Nous étudions dans cet article des espaces de moyennes définis par une méthode discrète d'interpolation. Après avoir démontré leur coïncidence, dans le cas général, avec les espaces$(A$_{o}, A_{1})_{Q; J}et$(A$_{0}, A_{1})_{Q;K}de C. Bennett ([3]), nous obtenons simplement les théorèmes de dualité en utilisant la méthode de [2] et aussi les arguments de [7]. Nous remercions le rapporteur dont les conseils nous ont permis en particulier de simplifier nos démonstrations.

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In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semi-classical expansion is in conflict with basic properties such as positive-semidefiniteness of the spectrum, and constraints of supersymmetry. Generic saddles are not only complex, but also possibly multi-valued, and even singular. This is in contrast to instanton solutions, which are real, smooth, and single-valued. The multi-valuedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to non-supersymmetric theories.

This erratum corrects an error arising in the proof of Proposition 6.4 in the article “On the density of geometrically finite Kleinian groups”

We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. These provide a solution to the long-standing problem of finding a good notion of Ricci flow through singularities, in the 3-dimensional case. We prove that Ricci flow with surgery, starting from a fixed initial condition, subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.

In this work, we study the stability of the expanding configurations for radiation gaseous stars. Such expanding configurations exist for the isentropic model and the thermodynamic model. In particular, we focus on the effect of the monatomic gas viscosity tensor on the expanding configurations. With respect to small perturbation, it is shown the self-similarly expanding homogeneous solutions of the isentropic model is unstable, while the linearly expanding homogeneous solutions of the isentropic model and the thermodynamic model are stable. This is an extensive study of the result in arXiv: 1605.08083 by Hadzic and Jang.

Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman-Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the sample size and it is not obvious how the variance function can be estimated when measurements are correlated. In such a high-dimensional nonparametric problem, we proposed two novel nonparametric estimators for genewise variance function and semiparametric estimators for measurement correlation, via solving a system of nonlinear equations. Their asymptotic normality is established. The finite sample property is

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Evolving smooth, compact hypersurfaces in Rn+1 with normal speed equal to a positive power k of the mean curvature improves a certain ‘isoperimetric difference’ for k > n.1. As singularities may develop before the volume goes to zero, we develop a weak level-set formulation for such flows and show that the above monotonicity is still valid. This proves the isoperimetric inequality for n 6 7. Extending this to complete, simply connected 3-dimensional manifolds with nonpositive sectional curvature, we give a new proof for the Euclidean isoperimetric inequality on such manifolds.

We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn’s linearization theorem.

Let G be a connected Lie group. We show that all characteristic classes of G are bounded—when viewed in the cohomology of the classifying space of the group G with the discrete topology—if and only if the derived group of the radical of G is simply connected in its Lie group topology. We also give equivalent conditions in terms of stable commutator length and distortion.

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Soit$T$un courant positif fermé sur un voisinage de 0 dans$C$^{n}. Nous montrons que$T$admet un cône tangent (limite de la famille de ses homothétiques), dès que les masses projectives$v$_{T}(r) convergent assez vite vers$V$_{T}(0) pour que ($v$_{T}(r)−$v$_{T}(0))/$r$soit localement sommable en$r$=0. Cette condition suffisante est optimale: nous construisons des courants de bidegré (1, 1) n'ayant pas de cône tangent, tels que l'intégrale de ($v$_{T}(r)−$v$_{T}(0))/$r$soit aussi peu divergente qu'on le souhaite. Lorsque$T$est le courant d'intégration sur un ensemble analytique, on vérifie que$v$_{T}(r)−$v$_{T}(0)=0$r$^{ε}), ce qui redonne le théorème de Thie-King sur l'existence du cône tangent.

An$L$^{1}-existence theorem is proved for the nonlinear stationary Boltzmann equation with hard forces and no small velocity truncation—only the Grad angular cut-off-in a setting between two coaxial rotating cylinders when the indata are given on the cylinders.

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We study analytic integrable deformations of the germ of a holomorphic foliation given by df=0 at the origin 0∈Cn,n≥3. We consider the case where f is a germ of an irreducible and reduced holomorphic function. Our central hypotheses is that, outside of a dimension ≤n−3 analytic subset Y⊂X, the analytic hypersurface Xf:(f=0) has only normal crossings singularities. We then prove that, as germs, such deformations also exhibit a holomorphic first integral, depending analytically on the parameter of the deformation. This applies to the study of integrable germs writing as ω=df+fη where f is quasi-homogeneous. Under the same hypotheses for Xf:(f=0) we prove that ω also admits a holomorphic first integral. Finally, we conclude that an integrable germ ω=adf+fη admits a holomorphic first integral provided that: (i) Xf:(f=0) is irreducible with an isolated singularity at the origin 0∈Cn,n≥3; (ii) the algebraic multiplicities of ω and f at the origin satisfy ν(ω)=ν(df). In the case of an isolated singularity for (f=0) the writing ω=adf+fη is always assured so that we conclude the existence of a holomorphic first integral. Some questions related to Relative Cohomology are naturally considered and not all of them answered.

Let X be a compact K\" ahler manifold and X be a simple normal crossing divisor. If X is the support of some effective X -ample divisor, we show <div class="gsh_dspfr"> X

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Fusion of images with same or different modalities has been conquering medical imaging field more rapidly due to the presence of highly accessible patients’ information in recent years. For example, cross platform non-rigid registration of CT with MRI images has found a significant role in different clinical application. In some instances labelling of anatomical features by medical experts are also involved to further improve the accuracy and authenticity of the registration. Being motivated by these, we propose a new algorithm to compute diffeomorphic hybrid multi-modality registration with large deformations. Our iterative scheme consists of mainly two steps. First, we obtain the optimal Beltrami coefficient corresponding to the diffeomorphic mapping that exactly superimposes the feature points. The second step detects the intensity difference in the framework of mutual information. A non-rigid deformation which minimizes the intensity difference is then obtained. Experiments have been carried out on both synthetic and real data. Results demonstrate the stability and efficacy of the proposed algorithm to obtain diffeomorphic image registration.

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