The projective translation equation and unramified 2-dimensional flows with rational vector fields

Let X=(x,y). Previously we have found all rational solutions of the 2-dimensional projective translation equation, or PrTE, (1-z)f(X)=f(f(Xz)(1-z)/z); here f(X)=(u(x,y),v(x,y)) is a pair of two (real or complex) functions. Solutions of this functional equation are called projective flows. A vector field of a rational flow is a pair of 2-homogenic rational functions. On the other hand, only special pairs of 2-homogenic rational functions give rise to rational flows. In this paper we are interested in all non-singular (satisfying the boundary condition) and unramified (without branching points, i.e. single-valued functions in C^2\{union of curves}) projective flows whose vector field is still rational. We prove that, up to conjugation with 1-homogenic birational plane transformation, these are of 6 types: 1) the identity flow; 2) one flow for each non-negative integer N - these flows are rational of level N; 3) the level 1 exponential flow, which is also conjugate to the level 1 tangent flow; 4) the level 3 flow expressable in terms of Dixonian (equianharmonic) elliptic functions; 5) the level 4 flow expressable in terms of lemniscatic elliptic functions; 6) the level 6 flow expressable in terms of Dixonian elliptic functions again. This reveals another aspect of the PrTE: in the latter four cases this equation is equivalent and provides a uniform framework to addition formulas for exponential, tangent, or special elliptic functions (also addition formulas for polynomials and the logarithm, though the latter appears only in branched flows). Moreover, the PrTE turns out to have a connection with Polya-Eggenberger urn models. Another purpose of this study is expository, and we provide the list of open problems and directions in the theory of PrTE; for example, we define the notion of quasi-rational projective flows which includes curves of arbitrary genus.Comment: 34 pages, 2 figure

Activity and abundance of methane-oxidizing bacteria in secondary forest and manioc plantations of Amazonian Dark Earth and their adjacent soils.

The oxidation of atmospheric CH4 in upland soils is mostly mediated by uncultivated groups of microorganisms that have been identified solely by molecular markers, such as the sequence of the pmoA gene encoding the -subunit of the particulate methane monooxygenase enzyme. The objective of this work was to compare the activity and diversity of methanotrophs in Amazonian Dark Earth soil (ADE, Hortic Anthrosol) and their adjacent non-anthropic soil

Le défi de la sécurité routière

La sécurité routière sensibilise chacun des acteurs qu’il soit un usager, un producteur de véhicule ou un ingénieur en charge des infrastructures. Il faut admettre que l’homme, de par sa constitution, arrive assez rapidement à ses limites physiologiques et psychologiques lorsque la conduite ou l’immersion dans la circulation atteint un certain niveau de complexité. D’autre part les formidables progrès de la technologie ont amené les véhicules à un niveau de performance qui permet d’éviter parfois que des situations dangereuses dégénèrent en catastrophe. Enfin les infrastructures ont un rôle à jouer et leur aménagement et adaptation peut contribuer grandement à améliorer la sécurité routière. L’ingénieur se doit de connaître le potentiel d’amélioration qui peut être mobilisé par une simple réduction de la dangerosité des abords de la route. Les connaissances et la normalisation ont progressé mais la mise en application reste liée à des considérations de priorité budgétaire. Si un audit de sécurité est établi et qu’il est complété par un calcul économique qui prend en compte le coût social des accidents la démonstration est immédiatement faite de l’urgence d’agir. Par une série d’exemples ont apprend comment améliorer la situation en corrigeant des défauts ou des erreurs

The Origin of Fe II Emission in AGN

We used a very large set of models of broad emission line (BEL) clouds in AGN to investigate the formation of the observed Fe II emission lines. We show that photoionized BEL clouds cannot produce both the observed shape and observed equivalent width of the 2200-2800A Fe II UV bump unless there is considerable velocity structure corresponding to a microturbulent velocity parameter v_turb > 100 km/s for the LOC models used here. This could be either microturbulence in gas that is confined by some phenomenon such as MHD waves, or a velocity shear such as in the various models of winds flowing off the surfaces of accretion disks. The alternative way that we can find to simultaneously match both the observed shape and equivalent width of the Fe II UV bump is for the Fe II emission to be the result of collisional excitation in a warm, dense gas. Such gas would emit very few lines other than Fe II. However, since the collisionally excited gas would constitute yet another component in an already complicated picture of the BELR, we prefer the model involving turbulence. In either model, the strength of Fe II emission relative to the emission lines of other ions such as Mg II depends as much on other parameters (either v_turb or the surface area of the collisionally excited gas) as it does on the iron abundance. Therefore, the measurement of the iron abundance from the FeII emission in quasars becomes a more difficult problem.Comment: 23 pages. Accepted by Ap

Kinetics of photoinduced ordering in azo-dye films: two-state and diffusion models

We study the kinetics of photoinduced ordering in the azo-dye SD1 photoaligning layers and present the results of modeling performed using two different phenomenological approaches. A phenomenological two state model is deduced from the master equation for an ensemble of two-level molecular systems. Using an alternative approach, we formulate the two-dimensional (2D) diffusion model as the free energy Fokker-Planck equation simplified for the limiting regime of purely in-plane reorientation. The models are employed to interpret the irradiation time dependence of the absorption order parameters extracted from the available experimental data by using the exact solution to the light transmission problem for a biaxially anisotropic absorbing layer. The transient photoinduced structures are found to be biaxially anisotropic whereas the photosteady and the initial states are uniaxial.Comment: revtex4, 34 pages, 9 figure

Formulation et optimisation des formules d'enrobés

La composition des enrobés influence de façon déterminante la durabilité et les performances des revêtements. A ce jour l'optimisation des formules pour mélanges bitumineux se fait encore par une approche trop empirique sur la base d'essais traditionnels qui souvent n'offrent qu'une faible corrélation avec les performances réelles des matériaux. L'élaboration d’une méthodologie de formulation couplée avec des essais de performance permettant d'obtenir des enrobés performants et durables constitue le but essentiel de ce projet de recherche. Cette méthode de formulation se base sur une approche volumique et sur des modèles analytiques capables de prévoir les performances des enrobés dans certains cas. En effet, il est possible de réaliser une étude de formulation, son optimisation et l’évaluation de ses performances à long terme en combinant un calcul de prévision et quelques essais complémentaires. D’autre part le choix judicieux d’essais de performances dont l’utilisation est diffusée en Suisse permet d’obtenir des informations importantes sur la performance et la durabilité des enrobés formulés. Le choix de ces essais doit encore être validé par une étude sur des planches en vraie grandeur qui est actuellement en cours

On the presentation of the LHC Higgs Results

We put forth conclusions and suggestions regarding the presentation of the LHC Higgs results that may help to maximize their impact and their utility to the whole High Energy Physics community.Comment: Conclusions from the workshops "Likelihoods for the LHC Searches", 21-23 January 2013 at CERN, "Implications of the 125 GeV Higgs Boson", 18-22 March 2013 at LPSC Grenoble, and from the 2013 Les Houches "Physics at TeV Colliders" workshop. 16 pages, 3 figures. Version 2: Comment added on the first publication of signal strength likelihoods in digital form by ATLA