The use of singular functions for the approximate conformal mapping of doubly-connected domains

Let f be the function which maps conformally a given doubly- connected domain onto a circular annulus. We consider the use of two closely related methods for determining approximations to f of the form fn (z) = z exp, ⎪⎩⎪⎨⎧⎭⎬⎫Σ−(z)uan1jjj where {uj} is a set of basis functions. The two methods are respectively a variational method, based on an extremum property of the function H(z) = f′(z)/f(z) - 1/z, and an orthononnalization method, based on approximating the function H by a finite Fourier series sum. The main purpose of the paper is to consider the use of the two methods for the mapping of domains having sharp corners, where corner singularities occur. We show, by means of numerical examples, that both methods are capable of producing approximations of high accuracy for the mapping of such "difficult" doubly-connected domains. The essential requirement for this is that the basis set {uj} contains singular functions that reflect the asymptotic behaviour of the function H in the neighbourhood of each "singular" corner

Numerical conformal mapping of exterior domains

The work of the present paper is closely related to the two numerical procedures described in [11], for determining approximations to the function which maps conformally a bounded simply-connected domain Ω1 , with boundary ∂Ω, onto the unit disc. Here, we consider the use of these procedures for the solution of the corresponding exterior problem, i.e. the problem of determining approximations to the mapping function which maps conformally the exterior domain Ω = compl(ΩI⋃∂Ω) onto the unit disc

Numerical techniques for conformal mapping onto a rectangle

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain onto a rectangle R, so that four specified points on are mapped Ω∂respectively onto the four vertices of R. In particular, we study the following two classes of methods for the mapping of domains of the form . (i) Methods which approximate where f is an approximation to the conformal map of Q onto the unit disc, and S is a simple Schwarz-Christoffel transformation. (ii) Methods based on approximating the conformal map of a certain symmetric doubly-connected domain onto a circular annulus. Keywords: Conforma

An orthonormalization method for the approximate conformal mapping of multiply-connected domains

We consider the use of an orthonormalization method for constructing approximations to one of the standard conformal maps for multiply-connected domains. The method has been used successfully in [12], but only for the mapping of doubly-connected domains. Our purpose here is to consider its application to the mapping of domains whose connectivity is greater than two

Properties and characterization of biodiesel from selected microalgea stains

The demand for alternative fuels has increased in the past several years[1]. Biofuels are gaining importance as significant substitutes for the depleting fossil fuels. The fact that biofuels are renewable fuels with very low emissions of CO2 in the lifecycle offers them a competitive advantage[2]. However, the first produced biodiesel derived from edible oil seed crops (first generation feedstocks), lurking a serious risk of disturbing the overall worldwide balance of food reserves and safety. The second generation feedstocks for biodiesel production obtained from non-edible oil seed crops, waste cooking oil, animal fats, etc., but these feedstocks are not sufficient to cover the present energy needs. Recent focus is on microalgae as the third generation feedstock[3]. Mi l d t t f l d b t th i lt ( ) b kih(l ) df h Microalgae do not compete for land, but they can grow in salty sea), brackish (lagoons) and fresh (lakes) water. Moreover, microalgae have high photosynthetic efficiency using solar energy, water and carbon dioxide to produce higher quantities of biomass than other feedstocks. In the present research work, two indigenous fresh water (ChlorF1, ChlorF2) and two marine (ChlorM1, ChlorM2) Chlorophyte strains have been cultivated successfully under laboratory conditions using commercial fertilizer (Nutrileaf 30-10-10, initial concentration=70 g/m3) as nutrient source. The produced biodiesel from the microalgae biomass achieved a range of 2.2 - 10.6% total lipid content and an unsaturated FAME content between 48 mol% and 59 mol%. The iodine value, the cetane number, the cold filter plugging point (CFPP) and the oxidative stability of the ultimate biodiesels were determined, based on the compositions of the four (4) microalgae strains and compared with the specifications in the EU and US standards, EN 14214 and ASTM D6751 respectively

