Related papers: Regularizing the Cross-Newell equation by re-modul…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
The second-order partial derivatives of the Coulomb potential of a point charge can be regularized using the Coulomb potential of a charge of the oblate spheroidal shape that a moving rest-frame-spherical charge acquires by the Lorentz…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
The conditions leading to a nontrivial renormalization of the topological charge in four--dimensional Yang--Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological…
We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant in the regulating…
Let $G=C_{p^n}$ be a finite cyclic p-group, and let $Hol(G)$ denote its holomorph. In this work, we find and characterize the regular subgroups of $Hol(G)$ that are mutually normalizing each other in the permutation group $Sym(G)$. We…
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange energy functional containing second-order derivatives of the unknown field. Such regularizations are featured in advanced micromagnetic models recently introduced…
In this note, we find an equivalent boundary integral equation to the classical $\bar{\partial}$-Neumann problem. The new equation contains an equivalent regularity to the global regularity of the $\bar{\partial}$-Neumann problem. We also…
A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
The paper is briefly dealing with greater or lesser misused normalization in self-modeling/multivariate curve resolution (S/MCR) practice. The importance of the correct use of the ode solvers and apt kinetic illustrations are elucidated.…
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques…