Diffeomorphic approximation of Sobolev homeomorphisms

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.Comment: 21 pages, 5 figure

Exponential instability in the fractional Calder\'on problem

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on problem and the truncated Hilbert transform.Comment: 17 page

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Covariant equations for the three-body bound state

The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including the Wigner rotations and rho-spin decomposition of the off-shell particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative rho-spin states of the off-shell particle.Comment: 57 pages, RevTeX, 6 figures, uses epsf.st

Mechanism of miR-222 and miR-126 regulation and its role in asbestos-induced malignancy

MiR-222 and miR-126 are associated with asbestos exposure and the ensuing malignancy, but the mechanism(s) of their regulation remain unclear. We evaluated the mechanism by which asbestos regulates miR-222 and miR-126 expression in the context of cancer etiology. An ‘in vitro’ model of carcinogen-induced cell transformation was used based on exposing bronchial epithelium BEAS-2B cells to three different carcinogens including asbestos. Involvement of the EGFR pathway and the role of epigenetics have been investigated in carcinogen-transformed cells and in malignant mesothelioma, a neoplastic disease associated with asbestos exposure. Increased expression of miR-222 and miR-126 were found in asbestos-transformed cells, but not in cells exposed to arsenic and chrome. Asbestos-mediated activation of the EGFR pathway and macrophages-induced inflammation resulted in miR-222 upregulation, which was reversed by EGFR inhibition. Conversely, asbestos-induced miR-126 expression was affected neither by EGFR modulation nor inflammation. Rather than methylation of the miR-126 host gene EGFL7, epigenetic mechanism involving DNMT1- and PARP1-mediated chromatin remodeling was found to upregulate of miR-126 in asbestos-exposed cells, while miR-126 was downregulated in malignant cells. Analysis of MM tissue supported the role of PARP1 in miR-126 regulation. Therefore, activation of the EGFR pathway and the PARP1-mediated epigenetic regulation both play a role in asbestos-induced miRNA expression, associated with in asbestos-induced carcinogenesis and tumor progression

Vanishing Theorems and String Backgrounds

We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions like for example that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition that a certain vector is parallel with respect to the Bismut connection.Comment: 25 pages, Late

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.Comment: 21 pages, no figure

Bounds on strong field magneto-transport in three-dimensional composites

This paper deals with bounds satisfied by the effective non-symmetric conductivity of three-dimensional composites in the presence of a strong magnetic field. On the one hand, it is shown that for general composites the antisymmetric part of the effective conductivity cannot be bounded solely in terms of the antisymmetric part of the local conductivity, contrary to the columnar case. So, a suitable rank-two laminate the conductivity of which has a bounded antisymmetric part together with a high-contrast symmetric part, may generate an arbitrarily large antisymmetric part of the effective conductivity. On the other hand, bounds are provided which show that the antisymmetric part of the effective conductivity must go to zero if the upper bound on the antisymmetric part of the local conductivity goes to zero, and the symmetric part of the local conductivity remains bounded below and above. Elementary bounds on the effective moduli are derived assuming the local conductivity and effective conductivity have transverse isotropy in the plane orthogonal to the magnetic field. New Hashin-Shtrikman type bounds for two-phase three-dimensional composites with a non-symmetric conductivity are provided under geometric isotropy of the microstructure. The derivation of the bounds is based on a particular variational principle symmetrizing the problem, and the use of Y-tensors involving the averages of the fields in each phase.Comment: 21 page

Gas-phase identification of (Z)-1,2-ethenediol, a key prebiotic intermediate in the formose reaction

Prebiotic sugars are thought to be formed on primitive Earth by the formose reaction. However, their formation is not fully understood and it is plausible that key intermediates could have formed in extraterrestrial environments and subsequently delivered on early Earth by cometary bodies. 1,2-Ethenediol, the enol form of glycolaldehyde, represents a highly reactive intermediate of the formose reaction and is likely detectable in the interstellar medium. Here, we report the identification and first characterization of (Z)-1,2-ethenediol by means of rotational spectroscopy. The title compound has been produced in the gas phase by flash vacuum pyrolysis of bis-exo-5-norbornene-2,3-diol at 750 °C, through a retro-Diels-Alder reaction. The spectral analysis was guided by high-level quantum-chemical calculations, which predicted spectroscopic parameters in very good agreement with the experiment. Our study provides accurate spectral data to be used for searches of (Z)-1,2-ethenediol in the interstellar space

Relativistic three-body bound states and the reduction from four to three dimensions

Beginning with an effective field theory based upon meson exchange, the Bethe-Salpeter equation for the three-particle propagator (six-point function) is obtained. Using the one-boson-exchange form of the kernel, this equation is then analyzed using time-ordered perturbation theory, and a three-dimensional equation for the propagator is developed. The propagator consists of a pre-factor in which the relative energies are fixed by the initial state of the particles, an intermediate part in which only global propagation of the particles occurs, and a post-factor in which relative energies are fixed by the final state of the particles. The pre- and post-factors are necessary in order to account for the transition from states where particles are off their mass shell to states described by the global propagator with all of the particle energies on shell. The pole structure of the intermediate part of the propagator is used to determine the equation for the three-body bound state: a Schr{\"o}dinger-like relativistic equation with a single, global Green's function. The role of the pre- and post-factors in the relativistic dynamics is to incorporate the poles of the breakup channels in the initial and final states. The derivation of this equation by integrating over the relative times rather than via a constraint on relative momenta allows the inclusion of retardation and dynamical boost corrections without introducing unphysical singularities.Comment: REVTeX, 21 pages, 4 figures, epsf.st