Afin de modéliser le flux sanguin dans les vaisseaux, l’équation de Stokes avec une viscosité variable est considérée dans une structure tubulaire mince, c’est à dire, dans une union de rectangles minces avec des hauteurs d’ordre ε et des bases d’ordre 1. Un développement asymptotique de la solution est construit. Dans le cas des perturbations aléatoires de la viscosité constante, nous prouvons que le premier terme de la vitesse est déterministe, alors que pour la pression, il est aléatoire, mais les espérances de la pression satisfont l’équation déterministe de Darcy. Les estimations pour la différence entre la solution exacte et son approximation asymptotique sont prouvées. Enfin, nous donnons quelques résultats numériques. Nous étendons les résultats à une structure tubulaire mince composée de deux rectangles minces avec des parois élastiques qui sont reliés par un domaine dont les parois sont rigides. Après une approche variationnelle du problème qui nous donne des résultats d’existence, d’unicité, de régularité, et certaines estimations, a priori, nous construisons une solution asymptotique. Nous présentons et résolvons les problèmes de tous les termes du développement asymptotique. Pour deux cas différents, nous décrivons l’ordre des étapes de résolution de l’algorithme du problème et nous construisons le terme principal du développement asymptotique. Et enfin, nous présentons une analyse variationnelle et asymptotique pour un cas plus général où la viscosité dépend du tenseur des déformations dans un canal mince. Par le biais des estimations a priori, nous justifions nos constructions asymptotiques, par l’obtention d’une petite erreur entre les solutions exactes et asymptotiques / In order to model the blood flow through vessels, the Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin rectangles with heights of order ε and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for the difference between the exact solution and its asymptotic approximation are proved. Finally, we give some numerical results. We extend the results for a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results and some a priori estimates, we construct an asymptotic solution. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. And finally, we present a variational and an asymptotic analysis for a more general case where the viscosity depends on the infinitesimal strain tensor in a thin channel. By means of the a priori estimates, we justify our asymptotic constructions, by obtaining a small error between the exact and the asymptotic solutions

Call number: LD2668 .T4 1986 R43 / Master of Science / Biological and Agricultural Engineering

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection.

Os modelos lineares generalizados duplos (MLGD), diferentemente dos modelos lineares generalizados (MLG), permitem o ajuste do parâmetro de dispersão da variável resposta em função de variáveis preditoras, aperfeiçoando a forma de modelar fenômenos. Desse modo, os mesmos são uma possível solução quando a suposição de que o parâmetro de dispersão constante não é razoável e a variável resposta tem distribuição que pertence à família exponencial. Considerando nosso interesse em seleção de variáveis nesta classe de modelos, estudamos o esquema de seleção de variáveis em dois passos proposto por Bayer e Cribari-Neto (2015) e, com base neste método, desenvolvemos um esquema para seleção de variáveis em até k passos. Para verificar a performance do nosso procedimento, realizamos estudos de simulação de Monte Carlo em MLGD. Os resultados obtidos indicam que o nosso procedimento para seleção de variáveis apresenta, em geral, performance semelhante ou superior à das demais metodologias estudadas sem necessitar de um grande custo computacional. Também avaliamos o esquema para seleção de variáveis em até \"k\" passos em um conjunto de dados reais e o comparamos com diferentes métodos de regressão. Os resultados mostraram que o nosso procedimento pode ser também uma boa alternativa quando possui-se interesse em realizar previsões. / The double generalized linear models (DGLM), unlike the generalized linear model (GLM), allow the fit of the dispersion parameter of the response variable as a function of predictor variables, improving the way of modeling phenomena. Thus, they are a possible solution when the assumption that the constant dispersion parameter is unreasonable and the response variable has distribution belonging to the exponential family. Considering our interest in variable selection in this class of models, we studied the two-step variable selection scheme proposed by Bayer and Cribari-Neto (2015) and, based on this method, we developed a scheme to select variables in up to k steps. To check the performance of our procedure, we performed Monte Carlo simulation studies in DGLM. The results indicate that our procedure for variable selection presents, in general, similar or superior performance than the other studied methods without requiring a large computational cost. We also evaluated the scheme to select variables in up to \"k\" steps in a set of real data and compared it with different regression methods. The results showed that our procedure can also be a good alternative when the interest is in making predictions.

