Related papers: Block regularisation of the logarithm central prob…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…
We prove refined space-time regularity for the classical stochastic Allen-Cahn equation with logarithmic potential. This allows to establish a random separation property, i.e. that the trajectories of the solution are strictly separated…
A new way how to calculate the off-shell renormalization functions within the $R^2$-gravity has been proposed. The one-loop renormalization group equations in the approach suggested have been constructed. The behaviour of effective…
We develop a mathematical theory of entropic regularisation of unbalanced optimal transport problems. Focusing on static formulation and relying on the formalism developed for the unregularised case, we show that unbalanced optimal…
We describe a method to discretize optimization problems arising in the regularization of linear inverse problem having compact forward operator defined on 3-D valed measures, compactly supported on a fixed set. The criterion is a quadratic…
Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators regularizing in all…
In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers of the unitarity problem…
For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…
Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
Consider the motion of a material point of unit mass in a central field determined by a homogeneous potential of the form $(-1/r^{\alpha})$, $\alpha>0,$ where $r$ being the distance to the centre of the field. Due to the singularity at…
For nearly a century the universal logarithmic behaviour of the mean velocity profile in a parallel flow was a mainstay of turbulent fluid mechanics and its teaching. Yet many experiments and numerical simulations are not fit exceedingly…
The arbitrariness in how the logarithm is defined within the QCD series for the inclusive electroproduction cross-section is shown to affect the summation to all orders in $\alpha_s$ of leading and successively-subleading logarithms within…
We discuss the statistical properties of a single vortex line in a perfect fluid. The partition function is calculated up to the end in the thin vortex approximation. It turns out that corresponding theory is renormalizable, and the…
In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An…
The problem of separation of variables in some coordinate systems obtained with the use of $L$-transformations is studied. Potentials are shown that allow separation of regular variables in a perturbed two-body problem. The potential…
Local oscillation of a function satisfying a H\"older condition is considered and it is proved that its growth is governed by a version of the Law of the Iterated Logarithm.
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions…