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 $G(t)=\alpha_1(t)I+\alpha_2(t)Q(t)$, $\alpha_1(t), \alpha_2(t)\in H(L)$, $Q(t)$ is a $2\times 2$ zero-trace polynomial matrix, and $I$ 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 $\rho$ zeros of the Baker-Akhiezer function ($\rho$ 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-$\rho$ polynomial and solution of a certain linear algebraic system of $\rho$ 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 $16^3\times 32$, $24^3\times32$ and $32^3\times 64$ at $\beta=6.0$. 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 figure

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