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Mathematical Formalism (mathematical + formalism)
Selected AbstractsMathematics in Economics: An Austrian Methodological CritiquePHILOSOPHICAL INVESTIGATIONS, Issue 1 2010Robert Wutscher Even the briefest and most superficial perusal of leading mainstream economics journals will attest to the degree that mathematical formalism has captured the economics profession. Whereas up to the early 20th century virtually all of the output of the dismal scientists was in the literary format, by the early 21st century this is not at all any longer the case. Mathematical formalism is supposed to serve economics, and yet now true economic insight has been crowded out by the math. If mainstream neoclassical economics is to come back to its proper path, a far less central role for mathematical economics, statistics and econometrics will have to be fashioned. [source] Using symbolic computing in building probabilistic models for atomsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2006Silviu Guiasu Abstract This article shows how symbolic computing and the mathematical formalism induced by maximizing entropy and minimizing the mean deviation from statistical equilibrium may be effectively applied to obtaining probabilistic models for the structure of atoms, using trial wave functions compatible with an average shell picture of the atom. The objective is not only to recover the experimental value of the ground state mean energy of the atom, but rather to better approximate the unknown parameters of these trial functions and to calculate both correlations between electrons and the amount of interdependence among different subsets of electrons of the atoms. The examples and numerical results refer to the hydrogen, helium, lithium, and beryllium atoms. The main computer programs, using the symbolic computing software MATHEMATICA, are also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Digitization and geo-referencing of botanical distribution mapsJOURNAL OF BIOGEOGRAPHY, Issue 7 2002Christian A. Schölzel Aim In many fields of research, valuable information is stored in atlases and maps which are only available as printed media. Scientists who are interested in computational analysis often seek to digitize the data to make it accessible for numerical calculations. In this paper, an approach using the example of digitizing distribution maps taken from plant-taxonomic atlases is described. For this purpose, a software tool has been built for application in the Sonderforschungsbereich 350 `Interactions between and Modelling of Continental Geosystems' at the University of Bonn. Its functionality has to be simple in use and capable of transforming fields drawn on geographical maps into grid data even where the type of map projection is unknown. Location As an example, plant distributions over Europe and Asia have been digitized. Methods To achieve this aim through an objective statistical analysis, the local deterministic approximation has been used for geo-referencing. Results For this reason the development of a new software tool was required. Although there is a large market for related software from Geographical Information Systems (GIS), none of the available GIS-programs appeared to be capable of geo-referencing maps with unidentified projections. Rather than to give a product comparison, this paper aims on the methodology and mathematical formalism. Main conclusions The developed algorithm is a handy tool to capture data from maps based on obscure projections. Valuable historical maps, which are problematic for standard GIS-programs, can be made accessible for modern research work. [source] Mathematics in Economics: An Austrian Methodological CritiquePHILOSOPHICAL INVESTIGATIONS, Issue 1 2010Robert Wutscher Even the briefest and most superficial perusal of leading mainstream economics journals will attest to the degree that mathematical formalism has captured the economics profession. Whereas up to the early 20th century virtually all of the output of the dismal scientists was in the literary format, by the early 21st century this is not at all any longer the case. Mathematical formalism is supposed to serve economics, and yet now true economic insight has been crowded out by the math. If mainstream neoclassical economics is to come back to its proper path, a far less central role for mathematical economics, statistics and econometrics will have to be fashioned. [source] Complex 1H,13C-NMR relaxation and computer simulation study of side-chain dynamics in solid polylysineBIOPOLYMERS, Issue 3 2005Alexey Krushelnitsky Abstract The side-chain dynamics of solid polylysine at various hydration levels was studied by means of proton spin,lattice relaxation times measurements in the laboratory and tilted (off-resonance) rotating frames at several temperatures as well as Monte Carlo computer simulations. These data were analyzed together with recently measured carbon relaxation data (A. Krushelnitsky, D. Faizullin, and D. Reichert, Biopolymers, 2004, Vol. 73, pp. 1,15). The analysis of the whole set of data performed within the frame of the model-free approach led us to a conclusion about three types of the side-chain motion. The first motion consists of low amplitude rotations of dihedral angles of polylysine side chains on the nanosecond timescale. The second motion is cis,trans conformational transitions of the side chains with correlation times in the microsecond range for dry polylysine. The third motion is a diffusion of dilating defects described in (W. Nusser, R. Kimmich, and F. Winter, Journal of Physical Chemistry, 1988, Vol. 92, pp. 6808,6814). This diffusion causes almost no reorientation of chemical bonds but leads to a sliding motion of side chains with respect to each other in the nanosecond timescale. This work evidently demonstrates the advantages of the simultaneous quantitative analysis of data obtained from different experiments within the frame of the same mathematical formalism, providing for the detailed description of the nature and geometry of the internal molecular dynamics. © 2005 Wiley Periodicals, Inc. Biopolymers 78: 129,139, 2005 This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com [source] | |||||||||||||