135 research outputs found

    Sharp mixed norm spherical restriction

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    Let d‚Č•2d\geq 2 be an integer and let 2d/(d‚ąí1)<q‚ȧ‚ąě2d/(d-1) < q \leq \infty. In this paper we investigate the sharp form of the mixed norm Fourier extension inequality \begin{equation*} \big\|\widehat{f\sigma}\big\|_{L^q_{{\rm rad}}L^2_{{\rm ang}}(\mathbb{R}^d)} \leq {\bf C}_{d,q}\, \|f\|_{L^2(\mathbb{S}^{d-1},{\rm d}\sigma)}, \end{equation*} established by L. Vega in 1988. Letting Ad‚äā(2d/(d‚ąí1),‚ąě]\mathcal{A}_d \subset (2d/(d-1), \infty] be the set of exponents for which the constant functions on Sd‚ąí1\mathbb{S}^{d-1} are the unique extremizers of this inequality, we show that: (i) Ad\mathcal{A}_d contains the even integers and ‚ąě\infty; (ii) Ad\mathcal{A}_d is an open set in the extended topology; (iii) Ad\mathcal{A}_d contains a neighborhood of infinity (q0(d),‚ąě](q_0(d), \infty] with q0(d)‚ȧ(12+o(1))dlog‚Ā°dq_0(d) \leq \left(\tfrac{1}{2} + o(1)\right) d\log d. In low dimensions we show that q0(2)‚ȧ6.76‚ÄČ;‚ÄČq0(3)‚ȧ5.45‚ÄČ;‚ÄČq0(4)‚ȧ5.53‚ÄČ;‚ÄČq0(5)‚ȧ6.07q_0(2) \leq 6.76\,;\,q_0(3) \leq 5.45 \,;\, q_0(4) \leq 5.53 \,;\, q_0(5) \leq 6.07. In particular, this breaks for the first time the even exponent barrier in sharp Fourier restriction theory. The crux of the matter in our approach is to establish a hierarchy between certain weighted norms of Bessel functions, a nontrivial question of independent interest within the theory of special functions.Comment: 21 page

    Comida e prazer: o lugar da gastronomia nos desejos do homem comtempor√Ęneo

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    Discute as no√ß√Ķes humanas de prazer relacionadas aos campos da alimenta√ß√£o e gastronomia. Investigo a g√™nese da sexualidade humana ao pesquisar a inaugura√ß√£o do prazer oral durante a amamenta√ß√£o segundo as teorias psicanal√≠ticas de Freud e parto para um mergulho detalhado na mudan√ßa de eixo entre as subjetividades modernas e contempor√Ęnea para, debru√ßado sobre a segunda, em sua condi√ß√£o espetacularizada em plena era digital, examinar os limites do prazer ligado √† alimenta√ß√£o. O projeto de pesquisa inclui, ainda, uma reflex√£o acerca do futuro da alimenta√ß√£o, visto que, consequ√™ncia da voraz ind√ļstria capitalista de alimentos industrializados e ultra-apressados, a sa√ļde humana est√° cada vez mais prejudicada, enquanto a comida caseira, a comida de verdade, perde seu lugar √† mesa. Uma coisa, por√©m, √© certa: o prazer de comer nunca sair√° de cena

    Olive tree (Olea europaea L.) diversity in traditional small farms of Ficalho, Portugal

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    The genetic diversity of ‚ÄúGama‚ÄĚ and ‚ÄúBico de Corvo‚ÄĚ, local cultivars of olive tree (Olea europaea) from seven traditional orchards of Ficalho (Alentejo region, Portugal), was studied to characterize the local diversity and assess the level of on farm diversity. Two different analytical systems were used: endocarp morphological characteristics and genetic analysis by microsatellite markers (Simple Sequence Repeats or SSR). The seven screened loci were polymorphic and allowed the identification of 23 distinct SSR profiles within the 27 trees analyzed. A total of 52 different alleles were scored, with an average of 7.43 alleles/SSR locus, and considerable genetic diversity was found. Neighbor-Joining algorithm cluster analysis and principal co-ordinate analysis (PCoA) allowed for the identification of the genetic relationships between several accessions. The 27 Olea accessions were clearly separated into three different groups. SSR analysis was more precise than endocarp characterization in the classification of genetic diversity among the olive tree cultivars. The study shows reasonable olive tree diversity in Ficalho, indicating that these traditional orchards are important reservoirs of old minor cultivars and incubators of new genotypesinfo:eu-repo/semantics/publishedVersio

