Related papers: Why Are Renormalons Always In The Same Place ?
We study the origin of non-analyticity in \alpha_s of a short-distance QCD observable to demonstrate that the infrared renormalons, the same-sign factorial growth of the perturbative expansion, is a universal phenomenon that originates…
The basis of renormalon calculus is briefly discussed. The method is applied to study QCD predictions for three sum rules of deep-inelastic scattering, namely for the Gross-Llewellyn Smith, Bjorken polarized and unpolarized sum rules. It is…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
A Radon-type transform called a cone transform that assigns to a given function its integral over various sets of cones has arisen in the last decade in the context of the study of Compton cameras used in Single Photon Emission Computed…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
The aim of this paper is to present inversion methods for the classical Radon transform which is defined on a family of $k$ dimensional planes in $\Bbb R^{n}$ where $1\leq k\leq n - 2$. For these values of $k$ the dimension of the set…
The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…
Known results on two-dimensional quantum electrodynamics (QED_2) have been used to study the dependence of functional renormalization group equations on renormalization schemes and approximations applied for its bosonized version. It is…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
The possibility is discussed that existence of renormalon singularities is not the internal property of the specific field theory but depends on the renormalization scheme.
In the evolution of a genome, the gene sequence is sometimes rearranged, for example by transposition of two adjacent gene blocks. In biocombinatorics, one tries to reconstruct these rearrangement incidents from the resulting permutation.…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincar\`e maps in geometric models of well-known Lorenz attractor. Using both analytical and symbolic approaches, we study connections between…
The properties of a generalized version of the Borel Transform in infrared unstable theories with dynamical mass generation are studied. The reconstruction of the nonperturbative structure is unambiguous in this version. Various methods for…
We prove that Pade approximants yield increasingly accurate predictions of higher-order coefficients in QCD perturbation series whose high-order behaviour is governed by a renormalon. We also prove that this convergence is accelerated if…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
Perturbation series in QCD are generally asymptotic and suffer from so-called infrared renormalon ambiguities. In the context of the standard operator product expansion in MS-bar these ambiguities are compensated by matrix elements of…
Modifications of the QCD perturbative expansions by the subtraction of the dominant infrared renormalon have been proposed recently as attempts to solve the long-standing discrepancy between fixed-order and contour-improved perturbation…