Local conjugacy classes for analytic torus flows

If a real-analytic flow on the multidimensional torus close enough to linear has a unique rotation vector which satisfies an arithmetical condition Y, then it is analytically conjugate to linear. We show this by proving that the orbit under renormalization of a constant Y vector field attracts all nearby orbits with the same rotation vector.Comment: inc bib

Design of a Supersonic Nozzle

As new engines are built, the necessity of improving the initial design grows. The preliminary design of nozzles is one of the most important parts due to being the component that increases the speed of the flow even more than the rest of the engine. There are a lot of factors involved in the selection of the nozzle: the cruise speed intended for the aircraft, the cruise altitude and others. As the design methods evolved from paper drafts, in the beginning of the history of aviation, to digital designs, in the present days, the methods employed to do it also changed. The Method of Characteristics was one of the methods that gain some popularity around the 1980’s being first used in paper drafts and then with computer software. This dissertation utilizes the Method of Characteristics to design the supersonic section of the nozzle, and describes how such factors, as the altitude, influence the shape of the contour, as the main goal. The State of the art, chapter 2, introduces a brief description of the types of nozzles that exist and the application for each one of them. From the basics of thermodynamics to advanced Aerothermodynamics, it is explained the knowledge required to accomplish the results presented on chapter 5. The theoretical foundation, 3, explains the relationship between work and heat as well as the specific heat ratio, the speed of sound and the Mach number, the types of flow, the shocks, the expansion fans and how the variations of pressure affect the flow inside a nozzle. The Design method chapter lays out step by step how to apply the Method of Characteristics, starting with an introduction to the method, then a linear method to design the convergent section, requiring only a few step to do it, and the design of the divergent section of the nozzle, which is the hardest part to attain. The code, in MATLAB, behind the design, is also explained step by step. The Results chapter depicts what appears to the user when initiating the code and what inputs are required for the code to work and give results.There are three cases described and explained, where some variables were changed to observe the difference between those cases. The results of this dissertation indicated that the nozzle was operating with an overexpanded flow, and the convergent section could not achieve a choked flow at the throat, but the pressure decrease along the nozzle had a similar behavior to a choked isentropic supersonic flow.À medida que novos motores são construidos, a necessidade de melhorar os designs aumenta. O projeto preliminar dos bocais é muto importante visto que são um dos componentes que aumenta a velocidade do jato. Existem muitos fatores envolvidos na seleção de bocal propulsivos: a velocidade de cruzeiro pretendida para a aeronave, a altitude de cruzeiro e outros. Na história da aviação, o projeto preliminar evoluiu desde desenhos em papel para designs digitais, e da mesma maneira, as técnicas utilizadas também mudaram. O método das característricas foi um dos métodos que ganhou popularidade nos anos oitenta, empregue primeiramente em papel mas depois podendo ser aplicado juntamente com um software de cálculo. Esta dissertação aplica o Método das Característricas para fazer o design da parte supersónica do bocal, e descreve como alguns fatores, por exemplo, a altitude, influenciam o contorno do bocal, como objectivo principal. O Estado da Arte, capítulo 2, introduz uma breve descrição dos tipos de bocais propulsivos que existem e a aplicação de cada um deles. Os conhecimentos de termodinámica requeridos, desde o básico até ao avançado para conseguir obter os resultados presentes no capítulo 5 são demonstrados no capítulo 3. A fundação teórica explica a relação entre trabalho e calor, a razão de calor específicos, a velocidade do som, o número de Mach, os tipos de fluxo, os choques, a fan de expanção e como as variações de pressão afetam o fluxo de dentro do bocal propulsivo. O capítulo do método de design demonstra, passo por passo, como se aplica o método das Caracteristrícas, começando por uma introdução do que consiste, de seguida o método linear usado para o design da secção convergente, que é a parte simples, e depois o design da secção divergente, sendo esta a parte complexa. O código, em MATLAB, utilizado para o design, também é explicado passo por passo. O capítulo dos resultados demostra o que aparece ao utilizador quando inicia o código e os inputs necessários para o código funcionar e fornecer resultados. Três casos são descritos e explicados, para isto algumas variavéis são mudadas para serem observadas as diferenças entre eles. Os resultados desta dissertação indicam que um bocal propulsivo opera com um fluxo sobre expandido, e que o fluxo na secção convergente nao atinge um estado estrangulado, mas o decrescimento de pressão ao longo do bocal tem um comportamento similar a um fluxo isentrópico, estrangulado e supersónico

A framework to quantify the quality-of-life value of progression-free survival in cancer clinical trials

