Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

Jacobi script v sign-functions and discrete Fourier transforms

Properties of the Jacobi script v sign3-function and its derivatives under discrete Fourier transforms are investigated, and several interesting results are obtained. The role of modulo N equivalence classes in the theory of script v sign-functions is stressed. An important conjecture is studied. © 2006 American Institute of Physics.

Radon emissions related to the granitic Precambrian shield in southern Brazil

The equivalent uranium (eU) activity concentration was analysed in selected granite samples at several sites in Porto Alegre, Southern Brazil, to obtain information on the radon (222Rn) generation by the aquifer rock matrices. Radon analyses of ground water and soil samples were also performed. Several samples exhibited a dissolved 222Rn activity concentration exceeding the World Health Organization maximum limit of 100 Bq l-1. The dissolved radon content in ground waters from the Fractured Precambrian Aquifer System exhibited a direct significant correlation with the eU in the rock matrices, which is a typical result of water-rock interactions. Variation in the soil's porosity was confirmed as an important factor for 222Rn release, as expected, due to its gaseous nature. Thus, although the calcic-alkaline to alkaline Precambrian granitoid rocks of the study area are important reservoirs for underground resources, they can release high amounts of radon gas into the liquid phase. © 2013 Copyright Taylor and Francis Group, LLC.

The use of radon (Rn-222) and volatile organic compounds in monitoring soil gas to localize NAPL contamination at a gas station in Rio Claro, Sao Paulo State, Brazil

This study focuses on the presence of radon (Rn-222) and volatile organic compounds (VOCs) in soil gases at a gas station located in the city of Rio Claro, Sao Paulo, Brazil, where a fossil fuel leak occurred. The spatial distribution results show a correlation between Rn-222 and VOCs, consistent with the fact that radon gas has a greater chemical affinity with organic phases than with water. This finding demonstrates that the presence of a residual hydrocarbon phase in an aquifer can retain radon, leading to a reduced radon content in the soil gas. The data in this study confirm the results of previous investigations, in which the method used in this study provided a preliminary fingerprint of a contaminated area. Furthermore, the data analysis time is brief, and only simple equipment is required. (C) 2014 Published by Elsevier Ltd.

Dissolved uranium, radium and radon evolution in the Continental Intercalaire aquifer, Algeria and Tunisia

Natural, dissolved U-238-series radionuclides (U, Ra-226, Rn-222) and activity ratios (A.R.s: U-234/U-238; Ra-228/Ra-226) in Continental Intercalaire (Cl) groundwaters and limited samples from the overlying Complexe Terminal (CT) aquifers of Algeria and Tunisia are discussed alongside core measurements for U/Th (and K) in the contexts of radiological water quality, geochemical controls in the aquifer, and water residence times. A redox barrier is characterised downgradient in the Algerian Cl for which a trend of increasing U-234/U-238 A.R.s with decreasing U-contents due to recoil-dominated U-234 solution under reducing conditions allows residence time modelling similar to 500 ka for the highest enhanced A.R. = 3.17. Geochemical modelling therefore identifies waters towards the centre of the Grand Erg Oriental basin as palaeowaters in line with reported C-14 and Cl-36 ages. A similar U-234/U-238 trend is evidenced in a few of the Tunisian CI waters. The paleoage status of these waters is affirmed by both noble gas recharge temperatures and simple modelling of dissolved, radiogenic He-4-contents both for sampled Algerian and Tunisian CI and CT waters. For the regions studied these waters therefore should be regarded as "fossil" waters and treated effectively as a non-renewable resource. (C) 2014 The Authors. Published by Elsevier Ltd.

Towards a Brazilian radon map: consortium radon Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Thoron and radon activity concentration in mineral waters of spas from southeastern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Nuclear structure studies in the xenon and radon region and the discovery of a new radon isotope by Penning trap mass spectrometry

