1,158 research outputs found
On the H\'enon-Lane-Emden conjecture
We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden
system
\hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N,
\hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when ,
. The main conjecture states that there is no non-trivial
non-negative solution whenever is under the critical Sobolev hyperbola,
i.e. .
We show that this is indeed the case in dimension N=3 provided the solution
is also assumed to be bounded, extending a result established recently by
Phan-Souplet in the scalar case.
Assuming stability of the solutions, we could then prove Liouville-type
theorems in higher dimensions.
For the scalar cases, albeit of second order ( and ) or of fourth
order ( and ), we show that for all dimensions in the
first case (resp., in the second case), there is no positive solution
with a finite Morse index, whenever is below the corresponding critical
exponent, i.e (resp., ).
Finally, we show that non-negative stable solutions of the full
H\'{e}non-Lane-Emden system are trivial provided \label{sysdim00}
N<2+2(\frac{p(b+2)+a+2}{pq-1}) (\sqrt{\frac{pq(q+1)}{p+1}}+
\sqrt{\frac{pq(q+1)}{p+1}-\sqrt\frac{pq(q+1)}{p+1}}).Comment: Theorem 4 has been added in the new version. 23 pages, Comments are
welcome. Updated version - if any - can be downloaded at
http://www.birs.ca/~nassif/ or http://www.math.ubc.ca/~fazly/research.htm
Quantum Electro and Chromodynamics treated by Thompson's heuristic approach
In this work we apply Thompson's method (of the dimensions and scales) to
study some features of the Quantum Electro and Chromodynamics. This heuristic
method can be considered as a simple and alternative way to the Renormalisation
Group (R.G.) approach and when applied to QED-lagrangian is able to obtain in a
first approximation both the running coupling constant behavior of alpha(mu)
and the mass m(mu).The calculations are evaluated just at d_c=4, where d_c is
the upper critical dimension of the problem, so that we obtain the logarithmic
behavior both for the coupling alpha and the excess of mass Delta m on the
energy scale mu. Although our results are well-known in the vast literature of
field theories,it seems that one of the advantages of Thompson's method, beyond
its simplicity is that it is able to extract directly from QED-lagrangian the
physical (finite) behavior of alpha(mu) and m(mu), bypassing hard problems of
divergences which normally appear in the conventional renormalisation schemes
applied to field theories like QED. Quantum Chromodynamics (QCD) is also
treated by the present method in order to obtain the quark condensate value.
Besides this, the method is also able to evaluate the vacuum pressure at the
boundary of the nucleon. This is done by assumming a step function behavior for
the running coupling constant of the QCD, which fits nicely to some quantities
related to the strong interaction evaluated through the MIT-bag model.Comment: RevTex, 25 pages, no figure
Parametrização do modelo CANEGRO para as cultivares brasileiras de cana-de-açúcar.
O objetivo do presente trabalho foi a parametrização do modelo CANEGRO para a as cultivares brasileiras IAC 91-1099 e SP 89 1115.Trabalho apresentado na V Mostra de Trabalhos de Estagiários e Bolsistas, Campinas, out. 2009
Study Of Inertia And Stoichiometric Effect On Surface Diffusion By Monte Carlo Method
In this work, we investigate the inertia and stoichiometric effect on surface diffusion of adsorbates particles. The study is done by means of Monte-Carlo simulation in the framework of the lattice gas model. Only first neighboring repulsive pair interaction is considered. We concentrate on the behaviour of the tracer diffusion coefficient Dt(θ), as a function of surface coverage θ in the case where two type of particles A and B are adsorbed. A and B are only different by their mass. The results shows that θt ordering phenomenon is not strongly influenced. However the diffusion process is decreased by inclusion of heavy particles.w.In this work, we investigate the inertia and stoichiometric effect on surface diffusion of adsorbates particles. The study is done by means of Monte-Carlo simulation in the framework of the lattice gas model. Only first neighboring repulsive pair interaction is considered. We concentrate on the behaviour of the tracer diffusion coefficient Dt(θ), as a function of surface coverage θ in the case where two type of particles A and B are adsorbed. A and B are only different by their mass. The results shows that θt ordering phenomenon is not strongly influenced. However the diffusion process is decreased by inclusion of heavy particles.w
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