Related papers: Invariant and Group Theoretical Integrations over …
We study the variety of complex $n$-dimensional Jordan algebras using techniques from Geometric Invariant Theory.
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
This is the first in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we construct a standard monomial basis for the arc space of the determinantal variety over $K$.…
We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to the metric. The main result of this paper is a generalized…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for theevaluation of Feynman diagrams. We describe the operational rules and illustrate the method…
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
We present the method of group foliation for constructing non-invariant solutions of partial differential equations on an important example of the Boyer-Finley equation from the theory of gravitational instantons. We show that the…
A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision…
We prove that the 2-hermitean matrix model and the complex-matrix model obey the same loop equations, and as a byproduct, we find a formula for Itzykzon-Zuber's type integrals over the unitary group. Integrals over U(n) are rewritten as…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the…
In this paper, we elucidate certain properties of the $(2n+1)$-dimensional Heisenberg group, and establish some theorems on the invariant differential operators on the group.
The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…
New exactly solvable problems have already been studied by using a modification of the factorization method introduced by Mielnik. We review this method and its connection with the traditional factorization method. The survey includes the…
This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is…
We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We curry the elementary arithmetic operations of addition and multiplication to give monotone injections on N, and describe & study the inverse monoids that arise from also considering their generalised inverses. This leads to well-known…
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…