Heutzutage gewähren hochpräzise Massenmessungen mit Penning-Fallen tiefe Einblicke in die fundamentalen Eigenschaften der Kernmaterie. Zu diesem Zweck wird die freie Zyklotronfrequenz eines Ions bestimmt, das in einem starken, homogenen Magnetfeld gespeichert ist. Am ISOLTRAP-Massenspektrometer an ISOLDE / CERN können die Massen von kurzlebigen, radioaktiven Nukliden mit Halbwertszeiten bis zu einigen zehn ms mit einer Unsicherheit in der Größenordnung von 10^-8 bestimmt werden. ISOLTRAP besteht aus einem Radiofrequenz-Quadrupol zum akkumulieren der von ISOLDE gelieferten Ionen, sowie zwei Penning-Fallen zum säubern und zur Massenbestimmung der Ionen. Innerhalb dieser Arbeit wurden die Massen von neutronenreichen Xenon- und Radonisotopen (138-146Xe und 223-229Rn) gemessen. Für elf davon wurde zum ersten Mal die Masse direkt bestimmt; 229Rn wurde im Zuge dieses Experimentes sogar erstmalig beobachtet und seine Halbwertszeit konnte zu ungefähr 12 s bestimmt werden. Da die Masse eines Nuklids alle Wechselwirkungen innerhalb des Kerns widerspiegelt, ist sie einzigartig für jedes Nuklid. Eine dieser Wechselwirkungen, die Wechselwirkung zwischen Protonen und Neutronen, führt zum Beispiel zu Deformationen. Das Ziel dieser Arbeit ist eine Verbindung zwischen kollektiven Effekten, wie Deformationen und Doppeldifferenzen von Bindungsenergien, sogenannten deltaVpn-Werten zu finden. Insbesondere in den hier untersuchten Regionen zeigen deltaVpn-Werte ein sehr ungewöhnliches Verhalten, das sich nicht mit einfachen Argumenten deuten lässt. Eine Erklärung könnte das Auftreten von Oktupoldeformationen in diesen Gebieten sein. Nichtsdestotrotz ist eine quantitative Beschreibung von deltaVpn-Werten, die den Effekt von solchen Deformationen berücksichtigt mit modernen Theorien noch nicht möglich.

La trasformata di Radon e la sua applicazione nella ricostruzione di immagini

Scopo di questo lavoro è mostrare una soluzione al problema della ricostruzione delle immagini basata sullo strumento matematico della trasformata di Radon. In un primo momento si introdurrà il problema legato ad un particolare ambito, quello medico; ci si focalizzerà, infatti sui principi di funzionamento della TAC (tomografia assiale computerizzata)e si cercherà di chiarire dal punto di vista fisico come la trasformata di Radon del coefficiente di attenuazione del materiale sia utile per visualizzare degli organi o comunque degli oggetti che altrimenti non potrebbero essere visibili, se non rompendo la struttura che li contiene. Dopo aver raccontato un po' di storia della TAC, sarà necessario quindi definire tale trasformata, le sue principali proprietà e trovare una formula per la sua inversione. Si mostrerà che la sola formula d'inversione non potrà essere utilizzata a livello pratico; si ricaverà allora un algoritmo di retroproiezione filtrata, basato sulla trasformata di Radon, applicato per visualizzare delle immagini tramite TAC.

Teorema di Radon-Nikodym e Statistica

Il presente elaborato vuole illustrare alcuni risultati matematici di teoria della misura grazie ai quali si sono sviluppate interessanti conseguenze nel campo della statistica inferenziale relativamente al concetto di statistica sufficiente. Il primo capitolo riprende alcune nozioni preliminari e si espone il teorema di Radon-Nikodym, sulle misure assolutamente continue, con conseguente dimostrazione. Il secondo capitolo dal titolo ‘Applicazioni alla statistica sufficiente’ si apre con le definizioni degli oggetti di studio e con la presentazione di alcune loro proprietà matematiche. Nel secondo paragrafo si espongono i concetti di attesa condizionata e probabilità condizionata in relazione agli elementi definiti nel paragrafo iniziale. Si entra nel corpo di questo capitolo con il terzo paragrafo nel quale definiamo gli insiemi di misura, gli insiemi di misura dominati e il concetto di statistica sufficiente. Viene qua presentato un importante teorema di caratterizzazione delle statistiche sufficienti per insiemi dominati e un suo corollario che descrive la relativa proprietà di fattorizzazione. Definiamo poi gli insiemi omogenei ed esponiamo un secondo corollario al teorema, relativo a tali insiemi. Si considera poi l’esempio del controllo di qualità per meglio illustrare la nozione di statistica sufficiente osservando una situazione più concreta. Successivamente viene introdotta la nozione di statistica sufficiente a coppie e viene enunciato un secondo teorema di caratterizzazione in termini di rapporto di verosimiglianza. Si procede quindi ad un confronto tra questi due tipi di sufficienza. Tale confronto viene operato in due situazioni differenti e porta a risultati diversi per ogni caso. Si conclude dunque l’elaborato marcando ancora l’effettiva bontà di una statistica sufficiente in termini di informazioni contenute al suo interno.