Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group

We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi's $\Gamma$-convergence techniques that optimal functions for a natural subcritical approximations of the Sobolev quotient concentrate energy at one point. In the second part of the paper, we try to restore the compactness by extending the celebrated Global Compactness result to the Heisenberg group via a completely different approach with respect to the original one by Struwe (Math. Z. 1984)

Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group

We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian operator on the Heisenberg-Weyl group Hn. Among other results, we prove that the weak solutions to such a class of problems are bounded and Hölder continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates

The Top Quark and the Higgs Boson Mass from LEP SLC and CDF Data

The impact of the new experimental data from LEP, SLC and CDF on the top quark mass and the Higgs boson mass is investigated. The determinations of m_{top} and of an upper bound on m_{Higgs} are given, taking into account the experimental error on the QED coupling constant \alpha_{em} and on the b-quark mass m_b. The relevance of higher order theoretical uncertainties is pointed out. briefly reviewed.Comment: Latex (6 Figures upon request, [email protected]

TOPAZ0 2.0 - A Program for Computing De-Convoluted and Realistic Observables Around the Z0Z^0 Peak

The program {\tt TOPAZ0} is designed for computing $Z^0$ parameters, de-convoluted and QED-dressed cross sections and forward-backward asymmetries of $e^+ e^-$ annihilation into fermion pairs and of Bhabha scattering around the $Z^0$ peak, over both a completely inclusive experimental set-up and a realistic one, i.e. with cuts on acollinearity, energy or invariant mass and angular acceptance of the outgoing fermions. The new version, 2.0, offers the possibility of imposing different experimental cuts on cross sections and forward-backward asymmetries in a single run, and includes radiative corrections whose effect can become relevant in view of the present and foreseen experimental accuracy. Moreover, an additional option is included, which allows an estimate of the theoretical uncertainty due to unknown higher-order effects, both of electroweak and QCD origin. With respect to the version 1.0, the code is available in the form of {\tt SUBROUTINE}, in order to render more viable the use of the program for aims not planned by the {\tt TOPAZ0} package itself.Comment: 12 pages, LateX, no macros, no figure

Four-Fermion Production in Electron-Positron Collisions

This report summarises the results of the four-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the calculation of four-fermion processes in electron-positron collisions at LEP-2 centre-of-mass energies are presented, concentrating on predictions for four main reactions: W-pair production, visible photons in four-fermion events, single-W production and Z-pair production. Based on a comparison of results derived within different approaches, theoretical uncertainties on these predictions are established.Comment: 150 pages, 73 figures, 45 table

Nonlocal Harnack inequalities in the Heisenberg group

We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group~\mathds{H}^n, whose prototype is the Dirichlet problem for the $p$-fractional subLaplace equation. These problems arise in many different contexts in quantum mechanics, in ferromagnetic analysis, in phase transition problems, in image segmentations models, and so on, when non-Euclidean geometry frameworks and nonlocal long-range interactions do naturally occur. \\ We prove general Harnack inequalities for the related weak solutions. Also, in the case when the growth exponent is $p=2$, we investigate the asymptotic behavior of the fractional subLaplacian operator, and the robustness of the aforementioned Harnack estimates as the differentiability exponent $s$ goes to $1$

Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group

We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlin- ear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian operator on the Heisenberg-Weyl group Hn. Among other results, we prove that the weak solutions to such a class of problems are bounded and Hölder continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates

TOPAZ0 4.0 - A new version of a computer program for evaluation of deconvoluted and realistic observables at LEP 1 and LEP 2

Description of the theoretical improvements included in the version 4.0 of the fitting code TOPAZ0, used at LEP for the indirect determination of the Standard Model parameters from radiative corrections

On a semianalytical and realistic approach to e+e- annihilation into fermion pairs and to Bhabha scattering within the minimal Standard Model at LEP energies

Theoretical formulation of the e+e- annihilation processes around the Z resonance, underlying the fitting program TOPAZ0 used by LEP collaborations and the LEP electroweak working group