Made available in DSpace on 2016-03-15T19:36:33Z (GMT). No. of bitstreams: 1 Nilton Inacio Domingues Junior.pdf: 2643612 bytes, checksum: 326f49f818932a8e26d3dc25d8e43064 (MD5) Previous issue date: 2011-08-23 / Fundo Mackenzie de Pesquisa / Aluminum alloys present low specific density, good strength, and high corrosion resistance under common environments. Aluminum-Copper 2024 alloy is one of the most widely used alloy in aircraft fuselage structures due to its good mechanical properties. The microstructure of the alloy was observed by optical microscopy showing elongated grains caused from the rolling process. Solution heat treatment was performed at 495, 505, and 515°C followed by water quenching. Afterwards, artificial aging was carried out at 190 and 208°C. Hardness measurements and tensile tests were performed to determine the mechanical properties of this material after heat treatments. Tensile and hardness tests exhibited similar mechanical properties for the alloy in the three solution temperatures (495, 505, and 515°C). In general, the increase of the strength due to aging was accompanied by a decrease in ductility of the alloy. The highest values of yield and ultimate strength were obtained in the solubilized alloy at 505°C and artificially aged at 208ºC/2h. A fatigue study on Al-2024 alloy was conducted under symmetric tension-compression at room temperature, using a rotating bending testing machine. S-N curve has not shown a typical fatigue limit, but a drop steadily with decreasing stress cycle. Specimen reached up to 7.8 x 106 cycles before fracture at 110.23 MPa. The fracture surfaces of specimens submitted to high stress and low number of cycles showed large quantity of precipitates and microvoids, while in specimens submitted to low stress and high number of cycles were observed the presence of cracks along the periphery of the fracture surface. The presence of pores was intercepted and pulled out of the matrix precipitates in the fracture surface during crack propagation of high cycle fatigue. / Ligas de alumínio apresentam baixa massa específica, relativamente alta resistência mecânica e elevada resistência à corrosão. A liga alumínio-cobre 2024 tem sido uma das ligas mais amplamente utilizada, principalmente em estruturas de aeronaves, devido às suas boas propriedades mecânicas. A microestrutura da liga observada por microscopia óptica apresentou grãos alongados decorrentes do processo de laminação. O tratamento térmico de solubilização na liga 2024 foi executado em três temperaturas diferentes a 495, 505 e 515°C seguido por resfriamento em água. Após a solubilização, envelhecimento artificial foi executado nas temperaturas de 190 e 208°C. Medidas de dureza e ensaios de tração foram feitos para determinar as propriedades mecânicas deste material após tratamentos térmicos. Ensaios de tração e medidas de dureza revelaram propriedades mecânicas similares para a liga 2024 nas três temperaturas de solubilização (495, 505 e 515°C). Em geral, o aumento na resistência mecânica decorrente do envelhecimento foi acompanhado pela diminuição da ductilidade da liga. Os valores mais elevados de limite de escoamento e de resistência foram obtidos na liga solubilizada a 505°C e envelhecida a 208°C/2h. Esta condição foi escolhida para a execução dos ensaios de fadiga e levantamento da curva S-N. O estudo de fadiga da liga 2024 foi conduzido sob ciclo reverso tensão-compressão à temperatura ambiente, utilizando uma máquina de fadiga flexo-rotativa. A curva S-N não apresentou um patamar de limite de fadiga típico dos aços, mas caiu continuamente com a diminuição do ciclo de tensão. O corpo-de-prova suportou mais de 7,8x106 ciclos antes de romper para ciclo de tensão de 110,23 MPa. As superfícies de fratura dos corpos-de-prova submetidos a tensões elevadas e baixo número de ciclos mostraram basicamente precipitados e microcavidades, enquanto que nas fraturas dos corpos-de-prova submetidos a tensões baixas e elevado número de ciclos observou-se a presença de trincas ao longo de toda a borda da superfície de fratura. Houve a presença de poros interceptados e precipitados arrancados da matriz na superfície da fratura durante a propagação da trinca por fadiga de alto ciclo.

