Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.

Genetic conectivity patterns in Holothuria Mammata considering different spatial scales

Dissertação de Mestrado, Biologia Marinha, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2015

Settlement patterns of mussel recruits at different temporal scales in the Peniche-Berlengas area (Southwest Portugal)

Dissertação de Mestrado, Biologia Marinha, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2015

Diatom-based characterization of iberian coastal environments at different time scales

Tese de doutoramento, Geologia (Geologia Económica e do Ambiente), Universidade de Lisboa, Faculdade de Ciências, 2014

Effects of sulphurization time on Cu2ZnSnS4 absorbers and thin films solar cells obtained from metallic precursors

We report the results of a study of the sulphurization time effects on Cu2ZnSnS4 absorbers and thin film solar cells prepared from dc-sputtered tackedmetallic precursors. Three different time intervals, 10 min, 30min and 60 min, at maximum sulphurization temperature were considered. The effects of this parameter' change were studied both on the absorber layer properties and on the final solar cell performance. The composition, structure, morphology and thicknesses of the CZTS layers were analyzed. The electrical characterization of the absorber layer was carried out by measuring the transversal electrical resistance of the samples as a function of temperature. This study shows an increase of the conductivity activation energy from 10 meV to 54meV for increasing sulphurization time from 10min to 60min. The solar cells were built with the following structure: SLG/Mo/CZTS/CdS/i-ZnO/ZnO:Al/Ni:Al grid. Several ac response equivalent circuit models were tested to fit impedance measurements. The best results were used to extract the device series and shunt resistances and capacitances. Absorber layer's electronic properties were also determined using the Mott–Schottky method. The results show a decrease of the average acceptor doping density and built-in voltage, from 2.0 1017 cm−3 to 6.5 1015 cm−3 and from 0.71 V to 0.51 V, respectively, with increasing sulphurization time. These results also show an increase of the depletion region width from approximately 90 nm–250 nm.

Cu2ZnSnS4 absorber layers obtained through sulphurization of metallic precursors: Graphite box versus sulphur flux

In this work we employed a hybrid method, combining RF-magnetron sputtering with evaporation, for the deposition of tailor made metallic precursors, with varying number of Zn/Sn/Cu (ZTC) periods and compared two approaches to sulphurization. Two series of samples with 1×, 2× and 4× ZTC periods have been prepared. One series of precursors was sulphurized in a tubular furnace directly exposed to a sulphur vapour and N2+5% H2 flux at a pressure of 5.0×10+4 Pa. A second series of identical precursors was sulphurized in the same furnace but inside a graphite box where sulphur pellets have been evaporated again in the presence of N2+5% H2 and at the same pressure as for the sulphur flux experiments. The morphological and chemical analyses revealed a small grain structure but good average composition for all three films sulphurized in the graphite box. As for the three films sulphurized in sulphur flux grain growth was seen with the increase of the number of ZTC periods whilst, in terms of composition, they were slightly Zn poor. The films' crystal structure showed that Cu2ZnSnS4 is the dominant phase. However, in the case of the sulphur flux films SnS2 was also detected. Photoluminescence spectroscopy studies showed an asymmetric broad band emission whichoccurs in the range of 1–1.5 eV. Clearly the radiative recombination efficiency is higher in the series of samples sulphurized in sulphur flux. We have found that sulphurization in sulphur flux leads to better film morphology than when the process is carried out in a graphite box in similar thermodynamic conditions. Solar cells have been prepared and characterized showing a correlation between improved film morphology and cell performance. The best cells achieved an efficiency of 2.4%.