Statin therapy, fitness, and mortality risk in middle-aged hypertensive male veterans

BACKGROUND Hypertension often coexists with dyslipidemia, accentuating cardiovascular risk. Statins are often prescribed in hypertensive individuals to lower cardiovascular risk. Higher fitness is associated with lower mortality, but exercise capacity may be attenuated in hypertension. The combined effects of fitness and statin therapy in hypertensive individuals have not been assessed. Thus, we assessed the combined health benefits of fitness and statin therapy in hypertensive male subjects. METHODS Peak exercise capacity was assessed in 10,202 hypertensive male subjects (mean age = 60.4±10.6 years) in 2 Veterans Affairs Medical Centers. We established 4 fitness categories based on peak metabolic equivalents (METs) achieved and 8 categories based on fitness status and statin therapy. RESULTS During the follow-up period (median = 10.2 years), there were 2,991 deaths. Mortality risk was 34% lower (hazard ratio (HR) = 0.66; 95% confidence interval (CI) = 0.59–0.74; P \u3c 0.001) among individuals treated with statins compared with those not on statins. The fitness-related mortality risk association was inverse and graded regardless of statin therapy status. Risk reduction associated with exercise capacity of 5.1–8.4 METs was similar to that observed with statin therapy. However, those achieving ≥8.5 METs had 52% lower risk (HR = 0.48; 95% CI = 0.37–0.63) when compared with the least-fit subjects (≤5 METs) on statin therapy. CONCLUSIONS The combination of statin therapy and higher fitness lowered mortality risk in hypertensive individuals more effectively than either alone. The risk reduction associated with moderate increases in fitness was similar to that achieved by statin therapy. Higher fitness was associated with 52% lower mortality risk when compared with the least fit subjects on statin therapy

Mechanical and electrochemical characterization of 3D printed orthodontic metallic appliances after in vivo ageing

Objectives: Three-dimensional (3D) printing technology is a promising technique for fabricating custom orthodontic metallic appliances. Aim of this study was to assess the effect of intraoral aging on the mechanical / electrochemical properties of 3D-printed orthodontic metallic appliances. Methods: Twelve molar orthodontic distalization appliances 3D-printed from cobalt chromium (Co-Cr) alloy were retrieved after intraoral use and twenty blocks fabricated under similar conditions were used as control. The samples' microstructural / elemental composition assessment was assessed with SEM/EDS, while their mechanical properties (modulus of elasticity [EIT], Martens hardness [HM] and the elastic index [ηIT]) were measured by instrumented indentation testing. Finally, the samples' electrochemical features were assessed with a potentiostat-connected cell arrangement in terms of open circuit potential (OCP), corrosion potential (Ez), current density (I300) and breaking potential (Epit). Results were analyzed by t-test / Mann-Whitney test (α = 0.05). Results: The used Co-Cr alloy was found to have a highly homogenous structure with no significant differences between retrieved and new specimens in HM (4037.7 ± 215.6 vs 4090.9 ± 259.8 N/mm2), EIT (120.0 ± 13.2 vs 123.8 ± 12.9 GPa), or nIT (28.4 ± 2.6 vs 28.6 ± 2.9 %) (P > 0.05 in all instances). Metallic surfaces retained the same oxidation tendency and oxide dissolution rate in passive region in both groups (P > 0.05 for OCP, Ez, and I300). However, intraorally-aged specimens had a significantly lower breakdown potential due to degraded protection efficacy of surface oxide (P = 0.003 for Epit). Significance: The tested 3D-printed Co-Cr orthodontic appliances present clinically-acceptable mechanical properties that remained unaffected by intraoral ageing, which however degraded the protection of surface oxide against pitting corrosion. Keywords: 3D printing; Co-Cr alloys; Corrosive resistance; Electrochemical behavior; Intraoral ageing; Orthodontic appliances