1,130,256 research outputs found
On the Solutions of infinite systems of linear equations
New theorems about the existence of solution for a system of infinite linear
equations with a Vandermonde type matrix of coefficients are proved. Some
examples and applications of these results are shown. In particular, a kind of
these systems is solved and applied in the field of the General Relativity
Theory of Gravitation. The solution of the system is used to construct a
relevant physical representation of certain static and axisymmetric solution of
the Einstein vacuum equations. In addition, a newtonian representation of these
relativistic solutions is recovered. It is shown as well that there exists a
relation between this application and the classical Haussdorff moment problem.Comment: Accepted for publication in General Relativity and Gravitatio
HighāOrder TimeāDependent Perturbation Theory for Classical Mechanics and for Other Systems of FirstāOrder Ordinary Differential Equations
A timeādependent perturbation solution is derived for a system of firstāorder nonlinear or linear ordinary differential equations. By means of an ansatz, justified a posteriori, the latter equations can be converted to an operator equation which is solvable by several methods. The solution is subsequently specialized to the case of classical mechanics. For the particular case of autonomous equations the solution reduces to a wellāknown one in the literature. However, when collision phenomena are treated and described in a classical āinteraction representationā the differential equations are typically nonautonomous, and the more general solution is required. The perturbation expression is related to a quantum mechanical one and will be applied subsequently to semiclassical and classical treatments of collisions
Structural stability of Supersonic solutions to the Euler-Poisson system
The well-posedness for the supersonic solutions of the Euler-Poisson system
for hydrodynamical model in semiconductor devices and plasmas is studied in
this paper. We first reformulate the Euler-Poisson system in the supersonic
region into a second order hyperbolic-elliptic coupled system together with
several transport equations. One of the key ingredients of the analysis is to
obtain the well-posedness of the boundary value problem for the associated
linearized hyperbolic-elliptic coupled system, which is achieved via a delicate
choice of multiplier to gain energy estimate. The nonlinear structural
stability of supersonic solution in the general situation is established by
combining the iteration method with the estimate for hyperbolic-elliptic system
and the transport equations together.Comment: The paper was revised substantially in this new version. In
particular, we constructed the new multiplier under general conditions on the
background solution
Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
We study the exact spectrum of the AdS4/CFT3 duality put forward by Aharony,
Bergman, Jafferis and Maldacena (ABJM). We derive thermodynamic Bethe ansatz
(TBA) equations for the planar ABJM theory, starting from "mirror" asymptotic
Bethe equations which we conjecture. We also propose generalization of the TBA
equations for excited states. The recently proposed Y-system is completely
consistent with the TBA equations for a large subsector of the theory, but
should be modified in general. We find the general asymptotic infinite length
solution of the Y-system, and also several solutions to all wrapping orders in
the strong coupling scaling limit. To make a comparison with results obtained
from string theory, we assume that the all-loop Bethe ansatz of N.G. and P.
Vieira is the valid worldsheet theory description in the asymptotic regime. In
this case we find complete agreement, to all orders in wrappings, between the
solution of our Y-system and generic quasi-classical string spectrum in AdS3 x
S.Comment: references added + minor changes; published versio
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