A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

Pathway Weathering in Granitoid Rocks from Central Region of Angola: Geochemical and Mineralogical Data

The Central Region of Angola is characterized by the abundance of granitoid rocks, whose weathering “in situ” originated the so-called residual soils. The textural, geochemical and mineralogical properties of these soils depend not only on the chemical composition of parent rock, but mainly on the local climatic and geomorphological characteristics. In the study area, sampling sites were selected, which extend from the region of Kwanza- Norte (Kassenda, Dondo) through Kwanza-Sul (Cangulo, Quibala and Waco Kungo) until the plateau of Huambo, where samples of fresh rock, weathered rock and its residual soil were collected along each weathering profile. Chemical analytical data were determined using X-ray fluorescence (XRF) analysis of the major and minor elements, whereas mineralogical data were determined using X-ray diffraction (XRD), on the samples of rock and on the respective residual soil. The results obtained and their comparative analysis between the sampling sites, as well as along each weathering profile is presented. This paper allows contributing to the knowledge of the geochemical weathering in tropical areas, as is the case of Angola

On a generalised model for time-dependent variance with long-term memory

The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.Comment: 6 pages, 4 figure

Evaluation of drug-resistant tuberculosis treatment outcome in Portugal, 2000-2016

Treatment of drug-resistant tuberculosis (TB), which is usually less successful than that of drug-susceptible TB, represents a challenge for TB control and elimination. We aimed to evaluate treatment outcomes and to identify the factors associated with death among patients with MDR and XDR-TB in Portugal. We assessed MDR-TB cases reported for the period 2000-2016, using the national TB Surveillance System. Treatment outcomes were defined according to WHO recommendations. We identified the factors associated with death using logistic regression. We evaluated treatment outcomes of 294 MDR- and 142 XDR-TB patients. The treatment success rate was 73.8% among MDR- and 62.7% among XDR-TB patients (p = 0.023). The case-fatality rate was 18.4% among MDR- and 23.9% among XDR-TB patients. HIV infection (OR 4.55; 95% CI 2.31-8.99; p < 0.001) and resistance to one or more second-line injectable drugs (OR 2.73; 95% CI 1.26-5.92; p = 0.011) were independently associated with death among MDR-TB patients. HIV infection, injectable drug use, past imprisonment, comorbidities, and alcohol abuse are conditions that were associated with death early on and during treatment. Early diagnosis of MDR-TB and further monitoring of these patients are necessary to improve treatment outcome.This work was developed under the scope of the project NORTE-01-0145-FEDER-000013 and NORTE-01-0145-FEDER-000023, supported by the Northern Portugal Regional Operational Programme (NORTE 2020), under the Portugal 2020 Partnership Agreement, through the European Regional Development Fund (FEDER) and projects PTDC/SAU-PUB/29521/2017. This work was partially supported by “Contratos-Programa” UIDB/50026/2020 and UIDB/04050/2020 funded by national funds through the FCT - Foundation for Science and Technology, I.P. OO is supported by the project NORTE-08-5369-FSE-000041, financed by the Operational Program NORTE 2020 and co-financed by the European Social Fund through a doctoral grant (UMINHO/BD/47/2016). This work was also supported by national funds through the FCT, I.P., under the project UIDB / 04750/2020

Improving the Knowledge on Seismogenic Sources in the Lower Tagus Valley for Seismic Hazard Purposes

The Lower Tagus Valley, that includes the metropolitan area of Lisbon, has been struck by several earthquakes which produced significant material damage and loss of lives. Their exact location remains unknown. Our goal is to shed some light into the seismogenic sources in the area using seismic reflection and geological data. In areas with no seismic coverage, potential-field data interpretation was carried out. Seismicity was overlaid to the potential seismogenic structures and high-resolution data was acquired in order to confirm which structures have been active into the Quaternary. Three major fault-zones affecting the Neogene were identified: V. F. Xira, Samora-Alcochete and Pinhal Novo. For the first fault, strong evidences suggest it is active. The other two fault-zones and other structures previously unknown can be correlated with several epicentres. Empirical relationships between maximum moment magnitude and fault area indicate that MW > 6.5 earthquakes can be expected for the larger structures

