On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

The decomposition of starch grains in soils: implications for archaeological residue analyses

Recent research involving starch grains recovered from archaeological contexts has highlighted the need for a review of the mechanisms and consequences of starch degradation specifically relevant to archaeology. This paper presents a review of the plant physiological and soil biochemical literature pertinent to the archaeological investigation of starch grains found as residues on artefacts and in archaeological sediments. Preservative and destructive factors affecting starch survival, including enzymes, clays, metals and soil properties, as well as differential degradation of starches of varying sizes and amylose content, were considered. The synthesis and character of chloroplast-formed 'transitory' starch grains, and the differentiation of these from 'storage' starches formed in tubers and seeds were also addressed. Findings of the review include the higher susceptibility of small starch grains to biotic degradation, and that protective mechanisms are provided to starch by both soil aggregates and artefact surfaces. These findings suggest that current reasoning which equates higher numbers of starch grains on an artefact than in associated sediments with the use of the artefact for processing starchy plants needs to be reconsidered. It is argued that an increased understanding of starch decomposition processes is necessary to accurately reconstruct both archaeological activities involving starchy plants and environmental change investigated through starch analysis. (C) 2004 Elsevier Ltd. All rights reserved.

Decomposition of nitrogen-15 labeled hoop pine harvest residues in subtropical Australia

Information on decomposition of harvest residues may assist in the maintenance of soil fertility in second rotation (2R) hoop pine plantations (Araucaria cunninghamii Aiton ex A. Cunn.) of subtropical Australia. The experiment was undertaken to determine the dynamics of residue decomposition and fate of residue-derived N. We used N-15-labeled hoop pine foliage, branch, and stem material in microplots, over a 30-mo period following harvesting. We examined the decomposition of each component both singly and combined, and used C-13 cross-polarization and magic-angle spinning nuclear magnetic resonance (C-13 CPMAS NMR) to chart C transformations in decomposing foliage. Residue-derived N-15 was immobilized in the 0- to 5-cm soil layer, with approximately 40% N-15 recovery in the soil from the combined residues by the end of the 30-mo period. Total recovery of N-15 in residues and soil varied between 60 and 80% for the combined-residue microplots, with 20 to 40% of the residue N-15 apparently lost. When residues were combined within microplots the rate of foliage decomposition decreased by 30% while the rate of branch and stem decomposition increased by 50 and 40% compared with rates for these components when decomposed separately. Residue decomposition studies should include a combined-residue treatment. Based on C-15 CPMAS NMR spectra for decomposing foliage, we obtained good correlations for methoxyl C, aryl C, carbohydrate C and phenolic C with residue mass, N-15 enrichment, and total N. The ratio of carbohydrate C to methoxyl C may be useful as an indicator of harvest residue decomposition in hoop pine plantations.

Synthesis and characterization of turbostratic carbons prepared by catalytic chemical vapour decomposition of acetylene

The turbostratic mesoporous carbon blacks were prepared by catalytic chemical vapour decomposition (CCVD) of acetylene using Ni/MgO catalysts prepared by co-precipitation. The relationship between deposition conditions and the nanostructures of resultant carbon black materials was investigated. It was found that the turbostratic and textural structures of carbon blacks are dependent on the deposition temperature and nickel catalyst loading. Higher deposition temperature increases the carbon crystallite unit volume V-nano and reduces the surface area of carbon samples. Moreover, a smaller V-nano is produced by a higher Ni loading at the same deposition temperature. In addition of the pore structure and the active metal surface area of the catalyst, the graphitic degree or electronic conductivity of the carbon support is also a key issue to the activity of the supported catalyst. V-nano is a very useful parameter to describe the effect of the crystalline structure of carbon blacks on the reactivity of carbon blacks in oxygen-carbon reaction and the catalytic activity of carbon-supported catalyst in ammonia decomposition semi-quantitatively. (C) 2006 Elsevier B.V. All rights reserved.

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.

On Hamilton cycle decomposition of 6-regular circulant graphs

The circulant graph Sn, where S ⊆ Zn \ {0}, has vertex set Zn and edge set {{x, x + s}|x ∈ Zn, s ∈ S}. It is shown that there is a Hamilton cycle decomposition of every 6-regular circulant graph Sn in which S has an element of order n.

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.