arXiv research

This paper classifies topological symmetry groups for Petersen family graphs.

New triangulations of quaternionic projective plane found with various symmetry groups.

Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of the complete graph K_{4r+3} in S^3.

We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.

Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.

For each $n\leq 6$, we characterize all the groups which can occur as either the orientation preserving topological symmetry group or the topological symmetry group of some embedding of $K_n$ in $S^3$.

Classifies scalar second-order PDEs with low-dimensional symmetry groups.

Using the theory of the symmetry group for PDEs [15, 17], we derive the symmetry group G associated to surfaces PDE. Several group invariant solutions of the surfaces PDE are given by solving a reduced system of partial differential equations.

Researchers found multiple surfaces with same topological and symmetry properties.

Optimal classification requires choosing the right group symmetries, contrary to intuition.

Origami patterns are classified based on their symmetry groups.

In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its topological symmetry group.

Let $X\in\mathbb{R}^{n}$. For $φ:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$ and $t\in\mathbb{R}$, we put $φ^{t}=t^{-1}φ(Xt)$. A projective flow is a solution to the projective translation equation $φ^{t+s}=φ^{t}\circφ^{s}$, $t,s\in\mathbb{R}$. The projective superflow is a projective flow with a rational vector field which, …

Study of symmetries in 3D Lie groups, determining index and moduli space properties.

Generalizes symmetries of curved manifolds.

Study of intrinsic symmetry groups of links, finding counterexamples.

This paper identifies all topological symmetry groups for Heawood family graphs.

Reduces equations for contact mechanical systems on Lie groups by exploiting symmetries.

The paper classifies and proves properties of symmetry breaking operators for specific groups.

The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular abstract graphs. This question has been answered for complete graphs; it is natu…

The paper shows symmetries of a geometric space for Coxeter groups.

This paper determines all possible topological symmetry groups of generalized Petersen graphs.

Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body problem: periodic motions where the n bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry…

One considers a special class of PDEs systems and one determines the associated symmetry group. Particulary, for the Blair system, one finds the symmetry group. A solutions of the Blair system gives a conformally flat contact metric structure and also it defines a "force-free" model of solar physics. By using the symme…

Symmetry groups help define solitons in curved spaces.

New triangulations of octonionic projective plane found with restricted symmetry groups.

We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry…

One applies the symmetry group theory for study the partial differential equations of Tzitzeica surfaces theory. One finds infinitesimal symmetries, Lagrangians and a new solution of Titzeica equation.

Develops non-parametric tests for group symmetry in data.

Develops tests for conditional symmetry under group actions.

In this paper, a symmetry classification of a $(2+1)$-nonlinear wave equation $u_{tt}-f(u)(u_{xx}+u_{yy})=0$ where $f(u)$ is a smooth function on $u$, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this $…

Using the symmetry group theory of second order PDEs, one finds the symmetry group associated to Tzitzeica surfaces partial differential equation. One studies the inverse problem and one shows that the Tzitzeica surfaces PDE is an Euler-Lagrange equation. One determines the variational symmetry group of the associated …

New framework discovers non-affine continuous symmetries in neural networks.

We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.

The paper studies cylindrical handlebody-knots of genus two with unique unknotting annuli and finds trivial symmetry groups.

In this paper, we study generalized symmetric Finsler spaces. We first study symmetry preserving diffeomorphisms, then we show that the group of symmetry preserving diffeomorphisms is a transitive Lie transformation group. Finally we give some existence theorems.

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G, there is an embedding Γ of some graph in a hyperbolic rational homology 3-sp…

We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in $S^3$.

Paper proves non-compact inaudibility of symmetry and commutativity.

Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular. In this work we consider unimodular solvable Lie groups and pro…

New neural networks learn graph symmetries.

Study finds maximal symmetry groups for CR structures with specific properties.

The paper calculates Veech groups for triangulable structures on the sphere.

Study 2D viscoelastic equations using Lie group theory.

We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the …

New approach to symmetries in teleparallel geometries with non-trivial isotropy groups.

New method detects symmetries beyond affine transformations.