Made available in DSpace on 2016-08-19T12:56:44Z (GMT). No. of bitstreams: 1 Dissertacao Daniel.pdf: 1759359 bytes, checksum: 8e118ed0eeb57413abe7a81e44a65d3f (MD5) Previous issue date: 2013-06-03 / Despite the advantages of bismuth film electrode for the determination of trace metals and organic compounds, the Cu²⁺ is an element that has problems when measured with this electrode, since its potential is very close to the Bi³⁺, causing overlapping of peaks. This work presents an alternative to eliminate the interference of Bismuth in the determination of copper in using bismuth film electrodes (BiFE), prepared ex situ mode. The ethanol fuel samples without pre-treatment and biodiesel samples previously digested were used in order to evaluate this electroanalytical procedure. The optimization of the parameters was performed using a complete factorial design 2³ with center point. After several voltammetric experiments, optimal conditions for the determination of Cu²⁺ were the following: Edep = -1.3 V; tpre = 120s; Frequency: 60 Hertz. The voltammograms using anodic stripping voltammetry method in the square wave mode and their corresponding standard addition curves indicated that the bismuth film electrode provides a sensitive and useful procedure for the determination of Cu²⁺ in biofuels. Experiments carried out by the successive addition of aliquots of a standard solution of Cu²⁺, yielded a linear response of peak current to the concentration of metal ion. Good detection limits have been obtained for the determination of Cu²⁺ in ethanol fuel, soybean oil and tallow biodiesels respectively (4.9 x 10ˉ⁸ mol Lˉ¹; 5.60 x 10ˉ⁸ mol Lˉ¹, 1.79 x 10ˉ⁸ mol Lˉ¹). The accuracy was assessed through recovery test (recoveries of 85.6% to 97.05%) and the precision was expressed by the coefficient of variation that ranged from 10% to 18%. The method was successfully applied to two different samples of biodiesel and ethanol fuel and analyzed in triplicate. / Apesar das vantagens do Eletrodo de Filme de Bismuto (BiFE), na determinação de metais traços e compostos orgânicos, o Cu²⁺ é um elemento que apresenta problemas quando quantificado com este eletrodo, uma vez que seu potencial é muito próximo ao do Bi³⁺, causando a sobreposição de picos. Este trabalho apresenta uma alternativa para eliminação da interferência do bismuto na determinação de Cu²⁺ em biocombustíveis (etanol e biodiesel), usando um BiFE, preparado no modo ex situ. As amostras de etanol combustível foram usadas sem tratamento prévio, enquanto as amostras de biodiesel foram previamente digeridas. A otimização dos parâmetros foi realizada com o uso do planejamento fatorial completo 2³ com ponto central. Após vários experimentos voltamétricos, as condições ideais para a determinação de Cu²⁺ foram: Edep = -1,3 V; tpré = 120 s; Frequência: 60 Hertz. Os voltamogramas e suas correspondentes curvas de adição padrão indicaram que o uso do BiFE com a técnica Voltametria de Redissolução Anódica (ASV), no modo onda quadrada, indicaram que o procedimento é adequado, útil e sensível para a determinação de Cu²⁺ em biocombustíveis. Os experimentos realizados, pela adição sucessiva de alíquotas da solução padrão de Cu²⁺ proporcionaram uma resposta linear entre a corrente de pico e a concentração do íon metálico. Bons limites de detecção foram obtidos para a determinação do Cu²⁺ em Etanol combustível, biodiesel de óleo de soja e de sebo respectivamente (4,90x10ˉ⁸ mol Lˉ¹; 5,60x10ˉ⁸ mol Lˉ¹; 1,79x10ˉ⁸mol Lˉ¹). A exatidão foi avaliada através do teste de recuperação (recuperações de 85,6% a 97,05%). A precisão, expressa pelo coeficiente de variação (CV: entre 10% e 18%) foi considerada boa. O método foi aplicado com sucesso em amostras reais de biodiesel e Etanol combustível.

