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A third consequence of switching to tetrahedral mensuration is Fuller's review of the standard "dimension" concept. Whereas "height, width and depth" have been promulgated as three distinct dimensions within the Euclidean context, each with its own independence, Fuller considered the tetrahedron a minimal starting point for spatial cognition.
Buckminster Fuller found that the cuboctahedron is the only polyhedron in which the distance between its center to the vertex is the same as the distance between its edges. In other words, it has the same length vectors in three-dimensional space, known as vector equilibrium . [ 8 ]
The first term in the RHS describes short-run impact of change in on , the second term explains long-run gravitation towards the equilibrium relationship between the variables, and the third term reflects random shocks that the system receives (e.g. shocks of consumer confidence that affect consumption). To see how the model works, consider two ...
Comparative statics is a tool of analysis in microeconomics (including general equilibrium analysis) and macroeconomics. Comparative statics was formalized by John R. Hicks (1939) and Paul A. Samuelson (1947) (Kehoe, 1987, p. 517) but was presented graphically from at least the 1870s.
The master equation exhibits detailed balance if each of the terms of the summation disappears separately at equilibrium—i.e. if, for all states k and ℓ having equilibrium probabilities and , =. These symmetry relations were proved on the basis of the time reversibility of microscopic dynamics ( microscopic reversibility ) as Onsager ...
Classical entropy is defined for a system in its own internal state of thermodynamic equilibrium, which is defined by state variables, with no non-zero fluxes, so that flux variables do not appear as state variables. But for a strongly non-equilibrium system, during a process, the state variables must include non-zero flux variables.
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
Cointegration is a statistical property of a collection (X 1, X 2, ..., X k) of time series variables. First, all of the series must be integrated of order d.Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated.