In the 18th century the most fertile equation of this kind was the vibrating string equation, derived by the French mathematician Jean Le Rond d'Alembert in 1747 and relating to rates of change of quantities arising in the vibration of a taut violin string (see Musical origins).
Uncertainty relations can be considered as statements about the spreads of the probability distributions of the several physical quantities arising from the same state.
Usually this method gives conditions on the averaged quantities arising in (4) whereas a Lyapunov method would give conditions on the sign of the same quantities.
Uncertainties in these quantities arising from the model form error are shown to be more significant than uncertainties arising from the model constant uncertainty.
The paper analyses equilibrium fares and quantities arising from collusion and competition on price (Bertrand) and quantity (Cournot), when the firms produce symmetrically differentiable services and have identical cost and goal functions.
Furthermore, questions about Aristotle's views about the nature of some of the species in quantity arise.
Here, the quantity arises as a natural scaling length for quantum transport where ε F is the Fermi energy in the source contact and m* is the effective mass of the charge carriers.
More precisely, using the notation of Figure 1, the three-population test statistic f3(C; A′, B′) estimates the sum of two directly competing terms: − αβF2(A″, B″), the negative quantity arising from admixture that we wish to detect, and α F2(A″, A) + β F2(B″, B) + F2(C, C″), a positive quantity from the "off-tree" drift branches.
Those calculations are made on a simplified model which takes into account the characteristic quantities which arise from an accurate asymptotic analysis of the nonlinear Schrödinger Poisson system.
Moreover, supergravity theories are more likely to be free from various inconsistent or "nonphysical" infinite quantities that usually arise in calculations involving quantum theories of gravity.
