Decompositions of complete graphs into theta graphs with fewer than ten edges

A theta graph is a graph consisting of three pairwise internally disjoint paths with common end points. Methods for decomposing the complete graph K-nu into theta graphs with fewer than ten edges are given.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Synthesis and characterization of mono- and bis-ligand zinc(II) and cadmium(II) complexes of the di-2-pyridylketone Schiff base of S-benzyl dithiocarbazate (Hdpksbz) and the X-ray crystal structures of the [Zn(dpksbz)2] and [Cd(dpksbz)NCS]2 complexes

New mono- and bis-chelated zinc(II) and cadmium(II) complexes of formula, [M(dpksbz)NCS] (dpksbz = anionic form of the di-2-pyridylketone Schiff base of S-benzyldithiocarbazate) and [M(dpksbz)(2)] (M = Zn-II, Cd-II) have been prepared and characterized. The structure of the bis-ligand complex, [Zn(dpksbZ)(2)] has been determined by X-ray diffraction. The complex has a distorted octahedral geometry in which the ligands are coordinated to the zinc(II) ion as uninegatively charged tridentate chelates via the thiolate sulfur atoms, the azomethine nitrogen atoms and the pyridine nitrogen atoms. The distortion from a regular octahedral geometry is attributed to the restricted bite angles of the Schiff base ligands. X-ray structural analysis shows that the [Cd(dpksbz)NCS](2) complex is a centrosymmetric dimer in which each of the cadmium(II) ions adopts a five-coordinate, approximately square-pyramidal configuration with the Schiff base acting as a tetradentate chelating agent coordinating a cadmium(II) ion via one of the pyridine nitrogen atoms, the azomethine nitrogen atom and the thiolate sulfur atom; the second pyridine nitrogen atom is coordinated to the other cadmium(II) ion of the dimer. The fifth coordination position around each cadmium(II) is occupied by an N-bonded thiocyanate ligand. (C) 2003 Elsevier Science Ltd. All rights reserved.

The preparation of zinc(II) and cadmium(II) complexes of the pentadentate N3S2 ligand formed from 2,6-diacetylpyridine and S-benzyldithiocarbazate (H2SNNNS) and the X-ray crystal structure of the novel dimeric [Zn2(SNNNS)2] complex

The pentadentate chelating agent, 2,6-diacetylpyridinebis(S-benzyldithiocarbazate) (H2SNNNS) reacts with zinc(II) and cadmium(II) ions forming stable complexes of empirical formula, [M(SNNNS)] (M=Zn2+, Cd2+; SNNNS2 =doubly deprotonated anionic form of the Schiff base). These complexes have been characterized by a variety of physico-chemical techniques. IR and H-1 NMR spectral evidence indicate that the Schiff base coordinates to the zinc(II) and cadmium(II) ions via the pyridine nitrogen atoms, the azomethine nitrogen atoms and the mercaptide sulfur atoms. The crystal and molecular structure of the zinc(II) complex has been determined by X-ray diffraction. The complex is a dimer in which the pyridine nitrogen atom,the azomethine nitrogen atom and the thiolate sulfur atom from one ligand coordinate to one of the zinc(II) ions whereas the azomethine and thiolate sulfur atoms from another ligand complete pentacoordination around the zinc(II) ion, the ligands being coordinated in their deprotonated forms. The coordination geometry about each zinc(II) can be considered as intermediate between a square-pyramid and trigonal-bipyramid. The cadmium(II) complex is also assigned with a dimeric structure. (C) 2003 Elsevier Ltd. All rights reserved.

Anomalous water absorption in porous materials

The absorption of fluid by unsaturated, rigid porous materials may be characterized by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of a material's resistance to exposure to fluids (especially moisture and reactive solutes) in aggressive environments. The complete isothermal absorption process is described by a nonlinear diffusion equation, with the hydraulic diffusivity being a strongly nonlinear function of the degree of saturation of the material. This diffusivity can be estimated from the sorptivity test. In a typical test the cumulative absorption is proportional to the square root of time. However, a number of researchers have observed deviation from this behaviour when the infiltrating fluid is water and there is some potential for chemo-mechanical interaction with the material. In that case the current interpretation of the test and estimation of the hydraulic diffusivity is no longer appropriate. Kuntz and Lavallee (2001) discuss the anomalous behaviour and propose a non-Darcian model as a more appropriate physical description. We present an alternative Darcian explanation and theory that retrieves the earlier advantages of the simple sorptivity test in providing parametric information about the material's hydraulic properties and allowing simple predictive formulae for the wetting profile to be generated.