Canonical decomposition of linear differential operators with selected differential Galois groups

We revisit an order-six linear differential operator having a solution which is a diagonal of a rational function of three variables. Its exterior square has a rational solution, indicating that it has a selected differential Galois group, and is actually homomorphic to its adjoint. We obtain the two corresponding intertwiners giving this homomorphism to the adjoint. We show that these intertwiners are also homomorphic to their adjoint and have a simple decomposition, already underlined in a previous paper, in terms of order-two self-adjoint operators. From these results, we deduce a new form of decomposition of operators for this selected order-six linear differential operator in terms of three order-two self-adjoint operators. We then generalize the previous decomposition to decompositions in terms of an arbitrary number of self-adjoint operators of the same parity order. This yields an infinite family of linear differential operators homomorphic to their adjoint, and, thus, with a selected differential Galois group. We show that the equivalence of such operators is compatible with these canonical decompositions. The rational solutions of the symmetric, or exterior, squares of these selected operators are, noticeably, seen to depend only on the rightmost self-adjoint operator in the decomposition. These results, and tools, are applied on operators of large orders. For instance, it is seen that a large set of (quite massive) operators, associated with reflexive 4-polytopes defining Calabi-Yau 3-folds, obtained recently by P. Lairez, correspond to a particular form of the decomposition detailed in this paper.Comment: 40 page

Dileptons in a coarse-grained transport approach

We calculate dilepton spectra in heavy-ion collisions using a coarse-graining approach to the simulation of the created medium with the UrQMD transport model. This enables the use of dilepton-production rates evaluated in equilibrium quantum-field theory at finite temperatures and chemical potentials.Comment: 4 pages, 2 figures, contribution to the proceedings of "The 15th International Conference on Strangeness in Quark Matter" (SQM 2015), 06-11 July in Dubna, Russi

On the large-Q^2 behavior of the pion transition form factor

We study the transition of non-perturbative to perturbative QCD in situations with possible violations of scaling limits. To this end we consider the singly- and doubly-virtual pion transition form factor $\pi^0\to\gamma\gamma$ at all momentum scales of symmetric and asymmetric photon momenta within the Dyson-Schwinger/Bethe-Salpeter approach. For the doubly virtual form factor we find good agreement with perturbative asymptotic scaling laws. For the singly-virtual form factor our results agree with the Belle data. At very large off-shell photon momenta we identify a mechanism that introduces quantitative modifications to Efremov-Radyushkin-Brodsky-Lepage scaling.Comment: 5 pages, 7 figures, v3:contents revised, version published in PL

Different but Equal: Total Work, Gender and Social Norms in the EU and US Time Use.

Overall, the issue of whether Europeans are lazy or Americans are crazy seems of second-order importance relative to understanding the determinants of individual behavior. Amore useful, scientific approach is to assume that underlying tastes are common to both continents, while technologies, institutions, or interpersonal influences like norms or externalities may differ and evolve differently. The fact that Americans work on weekends or more often at odd hours of the day may simply represent a bad equilibrium that no individual agent can improve upon—and would certainly not wish to deviate from, given what all others are doing. Especially if norms and other externalities are important, one should recognize that the invisible hand may lead agents to places like this.

Lateral-directional control of the x-15 airplane

Lateral directional control and stability characteristics of X-15 aircraf

Different but Equal: Total Work, Gender and Social Norms in EU and US Time Use.

Using time-diary data from 27 countries, we demonstrate a negative relationship between real GDP per capita and the female-male difference in total work time—the sum of work for pay and work at home. We also show that in rich non-Catholic countries on four continents men and women do the same amount of total work on average. Our survey results demonstrate that labor economists, macroeconomists, sociologists and the general public consistently believe that women perform more total work. The facts do not arise from gender differences in the price of time nor from differences in intra-family bargaining: Gender equality is not associated with marital status, and most of the variance in gender total work differences arises from within-couple differences. A theory of social norms could account for within-education group and within-region gender differences being smaller than inter-group differences. It is consistent with cross-national evidence from the World Values Surveys and various sets of microeconomic data.time use;gender differences;household production;paid work;

Globally nilpotent differential operators and the square Ising model

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $\infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property.Comment: 55 page