CuxSnSx+1 (x = 2, 3) thin films grown by sulfurization of metallic precursors deposited by dc magnetron sputtering

We report the results of the growth of Cu-Sn-S ternary chalcogenide compounds by sulfurization of dc magnetron sputtered metallic precursors. Tetragonal Cu2SnS3 forms for a maximum sulfurization temperature of 350 ºC. Cubic Cu2SnS3 is obtained at sulfurization temperatures above 400 ºC. These results are supported by XRD analysis and Raman spectroscopy measurements. The latter analysis shows peaks at 336 cm-1, 351 cm-1 for tetragonal Cu2SnS3, and 303 cm-1, 355 cm-1 for cubic Cu2SnS3. Optical analysis shows that this phase change lowers the band gap from 1.35 eV to 0.98 eV. At higher sulfurization temperatures increased loss of Sn is expected in the sulphide form. As a consequence, higher Cu content ternary compounds like Cu3SnS4 grow. In these conditions, XRD and Raman analysis only detected orthorhombic (Pmn21) phase (petrukite). This compound has Raman peaks at 318 cm-1, 348 cm-1 and 295 cm-1. For a sulfurization temperature of 450 ºC the samples present a multi-phase structure mainly composed by cubic Cu2SnS3 and orthorhombic (Pmn21) Cu3SnS4. For higher temperatures, the samples are single phase and constituted by orthorhombic (Pmn21) Cu3SnS4. Transmittance and reflectance measurements were used to estimate a band gap of 1.60 eV. For comparison we also include the results for Cu2ZnSnS4 obtained using similar growth conditions.

Influence of selenization pressure on the growth of Cu2ZnSnSe4 films from stacked metallic layers

Cu2ZnSnSe4 (CZTSe) is a p-type semiconductor with a high absorption coefficient, 104 to 105 cm-1, and is being seen as a possible replacement for Cu(In,Ga)Se2 in thin film solar cells. Yet, there are some fundamental properties of CZTSe that are not well known, one of them is its band gap. In order to resolve its correct value it is necessary to improve the growth conditions to ensure that single phase crystalline thin films are obtained. One of the problems encountered when growing CZTSe is the loss of Sn through evaporation of SnSe. Stoichiometric films are then difficult to obtain and usually there are other phases present. One possible way to overcome this problem is to increase the pressure of growth of CZTSe. This can be done by introducing an atmosphere of an inert gas like Ar or N2. In this work we report the results of morphological, structural and optical studies of the properties of CZTSe thin films grown by selenization of DC magnetron sputtered metallic layers under different Ar pressures. The films are analysed by SEM/EDS, Raman scattering and XRD.

Critical evaluation of outcome scales to assess outcome after lateral ankle ligament repair

Introduction: Several scores are commonly used to evaluate patients' postoperative satisfaction after lateral ankle ligament repair, including: AOFAS, FAAM, CAIT and CAIS. Comparing published studies in the literature is difficult, as the same patient can have markedly different results depending on which scoring system is used. The current study aims to address this gap in the literature by developing a system to compare these tests, to allow better analysis and comparison of published studies. Patients and methods: This is a retrospective cohort study of 47 patients following lateral ankle ligament repair using a modified Broström-Gould technique. All patients were operated between 2005 and 2010 by a single surgeon and followed the same post operative rehabilitation protocol. Six patients were excluded from the study because of concomitant surgery. Patients were assessed by an independent observer. We used the Pearson correlation coefficient to analyse the concordance of the scores, as well as scatter plots to assess the linear relationship between them. Results: A linear distribution between the scores was found when the results were analysed using scatter plots. We were thus able to use the Pearson correlation coefficient to evaluate the relationship between each of the different postoperative scores. The correlation was found to be above 0.5 in all cases except for the comparison between the CAIT and the FAAM for the activities of daily living (0.39). We were, therefore, able to compare the results obtained and assess the relative concordance of the scoring systems. The results showed that the more specific the scale is, the worst the score is and inversely. So the CAIT and the CAIS appeared to be more severe than the AOFAS and the FAAM measuring the activities of daily living. The sports subscale of the FAAM demonstrated intermediate results. Conclusion: This study outlines a system to compare different postoperative scores commonly used to evaluate outcome after ankle stabilization surgery. The impact of this study is that it makes comparison of published studies easier, even though they use a variety of different clinical scores, thus facilitating better outcome analysis of operative techniques.

