3,317 research outputs found
The Baker-Akhiezer function and factorization of the Chebotarev-Khrapkov matrix
A new technique is proposed for the solution of the Riemann-Hilbert problem
with the Chebotarev-Khrapkov matrix coefficient
, ,
is a zero-trace polynomial matrix, and is the unit matrix. This
problem has numerous applications in elasticity and diffraction theory. The
main feature of the method is the removal of the essential singularities of the
solution to the associated homogeneous scalar Riemann-Hilbert problem on the
hyperelliptic surface of an algebraic function by means of the Baker-Akhiezer
function. The consequent application of this function for the derivation of the
general solution to the vector Riemann-Hilbert problem requires finding of the
zeros of the Baker-Akhiezer function ( is the genus of the
surface). These zeros are recovered through the solution to the associated
Jacobi problem of inversion of abelian integrals or, equivalently, the
determination of the zeros of the associated degree- polynomial and
solution of a certain linear algebraic system of equations.Comment: 17 pages, 1 figur
A lattice study of the pentaquark states
We present a study of the pentaquark system in quenched lattice QCD using
diquark-diquark and kaon-nucleon local and smeared interpolating fields. We
examine the volume dependence of the spectral weights of local correlators on
lattices of size , and at
. We find that a reliable evaluation of the volume dependence of the
spectral weights requires accurate determination of the correlators at large
time separations. Our main result from the spectral weight analysis in the
pentaquark system is that within our variational basis and statistics we can
not exclude a pentaquark resonance. However our data also do not allow a clear
identification of a pentaquark state since only the spectral weights of the
lowest state can be determined to sufficient accuracy to test for volume
dependence. In the negative parity channel the mass extracted for this state is
very close to the KN threshold whereas in the positive parity channel is about
60% above.Comment: Manuscript expanded, discussion of two-pion system included, a
comment regarding Ref.13 was corrected, version to appear in Phys. Rev. D, 19
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Applying a CART-based approach for the diagnostics of mass appraisal models
In this paper an approach for automatic detection of segments where a regression model significantly underperforms and for detecting segments with systematically under- or overestimated prediction is introduced. This segmentational approach is applicable to various expert systems including, but not limited to, those used for the mass appraisal. The proposed approach may be useful for various regression analysis applications, especially those with strong heteroscedasticity. It helps to reveal segments for which separate models or appraiser assistance are desirable. The segmentational approach has been applied to a mass appraisal model based on the Random Forest algorithm.CART, model diagnostics, mass appraisal, real estate, Random forest, heteroscedasticity
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