Background: Progression-Free Survival (PFS) is a key outcome in cancer treatment trials, but its clinical value is unclear, particularly when there is a benefit on PFS but not for Overall Survival (OS). Considering PFS and Health-Related Quality-of-Life (HRQoL) together can help confirm PFS as a valuable outcome, but quantifying their relationship is challenging. Objective: To develop a new estimand that quantitatively combines PFS and HRQoL across the follow-up period for a patient: Time of Accumulated Quality of Life during PFS (TAQL PFS). Methods: The research involved literature reviews and development and evaluation of the TAQL PFS estimand. TAQL PFS incorporates PFS and HRQoL, considering HRQoL duration and intensity until a PFS event. A STATA command was developed for TAQL PFS analysis, which includes imputing censored PFS times, fitting mixed models, predicting HRQoL trajectories, and implementing bootstrapping for inference. The TAQL PFS analysis was validated using simulations and real-world trial data. Results: Among 13 studies, evidence of a link between progressive disease (PD) and HRQoL decline was mixed. A review of 20 colorectal cancer trials found a lack of standardisation in HRQoL assessment and reporting. It was unclear whether improved PFS or OS equated to HRQoL benefit, highlighting the need for a combined metric. Simulations confirmed sensitivity of TAQL PFS measure to PFS time and HRQoL scores and its robustness across different model specifications. TAQL PFS can be computed from published summary data using individual-level data reconstruction. Analysis of the ABC-02 trial identified PD as a factor in HRQoL decline and showed that extending PFS in the CisGem arm corresponded to a longer 12-month TAQL PFS across assessed HRQoL dimensions (treatment difference: 0.98-1.32 HRQoL-corrected PFS months, p<0.05). Conclusion: TAQL PFS combines PFS-HRQoL in a new way to quantify patient outcomes in cancer trials. It enhances the relevance of PFS as an outcome measure for clinicians, patients, and regulators. Further validation is needed to confirm robustness and generalisability across a range of cancer types and interventions

Values, beliefs and economic behaviors: a regional approach

The main goal of this paper is to identify relationships between value orientations, beliefs and economic behavior of agents, on one side, and differences between levels of economic development, on the other. Empirical analysis is based on a sample of Portuguese municipalities and correspondent parishes, organized in groups set by an urban versus rural typology and according to levels of development as measured by GDP per capita. Different value orientations, beliefs and behaviors were identified according to mostly either supply-side or demand-side, as well as predominantly State versus Private Sector orientations. Four clusters were thereby considered, which we generically named as corresponding to 'stabilization', 'economic nationalism', 'entrepreneurship' and 'consumerism'. These clusters are related to spatial dimensions considered. Parishes named 'rural', 'rural-urban' and 'urban' have shown (albeit in a small degree) a prevailing orientation to the State, whereas 'developing' parishes lean to private sector. Rural parishes are markedly consumerist, whereas in those said 'rural-urban' supply-side orientation prevails. Both 'urban' and 'developing' (correspondent to zones going through big recent changes) occupy, in this context, an intermediate position

The shading sign: is it exclusive of endometriomas?

To investigate if the shading sign is an exclusive MRI feature of endometriomas or endometrioid tumors, and to analyze its different patterns. Three hundred and fourty six women with adnexal masses who underwent 1.5/3-T MRI were included in this retrospective, board-approved study. The shading sign was found in 56 patients, but five cases were excluded due to lack of imaging follow-up or histological correlation. The final sample included 51 women. The type of tumor and the pattern of shading were recorded for each case. Thirty endometriomas and five endometrioid carcinomas were found. The remaining 16 cases corresponded to other benign and malignant tumors. The overall sensitivity, specificity, positive predictive value, and negative predictive value were 73%, 93%, 59%, and 96%, respectively. Restricting the analysis to cystic lesions without solid or fat component, sensitivity, specificity, positive predictive value, and negative predictive value were 73%, 96%, 94%, and 80%. Five shading patterns were identified: layering (15.7%), liquid-liquid level (11.8%), homogenous (45.1%), heterogeneous (11.8%), and focal/multifocal shading within a complex mass (19.6%). No significant correlation was found between these patterns and the type of tumor. The shading sign is not exclusive of endometriomas or endometrioid tumors. Homogenous shading was the most prevalent pattern in endometriomas and half of the cases with focal/multifocal shading within a complex mass were endometrioid carcinomas.info:eu-repo/semantics/publishedVersio

Aging in place, housing maintenance and reverse mortgages

We study the role of housing wealth in financing retirement consumption. In our model retirees: 1. derive utility benefits from remaining in their home (aging in place); and 2. choose in each period whether to maintain their house. The evidence that we present shows that these features are important in explaining the saving decisions of the elderly. The costs and the maintenance requirement of reverse mortgages (RMs) reduce (or eliminate) the benefits of the loans for retirees who wish to do less maintenance. We evaluate the impact of different loan features on retirees’ utility, cash-flows to lenders, and to the government agency that provides mortgage insurance. We show that combining RMs with insurance against a forced home sale (e.g. due to a move to a nursing home) is Pareto improving and can lead to increased demand for the loans due to product complementarities