Related papers: Symmetries and Invariant Differential Pairings
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.
Validation is a major challenge in differentiable programming. The state of the art is based on algorithmic differentiation. Consistency of first-order tangent and adjoint programs is defined by a well-known first-order differential…
In this paper the notion of an M-th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a…
I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…
This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication…
We study examples where conformal invariance implies triviality of the underlying quantum field theory.
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
The main purpose of this paper is to investigate several further interesting properties of symmetry for the p-adic invariant integral on Z_p.
We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in…
Skew-symmetric forms possess unique capabilities. The properties of closed exterior and dual forms, namely, invariance, covariance, conjugacy and duality, either explicitly or implicitly appear in all invariant mathematical formalisms. This…
Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
Chiral and conformal anomalies are fundamental phenomena that span multiple disciplines, including high-energy physics, condensed matter theory and cosmology. These anomalies play a crucial role in understanding fundamental interactions and…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…
The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…