Related papers: Regularization by {\epsilon}-metric
In a wide class of propagators regularized by the $\varepsilon$-metric [1], the $R$-operation is formulated. It is proved that the limit of renormalized Feynman integrals exists and is covariant. Possible applications in gravity are…
The aim of this paper is to numerically study the performance of a method of regularization. This technique was developed to solve the illposed problem of estimating a source-dimensional Poisson equation for two dimensions from measurements…
This paper has been withdrawn, as the explicit form of the propagator can be found in: V.V.Dodonov, I.A.Malkin and V.I.Man'ko, J.Phys.A 8 (1975) L19 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Int.J.Theor.Phys. 14 (1975) 37, Sec.3 V.V.Dodonov,…
The perturbative description of an electron propagating in a plane wave background is developed and loop corrections analysed. The ultraviolet divergences and associated renormalisation are studied using the sideband framework within which…
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…
We present a new proof of a recent $\epsilon$ regularity of G. Tian and J.Viaclovsky. Moreover, our idea also also works with a kind of $L^p, p<\dim M/2$ assumptions on the curvature.
The regularity theory for variational inequalities over polyhedral sets developed in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in the 90s has long become classics of variational analysis. But in the available proofs of…
Translation of the paper "Interpolation of linear spaces and maximum estimates for solutions to parabolic equations" published in Russian in the collected volume "Partial differential equations", Akad. Nauk SSSR, Sibirsk. Otdel., Inst.…
We investigate regularizations of distributional sections of vector bundles by means of nets of smooth sections that preserve the main regularity properties of the original distributions (singular support, wavefront set, Sobolev…
We discuss issues that arise in the regularisation of supersymmetric theories. (To appear in the book `Perspectives on Supersymmetry', World Scientific, Editor G. Kane.)
We resolve a long-standing open problem posed by Federer concerning the rectifiability of the integral geometric measure with exponent p >1, thereby settling a question that has persisted since its formulation. While the main theorem is…
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to $C^{1,1}$. Our approach is based on regularisations of the metric adapted to the causal structure.
Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles' motion at large scattering angle and,…
We present a new scheme for the general computation of cosmic propagators that allow to interpolate between standard perturbative results at low-k and their expected large-k resummed behavior. This scheme is applicable to any multi-point…
We consider realization and isomorphism problems for formal matrix rings over a given ring. Principal multiplier matrices of such rings play an important role in this case.\\ The work of A.A.Tuganbaev is supported by Russian Scientific…
The use of polarimetric techniques is nowadays widespread among solar and stellar astronomers. However, notwithstanding the recommandations that have often been made about the publication of polarimetric results in the astronomical…
The paper extends the 2003 radius of metric regularity theorem by Dontchev, Lewis & Rockafellar by providing an exact formula for the radius with respect to Lipschitz continuous perturbations in general Asplund spaces, thus, answering…
One reports the integral transform that determines the particle size distribution of a given sample from the small-angle scattering intensity under the assumption that the particle correlation function is a polynomial of degree M. The…