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Fractional calculus and fractional differential equations are popular in describing anomalous diffusion, ground water flow and transport, and the price fluctuation in finance, etc.
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Assuming a simple one-dimensional thermal diffusion, the ground temperature variation ΔT (z, t) is expressed as: where Δ T0 is the temperature variation amplitude at the surface, ω = 2π yr−1 is the angular frequency, and where κ is the thermal diffusivity.
Figure 2 shows T1 lipase crystal obtained by counter diffusion method (ground and space grown).
However, the major drawback of this ether is its easy diffusion in the ground water, its slow biological breakdown and its unpleasant odour.
The varying potential time behavior after a bulk concentration change has been explained by a different participation of the magnesium and calcium ions on the ground diffusion layer model (DLM).
As a result of weathering, diffusion into the ground water and adsorption by the peat, concentrations of As, Co, Cu, Fe, Hg, Mn, Ni, Zn, and S, as well as electrical conductivity were expected to be greater in the peat overlying black schist than in peat overlying felsic rocks and this difference was assumed to be strong in the bottom layers and to weaken near the surface.
In fact, the crucial role of spurring innovation played by cooperation activities in the process of knowledge creation and diffusion is well grounded in the economic literature, which emphasises, in particular, the relevance of relationships between research institutes and private companies in science-based sectors.
They concluded that the obtained stressing rate was consistent with magma intrusion into a vertical dyke rather than ground water diffusion.
Using that capacitary positive improving property and two new inequalities for generalized Ornstein Uhlenbeck generators, we show the essential self-adjointness of the ground state diffusion generator Lφ=L+2Γ/φ associated with two dimensional Euclidean quantum fields.
The concentration of pollutants in the atmosphere is determined by their transport, or mean velocity of movement through the atmosphere, their diffusion, chemical transformation, and ground deposition.
4 A network of diffusion tubes in the ground area showed no evidence of fumigation by sulphur dioxide, the predominant volcanic gas in the ash plume, in the last 3 weeks of the eruption (Personal communication: Peter Baxter, 2010).
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