A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the threefold tensor product of the basic realization of the Lie superalgebra osp(1 vertical bar 2) in terms of operators in one continuous and one Grassmanian variable. The basis vectors of the resulting Bannai-Ito algebra module involve Jacobi polynomials.
Padé approximation is the rational generalization of Hermite interpolating polynomial. On its own merits, it has earned a relevant place in the theory of constructive approximation. In this article, we will develop an exhaustive analysis of two-point Padé approximations to Herglotz-Riesz transforms. We study the convergence problem when the poles a...
status: published
status: published
Published in Journal of Synchrotron Radiation
A framework based on physical optics for simulating the effect of imperfect compound refractive lenses (CRLs) upon an X-ray beam is described, taking into account measured phase errors obtained from at-wavelength metrology. A CRL stack is modelled, with increasing complexity, as a single thin phase element, then as a more realistic compound element...
The q-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra osp(q) (1 | 2). It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these results will be extended to higher rank. The rank n - 2 q-Bannai-Ito algebra A(n)(q), which by the established isomorphism also ...
IEEE When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property that we call partial orthogonality. In this paper, we leverage partial orthogonality to develop a fast first-order method, based on the alternating direction method of...
A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace–Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the n-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy–Kovalevska...
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. We study the asymptotic behavior of the eigenvalues of Gaussian perturbations of large Hermitian random matrices for which the limiting eigenvalue density vanishes at a singular interior point or vanishes faster than a square root at a singular edge point. First, we show that the singul...
Let R[X] be the power series ring over a commutative ring R with identity. For f is an element of R[X], let A(f) denote the content ideal of f, i.e., the ideal of R generated by the coefficients of f. We show that if R is a Priifer domain and if g is an element of R[X] such that A(g) is locally finitely generated (or equivalently locally principal)...
