相关论文: Global approximants with renormalization scale inv…

We review how a specific resummation of the so-called "delta-expansion", applied to the QCD Lagrangian, transforms the ordinary perturbative expansion in $\alpha_s$ into an expansion in an arbitrary mass parameter, around the basic scale…

The problem of precise evaluation of the perturbative QCD predictions at moderate energies is considered. Substantial renormalization scheme dependence of the perturbative predictions obtained with the conventional renormalization group…

Deviations from scale invariance resulting from small perturbations of a general two dimensional conformal field theory are studied. They are expressed in terms of beta functions for renormalization of general couplings under local change…

A recently proposed method of estimating the asymptotic behaviour of QCD perturbation theory coefficients is critically reviewed and shown to contain numerous invalid mathematical operations and unsubstantiated assumptions. We discuss in…

We include the full second-order corrections to the static QCD potential in the analysis of the ttbar threshold cross section. There is an unexpectedly large difference between the QCD potential improved by the renormalization-group…

We explain that, like the usual Pad\'e approximants, the barycentric Pad\'e approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for every polynomial P there exists a power series S, with…

The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…

We present a new approach to determining the strong coupling $\alpha_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $\Lambda_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the…

For inversion-symmetric topological insulators and superconductors characterized by ${\mathbb Z}_{2}$ topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling…

Physical quantities in QCD do not depend upon $\alpha_s(Q)$. There is no way to measure $\alpha_s(Q)$ experimentally. If those statements sound shocking, please read on. They are actually well-known facts, though ones that are constantly…

Cosmography becomes non-predictive when cosmic data span beyond the red shift limit $z\simeq1 $. This leads to a \emph{strong convergence issue} that jeopardizes its viability. In this work, we critically compare the two main solutions of…

Accurate and efficient uncertainty quantification is essential for resilience assessment of modern power systems under high impact and low probability disturbances. Data driven sparse polynomial chaos expansion (DDSPCE) provides a…

General conditions controlling formation of incommensurate phases (IPs) in crystals undergoing reconstructive phase transitions (RPTs) are analyzed in the framework of a model free phenomenological approach. A universal trend to stabilizing…

We consider the distribution of a graph invariant of central similarity proximity catch digraphs (PCDs) based on one dimensional data. The central similarity PCDs are also a special type of parameterized random digraph family defined with…

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…

We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows…

Methods of Pad\'e approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors, and which is generalizing the well-known in Spectral theory Stieltjes transform (Markov function) of…

For a recent new numerical method for computing so-called robust Pad\'e approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called…

The coherent potential approximation, CPA, is a useful tool to treat systems with disorder. Cluster theories have been proposed to go beyond the translation invariant single-site CPA approximation and include some short range correlations.…

Determinantal Point Processes (DPPs), which originate from quantum and statistical physics, are known for modelling diversity. Recent research [Ghosh and Rigollet (2020)] has demonstrated that certain matrix-valued $U$-statistics (that are…