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The mathematical equations are derived based on geomechanics equilibrium and multiphase mass conversation.
The mathematical equations are derived in terms of symmetric tensors simplifying the constitutive relations.
Its mathematical equations are established and the numerical results both in the absence and in the presence of magnets are compared.
The resulting closed-form mathematical equations are converted to the commonly required flood frequency distributions for use in urban stormwater management studies.
Nomenclature is presented to identify different configurations, mathematical equations are provided that accurately model the force deflection relationships, and a pneumatic valve positioner application is demonstrated.
Stated boldly and bluntly, tautologies, contradictions and mathematical propositions (i.e., mathematical equations) are neither true nor false we say that they are true or false, but in doing so we use the words 'true' and 'false' in very different senses from the sense in which a contingent proposition is true or false.
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His mathematical equations were used, for instance, in forecasting supply and demand for vital materials like steel, or allocating scarce resources.
UNLESS you are like the character played by Matt Damon in "Good Will Hunting," solving complex mathematical equations is no walk in the park.
Thus, the matching of an automaton, or computer, with a real physical environment could result in the anticipation of the future, if certain mathematical equations were derived that minimized prediction error.
The mathematical equations were solved adapting an object oriented "Modelica language" framework in Dymola software tool.
Two sets of mathematical equations were derived from this model and tested.
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