A Generalization of Abel Inversion to non axisymmetric density distribution

Abel Inversion is currently used in laser-plasma studies in order to estimate the electronic density $n_e$ from the phase-shift map $\delta \phi$ obtained via interferometry. The main limitation of the Abel method is due to the assumption of axial symmetry of the electronic density, which is often hardly fulfilled. In this paper we present an improvement to the Abel inversion technique in which the axial symmetry condition is relaxed by means of a truncated Legendre Polinomial expansion in the azimutal angle. With the help of simulated interferograms, we will show that the generalized Abel inversion generates accurate densities maps when applied to non axisymmetric density sources

Dolbeault-Massey triple products of low degree

Let A=(A\u2022,\u2022, 02-A) be a differential bigraded algebra. We characterize non-vanishing Dolbeault-Massey triple products of low degree (see Theorems 3.1 and 3.2). We give some applications for the Dolbeault complex on a compact complex manifold

Complex symplectic structures and the del-delbar-lemma

In this paper, we study complex symplectic manifolds, i.e., compact complex manifolds X which admit a holomorphic (2,\ua00)-form \u3c3 which is d-closed and non-degenerate, and in particular the Beauville\u2013Bogomolov\u2013Fujiki quadric Q\u3c3 associated with them. We will show that if X satisfies the -lemma, then Q\u3c3 is smooth if and only if h2 , 0(X) = 1 and is irreducible if and only if h1 , 1(X) > 0

Degree Correlations in Random Geometric Graphs

Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree correlation function in terms of the clustering coefficient of the graphs for two-dimensional space in particular, with extensions to arbitrary finite dimension

Bott–Chern Laplacian on almost Hermitian manifolds

Let (M, J, g, ω) be a 2n-dimensional almost Hermitian manifold. We extend the definition of the Bott–Chern Laplacian on (M, J, g, ω) , proving that it is still elliptic. On a compact Kähler manifold, the kernels of the Dolbeault Laplacian and of the Bott–Chern Laplacian coincide. We show that such a property does not hold when (M, J, g, ω) is a compact almost Kähler manifold, providing an explicit almost Kähler structure on the Kodaira–Thurston manifold. Furthermore, if (M, J, g, ω) is a connected compact almost Hermitian 4-manifold, denoting by hBC1,1 the dimension of the space of Bott–Chern harmonic (1, 1)-forms, we prove that either hBC1,1=b- or hBC1,1=b-+1. In particular, if g is almost Kähler, then hBC1,1=b-+1, extending the result by Holt and Zhang (Harmonic forms on the Kodaira–Thurston manifold. arXiv:2001.10962, 2020) for the kernel of Dolbeault Laplacian. We also show that the dimensions of the spaces of Bott–Chern and Dolbeault harmonic (1, 1)-forms behave differently on almost complex 4-manifolds endowed with strictly locally conformally almost Kähler metrics. Finally, we relate some spaces of Bott-Chern harmonic forms to the Bott–Chern cohomology groups for almost complex manifolds, recently introduced in Coelho et al. (Maximally non-integrable almost complex structures: an h-principle and cohomological properties, arXiv:2105.12113, 2021)

Does the Mediterranean Sea influence the European summer climate? The anomalous summer 2003 as a testbed

The European summer 2003 presents a rare opportunity to investigate dynamical interactions in the otherwise variable European climate. Not only did air temperature show a distinct signal, but the Mediterranean sea surface temperature (SST) was also exceptionally warm. The traditional view of the role of the Mediterranean Sea in the climate system highlights the influence of the atmospheric circulation on the Mediterranean Sea. The question of whether the Mediterranean Sea feeds back on the atmospheric dynamics is of central importance. The case of the extremely anomalous summer 2003 allows for investigating the issue under realistic boundary conditions. The present study takes advantage of a newly developed regional coupled atmosphereocean model for this purpose. Experiments with prescribed historical versus climatological SST suggest that the local atmospheric circulation is not strongly sensitive to the state of the Mediterranean Sea, but its influence on the moisture balance and its role in the regional hydrological cycle is substantial. Warmer Mediterranean SSTs lead to enhanced evaporation and moisture transport in the atmosphere. Results of regional coupled simulations with different ocean initial conditions imply that because of the strong stratification of the surface waters in summer, the response time of the upper layers of the Mediterranean Sea to atmospheric forcing is rather short. It can be concluded that the role of the Mediterranean Sea in the European summer climate is mostly passive. In winter, however, since the upper layers of the Mediterranean Sea are well mixed, the memory of the Mediterranean SSTs stretches over longer time scales, which implies a potential for actively governing regional climate characteristics to some extent. © 2012 American Meteorological Society

On the Anti-invariant Cohomology of Almost Complex Manifolds

We study the space of closed anti-invariant forms on an almost complex manifold, possibly non-compact. We construct families of (non-integrable) almost complex structures on R4, such that the space of closed J-anti-invariant forms is infinite dimensional, and also 0- or 1-dimensional. In the compact case, we construct 6-dimensional almost complex manifolds with arbitrary large anti-invariant cohomology and a 2-parameter family of almost complex structures on the Kodaira–Thurston manifold whose anti-invariant cohomology group has maximum dimension