Decomposition of complete graphs into 5-cubes

Necessary conditions for the complete graph on n vertices to have a decomposition into 5-cubes are that 5 divides it - 1 and 80 divides it (it - 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for it even, thus completing the spectrum problem for the 5-cube and lending further weight to a long-standing conjecture of Kotzig. (c) 2005 Wiley Periodicals, Inc.

Effects of litter and fine root composition on their decomposition in a Rhodic Paleustalf under different land uses

Plant litter and fine roots are important in maintaining soil organic carbon (C) levels as well as for nutrient cycling. The decomposition of surface-placed litter and fine roots of wheat ( Triticum aestivum ), lucerne ( Medicago sativa ), buffel grass ( Cenchrus ciliaris ), and mulga ( Acacia aneura ), placed at 10-cm and 30-cm depths, was studied in the field in a Rhodic Paleustalf. After 2 years, = 60% of mulga roots and twigs remained undecomposed. The rate of decomposition varied from 4.2 year -1 for wheat roots to 0.22 year -1 for mulga twigs, which was significantly correlated with the lignin concentration of both tops and roots. Aryl+O-aryl C concentration, as measured by 13 C nuclear magnetic resonance spectroscopy, was also significantly correlated with the decomposition parameters, although with a lower R 2 value than the lignin concentration. Thus, lignin concentration provides a good predictor of litter and fine root decomposition in the field.

Synthesis and structure characterization of chromium oxide prepared by solid thermal decomposition reaction

Mesoporous chromium oxide (Cr2O3) nanocrystals were first synthesized by the thermal decomposition reaction of Cr(NO3)(3)(circle)9H(2)O using citric acid monohydrate (CA) as the mesoporous template agent. The texture and chemistry of chromium oxide nanocrystals were characterized by N-2 adsorption-desorption isotherms, FTIR, X-ray diffraction (XRD), UV-vis, and thermoanalytical methods. It was shown that the hydrate water and CA are the crucial factors in influencing the formation of mesoporous Cr2O3 nanocrystals in the mixture system. The decomposition of CA results in the formation of a mesoporous structure with wormlike pores. The hydrate water of the mixture provides surface hydroxyls that act as binders, making the nanocrystals aggregate. The pore structures and phases of chromium oxide are affected by the ratio of precursor-to-CA, thermal temperature, and time.