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Probing GPDs in Ultraperipheral Collisions
No full textInternational audienceUltraperipheral collisions in hadron colliders give new opportunites to investigate the hadron stucture through exclusive photoproduction processes. We describe the possibility of measuring the Generalized Parton Distributions in the Timelike Compton Scattering process and in the production of heavy vector meson
Search for extended γ-ray emission around AGN with H.E.S.S. and Fermi-LAT
No full textContext. Very-high-energy (VHE; E > 100 GeV) γ-ray emission from blazars inevitably gives rise to electron-positron pair production through the interaction of these γ-rays with the extragalactic background light (EBL). Depending on the magnetic fields in the proximity of the source, the cascade initiated from pair production can result in either an isotropic halo around an initially beamed source or a magnetically broadened cascade flux. Aims: Both extended pair-halo (PH) and magnetically broadened cascade (MBC) emission from regions surrounding the blazars 1ES 1101-232, 1ES 0229+200, and PKS 2155-304 were searched for using VHE γ-ray data taken with the High Energy Stereoscopic System (H.E.S.S.) and high-energy (HE; 100 MeV 10-12 G, this limits the production of pair haloes developing from electromagnetic cascades. For weaker magnetic fields, in which electromagnetic cascades would result in MBCs, EGMF strengths in the range (0.3-3)× 10-15 G were excluded for PKS 2155-304 at the 99% confidence level, under the assumption of a 1 Mpc coherence length
Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs
No full textThis paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduced in [8] which considers as test functions all those smooth processes which are tangent in mean. When restricted to the Markovian case, this definition induces a larger set of test functions, and reduces to the notion of stochastic viscosity solutions analyzed in [1, 2]. Our main result takes advantage of this enlargement of the test functions, and provides an easier proof of comparison. This is most remarkable in the context of the linear path-dependent heat equation. As a key ingredient for our methodology, we introduce a notion of punctual differentiation, similar to the corresponding concept in the standard viscosity solutions [3], and we prove that semimartingales are almost everywhere punctually differentiable. This smoothness result can be viewed as the counterpart of the Aleksandroff smoothness result for convex functions. A similar comparison result was established earlier in [8]. The result of this paper is more general and, more importantly, the arguments that we develop do not rely on any representation of the solution
Land use dynamics and the environment
No full textThis paper builds a benchmark framework to study optimal land use, encompassing land use activities and environmental degradation. We focus on the spatial externalities of land use as drivers of spatial patterns: land is immobile by nature, but local actions affect the whole space since pollution flows across locations resulting in both local and global damages. We prove that the decision maker problem has a solution, and characterize the corresponding social optimum trajectories by means of the Pontryagin conditions. We also show that the existence and uniqueness of time-invariant solutions are not in general guaranteed. Finally, a global dynamic algorithm is proposed in order to illustrate the spatial-dynamic richness of the model. We find that our simple set-up already reproduces a great variety of spatial patterns related to the interaction between land use activities and the environment. In particular, abatement technology turns out to play a central role as pollution stabilizer, allowing the economy to reach a time-invariant equilibrium that can be spatially heterogeneous
Optimal transportation under controlled stochastic dynamics
No full textInternational audienceWe consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale. The optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions. Our first main result is an extension of the Kantorovitch duality to this context. We also suggest a finite-difference scheme combined with the gradient projection algorithm to approximate the dual value. We prove the convergence of the scheme, and we derive a rate of convergence. We finally provide an application in the context of financial mathematics, which originally motivated our extension of the Monge-Kantorovitch problem. Namely, we implement our scheme to approximate no-arbitrage bounds on the prices of exotic options given the implied volatility curve of some maturity
Une coupe très intéressante dans le complément de l'éponge de Menger -itération 3-
No full textAn interesting cross-section inside the complement of the Menger sponge -iteration 3- (Une coupe très intéressante dans le complément de l'éponge de Menger -itération 3-
Le tapis de Sierpinski -itération 3-
No full textThe Sierpinski carpet -iteration 3- (Le tapis de Sierpinski -itération 3-