Related papers: Group analysis and renormgroup symmetries
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
In this paper, we are concerned with the first initial boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. As usual, the establishment of the a priori C^2 estimates is our main part. Based on…
A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.
Several methods are used to evaluate finite trigonometric sums. In each case, either the sum had not previously been evaluated, or it had been evaluated, but only by analytic means, e.g., by complex analysis or modular transformation…
We consider the problem of constructing matched groups such that the resulting groups are statistically similar with respect to their average values for multiple covariates. This group-matching problem arises in many cases, including…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In…
One common type of symmetry is when values are symmetric. For example, if we are assigning colours (values) to nodes (variables) in a graph colouring problem then we can uniformly interchange the colours throughout a colouring. For a…
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods, group-theoretic and coming from algebraic and arithmetic…
The isospectral renormalization group is a powerful method to analyze the spectrum of operators in quantum field theory. It was introduced in 1995 [see \cite{BachFrohlichSigal1995}, \cite{BachFrohlichSigal1998}] and since then it has been…
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal…
For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathbb Q[G]$. We give necessary and sufficient criteria for the existence of such relations and apply them to obtain relations between the…
Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to providing a new interpretation of the density matrix renormalization group: its…
We start by discussing some theoretical issues of renormalization group transformations and Monte Carlo renormalization group technique. A method to compute the anomalous dimension is proposed and investigated. As an application, we find…