Compositional data consist of known vectors such as compositions whose components are positive and defined in the interval (0,1) representing proportions or fractions of a whole, where the sum of these components must be equal to one. Compositional data is present in different areas, such as in geology, ecology, economy, medicine, among many others. Thus, there is great interest in new modeling approaches for compositional data, mainly when there is an influence of covariates in this type of data. In this context, the main objective of this thesis is to address the new approach of regression models applied in compositional data. The main idea consists of developing a marked method by penalized regression, in particular the Lasso (least absolute shrinkage and selection operator), elastic net and Spike-and-Slab Lasso (SSL) for the estimation of parameters of the models. In particular, we envision developing this modeling for compositional data, when the number of explanatory variables exceeds the number of observations in the presence of large databases, and when there are constraints on the dependent variables and covariates. / Dados composicionais consistem em vetores conhecidos como composições cujos componentes são positivos e definidos no intervalo (0,1) representando proporções ou frações de um todo, sendo que a soma desses componentes totalizam um. Tais dados estão presentes em diferentes áreas, como na geologia, ecologia, economia, medicina entre outras. Desta forma, há um grande interesse em ampliar os conhecimentos acerca da modelagem de dados composicionais, principalmente quando há a influência de covariáveis nesse tipo de dado. Nesse contexto, a presente tese tem por objetivo propor uma nova abordagem de modelos de regressão aplicada em dados composicionais. A ideia central consiste no desenvolvimento de um método balizado por regressão penalizada, em particular Lasso, do inglês least absolute shrinkage and selection operator, elastic net e Spike-e-Slab Lasso (SSL) para a estimação dos parâmetros do modelo. Em particular, visionamos o desenvolvimento dessa modelagem para dados composicionais, com o número de variáveis explicativas excedendo o número de observações e na presença de grandes bases de dados, e além disso, quando há restrição na variável resposta e nas covariáveis.

Tato práce se zabývá problematikou aerodynamického zatížení statorových lopatek turbodmychadla s variabilní geometrií turbíny a jeho následnou optimalizací. Metody výpočtového modelování tekutin jsou aplikovány s využitím komerčního softwaru ANSYS CFX. Výpočtový model celého turbínového stupně je použit pro analýzu aerodynamického zatížení statorových lopatek v několika polohách a pro různé operační podmínky. Provedená byla detailní analýza vlivu rozložení tlaku v turbínové skříni, úhlu natočení lopatky, jakož i vlivu distančních pinů na aerodynamické zatížení. Následně bylo vyvinuto experimentální zařízení pro přímé měření aerodynamického momentu statorových lopatek s využitím testovacího zařízení s názvem Gas Stand. Toto zařízení spaluje zemní plyn a dokáže vytvořit velmi stabilní podmínky proudění při vysokých teplotách, což umožňuje vyloučit vliv pulzací plynu, vibrací motoru, jakož i vlivu řídící strategie motoru na měřenou veličinu. Výsledky experimentu jsou následně porovnány s vypočtenou hodnotou pomocí CFD modelu a je dosažená velmi dobrá shoda. Validovaný CFD model je následně zredukován s využitím podmínek cyklické symetrie na model jen jednoho segmentu statoru a rotoru. Umožňuje to výrazně zvýšit produktivitu simulací a prozkoumat několik návrhových parametrů statoru v celém rozsahu pohybu statorových lopatek. Provedená analýza citlivosti těchto parametrů položila výborný základ pro jejich následnou optimalizaci a ukázala významný potenciál několika z nich. Na základě analýzy požadavků na aerodynamické zatížení statorových lopatek byla následně vytvořena definice ideálního zatížení, která byla ustavena jako cíl pro jeho optimalizaci. Použitých bylo několik optimalizačních strategií s využitím metody analýzy působících silových vektorů a jejich výsledky byly následně zhodnoceny a porovnány z více aspektů. Výsledné optimalizované řešení bylo následně přepočteno pomocí modelu celého turbínového stupně, čímž se prokázali jeho výborné vlastnosti z hlediska aerodynamického zatížení a zvýšení účinnosti ve spodní části charakteristiky.

