We examine quenched chiral logarithms in lattice QCD with overlap Dirac quarks. From our data of m π , we determine the coefficient of quenched chiral logarithm δ = 0.203(14), 0.176(17), 0.193(17) and 0.200(13) for lattices of sizes 8 × 24, 10 × 24, 12 × 24 and 16 × 32 respectively. Also, for the first three lattice sizes, we measure the index susceptibility of the overlap Dirac operator, and u...

Let ν be a positive Borel measure on R and pFq(a1, . . . , ap; b1, . . . , bq; s) be a generalized hypergeometric series. We define a generalized hypergeometric measure, μp,q := pFq(a1, . . . , ap; b1, . . . , bq; ν), as a series of convolution powers of the measure ν, and we investigate classes of probability distributions which are expressible as such a measure. We show that the Kemp family o...

The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered. A random measure is defined whose expectation approximates the unknown measure under suitable conditions. An estimator of the approximating measure is then ...

Sobolev and Hardy type inequalities play an important role in many areas of mathematics and mathematical physics. They have become standard tools in existence and regularity theories for solutions to partial differential equations, in calculus of variations, in geometric measure theory and in stability of matter. In analysis a number of inequalities like the Hardy–Littlewood– Sobolev inequality...

The present paper is mainly concerned with establishing conditions which .assure that all lattice regular measures have additional smoothness properties or that simply all two-valued such measures have such properties and are therefore Dirac measures. These conditions are expressed in terms of the general Wallman space. The general results are then applied to specific topological lattices, yiel...

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2, 2) gauge transformations acting on the spinor index of the wave functions. This local U(2, 2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory. 1 Connection between Local Gauge ...

The Thue–Morse (TM) sequence is defined via the binary substitution 1 7→ 11̄, 1̄ 7→ 1̄1; see [1, 4] and references therein for general background. The corresponding dynamical system is known to have mixed (pure point and singular continuous) spectrum [12, 15, 17], with a pure point part on the dyadic points and a singular continuous spectral measure in the form of a Riesz product. The latter coinc...