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Separation of variables in one partial integrable case of Goryachev
Separation of variables partial integrable case of Goryachev
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2010/12/28
We show that the equations of motion in one partial integrable case of Goryachev in the rigid body dynamics can be separated by the appropriate change of variables,the new variables x, y being hyperel...
$\ell^2$-Linear Independence for the System of Integer Translates of a Square Integrable Function
Linear Independence Square Integrable Function
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2010/11/15
We prove that if the system of integer translates of a square integrable function is $\ell^2$-linear independent then its periodization function is strictly positive almost everywhere. Indeed we show...
Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
Integrable Henon-Heiles Hamiltonians Poisson algebra approach
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2010/11/19
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable ...
Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization
partition functions integrable hierarchies Dyson gases
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2010/4/2
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms o...
On Non-Existence of Korovkin's Theorem in the Space of Lp-locally Integrable Functions
Linear positive operators Korovkin-type theorem Weighted Lp(loc) space
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2010/3/1
It is shown that a Korovkin-type theorem does not hold in the weighted space of Lp-locally integrable functions on the whole real axis.