Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Otimização com restrições de complementaridade: algoritmos e aplicações

Tese de Doutoramento em Engenharia Industrial e de Sistemas (PDEIS)

Detection of incipient left ventricular hypertrophy in mild to moderate arterial hypertension with normal electrocardiogram and echocardiogram: a new use for signal-averaged electrocardiography

OBJECTIVE: To assess signal-averaged electrocardiogram (SAECG) for diagnosing incipient left ventricular hypertrophy (LVH). METHODS: A study with 115 individuals was carried out. The individuals were divided as follows: GI - 38 healthy individuals; GII - 47 individuals with mild to moderate hypertension and normal findings on echocardiogram and ECG; and GIII - 30 individuals with hypertension and documented LVH. The magnitude vector of the SAECG was analyzed with the high-pass cutoff frequency of 40 Hz through the bidirectional four-pole Butterworth high-pass digital filter. The mean quadratic root of the total QRS voltage (RMST) and the two-dimensional integral of the QRS area of the spectro-temporal map were analyzed between 0 and 30 Hz for the frequency domain (Int FD), and between 40 and 250 Hz for the time domain (Int TD). The electrocardiographic criterion for LVH was based on the Cornell Product. Left ventricular mass was calculated with the Devereux formula. RESULTS: All parameters analyzed increased from GI to GIII, except for Int FD (GII vs GIII) and RMST log (GII vs GIII). Int TD showed greater accuracy for detecting LVH with an appropriate cutoff > 8 (sensitivity of 55%, specificity of 81%). Positive values (> 8) were found in 56.5% of the G II patients and in 18.4% of the GI patients (p< 0.0005). CONCLUSION: SAECG can be used in the early diagnosis of LVH in hypertensive patients with normal ECG and echocardiogram.

O regime de chuvas em Pesqueira

The authors studied the rainfall in Pesqueira (Pernambuco, Brasil) in a period of 48 years (1910 through 1957) by the method of orthogonal polynomials, degrees up to the fourth having been tried. None of them was significant, so that it seems that no trend is present. The mean observed was 679.00 mm., with standard error of the mean 205.5 mm., and a 30.3% coefficient of variation. The 95% level of probability would include annual rainfall from 263.9 up to 1094.1mm.

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

Associations between alcohol consumption and selected cytokines in a Swiss population-based sample (CoLaus study).

To assess the associations between alcohol consumption and cytokine levels (interleukin-1beta - IL-1β; interleukin-6 - IL-6 and tumor necrosis factor-α - TNF-α) in a Caucasian population. Population sample of 2884 men and 3201 women aged 35-75. Alcohol consumption was categorized as nondrinkers, low (1-6 drinks/week), moderate (7-13/week) and high (14+/week). No difference in IL-1β levels was found between alcohol consumption categories. Low and moderate alcohol consumption led to lower IL-6 levels: median (interquartile range) 1.47 (0.70-3.51), 1.41 (0.70-3.32), 1.42 (0.66-3.19) and 1.70 (0.83-4.39) pg/ml for nondrinkers, low, moderate and high drinkers, respectively, p<0.01, but this association was no longer significant after multivariate adjustment. Compared to nondrinkers, moderate drinkers had the lowest odds (Odds ratio=0.86 (0.71-1.03)) of being in the highest quartile of IL-6, with a significant (p<0.05) quadratic trend. Low and moderate alcohol consumption led to lower TNF-α levels: 2.92 (1.79-4.63), 2.83 (1.84-4.48), 2.82 (1.76-4.34) and 3.15 (1.91-4.73) pg/ml for nondrinkers, low, moderate and high drinkers, respectively, p<0.02, and this difference remained borderline significant (p=0.06) after multivariate adjustment. Moderate drinkers had a lower odds (0.81 [0.68-0.98]) of being in the highest quartile of TNF-α. No specific alcoholic beverage (wine, beer or spirits) effect was found. Moderate alcohol consumption is associated with lower levels of IL-6 and (to a lesser degree) of TNF-α, irrespective of the type of alcohol consumed. No association was found between IL-1β levels and alcohol consumption.

Sex difference and the role of leptin in the association between high-sensitivity C-reactive protein and adiposity in two different populations.

Elevated high-sensitivity C-reactive protein (hs-CRP) concentration is associated with an increased risk of cardiovascular disease but this association seems to be largely mediated via conventional cardiovascular risk factors. In particular, the association between hs-CRP and obesity has been extensively demonstrated and correlations are stronger in women than men. We used fractional polynomials-a method that allows flexible modeling of non linear relations-to investigate the dose/response mathematical relationship between hs-CRP and several indicators of adiposity in Caucasians (Switzerland) and Africans (Seychelles) surveyed in two population-based studies. This relationship was non-linear exhibiting a steeper slope for low levels of hs-CRP and a higher level in women. The observed sex difference in the relationship between hs-CRP and adiposity almost disappeared upon adjustment for leptin, suggesting that these sex differences might be partially mediated, by leptin. All these relationship were similar in Caucasians and Africans. This is the first report on a non-linear relation, stratified by gender, between hs-CRP and adiposity.

Second-Order Approximation to the Rotemberg Model around a Distorted Steady State

Less is known about social welfare objectives when it is costly to change prices, as in Rotemberg (1982), compared with Calvo-type models. We derive a quadratic approximate welfare function around a distorted steady state for the costly price adjustment model. We highlight the similarities and differences to the Calvo setup. Both models imply inflation and output stabilization goals. It is explained why the degree of distortion in the economy influences inflation aversion in the Rotemberg framework in a way that differs from the Calvo setup.

On Measuring the Efficiency of Monetary Policy

Cecchetti et al. (2006) develop a method for allocating macroeconomic performance changes among the structure of the economy, variability of supply shocks and monetary policy. We propose a dual approach of their method by borrowing well-known tools from production theory, namely the Farrell measure and the Malmquist index. Following FÄare et al (1994) we propose a decomposition of the efficiency of monetary policy. It is shown that the global efficiency changes can be rewritten as the product of the changes in macroeconomic performance, minimum quadratic loss, and efficiency frontier.

Ordering Policy Rules with an Unconditional Welfare Measure

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantitative research. It is shown that it is generally possible to derive a linear - quadratic problem that approximates the exact non-linear problem where the unconditional expectation of the objective is maximised and the steady-state is distorted. Thus, the measure of pol icy performance is a linear combinat ion of second moments of economic variables which is relatively easy to compute numerically, and can be used to rank alternative policy rules. The approach is applied to a simple Calvo-type model under various monetary policy rules.

An objective anisotropic elastic plastic model and Algorithm applicable to bone mechanics

The implicit projection algorithm of isotropic plasticity is extended to an objective anisotropic elastic perfectly plastic model. The recursion formula developed to project the trial stress on the yield surface, is applicable to any non linear elastic law and any plastic yield function.A curvilinear transverse isotropic model based on a quadratic elastic potential and on Hill's quadratic yield criterion is then developed and implemented in a computer program for bone mechanics perspectives. The paper concludes with a numerical study of a schematic bone-prosthesis system to illustrate the potential of the model.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.