

Three mu(1.5)-dicyanamide bridged Mn(II) and Co(II) complexes having molecular formula [Mn(dca)(2)(H2O)(2)](n)center dot(hmt)(n) (1), [Co(dca)(2) (H2O)(2)](n)center dot(hmt)(n) (2) and [Co(dca)(2)(bpds)](n) (3) [dca = dicyanamide; hmt = hexamethylenetetramine; bpds = 4,4'-bipyridyl disulfide] have been synthesized and characterized by single crystal X-ray diffraction study, low temperature (300-2 K) magnetic measurement and thermal behavior. The X-ray diffraction analysis of 1 and 2 reveals that they are isostructural, comprising of 1D coordination polymers [M(dca)(2)(H2O)(2)](n) [M = Mn(II), Co(II) for 1 and 2. respectively] with uncoordinated hmt molecules located among the chains. The [M(dca)(2)(H2O)(2)](n) chains and the lattice hint molecules are connected through H-bonds resulting in a 3D supramolecular architecture. The octahedral N4O2 chromophore surrounding the metal ion forms via two trans located water oxygens and four nitrogens from four nitrile dca. Complex 3 is a 1D chain formed by two mu(1.5)-dca and one bridging bpds. The octahedral N-6 coordination sphere surrounding the cobalt ions comprises four nitrogens from dca and two from bpds. Low temperature magnetic study indicates small antiferromagnetic coupling for all the complexes. Best fit parameters for 1: J = -0.17 cm(-1), g = -2.03 with R = 6.1 x 10(-4), for 2, J = -0.50 cm(-1), and for 3, J = -0.95 cm(-1). (c) 2005 Elsevier B.V. All rights reserved.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.