A Certain Subclass of Analytic Functions with Bounded Positive Real Part

For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in the class T(α,β). And we estimate the bounds of coefficients and solve Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.

On capped Higgs positivity cone

The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to the Wilson coefficients living in a convex cone,further including the nonpositivity part caps the cone from above.For Higgs scattering,a capped positivity cone was obtained using a simplified,linear unitarity condition without utilizing the full internal symmetries of Higgs scattering.Here,we further implement stronger nonlinear unitarity conditions from the UV,which generically gives rise to better bounds.We show that,for the Higgs case in particular,while the nonlinear unitarity conditions per se do not enhance the bounds,the fuller use of the internal symmetries do shrink the capped positivity cone significantly.

POSITIVE ENTIRE SOLUTIONS TO SINGULAR SEMILINEAR ELLIPTIC EQUATIONS OF MIXED TYPE

In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.

EXISTENCE AND ITERATIVE APPROXIMATIONS OF BOUNDED POSITIVE SOLUTIONS TO A NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

In this paper,we consider a nonlinear neutral differential equation.By the Schauder fixed point theorem,some sufficient conditions are obtained to ensure the existence of uncountably many bounded positive solutions.In addition,we give the iterative approximation sequences with errors for these positive solutions and establish some error estimates between the approximate and the positive solutions.

Positivity in electron-positron scattering:testing the axiomatic quantum field theory principles and probing the existence of UV states

We consider the positivity bounds on dimension-8 four-electron operators and study two related phenomenological aspects at future lepton colliders.First,if positivity is violated,probing such violations will revolutionize our understanding of the fundamental pillars of quantum field theory and the S-matrix theory.We observe that positivity violation at scales of 1-10 TeV can potentially be probed at future lepton colliders even if one assumes that dimension-6 operators are also present.Second,the positive nature of the dimension-8 parameter space often allows us to either directly infer the existence of UV-scale particles together with their quantum numbers or exclude them up to certain scales in a model-independent way.In particular,dimension-8 positivity plays an important role in the test of the Standard Model.If no deviations from the Standard Model are observed,it allows for simultaneous exclusion limits on all kinds of potential UV-complete models.Unlike the dimension-6 case,these limits apply regardless of the UV model setup and cannot be removed by possible cancellations among various UV contributions.This thus consists of a novel and universal test to confirm the Standard Model.We demonstrate with realistic examples how all the previously mentioned possibilities,including the test of positivity violation,can be achieved.Hence,we provide an important motivation for studying dimension-8 operators more comprehensively.