Os vidros metálicos baseados em Cu-Zr representam uma classe bastante promissora para a categoria de materiais estruturais, tendo em vista suas interessantes propriedades resultantes da natureza amorfa. Sabe-se que o oxigênio tem grande influência na formação da estrutura amorfa e consequentemente nas propriedades dessa classe de materiais. No presente trabalho, ligas amorfas baseadas em Cu-Zr foram analisadas termicamente a fim de se observar o comportamento das mesmas frente à contaminação com oxigênio. As análises térmicas foram realizadas em um equipamento de calorimetria exploratória diferencial (DSC), e as temperaturas características como de transição vítrea, cristalização, fusão e líquidus foram determinadas. Concluiu-se que conforme a literatura apresenta, o processo de cristalização é favorecido pela presença de oxigênio, causando uma queda na energia de ativação dos processos de cristalização das ligas trabalhadas. Através de ensaios que simularam tratamentos térmicos, cristalizou-se controladamente as amostras amorfas baseadas em Cu-Zr a fim de formar compósitos entre cristais e vidros metálicos buscando diminuir a fragilidade das ligas. / Cu-Zr-based bulk metallic glasses represent a very promising class of structural materials with interesting properties resulting from the amorphous nature. It is known that oxygen has a great influence on the formation of the amorphous structure and consequently on the properties of these materials. In the present work, Cu-Zr-based amorphous alloys were thermally analyzed in order to observe their behavior against oxygen contamination. Thermal analyzis were performed on a differential scanning calorimetry (DSC) equipment, and characteristic temperatures as glass transition, crystallization, melting and liquidus were determined. It was concluded that, according to the literature, the crystallization process is favored by the presence of oxygen, causing a decrease in the activation energy of the crystallization processes of the worked alloys. Through tests that simulated heat treatments, the amorphous samples were crystallized in order to form composites between crystals and metallic glasses in order to reduce the brittleness of the alloys.

Ce doctorat porte sur la fonctionnalisation de silices colloïdales en vue de la rétention de micropolluants métalliques dans des effluents. Les nanoparticules et microparticules ouvrent des potentialités d’application dans de nombreux secteurs industriels (chimie, environnement, pharmacie...). Ainsi, ces travaux de recherche portent sur la synthèse et la caractérisation de matériaux composites submicroniques : il s’agit de silices colloïdales sur lesquelles sont greffés des silanes ou supportés des polysaccharides. Une des applications de ces travaux de recherche porte sur l’adsorption de métaux de transition sur ces composites en solution aqueuse. Dans le cadre de ce doctorat, les caractéristiques des composites sont définies par leur morphologie de surface, par l’étude des groupements fonctionnels présents, par détermination de leurs surfaces spécifiques ainsi qu’en solution aqueuse par détermination de leurs diamètres hydrodynamiques et de leurs potentiels zéta. Dans un premier temps, la fonctionnalisation de la silice a permis le greffage de groupements carboxyliques et amines dont tes taux de greffage obtenus ont été respectivement de 0,47 µmol/m² et 3,86 µmol/m². En présence de groupements amines, le potentiel  des composites est positif jusqu’ à pH 9 alors qu’il est négatif dès pH 3 pour des silices non fonctionnalisées. Dans un second temps, la silice est supportée par du chitosane dont le degré de désacétylation est de 77%. Conjointement, l’encapsulation de la silice est réalisées par du chitosane sur lequel des fonctions carboxyliques ont été greffées. La morphologie des particules est alors modifiée, leurs diamètres hydrodynamiques sont plus élevés et leurs potentiels  sont positifs jusqu’ à pH basique. La rétention d’ions métalliques (Cu(II) et Ni(II)) par ces composites à différents pH est ensuite étudiée. Pour chacun des cations métalliques, les capacités d’adsorption sont déterminées ainsi que les cinétiques d’adsorption. L’application de plusieurs modèles d’isotherme d’équilibre a été réalisée. Dans le cas de Cu(II), à pH 5, les meilleures capacités d’adsorption sont obtenues pour des silices supportées par du chitosane greffé : la capacité de rétention des ions Cu(II) est de 270 mg/g à pH 5. De même, c’est ce composite qui permet la meilleurs rétention des ions Ni(II) à pH 7 avec une capacité d’adsorption de 263 m/g. Concernant la cinétique, le modèle de réaction de surface du pseudo-second ordre s’applique bien aux résultats expérimentaux. / This study is focused on the preparation of three types of silica-based composites for the capture of Cu(II) and Ni(II) ions. The first strategy consists in coating chitosan on colloidal fumed silica after acidic treatment yielding the composite SiO2+CS. The second strategy can be separated into two routes: the first one involves surface grafting of silica with aminopropyltriethoxysilane to obtaining silica particles covered by amino groups (SiO2(NH2)). The second one involves in surface condensation of triethoxysilylbutyronitrile, followed by acidic hydrolysis of the surface-bound nitrile groups affording silica particles covered by carboxyl groups (SiO2(CO2H)). In the last step, chitosan has been grafted on the surface bound NH2 or -CO2H groups yielding the composites SiO2(NH2)+CS or SiO2(CO2H)+CS. The third strategy involves in the modified CS surface with -CO2H groups, followed by coating