Hydrogeophysical data integration at larger scales: Application of Bayesian sequential simulation for the characterization of heterogeneous alluvial aquifers

Knowledge of the spatial distribution of hydraulic conductivity (K) within an aquifer is critical for reliable predictions of solute transport and the development of effective groundwater management and/or remediation strategies. While core analyses and hydraulic logging can provide highly detailed information, such information is inherently localized around boreholes that tend to be sparsely distributed throughout the aquifer volume. Conversely, larger-scale hydraulic experiments like pumping and tracer tests provide relatively low-resolution estimates of K in the investigated subsurface region. As a result, traditional hydrogeological measurement techniques contain a gap in terms of spatial resolution and coverage, and they are often alone inadequate for characterizing heterogeneous aquifers. Geophysical methods have the potential to bridge this gap. The recent increased interest in the application of geophysical methods to hydrogeological problems is clearly evidenced by the formation and rapid growth of the domain of hydrogeophysics over the past decade (e.g., Rubin and Hubbard, 2005).

On the Ewald method and the quartic Helmholtz free energy of an anharmonic metallic crystal

Thesis (M. Sc.) - Brock University, 1978.

Pressure dependence of spin fluctuations in metallic glasses Zrâ â Niâ â ,Zrâ â (Nix/Feâ â â -x)â â and /Zrx/feâ â â -x

The superconducting transition temperature Tc of metallic glasses ZrxFelOO-x (x=80, 75), Zr75(NixFelOO-x)25 (x=75, 50, 25), and CU2SZr75 were measured under quasi-hydrostatic pressure up to 8 OPa (80kbar). The volume (pressure) dependence of the electron-phonon coupling parameters Aep for CU25Zr75 was calculated using the McMillan equatio11. Using this volume dependence of Aep and the modified McMillan equation which incorporates spin-fluctuations, the volume dependence of the spin fluctuation parameter, Asf, was determined in Zr75Ni25, ZrxFelOO-x , a11d Zr75(NixFelOO-x)25. It was found that with increasing pressure, spinfluctuations are suppressed at a faster rate in ZrxFe lOO-x and Zr75(NixFelOO-x)25, as Fe concentration is increased. The rate of suppression of spin-fluctuations with pressure was also found to be higher in Fe-Zr glasses than in Ni-Zr glasses of similar composition.

Scales, networks and uncertainty : an examination of environmental policy-making in Ontario

Through a case-study analysis of Ontario's ethanol policy, this thesis addresses a number of themes that are consequential to policy and policy-making: spatiality, democracy and uncertainty. First, I address the 'spatial debate' in Geography pertaining to the relevance and affordances of a 'scalar' versus a 'flat' ontoepistemology. I argue that policy is guided by prior arrangements, but is by no means inevitable or predetermined. As such, scale and network are pragmatic geographical concepts that can effectively address the issue of the spatiality of policy and policy-making. Second, I discuss the democratic nature of policy-making in Ontario through an examination of the spaces of engagement that facilitate deliberative democracy. I analyze to what extent these spaces fit into Ontario's environmental policy-making process, and to what extent they were used by various stakeholders. Last, I take seriously the fact that uncertainty and unavoidable injustice are central to policy, and examine the ways in which this uncertainty shaped the specifics of Ontario's ethanol policy. Ultimately, this thesis is an exercise in understanding sub-national environmental policy-making in Canada, with an emphasis on how policy-makers tackle the issues they are faced with in the context of environmental change, political-economic integration, local priorities, individual goals, and irreducible uncertainty.

