By Alfonsas Juška
The major predicament of the e-book is research of organic strategies, the ultimate degree of that is mathematical modeling, i.e. quantitative presentation of the methods in rigorous mathematical phrases. it truly is detailed for non-mathematicians. Mathematical versions could be in comparison with experimental information hence verifying the validity of the versions and eventually of the preliminary assumptions and verbal descriptions of the tactics. The versions (usually within the type of mathematical equations) are completed painlessly through the schemes summarising verbal description of what's identified in regards to the methods. to unravel the equations software program is used. The step by step research ends up in particularly subtle types a few of them being unique. The ebook is helping the reader to enhance extra normal method of the issues. it can be valuable for skilled readers as well.
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Extra info for Analysis of biological processes: Verbal description, schemes, and mathematical models
To achieve experimental conditions as close as possible to those inside the hive, the accumulation of bees was determined by weighing the cage with them on it. The cage was suspended from an arm of a balance and let down above the brood chamber through a hole in the ceiling of the hive. It was possible to remove the queen from the cage without taking the latter from the hive. The cage was left over the brood chamber during the experiment, and the access to it for worker bees was not disturbed. Before the experiments, the cage had been kept in the same bee colony with the same laying queen.
Similar approach is applicable in modeling more sophisticated processes as schematized here, in Chap. 1)). The progress of the transition provides information on its duration. The rising curve of the process (see Fig. e. z' = a a −1 μ (exp( −μt ) − exp( −aμt ) ). 15) The random value t may be considered as the duration of the transition. The mean duration θ is ∞ θ = ∫ z ' tdt 0 or ∞ θ= ∫ 0 at a −1 μ (exp( −μt ) − exp( −aμt ) )dt = a +1 . e. the duration of the two-step transition is determined by that of the slower step (see Fig.
1007/97894-017-7373-7_4) contains supplementary material, which is available to authorized users. © Springer Science+Business Media Dordrecht 2015 A. 1007/978-94-017-7373-7_4 35 36 4 Transitions Y Y X X Y X X Y rate constant X x Y µ ⎯⎯→ y quantities dx = −μx dt states Fig. 1 Cartoon depicting volatilization of active molecules. Top, schematic representation of the molecules dispersed on the surface (state X) and those unbound from the surface (state Y). 2 Transitions As shown in Chap. 1) x being the changing quantity of the object, μ (μ > 0), the relative rate of the change, the “–” sign corresponds to the rate of change being negative.
Analysis of biological processes: Verbal description, schemes, and mathematical models by Alfonsas Juška