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Differential equation is the most basic mathematical theory and method to study the movement, evolution and change of things, objects and phenomena in natural sciences and social sciences.
This chapter presents the basics of the mapping techniques most often applied in practice, the most basic mathematical theories of stochastic simulation using Monte Carlo techniques, and the basic concept of the integrated fracture system characterization at site scales, as this knowledge is fundamental for developing and applying the discrete element methods (DEM) approach for rock engineering.
The chemical master equation (CME) is the most basic mathematical description of stochastic biomolecular reaction networks [ 1, 2].
The most basic mathematical model of the competition between populations was constructed by Alfred J. Lotka and Vito Volterra in 1925 and 1926 independently [ 13].
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He then argues that dreams, contrary to Descartes' own claims, should lead us to doubt even our most basic beliefs about mathematical truths.
Justification logic originated as part of a successful project to provide a constructive semantics for intuitionistic logic justification terms abstracted away all but the most basic features of mathematical proofs.
Thus number representation is the most basic level of numerical cognition upon which all other (more complex) numerical and mathematical thinking builds.
Among these interactions, the predator-prey interaction is the most basic one, and plenty of mathematical models have been established since the pioneering work by Lotka and Volterra [2, 3].
Indeed, these advances have established that the modern (quantitative) and traditional (descriptive) approaches are, in fact, easily interchangeable at the level of their most basic elements, with a little mathematical manipulation.
Mathematical modeling, perhaps the most basic tool in systems engineering, is a technique encountered in any branch of science that has become sufficiently quantitative.
In most cases, the classification is based on basic mathematical operations.
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