Related papers: The simplest Exotic Invariant (E3)

This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial…

A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems

Using the concept of constant evasion to different sorts of suitable binary relations, we establish many cardinal invariants derived from the established cardinal invariants $\mathfrak{e}^\mathrm{const}_{n}$ and…

A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.

We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k-1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is very…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

We give a formula of 3-dimensional invariant for a cyclic contact branched covering of the standard contact S^{3}.

We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.

The first examples of exceptional terminal singularities are constructed.

In this paper we present an iterative construction of irreducible polynomials over finite fields based upon repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…

We give a 3-page description of the Gassner invariant / representation of braids / pure braids, along with a description and a proof of its unitarity property.

An explicit example of an exotic symplectic $\mathbf{R}^6$ is given. Together with an earlier known example on $\mathbf{R}^4$, this yields an explicit exotic symplectic form on $\mathbf{R}^{2n}$ for all $n\geq2$.

Phase curves are the best technique to probe the three dimensional structure of exoplanets' atmospheres. In this chapter we first review current exoplanets phase curve observations and the particular challenges they face. We then describe…

It is shown in this paper that non-conforming finite elements on the triangle using $P^{1}$-nonconforming polynomials and $P^{2}$ -conforming polynomials can be easily built and used.They appear as an 'enriched' version of the standard…

We construct a hyperbolic sextic surface in P^3(C).

We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.

This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of…

In this note we give concise formulas, which lead to a simple and fast computer program that computes a powerful knot invariant. This invariant $\rho_1$ is not new, yet our formulas are by far the simplest and fastest: given a knot we write…

A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of…