In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two isotopy invariants: augmentation number via point-counting over finite field, for variety of Chekanov-Eliashberg differential graded algebra, ruling polynomial combinatorics decompositions front projection.

Formal methods have proved their usefulness for an-alyzing the security of protocols. Most existing resultsfocus on trace properties like secrecy or authentication.There are however several security properties, whichcannot be defined (or cannot be naturally defined) astrace properties and require the notion of observationalequivalence. Typical examples are anonymity, pri...

L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete classification up to isometry, and also their isometry groups. The key tool is the so-called canonical decomposition of hyperbolic manifolds.

Recently some results have been presented which show that certain kinds of deterministic descriptions and indeterministic descriptions are observationally equivalent (Werndl 2009a, Werndl 2011). These results prompt interesting philosophical questions, such as what exactly they show or whether the deterministic or indeterministic description is preferable. There is hardly any philosophical disc...

In this paper we introduce the concept of a behavior homomorphisms and isomorphisms and use it to present a uni.ed approach to the study of equivalence of di/erent behavior representations concentrating on a special representation we call normalized ARMA (NARMA) representation. c © 2001 Elsevier Science B.V. All rights reserved.

According to a previous result by S. V. Avgustinovich and the author, each factorial language admits a unique canonical decomposition to a catenation of factorial languages. In this paper, we analyze the appearance of the canonical decomposition of a catenation of two factorial languages whose canonical decompositions are given.

In the present paper, we point out that the basic result, which is the main tool, in [D. J. Wen, Projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators, Nonlinear Anal. 73 (2010) 2292–2297] has some fatal errors. Therefore, the results and algorithms in the above mentioned paper are no longer valid. To overcome with the problems in t...

We prove that QCD in the ǫ-regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential μ. To this aim we prove a theorem that relates integrals over fermionic and bosonic variables to super-Hermitian or super-Unitary groups also called superbosonisation. Our findings extend previous results for the equivalenc...

We give a list of canonical equivalence relations on discrete nets of the positive unit sphere of c0. This generalizes results of W. T. Gowers [1] and A. D. Taylor [5].