The Dirichlet problem for superdegenerate differential operators

Let $L$ be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of H\"ormander, we show that the Dirichlet problem associated with $L$ has a unique smooth classical solution. The proof uses the Malliavin calculus. At present, there appears to be no proof of this result using classical analytic techniques

Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index s=−1s=-1

This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\vec{u}_0,\theta_0)$ ($\nabla\cdot\vec{u}_0=0$) either in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\infty,\infty}}\times{B}^{-1,\epsilon}_{p,\infty}$ if $r\in[1,\infty]$, $\epsilon>0$ and $p\in(\frac{n}{2},\infty)$, where $B^{s,\epsilon}_{p,q}$ ($s\in\mathbb{R}$, $1\leq p,q\leq\infty$, $\epsilon>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s}_{p,q}$. We also prove that this system is well-posed for small initial data in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times({B}^{-1}_{\frac{n}{2},1}\cap{B^{-1,1}_{\frac{n}{2},\infty}})$.Comment: 18 page

Climate Model Intercomparisons: Preparing for the Next Phase

Since 1995, the Coupled Model Intercomparison Project (CMIP) has coordinated climate model experiments involving multiple international modeling teams. Through CMIP, climate modelers and scientists from around the world have analyzed and compared state-of-the-art climate model simulations to gain insights into the processes, mechanisms, and conswquences of climate variability and climate change

Strong cloud–circulation coupling explains weak trade cumulus feedback

Shallow cumulus clouds in the trade-wind regions cool the planet by reflecting solar radiation. The response of trade cumulus clouds to climate change is a key uncertainty in climate projections. Trade cumulus feedbacks in climate models are governed by changes in cloud fraction near cloud base with high-climate-sensitivity models suggesting a strong decrease in cloud-base cloudiness owing to increased lower-tropospheric mixing. Here we show that new observations from the EUREC4A (Elucidating the role of cloud-circulation coupling in climate) field campaign refute this mixing-desiccation hypothesis. We find the dynamical increase of cloudiness through mixing to overwhelm the thermodynamic control through humidity. Because mesoscale motions and the entrainment rate contribute equally to variability in mixing but have opposing effects on humidity, mixing does not desiccate clouds. The magnitude, variability and coupling of mixing and cloudiness differ markedly among climate models and with the EUREC4A observations. Models with large trade cumulus feedbacks tend to exaggerate the dependence of cloudiness on relative humidity as opposed to mixing and also exaggerate variability in cloudiness. Our observational analyses render models with large positive feedbacks implausible and both support and explain at the process scale a weak trade cumulus feedback. Our findings thus refute an important line of evidence for a high climate sensitivit

Un acercamiento al sistema educativo de suiza: currícula 21 y su implicancia en el desarrollo humano sostenible

The world societies go through a very rapid transformation like result, between other things, to the incorporation of the technologies to all the ambiences of the personal and social life. Switzerland as other countries is not foreign tothese changes and in the educational ambience, it offers across its Curricula 21 an alternative according to the current requirements. The education in Switzerland is a competence transferred in 26 Cantons that shape the Swiss Confederacy.Twenty-one Cantons of German speech received the Curricula 21 for the harmonization of the obligatory school in the frame of the interactional Concordat HarmoS. The target of the Concordat consists of improving the quality of theobligatory public education and overcoming the obstacles that make the educational mobility difficult between the cantons.Las sociedades mundiales atraviesan una transformación muy rápida como resultado, entre otras cosas, a la incorporación de las tecnologías a todos los ámbitos de la vida personal y social. Suiza al igual que otros países no es ajeno a estoscambios y en el ámbito educativo, ofrece a través de su Currícula 21 una alternativa acorde a las exigencias actuales. La educación en Suiza es una competencia transferida a los 26 Cantones que conforman la Confederación Helvética. Losveintiún Cantones de habla alemana recibieron la Currícula 21 para la armonización de la escuela obligatoria en el marco del Concordato intercantonal HarmoS. El objetivo del Concordato consiste en mejorar la calidad de la enseñanza públicaobligatoria y superar los obstáculos que dificultan la movilidad educacional entre los cantones

Conormal distributions in the Shubin calculus of pseudodifferential operators

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms and microlocal properties.Comment: 23 page

Minimal recipes for global cloudiness

Clouds are primary modulators of Earth’s energy balance. It is thus important to understand the links connecting variabilities in cloudiness to variabilities in other state variables of the climate system, and also describe how these links would change in a changing climate. A conceptual model of global cloudiness can help elucidate these points. In this work we derive simple representations of cloudiness, that can be useful in creating a theory of global cloudiness. These representations illustrate how both spatial and temporal variability of cloudiness can be expressed in terms of basic state variables. Specifically, cloud albedo is captured by a nonlinear combination of pressure velocity and a measure of the low-level stability, and cloud longwave effect is captured by surface temperature, pressure velocity, and standard deviation of pressure velocity. We conclude with a short discussion on the usefulness of this work in the context of global warming response studies

The influence of fractional diffusion in Fisher-KPP equations

We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable L\'evy process, the front position is exponential in time. Our results provide a mathe- matically rigorous justification of numerous heuristics about this model

Regularizing effect and local existence for non-cutoff Boltzmann equation

The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially inhomogeneous Boltzmann equation. In this paper, by sharpening the coercivity and upper bound estimates for the collision operator, establishing the hypo-ellipticity of the Boltzmann operator based on a generalized version of the uncertainty principle, and analyzing the commutators between the collision operator and some weighted pseudo differential operators, we prove the regularizing effect in all (time, space and velocity) variables on solutions when some mild regularity is imposed on these solutions. For completeness, we also show that when the initial data has this mild regularity and Maxwellian type decay in velocity variable, there exists a unique local solution with the same regularity, so that this solution enjoys the $C^\infty$ regularity for positive time

Preliminary design of a new high intensity injection system for GANIL.

http://accelconf.web.cern.ch/AccelConf/c89/papers/f6-12.pdfInternational audienc