We investigate the spectral properties of the Wilson Dirac operator in quenched QCD in the microscopic regime. We distinguish the topological sectors using the index as determined by the Wilson flow method. Consequently, the distributions of the low-lying eigenvalues of the Wilson Dirac operator can be compared in each of the topological sectors to predictions from random matrix theory applied ...

Allan C. Wilson studied genes [5], proteins, and body structures of animals and humans [6] in the US during the second half of the twentieth century. Wilson also studied human evolution [7] . Although morphology [8] and behaviors of humans [6] (Homo sapiens [9]) and great apes differ, Wilson found that they have biochemical and genetic similarities. Wilson and his colleagues calculated the time...

Two unitary integral transforms with a very-well poised 7F6-function as a kernel are given. For both integral transforms the inverse is the same as the original transform after an involution on the parameters. The 7F6-function involved can be considered as a non-polynomial extension of the Wilson polynomial, and is therefore called a Wilson function. The two integral transforms are called a Wil...

Mowat-Wilson syndrome (MWS) is a multiple congenital anomaly syndrome characterized by a distinct facial phenotype (high forehead, frontal bossing, large eyebrows, medially flaring and sparse in the middle part, hypertelorism, deep set but large eyes, large and uplifted ear lobes, with a central depression, saddle nose with prominent rounded nasal tip, prominent columella, open mouth, with M-sh...

We give a general expansion formula of functions in the Askey–Wilson polynomials and using the Askey–Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey–Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating funct...

We solve explicitly a closed, linear loop equation for the SU(2) Wilson loop average on a two-dimensional plane and generalize the solution to the case of the SU(N) Wilson loop average with an arbitrary closed contour. Futhermore, the flat space solution is generalized to any two-dimensional manifold for the SU(2) Wilson loop average and to any two-dimensional manifold of genus 0 for the SU(N) ...

Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which are deformations of those for the Wilson and Askey-Wilson polynomials in terms of a degree l (l = 1, 2, . . .) eigenpolynomial. These polynomials...