onto the non-modified silica nanoparticles to obtain the composite SiO2+CS(CO2H). The novel hybrid materials were characterized by IR spectroscopy, scanning electron microscopy, atomic force microscopy, and zeta potential measurements. Batch experiments were conducted to study the sorption performance of these composites for Cu(II) and Ni(II) removal from aqueous solution at optimum pH at 298 K. The kinetics were evaluated utilizing pseudo-first-order, pseudo-second-order, and intraparticle diffusion models. The adsorption kinetics followed the mechanism of the pseudo-second-order equation for all types of adsorbents. The adsorption isotherms were evaluated utilizing Langmuir, Freundlich, and Temkin models. The best interpretation for equilibrium data was given by Langmuir isotherm model. This study demonstrates that the adsorption capacities for Cu(II) ion is more efficient for the SiO2+CS (256 mg g-1) compared to SiO2(NH2) (75 mg g-1). However, the carboxyl grafted CS-coated silica (SiO2+CS(CO2H) exhibited an excellent adsorption capacity (333 mg g-1). In case of Ni(II), based on Langmuir isotherm the maximum adsorption capacity found to be 182 mg g-1for SiO2+CS, and 210 mg g-1 for SiO2(CO2H) + CS. Using single-metal solutions, these adsorbents were found to have an affinity for metal ions in order as Cu(II) > Ni(II). The adsorption of Cu(II) ion by SiO2+CS was affected by the nature of the respective anion. Application of these composite materials to remove Cu(II) and Ni(II) from aqueous solution was shown to be more efficient than the adsorption capacities of many sorbents probed by other research groups.

No description available.

No presente trabalho verificou-se a precisão de um critério que prevê composições de ligas vítreas aplicado ao sistema Zr-Ni-Cu. Este critério combina o parâmetro de instabilidade topológica (\'lâmbda\'), e o parâmetro termodinâmico (\'delta\' h) entre os elementos de liga. Os dois parâmetros correlacionam quantitativamente à composição química a tendência à formação de vidros metálicos. Este critério é uma ferramenta promissora e simples para guiar e reduzir o trabalho tedioso e intensivo de encontrar composições altas tendências a vitrificação em sistemas metálicos. Para comprovar a eficiência desta ferramenta, a metodologia foi calcular o parâmetro para o sistema de interesse e preparar ligas de acordo com algumas composições fornecidas. A metodologia de preparação das ligas seguiu a fusão a arco elétrico e subsequentemente o emprego das técnicas de resfriamento rápido, melt-spinning e splat-cooling, para a produção de fitas e discos metálicos respectivamente, e o coquilhamento para a produção de amostras maciças em forma de cunha. Para as amostras confeccionadas por melt-spinning e splat-cooling, verificou-se a precisão do critério de seleção através da quantificação das porcentagens de fases vítreas a partir de análises de difratogramas de raios-X e seus comportamentos térmicos a partir dos termogramas de análises por calorimetria exploratória diferencial (DSC). Já para as ligas coquilhadas em cunha, obtiveram-se alguns resultados com indícios de estruturas vítreas que foram caracterizadas por difração de raios-X e metalografia. Desta forma chegou-se à conclusão que o critério de seleção aplicado ao sistema Zr-Ni-Cu pode ser utilizado para o desenvolvimento de composições favoráveis à formação de vidro antes da produção das ligas. Conclui-se que o critério que combina o parâmetro de instabilidade topológica (\'lâmbda\' min) e o parâmetro termodinâmico (\'delta\' h) é uma ferramenta que pode ser utilizada como guia para encontrar as composições mais fáceis de formar vidro, reduzindo assim o trabalho experimental de tentativa e erro. / In the present work it was verified the accuracy of a proposed criterion to predict compositions of glassy alloys applied in the Zr-Ni-Cu system. This criterion combines the topological instability parameter (\'lâmbda\') and a thermodynamic parameter (\'delta\' h) among the alloying elements. The two parameters correlate quantitatively the chemical composition with the glass forming ability. This criterion is a promising and simple tool to guide and reduce the tedious and intensive work of finding good compositions of glasses in metallic systems. In an attempt to prove the efficiency of such tool, the methodology was to calculate the parameter for the system of interest and prepare alloys in accordance with the compositions provided by the tool. The methodology of preparation of the alloys followed the electric arc- melting and subsequent use of fast cooling techniques, melt-spinning and splat-cooling for the production of metallic ribbons and discs, respectively, and a wedge-shaped chiller mold to produce bulk metallic samples. For samples prepared from the melt-spinning and splat-cooling, it was verified the accuracy of the selection criteria by quantifying the percentage of glassy phases from X-ray diffractograms and their thermal behaviors from thermograms produced by differential scanning calorimetry (DSC). For alloys produced from the wedge-shaped mold, some results were obtained with evidence of vitreous structures that were characterized by X-ray diffraction and metallography. Therefore the conclusion is that the selection criteria applied to the system Zr-Ni-Cu can be used to develop favorable compositions for the formation of glasses before the production of the alloys. It is concluded that the selection criterion is a good tool and can be used as a guide to find the best glass forming alloys, thus reducing the experimental procedures of trial and error.

