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rigorous theory and numerical approximations
, 2008
"... We revisit existence and stability of twopulse solutions in the fifthorder Korteweg–de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations of pulses and prove convergence of iterations in a neighborhoo ..."
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We revisit existence and stability of twopulse solutions in the fifthorder Korteweg–de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations of pulses and prove convergence of iterations in a neighborhood of twopulse solutions. Second, we prove structural stability of embedded eigenvalues of negative Krein signature in a linearized KdV equation. Combined with stability analysis in Pontryagin spaces, this result completes the proof of spectral stability of the corresponding twopulse solutions. Eigenvalues of the linearized problem are approximated numerically in exponentially weighted spaces where embedded eigenvalues are isolated from the continuous spectrum. Approximations of eigenvalues and full numerical simulations of the fifthorder KdV equation confirm stability of twopulse solutions related to the minima of the effective interaction potential and instability of twopulse solutions related to the maxima points. 1
A Rigorous Theory of Infinite Limits
, 2000
"... We give rigorous definitions and theorems supporting the use of symbols for (various kinds of) infinity and unde nedness in calculations involving limits. Such calculations are often made on paper and blackboards, but are usually barred admission to textbooks on the grounds of insufficient pedigree. ..."
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We give rigorous definitions and theorems supporting the use of symbols for (various kinds of) infinity and unde nedness in calculations involving limits. Such calculations are often made on paper and blackboards, but are usually barred admission to textbooks on the grounds of insufficient pedigree
Rigorous Theory Of The Boltzmann Equation In The Lorentz Gas
, 1972
"... : The Boltzmann limit conjecture of Grad is discussed in general and proved for the Lorentz gas case (where the Boltzmann equation is linear). This is a reprint of an unpublished preprint of 1972, with one footnote added, one postscript (to quote the Lanford theorem), and improved with language edit ..."
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Cited by 31 (0 self)
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: The Boltzmann limit conjecture of Grad is discussed in general and proved for the Lorentz gas case (where the Boltzmann equation is linear). This is a reprint of an unpublished preprint of 1972, with one footnote added, one postscript (to quote the Lanford theorem), and improved with language editing. I reprint it in this form to make it accessible, as it has been quoted by other authors in later papers. The original preprint was commissioned for a book that eventually was not published. 1.  Introduction The Boltzmann equation is an approximation to the "true" evolution equation: this is due to the fact that in its derivation the following assumptions are made [1,2]: 1) only binary collisions are considered 2) "Molecular chaos" is assumed at all times: i.e. the high order correlation functions can be expressed in terms of the oneparticle distribution as: f(r 1 v 1 ; r 2 v 2 ; : : : ; r n v n ; t) = n Y i=1 f(r 1 v 1 ; t) (1:1) 3) in the computation of the collision term one ...
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Discovery of Grounded Theory
, 1967
"... Abstract: This paper outlines my concerns with Qualitative Data Analysis ’ (QDA) numerous remodelings of Grounded Theory (GT) and the subsequent eroding impact. I cite several examples of the erosion and summarize essential elements of classic GT methodology. It is hoped that the article will clarif ..."
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Cited by 2485 (12 self)
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Abstract: This paper outlines my concerns with Qualitative Data Analysis ’ (QDA) numerous remodelings of Grounded Theory (GT) and the subsequent eroding impact. I cite several examples of the erosion and summarize essential elements of classic GT methodology. It is hoped that the article
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 886 (35 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
The Theory of Economic Regulation
 The Bell Journal of Economics and Management Science
, 1971
"... The potential usex of public resources and powers to improve the economic stuius of economic groups (such as industries and occupations) are analyzed to provide a scheme of the demand for regulation. The characteristics of the political process which allow relatively small groups to obtain such regu ..."
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Cited by 1057 (1 self)
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such regulation is then sketched lo provide elemenls of a theory of supply of regulation. A variety of empirical evidence and illustration is also presented. W The state—the machinery and power of the state—is a potential resource or threat to every industry in the society. With its power to prohibit or compel
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 680 (13 self)
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A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on purely discrete state spaces only. In particular, various classes of hybrid automata induce finitary trace equivalence (or similarity, or bisimilarity) relations on an uncountable state space, thus permitting the application of various modelchecking techniques that were originally developed for finitestate systems.
A theory of fairness, competition and cooperation
 Quarterly Journal of Economics
, 1999
"... de/ls_schmidt/index.html ..."
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