Very special divisors on 4-gonal real algebraic curves

International audience

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Empirical evidence of S-curves in the Colombian

The Marshall-Lerner condition, the J-curve and S-curve have emerged as theoretical and empirical foundations developed for the study of the interaction between exchange rates and international patterns of bilateral trade -- They have a significant bearing on thedevelopment of public policy, and are of equal interest to the academic and professional communities -- The most recently developed of these theories, the S-Curve, is named after the theorized short-run behavior to be found in the cross-correlation function of the real exchange rate and the trade balance -- Considering this theoretical context, the paper seeks empirical evidence of the existence of the S-Curve in the bilateral trade in commodity and non-commodity goods between Colombia and the United States and Venezuela, its main trading partners, for the yearly quarters between 1994:1 and 2009:4

Distance and overcurrent relay coordination considering non standardized inverse time curves

Protective relaying comprehends several procedures and techniques focused on maintaining the power system working safely during and after undesired and abnormal network conditions, mostly caused by faulty events. Overcurrent relay is one of the oldest protective relays, its operation principle is straightforward: when the measured current is greater than a specified magnitude the protection trips; less variables are required from the system in comparison with other protections, causing the overcurrent relay to be the simplest and also the most difficult protection to coordinate; its simplicity is reflected in low implementation, operation, and maintenance cost. The counterpart consists in the increased tripping times offered by this kind of relays mostly before faults located far from their location; this problem can be particularly accentuated when standardized inverse-time curves are used or when only maximum faults are considered to carry out relay coordination. These limitations have caused overcurrent relay to be slowly relegated and replaced by more sophisticated protection principles, it is still widely applied in subtransmission, distribution, and industrial systems. In this work, the use of non standardized inverse-time curves, the model and implementation of optimization algorithms capable to carry out the coordination process, the use of different levels of short circuit currents, and the inclusion of distance relays to replace insensitive overcurrent ones are proposed methodologies focused on the overcurrent relay performance improvement. These techniques may transform the typical overcurrent relay into a more sophisticated one without changing its fundamental principles and advantages. Consequently a more secure and still economical alternative can be obtained, increasing its implementation area

Removal of paracetamol on biomass-derived activated carbon: Modeling the fixed bed breakthrough curves using batch adsorption experiments

The remediation of paracetamol (PA), an emerging contaminant frequently found in wastewater treatment plants, has been studied in the low concentration range (0.3–10 mg L−1) using as adsorbent a biomass-derived activated carbon. PA uptake of up to 100 mg g−1 over the activated carbon has been obtained, with the adsorption isotherms being fairly explained by the Langmuir model. The application of Reichemberg and the Vermeulen equations to the batch kinetics experiments allowed estimating homogeneous and heterogeneous diffusion coefficients, reflecting the dependence of diffusion with the surface coverage of PA. A series of rapid small-scale column tests were carried out to determine the breakthrough curves under different operational conditions (temperature, PA concentration, flow rate, bed length). The suitability of the proposed adsorbent for the remediation of PA in fixed-bed adsorption was proven by the high PA adsorption capacity along with the fast adsorption and the reduced height of the mass transfer zone of the columns. We have demonstrated that, thanks to the use of the heterogeneous diffusion coefficient, the proposed mathematical approach for the numerical solution to the mass balance of the column provides a reliable description of the breakthrough profiles and the design parameters, being much more accurate than models based in the classical linear driving force.

Conversion of a Micro, Glow-Ignition, Two-Stroke Engine from Nitromethane-Methanol Blend Fuel to Military Jet Propellant (JP-8)

The goal of the thesis "Conversion of a Micro, Glow-Ignition, Two-Stroke Engine from Nitromethane-Methanol Blend Fuel to Military Jet Propellant (JP-8)" was to demonstrate the ability to operate a small engine on JP-8 and was completed in two phases. The first phase included choosing, developing a test stand for, and baseline testing a nitromethane-methanol-fueled engine. The chosen engine was an 11.5 cc, glow-ignition, two-stroke engine designed for remote-controlled helicopters. A micro engine test stand was developed to load and motor the engine. Instrumentation specific to the low flow rates and high speeds of the micro engine was developed and used to document engine behavior. The second phase included converting the engine to operate on JP-8, completing JP-8-fueled steady-state testing, and comparing the performance of the JP-8-fueled engine to the nitromethane-methanol-fueled engine. The conversion was accomplished through a novel crankcase heating method; by heating the crankcase for an extended period of time, a flammable fuel-air mixture was generated in the crankcase scavenged engine, which greatly improved starting times. To aid in starting and steady-state operation, yttrium-zirconia impregnated resin (i.e. ceramic coating) was applied to the combustion surfaces. This also improved the starting times of the JP-8-fueled engine and ultimately allowed for a 34-second starting time. Finally, the steady-state data from both the nitromethane-methanol and JP-8-fueled micro engine were compared. The JP-8-fueled engine showed signs of increased engine friction while having higher indicated fuel conversion efficiency and a higher overall system efficiency. The minimal ability of JP-8 to cool the engine via evaporative effects, however, created the necessity of increased cooling air flow. The conclusion reached was that JP-8-fueled micro engines could be viable in application, but not without additional research being conducted on combustion phenomenon and cooling requirements.

