Signal Transceiver Transit Times and Propagation Delay Corrections for Ranging and Georeferencing Applications

The accuracy of ranging measurements depends critically on the knowledge of time delays undergone by signals when retransmitted by a remote transponder and due to propagation effects. A new method determines these delays for every single pulsed signal transmission. It utilizes four ground-based reference stations, synchronized in time and installed at well-known geodesic coordinates and a repeater in space, carried by a satellite, balloon, aircraft, and so forth. Signal transmitted by one of the reference bases is retransmitted by the transponder, received back by the four bases, producing four ranging measurements which are processed to determine uniquely the time delays undergone in every retransmission process. A minimization function is derived comparing repeater's positions referred to at least two groups of three reference bases, providing the signal transit time at the repeater and propagation delays, providing the correct repeater position. The method is applicable to the transponder platform positioning and navigation, time synchronization of remote clocks, and location of targets. The algorithm has been demonstrated by simulations adopting a practical example with the transponder carried by an aircraft moving over bases on the ground.CNPq Agency (Brazil)Brazil agency CNPqBrazil agency CAPESBrazil agency CAPE

Sets of weak sequential continuity for polynomials in Banach spaces

Esta dissertação tem por objetivo a apresentação de um estudo em espaços de Banach sobre os conjuntos nos quais determinados polinômios homogêneos contínuos são fracamente sequencialmente contínuos. Algumas propriedades desses conjuntos são estudadas e ilustradas com exemplos, em maior parte no espaço $l_p$. Obtemos um fórmula para o conjunto de continuidade sequencial fraca do produto de dois polinômios e algumas consequências. Resultados mais fortes são obtidos quando restringimos nossos espaços de Banach a espaços com FDD incondicional e/ou separáveis. Os resultados estudados aqui foram obtidos por R. Aron e V. Dimant em: Aron, R. & Dimant, V., Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299.This work has the purpose of presenting a study on Banach spaces about sets in which determined homogeneous continuous polynomials are weakly sequentially continuous. Some properties of these sets are studied and illustrated with examples, most in the space $l_p$. We obtain a formula for the weak sequential continuity set of the product of two polynomials, and some consequences. Stronger results are obtained when we restrict our Banach spaces to spaces with unconditional FDD and/or separable. The results studied here were obtained by R. Aron and V. Dimant in: Aron, R. & Dimant, V., {Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299

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Utilizamos neste trabalho um exemplo dado por Marík e apresentado por Karták para mostrar que a integral de Henstock-Kurzweil e a 'M.IND.1'-integral não são invariantes por rotações. A seguir é apresentada uma definição abstrata de integral e é discutida a incompatibilidade entre o Teorema da Divergência e o Teorema de Fubini quando grande generalidade é requerida. Finalmente é introduzida uma nova integral não-absoluta baseada em partições triangulares do domínio, que admite fórmula de mudança de variáveis com respeito a tranformações lineares, satisfaz o Teorema da Divergência com grande generalidade e apresenta boas relações com a integral de Lebesgue. Algumas propriedades de convergência são estudadas para esta integral.not availabl

Sets of weak sequential continuity for polynomials in Banach spaces

Esta dissertação tem por objetivo a apresentação de um estudo em espaços de Banach sobre os conjuntos nos quais determinados polinômios homogêneos contínuos são fracamente sequencialmente contínuos. Algumas propriedades desses conjuntos são estudadas e ilustradas com exemplos, em maior parte no espaço $l_p$. Obtemos um fórmula para o conjunto de continuidade sequencial fraca do produto de dois polinômios e algumas consequências. Resultados mais fortes são obtidos quando restringimos nossos espaços de Banach a espaços com FDD incondicional e/ou separáveis. Os resultados estudados aqui foram obtidos por R. Aron e V. Dimant em: Aron, R. & Dimant, V., Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299.This work has the purpose of presenting a study on Banach spaces about sets in which determined homogeneous continuous polynomials are weakly sequentially continuous. Some properties of these sets are studied and illustrated with examples, most in the space $l_p$. We obtain a formula for the weak sequential continuity set of the product of two polynomials, and some consequences. Stronger results are obtained when we restrict our Banach spaces to spaces with unconditional FDD and/or separable. The results studied here were obtained by R. Aron and V. Dimant in: Aron, R. & Dimant, V., {Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299

On approximation properties in Lipschitz-free spaces over groups

We study Lipschitz-free spaces over compact and uniformly discrete metric spaces enjoying certain high regularity properties - having group structure with left-invariant metric. Using methods of harmonic analysis we show that, given a compact metrizable group $G$ equipped with an arbitrary compatible left-invariant metric $d$, the Lipschitz-free space over $G$, \F(G,d), satisfies the metric approximation property. We show also that, given a finitely generated group $G$, with its word metric $d$, from a class of groups admitting a certain special type of combing, which includes all hyperbolic groups and Artin groups of large type, \F(G,d) has a Schauder basis. Examples and applications are discussed. In particular, for any net $N$ in a real hyperbolic $n$-space $\mathbb{H}^n$, \F(N) has a Schauder basis.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2017/18623-5, 2016/25574-

ON THE GEOMETRY OF BANACH SPACES OF THE FORM Lip0(C(K))

We investigate the problem of classifying the Banach spaces Lip0(C(K)) for Hausdorff compacta K. In particular, sufficient conditions are established for a space Lip0(C(K)) to be isomorphic to Lip0(c0(Γ )) for some uncountable set ΓFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2016/25574-82017/18623-

On Lipschitz-free spaces over spheres of Banach spaces

We prove that, for each Banach space X which is isomorphic to its hyperplanes, the Lipschitz-free spaces over X and over its sphere are isomorphic.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2016/25574-82017/18623-