Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation

We study the electromagnetic Helmholtz equation \notag (\nabla + ib(x))^{2}u(x) + n(x)u(x) = f(x), \quad x\in\Rd with the magnetic vector potential $b(x)$ and $n(x)$ a variable index of refraction that does not necessarily converge to a constant at infinity, but can have an angular dependency like $n(x) \to n_{\infty}(\frac{x}{|x|})$ as $|x|\to\infty$. We prove an explicit Sommerfeld radiation condition \notag \int_{\Rd} |\D u - in_{\infty}^{1/2}\frac{x}{|x|}u|^{2} \frac{dx}{1+|x)} < + \infty for solutions obtained from the limiting absorption principle and we also give a new energy estimate \notag \int_{\Rd}| \nabla_{\omega}n_{\infty}(\frac{x}{|x|})|^{2}\frac{|u|^{2}}{1+|x|} dx < +\infty, which explains the main physical effect of the angular dependence of $n$ at infinity and deduces that the energy concentrates in the directions given by the critical points of the potential

Towards precision SZ cluster cosmology: from Planck to the Simons Observatory

As demonstrated by Planck, SPT, and ACT, the abundance of Sunyaev-Zeldovich-detected galaxy clusters across mass and redshift is a powerful cosmological probe. Upcoming experiments such as the Simons Observatory (SO) will detect over an order of magnitude more objects than what previous experiments have found, thereby providing an unprecedented constraining potential. However, in order for this potential to be realised, the cluster detection and analysis pipelines will have to be built and understood to a much higher level of accuracy than has been demonstrated to date. Here we discuss ongoing efforts towards the accurate modelling of tSZ cluster counts, focusing on several improvements regarding optimisation bias, covariance estimation, and foreground deprojection, which are implemented in the publicly-available SZiFi package. Next, we briefly discuss the application of these improved cluster detection methods to Planck data. Finally, we introduce cosmocnc, a new cluster number count likelihood code that will be publicly available soon.Comment: To appear in Proc. of the mm Universe 2023 conference, Grenoble (France), June 2023, published by F. Mayet et al. (Eds), EPJ Web of conferences, EDP Science

Neska kirolarien egoera eskola garaitik goi mailako txapelketeraino

33 p. : il. - E-mail del autor: [email protected] eskubideak aldarrikatuz, mugimendu feministek bide latza ibili dute. Urte askotan zehar, eta gaur egun ere, gizarteak barneratuta duen matxismoaren aurka borrokatu da, gehiengoaren ideal eta estereotipoen aurka jokatuz. Gizartean nesken diskriminazio egoerak gutxitu direla eta sexuen eskubide eta aukerak berdintzen doazela dioten arren, egundoko ibilbidea geratzen da. Beraz, elkarrizketa batzuen bidez, gaur egun goi mailako kirolarien artean neskek bizitzen dituzten diskriminazio egoerak aztertuko ditugu. Beren kiroleko lehen urteetatik gogoratzen dutena egungoarekin alderatuko da, azkenik diskriminazio egoera ezberdinetatik ateratzeko aukera posibleak identifikatuz. Hurrengo lerroetan zehar sexu eta genero kontzeptuak azalduko dira, estereotipoek sexu diskriminazioan eduki ditzakeen ondorioak aipatuz. Ondoren, neskek hezkuntzan bizi izandako eskubide eta aukera gora-beherak gainetik aipatuko dira, garrantzi handia eduki zuten zenbait lege eta hezkuntza erreforma argituz. Azkenik, neskek kirol munduan edukitako garapenari errepaso labur bat emango zaio. Elkarrizketak eta hauetatik lorturiko emaitzak aztertu ondoren, argi ikus daiteke neska kirolariek, beren egunerokoan, diskriminazio egoera ezberdin ugari bizi dituztela. Hala ere, egoera honen analisi hobe bat egiteko denbora gehiago, elkarrizketatuen kopuru handiagoa eta hauek praktikatzen duten kirol aniztasun zabalagoa beharko genuke

Aplicación del test gráfico de L.Corman en niños y niñas de 5 años

Treball de Final de Grau en Mestre o Mestra d'Educació Infantil. Codi: MI1040. Curs acdèmic 2014-201

The forward problem for the electromagnetic Helmholtz equation

157 p.[EN]We consider the Helmholtz equation in Rd, d 3, with electric and magnetic potentials. The aim of this thesis is to study the direct problem of such an equation for potentials that decay at in nity, but also have singularities at the origin. We use integration by parts to achieve this. A main tool is a multiplier method in spirit of the so called Morawetz estimate. We prove that there exists a unique solution of this equation such that satis es some a-priori estimates together with some Sommerfeld radiation condition. We then deduce some extra information about the behavior of the solution for di erent classes of electric and magnetic potentials, which allows us to derive some applications related to the spectral properties for the magnetic Schr odinger operator.[ES]El objetivo principal de esta tesis es estudiar el problema directo de la ecuación de Helmholtz con potenciales eléctrico y magnético. Consideramos potenciales que permiten singularidades en el origen y con un cierto decaimiento en el infinito. Para ello utilizamos la integración por partes y el método del multiplicador basándonos en los introducidos por Morawetz. Para distintos tipos de potenciales, probamos que existe una única solución de la ecuación de Helmholtz electromagnética tal que satisface una cierta condición de radiación de Sommerfeld y algunas estimaciones a-priori. Esto nos permite dar información extra sobre el comportamiento de la solución en el infinito, concluyendo algunas propiedades del espectro del operador de Schrödinger magnéticoMinisterio de Ciencia e Innovación, Gobierno de España: Fellowship AP2007-02659 of FPU program FPU,2008 Grant for a four-month stay at the Mathematical Sciences Research Institute (MSRI),Berkeley, August 2010 - December 2010. FPU program (Fellowship AP2007-02659). Grant for a two-month stay at the Department of Mathematics and Statistics of theUniversity of Helsinki, September 2011 - October 2011. FPU program (Fellowship AP2007-02659). European Research Council (ERC) Advanced Grant-Mathematical foundations (ERC-AG-PE1), November 2011-December 201