Some basic concepts are discussed to derive renormalisation factors of local lattice operators relevant to deep inelastic structure functions and to other measurable quantities. These Z factors can be used to relate matrix elements measured by lattice techniques to their continuum counterparts. We discuss the O(a) improvement of point and one–link lattice quark operators. Suitable bases of impr...

We present a semiclassical calculation of the generalized form factor Kab(tau) which characterizes the fluctuations of matrix elements of the operators a and b in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f = 2 degrees of ...

We study Darboux-Bäcklund transformations (DBTs) for the q-deformed Korteweg-de Vries hierarchy by using the q-deformed pseudodifferential operators. We identify the elementary DBTs which are triggered by the gauge operators constructed from the (adjoint) wave functions of the hierarchy. Iterating these elementary DBTs we obtain not only q-deformed Wronskian-type but also binary-type representa...

We study the $d^2 \Gamma_d /(d\omega d\cos\theta_d) $, $d\Gamma_d /d\cos\theta_d$ and $ d\Gamma_d /dE_d distributions, which are defined in terms of visible energy polar angle charged particle from $\tau-$decay $b\to c \tau\, (\mu \bar \nu_\mu \nu_\tau,\pi \nu_\tau,\rho\nu_\tau) \bar\nu_\tau$ reactions. The first two contain information on transverse tau-spin, tau-angular tau-angular-spin asymm...

In [5], D. Lanphier used differential operators studied by Maass [6] to prove the above van der Pol identity (2). He also obtained several van der Pol-type identities using the Maass operators and thereby obtained new congruences for the Ramanujan’s tau-function. In [9], D. Niebur derived a formula for τ(n) similar to the classical ones of Ramanujan and van der Pol, but has the feature that hig...

This article is divided into two parts. In the first part we present a general theory of the dyadic lattices. In the second part we show several applications of this theory to harmonic analysis: a decomposition of an arbitrary measurable function in terms of its local mean oscillations, and a pointwise bound of CalderónZygmund operators by sparse operators. Table of

The study of random fixed points has been an active area of contemporary research in mathematics. Some of the recent works in this field are noted in [1, 2, 3, 11]. In particular, random iteration schemes leading to random fixed points were introduced in [3]. After that, random iterations for finding solutions of random operator equations and fixed points of random operators have been discussed...