E-polynomial of SL(2,C)-character varieties of complex curves of genus 3.

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g = 3 into SL(2, C), and also of the moduli space of twisted representations. The case of genus g = 1, 2 has already been done in [12]. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.

Centile curves and reference values for height, body mass, body mass index and waist circumference of peruvian children and adolescents

This study aimed to provide height, body mass, BMI and waist circumference (WC) growth centile charts for school-children, aged 4–17 years, from central Peru, and to compare Peruvian data with North-American and Argentinean references. The sample consisted of 8753 children and adolescents (4130 boys and 4623 girls) aged 4 to 17 years, from four Peruvian cities: Barranco, La Merced, San Ramón and Junín. Height, body mass and WC were measured according to standardized techniques. Centile curves for height, body mass, BMI and WC were obtained separately for boys and girls using the LMS method. Student t-tests were used to compare mean values. Overall boys have higher median heights than girls, and the 50th percentile for body mass increases curvilinearly from 4 years of age onwards. In boys, the BMI and WC 50th percentiles increase linearly and in girls, the increase presents a curvilinear pattern. Peruvian children are shorter, lighter and have higher BMI than their counterparts in the U.S. and Argentina; in contrast, age and sex-specific WC values are lower. Height, body mass and WC of Peruvian children increased with age and variability was higher at older ages. The growth patterns for height, body mass, BMI and WC among Peruvian children were similar to those observed in North-American and Argentinean peers.

Learning curves: analysing pace and challenge in four successful puzzle games

The pace at which challenges are introduced in a game has long been identified as a key determinant of both the enjoyment and difficulty experienced by game players, and their ability to learn from game play. In order to understand how to best pace challenges in games, there is great value in analysing games already demonstrated as highly engaging. Play-through videos of four puzzle games (Portal, Portal 2 Co-operative mode, Braid and Lemmings), were observed and analysed using metrics derived from a behavioural psychology understanding of how people solve problems. Findings suggest that; 1) the main skills learned in each game are introduced separately, 2) through simple puzzles that require only basic performance of that skill, 3) the player has the opportunity to practice and integrate that skill with previously learned skills, and 4) puzzles increase in complexity until the next new skill is introduced. These data provide practical guidance for designers, support contemporary thinking on the design of learning structures in games, and suggest future directions for empirical research.

An alternative methodology for fitting selectivity curves to pre-defined distributions

A non-linear least-squares methodology for simultaneously estimating parameters of selectivity curves with a pre-defined functional form, across size classes and mesh sizes, using catch size frequency distributions, was developed based on the model of Kirkwood and Walker [Kirkwood, G.P., Walker, T.L, 1986. Gill net selectivities for gummy shark, Mustelus antarcticus Gunther, taken in south-eastern Australian waters. Aust. J. Mar. Freshw. Res. 37, 689-697] and [Wulff, A., 1986. Mathematical model for selectivity of gill nets. Arch. Fish Wiss. 37, 101-106]. Observed catches of fish of size class I in mesh m are modeled as a function of the estimated numbers of fish of that size class in the population and the corresponding selectivities. A comparison was made with the maximum likelihood methodology of [Kirkwood, G.P., Walker, T.I., 1986. Gill net selectivities for gummy shark, Mustelus antarcticus Gunther, taken in south-eastern Australian waters. Aust. J. Mar. Freshw. Res. 37, 689-697] and [Wulff, A., 1986. Mathematical model for selectivity of gill nets. Arch. Fish Wiss; 37, 101-106], using simulated catch data with known selectivity curve parameters, and two published data sets. The estimated parameters and selectivity curves were generally consistent for both methods, with smaller standard errors for parameters estimated by non-linear least-squares. The proposed methodology is a useful and accessible alternative which can be used to model selectivity in situations where the parameters of a pre-defined model can be assumed to be functions of gear size; facilitating statistical evaluation of different models and of goodness of fit. (C) 1998 Elsevier Science B.V.