Verbindungen mit einer Vielzahl von Oberflächeneinheiten (Multimere) sind im Hinblick auf eine nuklearmedizinische Anwendung von besonderem Interesse, da durch definierte Strukturmodifizierung das Bindungsverhalten an bestimmte Zielstrukturen, die Löslichkeit und damit die Bioverteilung und Pharmakokinetik beeinflusst werden können. Baut man eine Verbindung so auf, dass sich im Inneren ein metallbindendes Zentrum befindet, ergibt sich einerseits die Möglichkeit, das Radiometall chemisch stabil zu binden, andererseits durch genannte Oberflächenfunktionalisierung eine spezifische Bindung im Zielgewebe zu erreichen. Im Rahmen dieser Arbeit wurden neuartige mehrfunktionale Verbindungen mit einer Cyclam-Kerneinheit synthetisiert. Cyclam bildet mit Cu(II)-Ionen äußerst stabile Komplexe, was im Hinblick auf eine radiopharmazeutische Anwendung der Radiometallkomplexe von 64Cu oder 67Cu für diagnostische und therapeutische Zwecke äußerst interessant ist. Für eine symmetrische Mehrfachfunktionalisierung wurde auf ein Tetraamin mit Cyclamkern zurückgegriffen. Die Kupplung von vier Dansylchlorid-Einheiten war erfolgreich. Über geschützte Glucosyl-Isothiocyanate wurden Derivate mit vier Zuckereinheiten gewonnen. Nach der Entfernung der Schutzgruppen wurde die Bindung an das kohlenhydratbindende Lektin Concanavalin A mittels isothermer Kalorimetrie bestimmt. Es war ein deutlicher Anstieg der Stabilitätskonstante K im Vergleich zu den monomeren Zuckern zu beobachten. Die Kinetik der Cu(II)-Komplexierung wurde UV/Vis-spektroskopisch bestimmt. Wegen der langsamen Cu-Komplexierungskinetik der Thioharnstoff-verbrückten Glycodendrimere wurde der Schwerpunkt bei den nachfolgenden Untersuchungen zur Kupplung von Peptiden über Amidbindungen gelegt. Nach zahlreichen erfolglosen Kupplungsversuchen von Peptiden mit einer freien Aminogruppe an Cyclamtetrapropionsäure im organischen Medium wurden im wässrigen Milieu Cyclamderivate mit ein bis zu drei Peptideinheiten durch Peptidkupplung erzeugt. Die Synthese kupplungsfähiger Peptidisothiocyanate blieb erfolglos. Schließlich führte eine Michael-Addition von Acrylamid-Arg-Tyr-OH und Acrylamid-Neurotensin(8-13)-OH an Cyclam zu den gewünschten tetrameren Verbindungen. Das Neurotensintetramer mit vier zielsuchenden Einheiten wurde für weiterführende radiochemische und radiopharmakologische Untersuchungen eingesetzt. Es kann unter milden Bedingungen sehr effizient mit 64Cu radiomarkiert werden, wobei eine spezifische Aktivität von 12 GBq pro µmol und Markierungsausbeuten von durchschnittlich 95-98% erzielt werden können. Erwartungsgemäß werden die Neurotensineinheiten unter diesen Bedingungen abgebaut, wobei im Vergleich zu freiem H-Neurotensin(8-13)-OH, welches innerhalb von zwei Minuten abgebaut wird, die In-vivo-Halbwertszeit des Tetramers 34 Minuten beträgt. Es konnte keine Transmetallierung beziehungsweise Transchelatisierung beobachtet werden, was die Stabilität des Komplexes zeigt. PET-Untersuchungen nach Applikation des 64Cu-markierten Neurotensin-Tetramers wiesen eine erhöhte Anreicherung von radioaktiver Substanz in Tumoren von LoVo- und HT29-Mäusen nach. Um zu unsymmetrischen Cyclamderivaten mit dem Ziel der gleichzeitigen Einführung zielsuchender, löslichkeitsvermittelnder und fluoreszierender Einheiten zu gelangen, wurden unterschiedliche Schutzgruppen eingesetzt. Die Blockierung primärer Aminogruppen eines Cyclam-Derivates mit MMTr-, Boc- und Z-Schutzgruppen lieferte Produkte, die sauber isoliert, aber nicht selektiv entschützt werden konnten. Daher wurden die Aminstickstoffatome des Cyclams direkt geschützt. Ausgehend von Cyclam-Boc3 konnten über Kupplungsreaktionen Aminosäure- und Dipeptidmethylester als unsymmetrische Cyclamderivate gewonnen werden. Damit ist ein Syntheseweg entwickelt worden, der die Darstellung unsymmetrischer Cyclamderivate mit einer definierten Anzahl von gewünschten biologisch aktiven Molekülen beziehungsweise löslichkeitsvermittelnder oder fluoreszierender Einheiten gestattet.