Intra-urban variation in tuberculosis and community socioeconomic deprivation in Lisbon metropolitan area: a Bayesian approach

Background: Multidrug resistant tuberculosis (MDR-TB) is a recognized threat to global efforts to TB control and remains a priority of the National Tuberculosis Programs. Additionally, social determinants and socioeconomic deprivation have since long been associated with worse health and perceived as important risk factors for TB. This study aimed to analyze the spatial distribution of non-MDR-TB and MDR-TB across parishes of the Lisbon metropolitan area of Portugal and to estimate the association between non-MDR-TB and MDR-TB and socioeconomic deprivation. Methods: In this study, we used hierarchical Bayesian spatial models to analyze the spatial distribution of notification of non-MDR-TB and MDR-TB cases for the period from 2000 to 2016 across 127 parishes of the seven municipalities of the Lisbon metropolitan area (Almada, Amadora, Lisboa, Loures, Odivelas, Oeiras, Sintra), using the Portuguese TB Surveillance System (SVIG-TB). In order to characterise the populations, we used the European Deprivation Index for Portugal (EDI-PT) as an indicator of poverty and estimated the association between non-MDR-TB and MDR-TB and socioeconomic deprivation. Results: The notification rates per 10,000 population of non-MDR TB ranged from 18.95 to 217.49 notifications and that of MDR TB ranged from 0.83 to 3.70. We identified 54 high-risk areas for non-MDR-TB and 13 high-risk areas for MDR-TB. Parishes in the third [relative risk (RR) = 1.281, 95% credible interval (CrI): 1.021–1.606], fourth (RR = 1.786, 95% CrI: 1.420–2.241) and fifth (RR = 1.935, 95% CrI: 1.536–2.438) quintile of socioeconomic deprivation presented higher non-MDR-TB notifications rates. Parishes in the fourth (RR = 2.246, 95% CrI: 1.374–3.684) and fifth (RR = 1.828, 95% CrI: 1.049–3.155) quintile of socioeconomic deprivation also presented higher MDR-TB notifications rates. Conclusions: We demonstrated significant heterogeneity in the spatial distribution of both non-MDR-TB and MDR-TB at the parish level and we found that socioeconomically disadvantaged parishes are disproportionally affected by both non-MDR-TB and MDR-TB. Our findings suggest that the emergence of MDR-TB and transmission are specific from each location and often different from the non-MDR-TB settings. We identified priority areas for intervention for a more efficient plan of control and prevention of non-MDR-TB and MDR-TB. Graphical Abstract: [Figure not available: see fulltext.] © 2022, The Author(s).This work has been funded by National funds, through the Foundation for Science and Technology (FCT)—project UIDB/50026/2020, UIDP/50026/2020 and PTDC/SAU-PUB/29521/2017. This study was also supported by FEDER through the Operational Programme Competitiveness and Internationalization and national funding through the Foundation for Science and Technology—FCT (Portuguese Ministry of Science, Technology and Higher Education) under the Unidade de Investigação em Epidemiologia—Instituto de Saúde Pública da Universidade do Porto (EPIUnit) (UIDB/04750/2020). Ana Isabel Ribeiro was supported by National Funds through FCT, under the programme of ‘Stimulus of Scientific Employment—Individual Support’ within the contract CEECIND/02386/2018

Statistical mixing and aggregation in Feller diffusion

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.Comment: 16 pages, 3 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen

Object-oriented Programming Laws for Annotated Java Programs

Object-oriented programming laws have been proposed in the context of languages that are not combined with a behavioral interface specification language (BISL). The strong dependence between source-code and interface specifications may cause a number of difficulties when transforming programs. In this paper we introduce a set of programming laws for object-oriented languages like Java combined with the Java Modeling Language (JML). The set of laws deals with object-oriented features taking into account their specifications. Some laws deal only with features of the specification language. These laws constitute a set of small transformations for the development of more elaborate ones like refactorings

Reação de espécies de Piper a dois isolados de Nectria haematococca f. sp. piperis.

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