The Hungarian mathematician Csiszar, winner of Shannon prize, had also proved that for a group of information which is not contradictory, there exist unique entropy maximization models and their mathematical forms are exponential functions.
If we regard the initial allocation of emission permits as an uncertain problem, according to entropy maximization theorem, its probability distribution is the one which has maximum entropy and the mathematical forms are exponential functions.
The response of the wave properties of a particle to an external force follows a basic law of quantum mechanics that, in its mathematical form, is known as the Schrödinger equation.
A mathematical form is found for relating one parameter, such as time, to another.
Rice (1995) analyses this process and argues that the mathematical form is uniquely determined by its memoryless property.
As in the classical theory of plates (non-porous), the solutions are approximate and their mathematical form is chosen.
The models are parametric with parameters explicitly determined by the underlying physical mechanisms and are canonical, i.e., their mathematical form is independent of the physical environment.
Still, we let Φ i denote the flux-sum of metabolite i, and its mathematical form is given by Φ i = 0.5 (mathop sum nolimits_{j} left| {S_{ij} v_{j} } right|).
This constitutive model due to high performance in constitutive modeling and simplicity of its mathematical form is applied to pressurized thick-walled cylinders in order to find a closed-form analytical solution for their analysis.
There is an ongoing scholarly debate about whether Kant's conception of mathematical form is a direct expression of the narrow-mindedness of his logical theory, or instead a direct expression of the striking originality of his philosophy of mathematics (Parsons 1983, Friedman 1992, Hanna 2002, Shabel 2003, Hanna 2006b, ch. 6, Shabel 2006).
