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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 ]
Fuller, R. Buckminster (1975). "Vector Equilibrium". Everything I Know Sessions. Philadelphia. Kenner, Hugh (1976). Geodesic Math and How to Use It. University of California Press. ISBN 978-0520029248. Verheyen, H. F. (1989). "The complete set of Jitterbug transformers and the analysis of their motion". Computers and Mathematics with Applications.
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 ...
The structural equilibrium model can be solved using the GE package in R. Below, we illustrate the above structural equilibrium model through a linear programming example, [16] with the following assumptions: (1) There are 3 types of primary factors, with quantities given by = (,,). These 3 primary factors can be used to produce a type of product.
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.