7,278 research outputs found
A Note on the Monge-Kantorovich Problem in the Plane
The Monge-Kantorovich mass-transportation problem has been shown to be
fundamental for various basic problems in analysis and geometry in recent
years. Shen and Zheng (2010) proposed a probability method to transform the
celebrated Monge-Kantorovich problem in a bounded region of the Euclidean plane
into a Dirichlet boundary problem associated to a nonlinear elliptic equation.
Their results are original and sound, however, their arguments leading to the
main results are skipped and difficult to follow. In the present paper, we
adopt a different approach and give a short and easy-followed detailed proof
for their main results
Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation
The Bertrand's theorem is extended, i.e. closed orbits still may exist for
other central potentials than the power law Coulomb potential and isotropic
harmonic oscillator. It is shown that for the combined potential
(), when (and only when) is the Coulomb
potential or isotropic harmonic oscillator, closed orbits still exist for
suitable angular momentum. The correspondence between the closeness of
classical orbits and the existence of raising and lowering operators derived
from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug
THE INFLUENCE OF RESEARCH AND PRACTICE OF VOCATIONAL EDUCATION SERVICE ON RURAL REVITALIZATION STRATEGY ON RELIEVING AUDIENCE’S PSYCHOLOGICAL ANXIETY
THE INFLUENCE OF RESEARCH AND PRACTICE OF VOCATIONAL EDUCATION SERVICE ON RURAL REVITALIZATION STRATEGY ON RELIEVING AUDIENCE’S PSYCHOLOGICAL ANXIETY
transitions in the light cone sum rules with the chiral current
semi-leptonic decays to the light scalar meson, , are investigated in the QCD
light-cone sum rules (LCSR) with chiral current correlator. Having little
knowledge of ingredients of the scalar mesons, we confine ourself to the two
quark picture for them and work with the two possible Scenarios. The resulting
sum rules for the form factors receive no contributions from the twist-3
distribution amplitudes (DA's), in comparison with the calculation of the
conventional LCSR approach where the twist-3 parts play usually an important
role. We specify the range of the squared momentum transfer , in which the
operator product expansion (OPE) for the correlators remains valid
approximately. It is found that the form factors satisfy a relation consistent
with the prediction of soft collinear effective theory (SCET). In the effective
range we investigate behaviors of the form factors and differential decay
widthes and compare our calculations with the observations from other
approaches. The present findings can be beneficial to experimentally identify
physical properties of the scalar mesons.Comment: 22 pages,16 figure
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