Related papers: Group analysis and renormgroup symmetries
We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…
In this paper we establish a comparison result through symmetrization for solutions to some boundary value problems involving the fractional Laplacian. This allows to get sharp estimates for the solutions, obtained by comparing them with…
For certain hierarchical structures, one can study the percolation problem using the renormalization-group method in a very precise way. We show that the idea can be also applied to two-dimensional planar lattices by regarding them as…
Calculating multiple zeta values at arguments of any sign in a way that is compatible with both the quasi-shuffle product as well as meromorphic continuation, is commonly referred to as the renormalisation problem for multiple zeta values.…
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
Applications of the principle of reduction of couplings to the standard model and supersymmetric grand unified theories are reviewed. Phenomenological applications of renormalization group invariant sum rules for soft supersymmetry-breaking…
New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and…
We use renormalization group summed perturbation theory (RGSPT) to improve perturbation series in quantum chromodynamics in the determination of some of the standard model parameters.
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a…
The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…
We propose a theoretical formulation of protected edge modes in the language of quantum field theories based on the contemporary understanding of the renormalization group. We use bulk and boundary renormalization arguments which have never…