Search results for "Trivia"

Simple Facts Concerning Nambu Algebras

1998

A class of substitution equations arising in the extension of Jacobi identity for $n$-gebras is studied and solved. Graded bracket and cohomology adapted to the study of formal deformations are presented. New identities in the case of Nambu-Lie algebras are proved. The triviality in the Gerstenhaber sense of certain deformed n-skew-symmetric brackets, satisfying the Leibniz rule with respect to a star-product, is shown for n≥ 3.

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.

Reduction to finite dimensions of continuous systems having only a few amplified modes

2008

In the approach of Guckenheimer and Knobloch the amplitudes of trajectories on the unstable manifold 0 are the pivotal quantities. This places a certain restriction on the applicability of this approach, as only neighbourhoods of 0 of the unstable manifold of 0 are accessible, which have a one-to-one projection into their tangent at 0, the linear space spanned by the amplified modes. This restriction may be lifted, using the arc lengths of trajectories instead.

New solutions of the hamiltonian and diffeomorphism constraints of quantum gravity from a highest weight loop representation

1991

Abstract We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space.

Macroscopic conductivity of free fermions in disordered media

2014

We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint. We show, in particular, the existence and finiteness of the conductivity measure $\mu _{\mathbf{\Sigma }}$ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, $\mu _{\mathbf{\Sigma }}$ converges in the weak$^{\ast } $-topology to the trivial measure in the case of perfect insulators (strong disorder, compl…

Two Dimensional Quantum Chromodynamics as the Limit of Higher Dimensional Theories

1994

We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.

Population dynamics based on ladder bosonic operators

2021

Abstract We adopt an operatorial method, based on truncated bosons, to describe the dynamics of populations in a closed region with a non trivial topology. The main operator that includes the various mechanisms and interactions between the populations is the Hamiltonian, constructed with the density and transport operators. The whole evolution is derived from the Schrodinger equation, and the densities of the populations are retrieved from the normalized expected values of the density operators. We show that this approach is suitable for applications in very large domain, solving the computational issues that typically occur when using an Hamiltonian based on fermionic ladder operators.

Elements of General Representation Theory

1982

In Chapter V, classical representation theory was studied. This is the theory of the group-ring KG and the KG-modules, where K is an algebraically closed field of characteristic 0. (Many theorems remain valid under the hypothesis that K is algebraically closed and that char K does not divide the order of G). In this case, KG is semisimple and all KG-modules are completely reducible. For many purposes it is therefore sufficient to handle the irreducible representations.

Galilée, une soûlographie

2019

Galilée, un signe à tout faire

2014

Que l’on souhaite faire oeuvre de science, prévaloir une opinion, susciter une émotion, valoriser un produit, la vie et l’oeuvre du mathématicien, physicien et astronome italien Galileo Galilei s’acommodent de bien des manières. Comment cette trivialité manifeste participe-t-elle du « mythe » ?