Related papers: Regularization of self inductance
We continue the program initiated in a previous work, of applying integro-differential methods to Neumann Homogenization problems. We target the case of linear periodic equations with a singular drift, which includes (with some regularity…
Invariants are the predominant approach to verify the correctness of loops. As an alternative, loop contracts, which make explicit the premise and conclusion of the underlying induction proof, can sometimes capture correctness conditions…
We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions.…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
In this paper, we study two-loop contribution to the effective action of a two-dimensional sigma model. We derive a new formula, which can be applicable to a regularization of general type. As examples, we obtain known results for…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional 'orbit method', keep T-duality manifest throughout. In particular, we apply the Rankin-Selberg-Zagier approach to…
We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently…
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
Loewner's equation provides a way to encode a simply connected domain or equivalently its uniformizing conformal map via a real-valued driving function of its boundary. The first main result of the present paper is that the Dirichlet energy…
Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the UV-divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast…
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…
We present an invariant regularisation scheme to compute two dimensional induced gauge theory actions, that is local in Polyakov's variables, but nonlocal in the original gauge potentials. Our method sheds light on the locality of this…
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
We propose a regularization method to solve a nonlinear ill-posed problem connected to inversion of data gathered by a ground conductivity meter.