We consider the application of regularization by dimensional reduction to NLO corrections of hadronic processes. The general collinear singularity structure is discussed, the origin of the regularization-scheme dependence is identified and transition rules to other regularization schemes are derived. PACS: 11.10.Gh, 11.15.-q, 12.38.Bx, 12.60.Jv

Solodkiı̆ (1998) applied the modified projection scheme of Pereverzev (1995) for obtaining error estimates for a class of regularization methods for solving ill-posed operator equations. But, no a posteriori procedure for choosing the regularization parameter is discussed. In this paper, we consider Arcangeli’s type discrepancy principles for such a general class of regularization methods with m...

We present a novel variational method to non rigid registration of multi-modal data. A suitable deformation will be determined via the minimization of a morphological, i.e., contrast invariant, matching functional along with an appropriate regularization energy. Here we want to give special focus on the practical issues involving scale-space methods, regularization of the corresponding gradient...

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (“quantum mechanical path integrals in curved space”) dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by 1 8 h̄R. E-mail: [email protected] E-...

We describe two regularization techniques based on optimal control for solving two types of ill-posed problems. We include convergence proofs of the regularization method and error estimates. We illustrate our method through problems in signal processing and parameter identification using an efficient Riccati solver. Our numerical results are compared to the same examples solved using Tikhonov ...

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy principle, in general, does not yield uniform with respect to the data convergence. An a priori choice of the regularization parameter is proposed and justified for ...

The generalized second-order partial derivatives of 1/r , where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a spheroidal-regularization expression is illustrated on an ...

We extend the dipole formalism of Catani and Seymour to QCD processes involving heavy fermions. We give the appropriate subtraction terms together with their integrated counterpart. All calculations are done within dimensional regularization. Our formulae can be used with three variants of dimensional regularization (conventional dimensional regularization, the ’t Hooft-Veltman scheme or the fo...

We prove that three-dimensional N = 1 supersymmetric Yang-Mills-ChernSimons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfiel...