A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Minimally invasive video-assisted thyroid surgery: how can we improve the learning curve?

Objective. Minimally invasive video-assisted thyroidectomy (MIVAT) is a technically demanding procedure and requires a surgical team skilled in both endocrine and endoscopic surgery. A time consuming learning and training period is mandatory at the beginning of the experience. The aim of our report is to focus some aspects of the learning curve of the surgeon who practices video-assisted thyroid procedures for the first time, through the analysis of our preliminary series of 36 cases. Patients and methods. From September 2004 to April 2005 we selected 36 patients for minimally invasive video-assisted surgery of the thyroid. The patients were considered eligible if they presented with a nodule not exceeding 35mm in maximum diameter; total thyroid volume within normal range; absence of biochemical and echographic signs of thyroiditis. We analyzed surgical results, conversion rate, operating time, post-operative complications, hospital stay, cosmetic outcome of the series. Results. We performed 36 total thyroidectomy. The procedure was successfully carried out in 33/36 cases. Post-operative complications included 3 transient recurrent nerve palsies and 2 transient hypocalcemias; no definitive hypoparathyroidism was registered. All patients were discharged 2 days after operation. The cosmetic result was considered excellent by most patients. Conclusions. Advances in skills and technology have enabled surgeons to reproduce most open surgical techniques with video-assistance or laparoscopically. Training is essential to acquire any new surgical technique and it should be organized in detail to exploit it completely.

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The proposed a posteriori error estimator is validated by numerical experiments, illustrating its reliability and efficiency for a range of test problems.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Pairings: Quintets and Duos from the Collaborative Piano Repertoire

Chamber music with piano comprises some of the greatest masterpieces in the Western canon. The works range from duo sonatas with various instruments through septets. In regard to duo sonatas, the violin is the instrument most frequently paired with the piano. Of all the chamber works for larger ensembles, the most popular is the quintet. In this dissertation, I will be exploring the similarities and differences between the duo sonatas and quintets of a given composer. I will be surveying Robert Schumann’s Piano Quintet in E-flat Major, Op. 44 along with his Violin and Piano Sonata in A Minor, Op. 105. The next pairing will be Johannes Brahms’ Piano Quintet in F Minor, Op. 34 and his Piano and Violin Sonata in D Minor, Op. 108. Dmitri Shostakovich’s Piano Quintet in G Minor, Op. 57 and his Cello and Piano Sonata in D Minor, Op. 40 will be the last two works examined in this dissertation. This dissertation project consisted of three recitals, presented in the Gildenhorn Recital Hall at the Clarice Smith Performing Arts Center of the University of Maryland. The recitals featured works by Johannes Brahms, Robert Schumann and Dmitri Shostakovich and took place on March 14, 2014, February 13, 2015 and November 22, 2015. All three recitals were recorded on compact discs, which can be accessed at the Digital Repository at the University of Maryland (DRUM) and at the University of Maryland Hornbake Library.

Estimating the demand curve for sustainable use of pesticides from contingent-valuation data

Stated-preference valuation techniques are often used to assess consumers' willingness-to-pay for food items produced in farming systems that adopt a sustainable use of pesticides (SUP). We propose an innovative valuation methodology in which dichotomous-choice contingent valuation is used to estimate the demand curve (price-quantity relationship) for such food items where price means price premium for the SUP output, quantity is the probability of choosing SUP and the conventional food product is kept available in the market at the current market price. This methodology can be used to evaluate market differentiation as a policy option to promote the SUP. The methodology is tested with data from a sample of urban consumers of fruits and vegetables in Portugal. The estimated demand curve is used to define the price level maximizing the total premium revenue for the SUP sector as a whole. This optimal level of the price premium is €77.55 (or 163% of the value of the monthly basket of fruits and vegetables at current prices). Adopting the optimal price premium will decrease the number of consumers of SUP food by 54%. The reduction is even higher for low income consumers (80%) leaving them more exposed to the risks of pesticide use.

Using a CGE Model to Identify the Policy Trade-Off between Unemployment and Inflation: The Efficient Phillips Curve

This paper provides a new reading of a classical economic relation: the short-run Phillips curve. Our point is that, when dealing with inflation and unemployment, policy-making can be understood as a multicriteria decisionmaking problem. Hence, we use so-called multiobjective programming in connection with a computable general equilibrium (CGE) model to determine the combinations of policy instruments that provide efficient combinations of inflation and unemployment. This approach results in an alternative version of the Phillips curve labelled as efficient Phillips curve. Our aim is to present an application of CGE models to a new area of research that can be especially useful when addressing policy exercises with real data. We apply our methodological proposal within a particular regional economy, Andalusia, in the south of Spain. This tool can give some keys for policy advice and policy implementation in the fight against unemployment and inflation.

A rolling-gliding wear simulator for the investigation of tribological material pairings for application in total knee arthroplasty

Background: Material wear testing is an important technique in the development and evaluation of materials for use in implant for total knee arthroplasty. Since a knee joint induces a complex rolling-gliding movement, standardised material wear testing devices such as Pin-on-Disc or Ring-on-Disc testers are suitable to only a limited extent because they generate pure gliding motion only.Methods: A rolling-gliding wear simulator was thus designed, constructed and implemented, which simulates and reproduces the rolling-gliding movement and loading of the knee joint on specimens of simplified geometry. The technical concept was to run a base-plate, representing the tibia plateau, against a pivoted cylindrical counter-body, representing one femur condyle under an axial load. A rolling movement occurs as a result of the friction and pure gliding is induced by limiting the rotation of the cylindrical counter-body. The set up also enables simplified specimens handling and removal for gravimetrical wear measurements. Long-term wear tests and gravimetrical wear measurements were carried out on the well known material pairings: cobalt chrome-polyethylene, ceramic-polyethylene and ceramic-ceramic, over three million motion cycles to allow material comparisons to be made.Results: The observed differences in wear rates between cobalt-chrome on polyethylene and ceramic on polyethylene pairings were similar to the differences of published data for existing material-pairings. Test results on ceramic-ceramic pairings of different frontal-plane geometry and surface roughness displayed low wear rates and no fracture failures.Conclusions: The presented set up is able to simulate the rolling-gliding movement of the knee joint, is easy to use, and requires a minimum of user intervention or monitoring. It is suitable for long-term testing, and therefore a useful tool for the investigation of new and promising materials which are of interest for application in knee joint replacement implants. © 2010 Richter et al; licensee BioMed Central Ltd.

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

Automorphism groups of non-orientable elliptic-hyperelliptic Klein surfaces with boundary

A classical study about Klein and Riemann surfaces consists in determining their groups of automorphisms. This problem is very difficult in general,and it has been solved for particular families of surfaces or for fixed topological types. In this paper, we calculate the automorphism groups of non-orientable bordered elliptic-hyperelliptic Klein surfaces of algebraic genus p> 5.

Economic development and Environmental quality: The environmental Kuznets curve for water pollution

The main aim of this study was to analyze evidence of an environmental Kuznets curve for water pollution in the developing and developed countries. The study was conducted based on a panel data set of 54 countries – that were categorized into six groups of “developed countries”, “developing countries”, “developed countries with low income”, “developed countries with high income” and “coastal countries”- between the years 1995 to 2006. The results do not confirm the inverted U-shape of EKC curve for the developed countries with low income. Based on the estimated turning points and the average GDP per capita, the study revealed at which point of the EKC the countries are. Furthermore, impacts of capital-and-labor ratio as well as trade openness are drawn by estimating different models for the EKC. The magnitude role of each explanatory variable on BOD was calculated by estimating the associated elasticity.

Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Sensitivity analysis in optimized parametric curve fitting

Purpose – Curve fitting from unordered noisy point samples is needed for surface reconstruction in many applications -- In the literature, several approaches have been proposed to solve this problem -- However, previous works lack formal characterization of the curve fitting problem and assessment on the effect of several parameters (i.e. scalars that remain constant in the optimization problem), such as control points number (m), curve degree (b), knot vector composition (U), norm degree (k), and point sample size (r) on the optimized curve reconstruction measured by a penalty function (f) -- The paper aims to discuss these issues -- Design/methodology/approach - A numerical sensitivity analysis of the effect of m, b, k and r on f and a characterization of the fitting procedure from the mathematical viewpoint are performed -- Also, the spectral (frequency) analysis of the derivative of the angle of the fitted curve with respect to u as a means to detect spurious curls and peaks is explored -- Findings - It is more effective to find optimum values for m than k or b in order to obtain good results because the topological faithfulness of the resulting curve strongly depends on m -- Furthermore, when an exaggerate number of control points is used the resulting curve presents spurious curls and peaks -- The authors were able to detect the presence of such spurious features with spectral analysis -- Also, the authors found that the method for curve fitting is robust to significant decimation of the point sample -- Research limitations/implications - The authors have addressed important voids of previous works in this field -- The authors determined, among the curve fitting parameters m, b and k, which of them influenced the most the results and how -- Also, the authors performed a characterization of the curve fitting problem from the optimization perspective -- And finally, the authors devised a method to detect spurious features in the fitting curve -- Practical implications – This paper provides a methodology to select the important tuning parameters in a formal manner -- Originality/value - Up to the best of the knowledge, no previous work has been conducted in the formal mathematical evaluation of the sensitivity of the goodness of the curve fit with respect to different possible tuning parameters (curve degree, number of control points, norm degree, etc.)

Maximum Principle for Elliptic and Parabolic Equations

Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.