4,028 research outputs found

    Enzyme activity in terrestrial soil in relation to exploration of the Martian surface

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    Urease activity in soil is persistent for long periods under low water, low temperature, and sterile regimes, and it was suggested that some form of enzyme-protective mechanism exists in soil. Dublin soil was extracted by sonication in water followed by adding a mixture of salts. Urease activity is associated with the organo-mineral complex thus obtained and is resistant to the activities of proteolytic enzymes. Clay free soil organic matter prepared subsequently by filtration also exhibits urease activity which is resistant to proteolysis. Models consisting of enzymes with bentonite and lignin were found to mimic this resistance to proteolysis. A model system is presented which suggests both the origin and location of soil ureases and a reason for their persistence in nature

    An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps

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    We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials defining the prolongation of the three parallel sides of a hexagon. On the vertices of such a hexagon lie the indeterminacy points of the KHK map. This result is obtained analysing the structure of the singular fibres of the known invariant. We apply this construction to several examples, and we prove that a similar result holds true for a case outside the hypotheses of the main theorem, leading us to conjecture that further extensions are possible.Comment: 30 pages, 7 figure

    Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps

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    In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and Discrete Darboux Polynomials and relies on the use of symbolic algebra tools. Given sufficient computing power, all rational preserved integrals can be found. We show, in two examples, how to use this method to detect and determine preserved measures and integrals of the considered rational maps.Comment: 8 pages, 1 Figur
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