A comparison of functional behaviour assessment rating scales in a sample of children and youth with autism spectrum disorders

This study sought to compare the results of the Motivation Assessment Scale (MAS; Durand & Crimmins, 1988), Questions About Behavior Function Scale (QABF; Matson & Vollmer, 1996) and Functional Analysis Screening Tool (FAST; Iwata & Deleon, 1996), when completed by parent informants in a sample of children and youth with autism spectrum disorders (ASD) who display challenging behaviour. Results indicated that there was low agreement between the functional hypotheses derived from each of three measures. In addition, correlations between functionally analogous scales were substantially lower than expected, while correlations between non-analogous subscales were stronger than anticipated. As indicated by this study, clinicians choosing to use FBA questionnaires to assess behavioural function, may not obtain accurate functional hypotheses, potentially resulting in ineffective intervention plans. The current study underscores the caution that must be taken when asking parents to complete these questionnaires to determine the function(s) of challenging behaviour for children/youth with ASD.

Indirect Bonding Method: in vitro Comparison of the Shear Bond Strength between Metallic Orthodontic Brackets and Different Porcelain Surface Preparations

Introduction : La force d’adhésion à l'interface métal-céramique avec les résines auto-polymérisantes destinées au collage indirect des boîtiers orthodontiques n'a pas été évaluée à ce jour et un protocole clinique basé sur la littérature scientifique est inexistant. Objectifs : 1) Comparer la force de cisaillement maximale entre des boîtiers métalliques et des surfaces en porcelaine préparées selon différentes méthodes; 2) Suggérer un protocole clinique efficace et prévisible. Matériel et méthodes : Quatre-vingt-dix disques en leucite (6 groupes; n = 15/groupe) ont été préparés selon 6 combinaisons de traitements de surface : mécaniques (+ / - fraisage pour créer les rugosités) et chimiques (acide fluorhydrique, apprêt, silane). Des bases en résine composite Transbond XT (3M Unitek, Monrovia, California) faites sur mesure ont été collées avec le système de résine adhésive auto-polymérisante Sondhi A + B Rapid Set (3M Unitek, Monrovia, California). Les échantillons ont été préservés (H2O/24hrs), thermocyclés (500 cycles) et testés en cisaillement (Instron, Norwood, Massachusetts). Des mesures d’Index d’adhésif résiduel (IAR) ont été compilées. Des tests ANOVAs ont été réalisés sur les rangs étant donné que les données suivaient une distribution anormale et ont été ajustés selon Tukey. Un Kruskall-Wallis, U-Mann Whitney par comparaison pairée et une analyse de Weibull ont aussi été réalisés. Résultats : Les médianes des groupes varient entre 17.0 MPa (- fraisage + acide fluorhydrique) à 26.7 MPa (- fraisage + acide fluorhydrique + silane). Le fraisage en surface ne semble pas affecter l’adhésion. La combinaison chimique (- fraisage + silane + apprêt) a démontré des forces de cisaillement significativement plus élevées que le traitement avec (- fraisage + acide fluorhydrique), p<0,05, tout en possédant des forces similaires au protocole typiquement suggéré à l’acide fluorhydrique suivi d’une application de silane, l’équivalence de (- fraisage + acide fluorhydrique + silane). Les mesures d’IAR sont significativement plus basses dans le groupe (- fraisage + acide fluorhydrique) en comparaison avec celles des 5 autres groupes, avec p<0,05. Malheureusement, ces 5 groupes ont des taux de fracture élévés de 80 à 100% suite à la décimentation des boîtiers. Conclusion : Toutes les combinaisons de traitement de surface testées offrent une force d’adhésion cliniquement suffisante pour accomplir les mouvements dentaires en orthodontie. Une application de silane suivie d’un apprêt est forte intéressante, car elle est simple à appliquer cliniquement tout en permettant une excellente adhésion. Il faut cependant avertir les patients qu’il y a un risque de fracture des restorations en céramique lorsque vient le moment d’enlever les broches. Si la priorité est de diminuer le risque d’endommager la porcelaine, un mordançage seul à l’acide hydrofluorique sera suffisant.