After mineral exploitation the residual grinded and milled material, rich in sulphide minerals and heavy metals, is often left exposed to the atmospheric variables. This weathered mine waste material can lead to the formation of acid mine drainage (AMD) which has negative effects to the environment. The fractionation of stable isotope of metals such as Cu and Fe can be measured using innovative analytical techniques developed recently and could offer a detailed hindsight of the geochemical processes occurring in mine contaminated sites. Tailings profiles from Northern Sweden with high content of Cu and Fe sulphides and in different stages of weathering and/or remediation, along with plant and soil samples from a phytoremediation test site in Ronneburg, Germany were analysed using MC-ICP-MS to measure the isotope ratios of 65Cu/63Cu and 56Fe/54Fe. The analytical method used requires anion exchange chromatography to extract Cu and Fe from a complex matrix prior to the proper isotope ratio measurement. The samples from the tailings profile were useful to interpret the geochemical processes that can lead to a fractionation of Cu and Fe in the field, since redox-driven reactions such as rock oxidation and mineral precipitation are present in such environment. This study shows that precipitation of covellite in a redox-boundary zone in a mine tailings can cause a clear fractionation of Cu (Δ65Curock-covellite= -5.66±0.05‰) and a depletion of the lighter Cu isotope in the oxidised areas of the tailings due to dissolution of the remaining Cu-sulphides. Precipitation of Fe(oxy)hydroxides as a result of the oxidation process of sulphide-bearing rocks can also fractionate Fe, being the precipitated mineral slightly enriched in 56Fe.The influence of soil bacteria and plant uptake in the fractionation of Cu and Fe was investigated in pot and field experiments at the Ronneburg site, where organic amendments were used. The results showed that the plant material was enriched in the lighter Fe isotope compared to the substrate used in the pot and field experiments, in spite of the application of a bacterial consortium. Cu isotope fractionation is more susceptible to the changes in the amendments used, being those bacterial consortium, mychorriza or compost than Fe isotope fractionation. There are differences in the fractionation values in pot and field trials, regardless of the type of organic amendment applied. As an overall view, leaves are enriched in the heavier Cu isotope compared to the soils, regardless of the amendment usedThe application of the results obtained in this work would help not only to offer a view in the cycle of Fe and Cu in the surface environment, and the understanding of the (bio)geochemical processes occurring in sulphide soil surfaces. But also in the way that current remediation techniques of metal contaminated sites could be evaluated, having in mind that simplified systems show a different Cu and Fe fractionation compared to natural systems where more variables are needed to take into account.

No description available.

No description available.