Least effort, principle

Second, considerable effort has been expended to create 13C NMR reference data systems that will enable spectroscopists to extract structural information from their experimental results by comparing them with documented spectra of related compounds data banks stored in computers have been compiled and are accessible for substructure searches (510-519). The advent of these facilities means that SCS evaluations have been-at least in principle-outstripped in an important field of their application, namely in their use for establishing molecular constitution and assigning signals. In cases of doubt one should rely... 

The principle of least effort.—The principle of least action underlies all these rules, and it is of great service, and of wide application. P. L. M. Maupertius foreshadowed the idea in 1747 All natural changes take place in such a way that the existing state of things suffers the least possible change or, as W. D. Bancroft (1911) expressed it A system tends to change so as to minimize the effects of an external disturbing force. This has been called the principle of the... 

The idea that laws of nature should satisfy a principle of simplicity goes back at least to the Greek philosophers [436], The anthropomorphic concept that the engineering skill of a supreme creator should result in rules of least effort or of most efficient use of resources leads directly to principles characterized by mathematical extrema. For example, Aristotle (De Caelo) concluded that planetary orbits must be perfect circles, because geometrical perfection is embodied in these curves ... of lines that return upon themselves the line which bounds the circle is the shortest. That movement is swiftest which follows the shortest line . Hero of Alexandria ( Catoptrics) proved perhaps the first scientific minimum principle, showing that the path of a reflected ray of light is shortest if the angles of incidence and reflection are equal. 

Titration curves have the virtue of simplicity, while thermodynamic models have, at least in principle, greater capacity to be adapted to changing process conditions. In practice, the amount of effort required to develop a thermodynamic model based on real chemical species and physical properties is usually prohibitive. Semiempirical models based on notional species and concentration equilibria can be developed quite readily (Gustafsson and Waller, 1983). However, these have extrapolation properties identical to the original titration curves. In both cases the pH of a mixture of components can be predicted accurately, subject to the assumptions that mixing two solutions of equal pH results in a solution with the same pH and the pH measurement is ideal (Gustafsson, 1982 Luyben, 1990). The validity of this assumption is discussed in Walsh (1993). 

G. K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, 1949. 

There is already a large number of different conductive polymers. A typical monomer is 3-methylthiophene, which can be electrically polymerized to a polymer coupled by the 2-and 5-positions of the monomer. In the oxidized form, usually called doped , the chains contain positive charges at about every fourth monomer unit. In order to keep the polymer layer electrically neutral, also counter anions should be present in the polymer matrix. It is analytically interesting that the diffusion rate of these counter anions controls the rate of oxidation and reduction of the polymer, and the diffusion rate depends on the size, degree of solvation etc. of the anion. Hence, by a suitable choice of the polymer, it should be possible, at least in principle, to tailor-make sensors for different anions. In addition, it has been shownthat electrically neutral polymers can be incorporated from the solution into the polymer matrix during the polymerization process. This of course extends enormously the possibilities for developing selective sensors without undue efforts to synthesize new electrically polymerizable monomers. 

Chemical analysis of composite systems is often severely restricted by the invalidity of the co-existence principle (although there are a few cases known in which estimations are made possible just because of the occurrence of chemical induction). Therefore, many efforts have been directed at exploring at least qualitatively the source of errors caused by induced reactions. That is why our present knowledge about such reactions is rather qualitative in nature. 

Yet it is on the issues of reproducibility and instrumentation that Occult Chemistry failed to persuade, at least outside of Theosophical circles and the small group of scientists in recent years who have been willing to work entirely at the level of theory. Besant and Leadbeater could move beyond older models of science, which based themselves upon deductions from revealed principles (alchemical or scientific deductions from the writings of the Hermetic tradition, for instance, or from the revelations of H. P. Blavatsky), by turning to experimentation. Not surprisingly, their form of experimentation did not admit of reproducibility. In spite of efforts by Stephen Phillips to conduct blind trials using a Buddhist clairvoyant to confirm Besant and Lead-beater s micro-psi visions (1996,48), direct experience is neither convincingly verifiable nor falsifiable. 

Optimization pervades the fields of science, engineering, and business. In physics, many different optimal principles have been enunciated, describing natural phenomena in the fields of optics and classical mechanics. The field of statistics treats various principles termed maximum likelihood, minimum loss, and least squares, and business makes use of maximum profit, minimum cost, maximum use of resources, minimum effort, in its efforts to increase profits. A typical engineering problem can be posed as follows A process can be represented by some equations or perhaps solely by experimental data. You have a single performance criterion in mind such as minimum cost. The goal of optimization is to find the values of the variables in the process that yield the best value of the performance criterion. A trade-off usually exists between capital and operating costs. The described factors—process or model and the performance criterion—constitute the optimization problem. ... 

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