Search results for " Mathematical"
showing 10 items of 686 documents
Magnetic Monopole Search with the Full MoEDAL Trapping Detector in 13 TeV pp Collisions Interpreted in Photon-Fusion and Drell-Yan Production
2019
MoEDAL is designed to identify new physics in the form of stable or pseudostable highly ionizing particles produced in high-energy Large Hadron Collider (LHC) collisions. Here we update our previous search for magnetic monopoles in Run 2 using the full trapping detector with almost four times more material and almost twice more integrated luminosity. For the first time at the LHC, the data were interpreted in terms of photon-fusion monopole direct production in addition to the Drell-Yan-like mechanism. The MoEDAL trapping detector, consisting of 794 kg of aluminum samples installed in the forward and lateral regions, was exposed to 4.0 fb$^{-1}$ of 13 TeV proton-proton collisions at the LHC…
Diseased Social Predators
2017
Social predators benefit from cooperation in the form of increased hunting success, but may be at higher risk of disease infection due to living in groups. Here, we use mathematical modeling to investigate the impact of disease transmission on the population dynamics benefits provided by group hunting. We consider a predator-prey model with foraging facilitation that can induce strong Allee effects in the predators. We extend this model by an infectious disease spreading horizontally and vertically in the predator population. The model is a system of three nonlinear differential equations. We analyze the equilibrium points and their stability as well as one- and two-parameter bifurcations. …
Non-equivariant cylindrical contact homology
2013
It was pointed out by Eliashberg in his ICM 2006 plenary talk that the integrable systems of rational Gromov-Witten theory very naturally appear in the rich algebraic formalism of symplectic field theory (SFT). Carefully generalizing the definition of gravitational descendants from Gromov-Witten theory to SFT, one can assign to every contact manifold a Hamiltonian system with symmetries on SFT homology and the question of its integrability arises. While we have shown how the well-known string, dilaton and divisor equations translate from Gromov-Witten theory to SFT, the next step is to show how genus-zero topological recursion translates to SFT. Compatible with the example of SFT of closed …
The spatial dimension of the French private rental markets: Evidence from microgeographic data in 2015
2021
International audience; This article draws on data collected by local rental observatories in 12 French urban units in 2015 to analyze the spatial dimension of hedonic rental prices in the private rental market through (i) the spatial heterogeneity between urban units and (ii) the wide variety of contextual and locational characteristics (socio-economic, environmental (dis)amenity, and accessibility) and flexible specifications to capture their potential non-linear influence on rent. Based on a joint test of equality of coefficients across all urban units, we find that hedonic prices differ for 75% of the characteristics, thereby justifying a detailed analysis of heterogeneity. Lyon, Nice, …
Languages associated with saturated formations of groups
2013
International audience; In a previous paper, the authors have shown that Eilenberg's variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.; Dans un article précédent, les auteurs avaient montré comment étendre le théorème des variétés d'Eilenberg à des structures plus g…
Hajłasz–Sobolev imbedding and extension
2011
Abstract The author establishes some geometric criteria for a Hajlasz–Sobolev M ˙ ball s , p -extension (resp. M ˙ ball s , p -imbedding) domain of R n with n ⩾ 2 , s ∈ ( 0 , 1 ] and p ∈ [ n / s , ∞ ] (resp. p ∈ ( n / s , ∞ ] ). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α -cigar domain with α ∈ ( 0 , 1 ) if and only if F ˙ p , ∞ s ( R 2 ) | Ω = M ˙ ball s , p ( Ω ) for some/all s ∈ [ α , 1 ) and p = ( 2 − α ) / ( s − α ) , where F ˙ p , ∞ s ( R 2 ) | Ω denotes the restriction of the Triebel–Lizorkin space F ˙ p , ∞ s ( R 2 ) on Ω .
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
2016
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.
Monotonicity and local uniqueness for the Helmholtz equation
2017
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…
An optimal Poincaré-Wirtinger inequality in Gauss space
2013
International audience; Let $\Omega$ be a smooth, convex, unbounded domain of $\mathbb{R}^N$. Denote by $\mu_1(\Omega)$ the first nontrivial Neumann eigenvalue of the Hermite operator in $\Omega$; we prove that $\mu_1(\Omega) \ge 1$. The result is sharp since equality sign is achieved when $\Omega$ is a $N$-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincaré-Wirtinger inequality for functions belonging to the weighted Sobolev space $H^1(\Omega,d\gamma_N)$, where $\gamma_N$ is the $N$% -dimensional Gaussian measure.
A note on Sobolev isometric immersions below W2,2 regularity
2017
Abstract This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W 2 , 2 setting. We show that the Hessian of each coordinate function of a W 2 , p , p 2 , isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W 2 , p , p 2 , isometric immersion from a bounded domain of R 2 into R 3 that has multiple singularities.