Search results for "invariants"
showing 10 items of 36 documents
Comment on “Topological invariants, instantons, and the chiral anomaly on spaces with torsion”
1999
In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].
A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality
2019
AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s so…
La linguistique cognitive existe-t-elle ?
2009
International audience; La présente contribution est consacrée à la question du statut théorique et de la légitimité même de la notion de ‘linguistique cognitive'. Sont tout d'abord rappelées (§ 1) les conditions historiques d'émergence, aux Etats-Unis, des deux grands courants de la linguistique dite ‘cognitive' : la grammaire générative (qui s'inscrit dans le paradigme ‘computo-représentationnel symbolique' du cognitivisme classique) et les grammaires cognitives (se réclamant d'un paradigme ‘constructiviste'). Puis (§ 2) est défendue l'idée qu'une théorie linguistique ne saurait se dire ‘cognitive' si elle ne cherche pas à relier explicitement les significations et les concepts, ce qui co…
The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras
2016
We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.
Symplectic Applicability of Lagrangian Surfaces
2009
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equa- tions. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
Une nouvelle méthode constructive des lois de comportement des matériaux composites à l'aide de la théorie des invariants
2005
International audience; On propose une nouvelle méthode constructive, systématique et générale des lois de comportement des milieux anisotropes appuyée sur la Théorie des invariants. On peut résumer la démarche adoptée de la manière suivante : l'ensemble V des variables et le groupe (fini) S des symétries matérielles étant supposés connus, on donne une borne au nombre des éléments d'une famille des générateurs possibles des invariants polynominaux de V sous S ; on donne la méthode pour construire ces élements ; on écrit sous une forme induisant une certaine unicité, dite forme normale, la décomposition de tout invariant polynominal de V sous S. Enfin à l'aide des critères de tensorialité, o…
Topological Hamiltonian as an exact tool for topological invariants
2012
We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show that topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
Defining relations of the noncommutative trace algebra of two 3×3 matrices
2006
The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$ generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all traces of products of generic matrices, $n,d\geq 2$. It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra $S$ of the center $C_{nd}$. For $n=3$ and $d=2$ we have found explicitly such a subalgebra $S$ and a set of free generators of the $S$-module $T_{32}$. We give also a set of defining relations of $T_{32}$ as an algebra and a Groebner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit prese…
A new constructive method using the theory of invariants to obtain material behavior laws
2006
International audience; The aim of this paper is to present a constructive method to derive mechanical behavior laws using the Theory of Invariants and Continuum Thermodynamics. More precisely, we want to construct, in a general way, the state or dissipation potential in a polynomial form given a set of variables V and the material symmetry group S. For this purpose, we show how to obtain a set of generators for the S-invariant polynomials of V. Then, using the Grœbner basis concept, we write all the decompositions of a polynomial of a given degree.
A constructive approach of invariants of behavior laws with respect to an infinite symmetry group – Application to a biological anisotropic hyperelas…
2014
Abstract In this paper, six new invariants associated with an anisotropic material made of one fiber family are calculated by presenting a systematic constructive and original approach. This approach is based on the development of mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Definition of the generalized Reynolds Operator. • Calculation of an integrity basis for invariant polynomials. • Comparison between the new (constructed) invariants and the classical ones.