    O M√ČTODO DE REDU√á√ÉO AO ABSURDO NO LIVRO I DO ELEMENTOS DE EUCLIDES

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    Historicamente o m√©todo de redu√ß√£o ao absurdo, tamb√©m conhecido como mecanismo indireto de demonstra√ß√£o ou nega√ß√£o, aparece na matem√°tica como uma das ferramentas de grande poder para o desenvolvimento e fortalecimento desta ci√™ncia. Mesmo sem ter sua origem bem definida e em meio √†s cr√≠ticas, de escritores da antiguidade at√© a atualidade, a t√©cnica de redu√ß√£o ao absurdo foi e ainda permanece sendo aplicada no trabalho de diversos matem√°ticos e, principalmente na obra de inestim√°vel valor para a matem√°tica de todos os tempos, o Elementos de Euclides. Esta valorosa obra, composta por treze volumes, destinada principalmente ao estudo de geometria elementar, exerceu e continua a exercer vasta influ√™ncia no conhecimento cient√≠fico e apresenta pela primeira vez o m√©todo revolucion√°rio na hist√≥ria da matem√°tica, que √© o m√©todo dedutivo e axiom√°tico, respons√°vel por caracterizar a matem√°tica at√© mesmo nos dias de hoje. E √© sobre esta obra que nos inclinaremos √† procura das proposi√ß√Ķes do livro I nas quais Euclides aplica o m√©todo indireto de demonstra√ß√£o, com o intuito de descrever algumas delas, em linguagem atual, e identificar as demais. Caracterizando assim o objetivo deste trabalho, que servir√° de base posteriormente para o desenvolvimento de outro, que √© o de catalogar as proposi√ß√Ķes nas quais Euclides emprega em sua obra o racioc√≠nio indireto de demonstra√ß√£o, isto √©, identificar rela√ß√Ķes entre as proposi√ß√Ķes que s√£o marcadas por este m√©todo. Para alcan√ßar os objetivos aqui mencionados, utilizou-se a pesquisa de car√°ter bibliogr√°fico, em que foram consultados livros e artigos publicados que abordem o assunto em quest√£o

    Omnibus survey of pupils and their parents or carers: wave 5: Research report: March 2019

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    Brazilian productivity of eucalyptus trees is one of the highest in the world, and it has sustainable and viable conditions to supply the demand for woody biomass in a large quantity and diversity. This favorable situation makes Brazil one of the countries with the greatest potential for the production development of torrefied woody biomass on a commercial scale. Torrefaction is a mild pyrolysis applied to increase the energy quality of the feedstock. The aim of this study was to evaluate the Brazilian potential of woody biomass torrefaction for energy purposes. An experimental study was performed evaluating this thermal treatment of eucalyptus wood chips on a semi-continuous screw reactor developed by a Brazilian university. The results showed the increases in the energy quality of eucalyptus wood chips as a function of torrefaction temperature and time. This thermal treatment was technically feasible for the hygroscopicity reduction and the increases of fixed carbon and calorific values of the woody biomass

    WOOD DRYERS: A SUSTAINABLE ALTERNATIVE FOR INCREASED CHARCOAL PRODUCTION

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    The aim of the study was to evaluate the technical and economic viability of a wood dryer in the charcoal production. Drying was carried out for 72 hours using wood from Eucalyptus sp. in two classes of diameter. The average admission temperature of combustion gases in the dryer was 100-150¬ļC. It was determined the mass of water withdrawn by drying and estimated the amount of wood that would be consumed during the pyrolysis to remove the same amount of water, being this wood converted into charcoal mass. In the economic analysis were determined the indicators net present value, internal rate of return and discounted payback. The dryer presented technical feasibility, reducing wood moisture by 8% and, consequently, increasing the charcoal productivity by 3.3%, and economic viability, with good financial indicators for current market conditions, including a discounted payback of 6 years. In this way, the use of a wood dryer was presented as an efficient way to take advantage of an environmental liability of pyrolysis, which contributes to the increase of sustainability in the charcoal production
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