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Exact Solutions and Applications
2017This chapter considers the construction of the few known and some new explicit solutions to the shape equation. For example, a review of the available experimental facts concerning nerve fibers suggests that their form can be adequately modelled by Delaunay unduloids. We present parameterizations of these surfaces in terms of the geometrical parameters
Ivaïlo M. Mladenov +1 more
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AIP Conference Proceedings, 2012
Inflationary universe model in the context of an exact intermediate solution is studied. General conditions required for these models to be realizable are discussed.
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Inflationary universe model in the context of an exact intermediate solution is studied. General conditions required for these models to be realizable are discussed.
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2014
Publisher Summary A matrix is denoted by A. The i-th row of A is denoted by Ai, the i-th column by A.i, the column of the absolute terms (right sides) by A.f. To eliminate x1, one derives from Aa system B in which the first column vanishes. For this purpose, the first row is multiplied by the leading coefficient a21 of the second row and the second ...
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Publisher Summary A matrix is denoted by A. The i-th row of A is denoted by Ai, the i-th column by A.i, the column of the absolute terms (right sides) by A.f. To eliminate x1, one derives from Aa system B in which the first column vanishes. For this purpose, the first row is multiplied by the leading coefficient a21 of the second row and the second ...
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2002
We first give a brief review of the basic observational facts (Olbers’ paradox, Hubble recession, microwave background radiation) and assumptions (cosmological principle) that lead to our present picture of the universe. We then formulate our assumptions in mathematical terms and deduce the basic geometric properties of any model satisfying the ...
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We first give a brief review of the basic observational facts (Olbers’ paradox, Hubble recession, microwave background radiation) and assumptions (cosmological principle) that lead to our present picture of the universe. We then formulate our assumptions in mathematical terms and deduce the basic geometric properties of any model satisfying the ...
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2008
In conclusion we have seen that sometimes quite simple mathematics may lead to a rich body of physical informations. I think that new interesting results can be obtained through different analytic continuation of these calculations. It would be also useful to use more sophisticated Ansatze as well as to consider the dynamic poperties of systems with ...
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In conclusion we have seen that sometimes quite simple mathematics may lead to a rich body of physical informations. I think that new interesting results can be obtained through different analytic continuation of these calculations. It would be also useful to use more sophisticated Ansatze as well as to consider the dynamic poperties of systems with ...
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2008
Harmonic maps theory include some examples of non linear field theories of physical interest, among which stationary axisymmetric electrovacuum Einstein equations. After a short review of such applications, we concentrate on the so called CPn models. This is a very nice example of an harmonic physical problem, about which much is known.
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Harmonic maps theory include some examples of non linear field theories of physical interest, among which stationary axisymmetric electrovacuum Einstein equations. After a short review of such applications, we concentrate on the so called CPn models. This is a very nice example of an harmonic physical problem, about which much is known.
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1997
This chapter evaluates some of the simplified Schrödinger equations obtained in the previous chapter, and presents explicit solutions for the energy levels and the corresponding wavefunctions. It begins by looking at the free particle and the particle in a box.
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This chapter evaluates some of the simplified Schrödinger equations obtained in the previous chapter, and presents explicit solutions for the energy levels and the corresponding wavefunctions. It begins by looking at the free particle and the particle in a box.
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