A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem

Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order. We also pedagogically discuss how the method complies with gauge symmetry using one- and two-loop examples in QED and QCD.

Superoscillations and Analytic Extension in Schur Analysis

We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of R-functions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

Estimates for initial coefficients of certain bi-univalent functions

Estimates are obtained for the initial coefficients of a normalized analytic function f in the unit disk D such that f and the analytic extension of f-1 to D belong to certain subclasses of univalent functions. The bounds obtained improve some existing known bounds.

Analytic Extension of Riemannian Analytic Manifolds and Local Isometries

This article deals with a locally given Riemannian analytic manifold. One of the main tasks is to define its regular analytic extension in order to generalize the notion of completeness. Such extension is studied for metrics whose Lie algebra of all Killing vector fields has no center. The generalization of completeness for an arbitrary metric is given, too. Another task is to analyze the possibility of extending local isometry to isometry of some manifold. It can be done for metrics whose Lie algebra of all Killing vector fields has no center. For such metrics there exists a manifold on which any Killing vector field generates one parameter group of isometries. We prove the following almost necessary condition under which Lie algebra of all Killing vector fields generates a group of isometries on some manifold. Let g be Lie algebra of all Killing vector fields on Riemannian analytic manifold, h⊂g is its stationary subalgebra, z⊂g is its center and [g,g] is commutant. G is Lie group generated by g and is subgroup generated by h⊂g. If h∩(z+[g;g])=h∩[g;g], then H is closed in G.

Making sense of climate: A meta-analytic extension of the competing values framework

Organizational climate research has surged recently, but the disbursement of research contributions across domains has made it difficult to draw conclusions about climate and its connections with performance. To make sense of the climate literature, we used the competing values framework (CVF) to classify domain-specific climates into four climate types (clan, adhocracy, hierarchy, and market climates). We did so by conceptually linking domain-specific climates that are manifestations of the same underlying strategic values. We then conducted meta-analyses to examine the magnitudes, mechanisms, and moderators of the individual and group-level associations between the CVF climates and performance. These meta-analyses revealed positive climate–performance associations for each climate type and supported job attitudes as a common mediator. We also examined several methodological moderators of climate–performance relationships, testing the source of climate and performance measures, the temporal assessment of these constructs, and the level of within-group agreement in climate measures as possible boundary conditions.