Related papers: The simplest Exotic Invariant (E3)
This paper is a continuation of previous work of the authors. We extend one of the theorems that gave a way to construct equilateral triangles whose vertices have integer coordinates to the general situation. An approximate extrapolation…
We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…
We present two different constructions of invariants for Legendrian knots in the standard contact space $\R^3$. These invariants are defined combinatorially, in terms of certain planar projections, and are useful in distinguishing…
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we…
Given a symplectomorphism f of a symplectic manifold X, one can form the `symplectic mapping cylinder' $X_f = (X \times R \times S^1)/Z$ where the Z action is generated by $(x,s,t)\mapsto (f(x),s+1,t)$. In this paper we compute the Gromov…
A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…
In this short note, we give an algorithm to get an explicit expression of the Luroth invariant in terms of the Dixmier-Ohno invariants. We also get the explicit factorized expression on the locus of Ciani quartics in terms of the…
Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.
The exoplanet field now abounds with new discoveries of planets and planetary systems. It is of great interest for the scientific community to understand the compositions and internal structures of these new planets outside our own solar…
Extensible variants improve the modularity and expressiveness of programming languages: they allow program functionality to be decomposed into independent blocks, and allow seamless extension of existing code with both new cases of existing…
It is shown that fractional $Z_3$-superspace is isomorphic to the $q\to\exp(2\pi i/3)$ limit of the braided line. $Z_3$-supersymmetry is identified as translational invariance along this line. The fractional translation generator and its…
We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and -- possibly coupled -- laws, including piezoelectricity…
This paper makes no sense. It only increases the entropy of our universe. It has been withdrawn by the author.
We study the structure of the algebra of polynomial invariants for the usual conjugation action of the complex special, SO_n, and general, O_n, orthogonal group on the space of traceless n by n complex matrices. (Note that these two…
We study low order terms of Emerton's spectral sequence for simply connected, simple groups. As a result, for real rank 1 groups, we show that Emerton's method for constructing eigenvarieties is successful in cohomological dimension 1. For…
An explicit form of first order PDE for invariants of binary form are found. By solving the equation a minimal generation set for a ring of invariants and theirs syzygies are calculated in the cases $n\leq 6$ and $n=8.$
Some forms of Lie algebras of types E_6, E_7, and E_8 are constructed using the exterior cube of a rank 9 finitely generated projective module.
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
At present the theory of skew-symmetric exterior differential forms has been developed. The closed exterior forms possess the invariant properties that are of great importance. The operators of the exterior form theory lie at the basis of…