The result in this paper undercuts the major applications of the Kaldor-Hicks reasoning in the standard Chicago school (wealth maximization) of law and economics, cost–benefit analysis, policy analysis, and related parts of applied welfare economics.
This a reprint of an applied math paper connecting the notion of arbitrage and the Lagrange multipliers of mathematical economics. The paper has a simple application showing that a circular gear train (all in the same plane) with an odd number of gears is rigid (cannot move) like the graphic to the left.
In financial arithmetic and in the appraisal literature, it has been noticed that the basic formulas occur in pairs, one being the reciprocal of the other. This Part II of the series-parallel duality post shows that these reciprocal formulas are an example of the SP duality normally associated with electrical circuit theory.
This post describes the duality between the usual (series) addition and the dual parallel addition. This duality is normally considered in electrical circuit theory and combinatorics, but it has a much wider applications. In Part I of this post, the focus is on developing series-parallel dual formulas—in contrast to the usual focus on formulas using only the series sum.
Double-entry bookkeeping illustrates one of the most astonishing examples of intellectual insulation between disciplines—the very opposite of intellectual trespassing.
Although double-entry bookkeeping (DEB) has been used in the business world for 5 centuries, the mathematical formulation of the double entry method is almost completely unknown. The correct mathematical formulation allows the generalization from the value scalars of ordinary DEB to multi-dimensional accounting using vectors–which is the topic of this post.