Trees, bialgebras and intrinsic numerical algorithms

Preliminary work about intrinsic numerical integrators evolving on groups is described. Fix a finite dimensional Lie group G; let g denote its Lie algebra, and let Y(sub 1),...,Y(sub N) denote a basis of g. A class of numerical algorithms is presented that approximate solutions to differential equations evolving on G of the form: dot-x(t) = F(x(t)), x(0) = p is an element of G. The algorithms depend upon constants c(sub i) and c(sub ij), for i = 1,...,k and j is less than i. The algorithms have the property that if the algorithm starts on the group, then it remains on the group. In addition, they also have the property that if G is the abelian group R(N), then the algorithm becomes the classical Runge-Kutta algorithm. The Cayley algebra generated by labeled, ordered trees is used to generate the equations that the coefficients c(sub i) and c(sub ij) must satisfy in order for the algorithm to yield an rth order numerical integrator and to analyze the resulting algorithms

Computations involving differential operators and their actions on functions

The algorithms derived by Grossmann and Larson (1989) are further developed for rewriting expressions involving differential operators. The differential operators involved arise in the local analysis of nonlinear dynamical systems. These algorithms are extended in two different directions: the algorithms are generalized so that they apply to differential operators on groups and the data structures and algorithms are developed to compute symbolically the action of differential operators on functions. Both of these generalizations are needed for applications

U.S. Energy Policy and the Presumption of Market Failure

The article presents an analysis of U.S. energy policy, focusing on the question of whether it is able to correct market failures in terms of alternative energy sources. The question of whether any such market failures exist is said to be a separate question, and an argument is presented that governments generally are not competent to fix such problems even when they do exist. A discussion of U.S. energy policy from the early 1970s to the 21st century is presented. Programs designed to encourage technological innovations such as biofeuls, nuclear fusion, and electric vehicles are analyzed

The Apollo Fallacy and its Effect on U.S. Energy Policy

US Policy makers have made continual references to the Apollo Program as a model for development of alternative energy technologies. This model, however, is inappropriate for energy policy, and its use is termed the Apollo fallacy. The goal of the Apollo Program was the demonstration of engineering prowess while any alternative energy technology must succeed in the marketplace. Several Apollo-like energy programs have been tried and all have failed at high cost. It is argued that the use of Apollo has political benefits but that it is detrimental to the adoption of potentially effective energy policies

Determinants of share price movements in emerging equity markets: some evidence from America\u27s past

Emerging equity markets are plagued by poor information, which is a barrier to outside shareholder participation. This paper examines the determinants of share prices of two United States companies over a 14-year period during the late 19th century, when America had an emerging equity market. These two companies withheld all information on profits and assets until the end of the period, yet traded regularly. Overall, the evidence suggests that outside investors received sufficient compensation for their ignorance, and that these outsiders set the market price. An event study shows that when information about company assets was revealed, market returns were significantly changed

If Ethanol is the Answer, What is the Question

Since 2005, in the face of rising oil and gasoline prices, many Americans have looked to plant-based fuels, particularly ethanol, as the answer to our energy dilemmas. Section III examines the issues connected specifically to ethanol, how market forces as well as government subsidies have worked to make corn-based ethanol economically viable at times, why that viability has been lost in recent months even with subsidies, and further, why ethanol from corn on the scale the legislation demands is impractical. Clearly it would be technically possible to produce the mandated 15 billion gallons of ethanol, and distilling capacity will nearly reach that level shortly, but the economics of corn-derived ethanol suggest that, absent massive subsidies or coercion, this effort will not be economically sound for producers or consumers. (Indeed, high capital costs are an issue for the mandated innovation of cellulosic ethanol, and part of the reason that technology is not yet considered economically viable.) ... The federal subsidy is still 51 cents per gallon, equivalent to $ 1.43 per bushel (assuming 2.8 gallons per bushel), although as noted earlier there may be state subsidies as well. Major meat producing firms as well as users of corn-based products such as high fructose corn syrup, have noted the impacts on their businesses and in turn lobbied against fulfillment of the larger corn ethanol mandates

The Dynamics of the Hungarian Hyperinflation, 1945-6: A New Perspective

From late 1945 through the middle of 1946, Hungary experienced the most gigantic inflation of modern history. But in August 1946, the astronomical price increases stopped, and lasting price stability followed. Indeed, the contrast is so dramatic that it is viewed by some as an economic miracle surpassing even the post-war German Wirschaftswunder. On the surface, the Hungarian hyperinflation, which witnessed a depreciation of the currency unit, the pengo of about 10-27, seems a kind of madness that raises two interlinked questions: First, how could such a fantastic destruction in the value of a currency take place, and second, what possible motive could anyone have for creating this inflation or at least for allowing it to happen

When is Command-and-Control Efficient? Institutions, Technology and the Comparative Efficiency of Alternative Regulatory Regimes for Environmental Protection

The nominal efficiency of a regulatory regime is determined by comparing its social costs and benefits; the regime is nominally efficient if it produces benefits in excess of its costs. Thus, a regulatory regime can be at once nominally efficient and relatively inefficient. A regulatory regime that is nominally efficient in the early days of pollution-control efforts, when increments of environmental quality are relatively cheap, may (but will not necessarily) grow less efficient over time - producing less return on each dollar invested - as increments of environmental quality grow increasingly expensive. A regulatory regime that is more efficient in one institutional and technological setting may be less efficient (or inefficient) in another. In reality, however, this outcome will occur only under certain conditions; specifically, when the regulatory regime as a whole is more efficient. The discussion begins, for the sake of comparison, with a brief review of the conventional story of the Clean Air Act\u27s regulatory regime. In addition, in 1987 the EPA wrapped up a small-scale and temporary but highly successful experiment in tradable rights to lead-content in gasoline. Like other institutions in society, those of environmental protection (including the regulatory regime itself) tend to evolve slowly, incrementally, and inconsistently. In large measure, the choice of regulatory regime depends on the goals and concerns of policy-makers