Search results for "Algebraic Geometry"
showing 10 items of 356 documents
The J-invariant, Tits algebras and Triality
2012
In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map and Grothendieck's $\gamma$-filtration. As an application we recover some known results on the $J$-invariant of quadratic forms of small dimension; we describe all possible values of the $J$-invariant of an algebra with orthogonal involution up to degree 8 and give explicit examples; we establish several relations between the $J$-invariant of an algebra $A$ with orthogonal involution and the $J$-invariant of the corresponding quadratic form over the functi…
Algebraic groups as difference Galois groups of linear differential equations
2019
We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field $\mathbb{C}(x)$ with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main result is that every linear algebraic group, considered as a difference algebraic group, occurs as the difference Galois group of some linear differential equation over $\mathbb{C}(x)$.
Steiner systems and configurations of points
2020
AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…
A second-order differential equation for the two-loop sunrise graph with arbitrary masses
2011
We derive a second-order differential equation for the two-loop sunrise graph in two dimensions with arbitrary masses. The differential equation is obtained by viewing the Feynman integral as a period of a variation of a mixed Hodge structure, where the variation is with respect to the external momentum squared. The fibre is the complement of an elliptic curve. From the fact that the first cohomology group of this elliptic curve is two-dimensional we obtain a second-order differential equation. This is an improvement compared to the usual way of deriving differential equations: Integration-by-parts identities lead only to a coupled system of four first-order differential equations.
Real Algebraic Geometry
2011
144 Pages; Cet ouvrage constitue les actes de la conférence de Géométrie Algébrique Réelle qui a eu lieu à Rennes du 20 au 24 Juin 2011
Effect of the loading rate on ultimate strength of composites. Application: Pressure vessel slow burst test
2013
International audience; The strength of unidirectional elastic fibre composites is shown to depend on the loading rate as the viscoelastic nature of the matrix results in a fall in breaking load as the rate is reduced. The simulation of the accumulation of fibre breaks leading to failure, takes into account all physical phenomena involved fibre failure, including the stochastic nature of fibre strength, stress transfer through the matrix between reinforcements, interfacial debonding and the viscoelastic nature of the matrix. The kinetics of composite failure are seen to involve the initial formation of random fibre breaks which at higher loads coalesce into clusters of broken fibres. The ra…
Glass fibre strength distribution determined by common experimental methods
2002
The tensile strength of brittle fibres is routinely described by the Weibull distribution. The parameters of the distribution can be obtained from tests on single fibres and fibre bundles or from model composite tests. However, there is growing evidence that the distribution parameters obtained by different experimental techniques differ systematically. In order to investigate the possible causes of such discrepancies, single-fibre tension, fibre bundle, and single-fibre fragmentation tests are employed in this study to obtain strength distribution of commercial E-glass fibres. The results reveal parameter dependence on the approach used to extract the distribution parameters from experimen…
Strong enhancement of the Breit-Wigner-Fano Raman line in carbon nanotube bundles caused by plasmon band formation
2002
We investigate the origin of the Breit-Wigner-Fano line in the Raman spectra of individual single-walled carbon nanotubes and their bundles. Using confocal Raman microscopy and atomic-force microscopy we found that the Breit-Wigner-Fano line intensity increases strongly with the bundle thickness. We confirmed this result by Raman investigations of partially decomposed bundles, which were additionally investigated by transmission electron microscopy. Our random-phase approximation based theory, which identifies the Breit-Wigner-Fano line as an excited band of plasmon-phonon modes, is fully consistent with the experimental results.
Nonisotrivial families over curves with fixed point free automorphisms
2005
We construct for any smooth projective curve of genus $q\ge 2$ with a fixed point free automorphism a nonisotrivial family of curves. Moreover we study the space of modular curves and that of parameters.
The structure of the moduli spaces of toric dynamical systems
2023
We consider complex-balanced mass-action systems, or toric dynamical systems. They are remarkably stable polynomial dynamical systems arising from reaction networks seen as Euclidean embedded graphs. We study the moduli spaces of toric dynamical systems, called the toric locus: given a reaction network, we are interested in the topological structure of the set of parameters giving rise to toric dynamical systems. First we show that the complex-balanced equilibria depend continuously on the parameter values. Using this result, we prove that the toric locus of any toric dynamical system is connected. In particular, we emphasize its product structure: it is homeomorphic to the product of the s…