A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

Dimensionando e caracterizando a agricultura familiar no circuito das frutas, São Paulo.

O perfil da agricultura familiar no Circuito das Frutas, Estado de São Paulo, no ano de 2018, foi analisado e tendo como material empírico 1.373 declarações de aptidão ao PRONAF subdivididas em três situações diferentes: DAPs ativas, expiradas e canceladas. Os resultados mostraram que os fruticultores totalizaram 798. Observou-se que o número de DAPs com prazos de validade vencidos (61,4%) supera as ativas (33,7%). Para as três situações, observou-se que a maioria dos fruticultores não são socialmente organizados; quanto a renda bruta do imóvel com frutíferas verificaram-se diferenças entre os estratos com predomínio de 30,5% das ativas, entre 30 a 60 mil reais e das canceladas, entre 60 e 90 mil reais (35,7%), bem distante do limite de 415 mil reais definido pelo Conselho Monetário. Ações dos agentes locais se fazem necessárias para resgatar os produtores com DAPs expiradas para o universo de agricultores familiares, bem como a orientação aos produtores sobre as vantagens de se vincularem a associações e cooperativas a fim de garantir melhores condições na compra de insumos e abertura de canais de comercialização para sua produção.Publicado também em: In: CONGRESSO DA SOCIEDADE BRASILEIRA DE ECONOMIA, ADMINISTRAÇÃO E SOCIOLOGIA RURAL, 57., 2019, Ilhéus. Agricultura, alimentação e desenvolvimento: anais eletrônicos. Ilhéus: SOBER, 2019. Disponível em:

Multiwavelength Observations of the Gamma-Ray Blazar PKS 0528+134 in Quiescence

We present multiwavelength observations of the ultraluminous blazar-type radio loud quasar PKS 0528+134 in quiescence during the period July to December 2009. Significant flux variability on a time scale of several hours was found in the optical regime, accompanied by a weak trend of spectral softening with increasing flux. We suggest that this might be the signature of a contribution from the accretion disk at the blue end of the optical spectrum. The optical flux is weakly polarized with rapid variations of the degree and direction of polarization, while the polarization of the 43 GHz radio core remains steady. Optical spectropolarimetry suggests a trend of increasing degree of polarization with increasing wavelength, providing additional evidence for an accretion disc contribution towards the blue end of the optical spectrum. We constructed four SEDs indicating that even in the quiescent state, the bolometric luminosity of PKS 0528+134 is dominated by its gamma-ray emission. A leptonic single-zone jet model produced acceptable fits to the SEDs with contributions to the high-energy emission from synchrotron self-Compton radiation and Comptonization of direct accretion disk emission. Fit parameters close to equipartition were obtained. The moderate variability on long time scales implies the existence of on-going particle acceleration, while the observed optical polarization variability seems to point towards a turbulent acceleration process. Turbulent particle acceleration at stationary features along the jet therefore appears to be a viable possibility for the quiescent state of PKS 0528+134.Comment: Accepted for Publication in The Astrophysical Journal. - Acknowledgement adde

Multifrequency Photo-polarimetric WEBT Observation Campaign on the Blazar S5 0716+714: Source Microvariability and Search for Characteristic Timescales

Here we report on the results of the WEBT photo-polarimetric campaign targeting the blazar S5~0716+71, organized in March 2014 to monitor the source simultaneously in BVRI and near IR filters. The campaign resulted in an unprecedented dataset spanning $\sim 110$\,h of nearly continuous, multi-band observations, including two sets of densely sampled polarimetric data mainly in R filter. During the campaign, the source displayed pronounced variability with peak-to-peak variations of about $30\%$ and "bluer-when-brighter" spectral evolution, consisting of a day-timescale modulation with superimposed hourlong microflares characterized by $\sim 0.1$\,mag flux changes. We performed an in-depth search for quasi-periodicities in the source light curve; hints for the presence of oscillations on timescales of $\sim 3$\,h and $\sim 5$\,h do not represent highly significant departures from a pure red-noise power spectrum. We observed that, at a certain configuration of the optical polarization angle relative to the positional angle of the innermost radio jet in the source, changes in the polarization degree led the total flux variability by about 2\,h; meanwhile, when the relative configuration of the polarization and jet angles altered, no such lag could be noted. The microflaring events, when analyzed as separate pulse emission components, were found to be characterized by a very high polarization degree ($> 30\%$) and polarization angles which differed substantially from the polarization angle of the underlying background component, or from the radio jet positional angle. We discuss the results in the general context of blazar emission and energy dissipation models.Comment: 16 pages, 17 Figures; ApJ accepte

Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques

The Necessary and Sufficient Conditions for Representing Lipschitz Bivariate Functions as a Difference of Two Convex Functions

In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this algorithm is a sequence of pairs of convex functions that converge uniformly to a pair of convex functions if the conditions of the formulated theorems are satisfied. A geometric interpretation is also given

A Variable-Density Absorption Event in NGC 3227 mapped with Suzaku and Swift

The morphology of the circumnuclear gas accreting onto supermassive black holes in Seyfert galaxies remains a topic of much debate. As the innermost regions of Active Galactic Nuclei (AGN) are spatially unresolved, X-ray spectroscopy, and in particular line-of-sight absorption variability, is a key diagnostic to map out the distribution of gas. Observations of variable X-ray absorption in multiple Seyferts and over a wide range of timescales indicate the presence of clumps/clouds of gas within the circumnuclear material. Eclipse events by clumps transiting the line of sight allow us to explore the properties of the clumps over a wide range of radial distances from the optical/UV Broad Line Region (BLR) to beyond the dust sublimation radius. Time-resolved absorption events have been extremely rare so far, but suggest a range of density profiles across Seyferts. We resolve a weeks-long absorption event in the Seyfert NGC 3227. We examine six Suzaku and twelve Swift observations from a 2008 campaign spanning 5 weeks. We use a model accounting for the complex spectral interplay of three differently-ionized absorbers. We perform time-resolved spectroscopy to discern the absorption variability behavior. We also examine the IR-to-X-ray spectral energy distribution (SED) to test for reddening by dust. The 2008 absorption event is due to moderately-ionized ($\log \xi\sim 1.2-1.4$) gas covering 90% of the line of sight. We resolve the density profile to be highly irregular, in contrast to a previous symmetric and centrally-peaked event mapped with RXTE in the same object. The UV data do not show significant reddening, suggesting that the cloud is dust-free. The 2008 campaign has revealed a transit by a filamentary, moderately-ionized cloud of variable density that is likely located in the BLR, and possibly part of a disk wind.Comment: Accepted for publication by A&