The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey-Wilson second order q-difference operator. The kernel is called the Askey-Wilson function. In this paper an explicit expansion formula for the Askey-Wilson function in terms of Askey-Wilson polynomials is proven. With this expansion form...

An analogue for composite moduli m ≥ 2 of the Wilson quotient is studied. Various congruences are derived, and the question of when these quotients are divisible by m is investigated; such an m will be called a “Wilson number”. It is shown that numbers in certain infinite classes cannot be Wilson numbers. Eight new Wilson numbers up to 500 million were found.

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Gradient Flow Exact Renormalization Group (GFERG) is a framework to define the Wilson action via gradient flow equation. We study fixed point structure of GFERG equation associated with general for scalar field theories and show that it same as conventional Wilson-Polchinski (WP) in general. Furthermore, we discuss has similar RG around WP illustrate these results $O(N)$ non-linear sigma model ...

We present results of quenched SU(3) hadron spectroscopy comparing O(a) improved Wilson (Clover) fermions with conventional Wilson fermions. The configurations were generated using an O(a) improved 6-link SU(3) pure gauge action at β’s corresponding to lattice spacings of 0.15, 0.18, 0.20, 0.33, and 0.43 fm. We find evidence that fermionic scaling violations are consistent with O(a) for Clover ...

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...