Centile curves and reference values for height, body mass, body mass index and waist circumference of peruvian children and adolescents

This study aimed to provide height, body mass, BMI and waist circumference (WC) growth centile charts for school-children, aged 4–17 years, from central Peru, and to compare Peruvian data with North-American and Argentinean references. The sample consisted of 8753 children and adolescents (4130 boys and 4623 girls) aged 4 to 17 years, from four Peruvian cities: Barranco, La Merced, San Ramón and Junín. Height, body mass and WC were measured according to standardized techniques. Centile curves for height, body mass, BMI and WC were obtained separately for boys and girls using the LMS method. Student t-tests were used to compare mean values. Overall boys have higher median heights than girls, and the 50th percentile for body mass increases curvilinearly from 4 years of age onwards. In boys, the BMI and WC 50th percentiles increase linearly and in girls, the increase presents a curvilinear pattern. Peruvian children are shorter, lighter and have higher BMI than their counterparts in the U.S. and Argentina; in contrast, age and sex-specific WC values are lower. Height, body mass and WC of Peruvian children increased with age and variability was higher at older ages. The growth patterns for height, body mass, BMI and WC among Peruvian children were similar to those observed in North-American and Argentinean peers.

Maturation curves of sweet sorghum genotypes.

O sorgo sacarino [Sorghum bicolor (L.) Moench] se destaca como cultura complementar à cana-de-açúcar Saccharum spp. na produção de etanol, uma vez que este possui colmos suculentos com presença de açúcares diretamente fermentescíveis. Em decorrência deste fato, existe a necessidade de se analisar as propriedades do sorgo, a fim de atender às demandas da agroindústria. No presente trabalho, buscou-se desenvolver e estudar as curvas de maturação de sete cultivares de sorgo sacarino em dez épocas de colheita. Os resultados mostram que houve diferença significativa para cultivares e épocas de colheita para todos os parâmetros (p≤0,01). Quanto aos teores de açúcares, as cultivares BRS508, XBWS80147 e CMSXS629 apresentaram as maiores médias para as variáveis açúcares redutores totais (ART) e açúcares totais recuperáveis (ATR). Em relação à produção de etanol por tonelada de biomassa, as cultivares BRS 508 e a CMSXS629 apresentaram os melhores resultados.

The Hitchin map for one-nodal base curves of compact type

Studying moduli spaces of semistable Higgs bundles (E, \phi) of rank n on a smooth curve C, a key role is played by the spectral curve X (Hitchin), because an important result by Beauville-Narasimhan-Ramanan allows us to study isomorphism classes of such Higgs bundles in terms of isomorphism classes of rank-1 torsion-free sheaves on X. This way, the generic fibre of the Hitchin map, which associates to any semistable Higgs bundle the coefficients of the characteristic polynomial of \phi, is isomorphic to the Jacobian of X. Focusing on rank-2 Higgs data, this construction was extended by Barik to the case in which the curve C is reducible, one-nodal, having two smooth components. Such curve is called of compact type because its Picard group is compact. In this work, we describe and clarify the main points of the construction by Barik and we give examples, especially concerning generic fibres of the Hitchin map. Referring to Hausel-Pauly, we consider the case of SL(2,C)-Higgs bundles on a smooth base curve, which are such that the generic fibre of the Hitchin map is a subvariety of the Jacobian of X, the Prym variety. We recall the description of special loci, called endoscopic loci, such that the associated Prym variety is not connected. Then, letting G be an affine reductive group having underlying Lie algebra so(4,C), we consider G-Higgs bundles on a smooth base curve. Starting from the construction by Bradlow-Schaposnik, we discuss the associated endoscopic loci. By adapting these studies to a one-nodal base curve of compact type, we describe the fibre of the SL(2,C)-Hitchin map and of the G-Hitchin map, together with endoscopic loci. In the Appendix, we give an interpretation of generic spectral curves in terms of families of double covers.

Elementary properties of Modular curves and Modular forms

Lo scopo di questa tesi è introdurre in breve le prime proprietà delle curve modulari e delle forme modulari, per poi mostrarne alcune applicazioni archetipiche. Per farlo, dopo aver richiamato alcune nozioni utili nel primo capitolo, sviluppiamo, nel secondo capitolo, la teoria di base delle curve modulari compatte come superfici di Riemann, calcolandone il genere nel caso dei sottogruppi principali di congruenza. Dunque, nel terzo capitolo, dopo un estesa trattazione dell'esempio delle forme modulari rispetto al gruppo modulare, viene calcolata la dimensione degli spazi delle forme intere e delle forme cuspidali rispetto a un sottogruppo di indice finito del gruppo modulare. Questo capitolo si conclude con tre esempi di applicazione della teoria esposta, tra i quali spiccano la dimostrazione del Grande Teorema di Picard e del Teorema dei quattro quadrati di Jacobi.