Dans ce mémoire de thèse, nous présentons la conception, l'analyse de la stabilité, les simulations numériques et aussi les résultats des expérimentes concernant différents contrôleurs de vitesse mécanique du moteur à réluctance variable (MRV).Dans les deux premiers chapitres une brève description de la physique et de la construction du MRV est présenté ainsi que le problème du contrôle d'être abordé, c'est la commande de vitesse sans capteur. Il est aussi présenté l'état de l'art de ce problème et certains des solutions proposées dans d'autres travaux. On propose notre solution et on présente un petit résumé des articles scientifiques qui ont été publiés dans des magazines et des conférences.Dans le chapitre numéro trois est présenté le design du contrôleur adaptatif et sans capteur du MRV. On suppose, dans une première étape que seule la vitesse mécanique est inconnue et la stabilité exponentielle uniforme des erreurs de suivement est obtenue. Dans une deuxième étape, les conditions d'opération sont aggravées et, en plus de la vitesse, les paramètres physiques sont également supposées inconnues, la stabilité asymptotique uniforme est obtenue dans ce cas. L'estimation des paramètres du MRV est garantie grâce à la condition de persistance d'excitation. Cette commande se compose de deux boucles, une boucle interne basée sur un contrôleur de type PI2D qui est particulièrement intéressant parce qu'il est libre de modèle; cette boucle entraîne les variables mécaniques -la position et la vitesse- vers une référence désirée. Une deuxième boucle de contrôle externe prend le courant électrique vers un ' "courant de référence virtuelle" qui est généré sur la base d'une approche de partage de couple. Le contrôleur propose est testé au niveau de simulations numériques qui sont également présentés.Dans le quatrième chapitre, une nouvelle approche de modélisation du MRV est utilisée pour concevoir le contrôleur. Dans ce scénario, on suppose que l'ensemble de l'état et tous les paramètres physiques sont disponibles, cette approche est pensée pour être adapté au contrôleur basé sur observateur, recherche qui est en cours de développement. Le contrôleur est composé de deux boucles, également que celui qui a été mentionné précédemment. Ce contrôleur est sélectionné parce qu'il est approprié pour le contrôle d'équivalence vraie, qui il s'agit de remplacer les «mesures physiques» provenant d'un capteur par les «observations» provenant d'un observateur. La mise en oeuvre numérique est effectuée sur Simulink de Matlab.Enfin, dans le chapitre cinq, les résultats expérimentaux qui ont été effectués pour évaluer la performance des contrôleurs proposés -ce sont les PI2D et adaptatif PI2D pour le modèle simplifie ainsi que le PID pour le nouveau approche de modélisation- sont présentés. Dans la première partie, une brève description de la construction du banc de tests utilisé est présenté ainsi que quelques-unes caractéristiques techniques. Trois différentes profils de vitesse sont imposées à chacun des contrôleurs proposés -ce sont la tangente hyperbolique, la rampe saturée et la référence sinusoïdal- et de bonnes résultats sont obtenus en considérant que la variable contrôlée est la vitesse. Le dernier chapitre correspond aux conclusions de la recherche effectuée ainsi qu'aux travaux futurs. / In this thesis dissertation we present the design, stability analysis, numerical simulations and physical experiments of different controllers designed to drive the mechanical velocity of the switched reluctance motor (SRM). In the First and Second Chapters a brief description of the physics and construction of the SRM is presented, as well as the problem of control to be aboard, that is the velocity sensorless control of motors and the state of the art of this problem. The proposed solution is introduced and a summary of the published papers as well as the contribution are also presented.In the Chapter number three is presented the velocity sensorless and adaptive control of the SRM. It is assumed, in a first stage, that only mechanical velocity is unknown, uniform exponential stability of the errors is achieved in this scenario. In a second stage, conditions are stressed and in addition to the velocity, physical parameters are also assumed unknown, uniform asymptotical stability is achieved in this case and parameters estimation is guaranteed under a persistence of excitation condition. This controller consists of two loops, an internal loop based on a PI2D–type controller which is of particular interest given it is free-model; this loop drives the mechanical variables –that is position and velocity- towards a desired reference. An external control loop takes the electrical current towards a ‘’virtual” current reference which is generated based on a torque share approach. The controller is tested on numerical simulations, which are also presented.In the fourth chapter, a new approach on the modeling of the SRM is utilized to design the controller, in this scenario is assumed that the whole state and all the physical parameters are available, however this approach is thought to be suitable to observer based controller, whose ongoing research is being performed. The controller is composed by two loops, similarly to the one mentioned previously. This controller is selected because it is suitable for certainty equivalence control, that is, to substitute the “measurements” by the “observations” coming from a virtual sensor. Numerical implementation is performed on Simulink of Matlab.Finally, in the Chapter five, the experimental results carried out to evaluate the performance of the proposed controllers are presented, these are the PI2D and the adaptive PI2D controllers for the simplified model and the $PID$ controller for the novel modeling approach. In the first part, a brief description of the construction of the utilized bench is presented as well as the some technical characteristics. Three different velocity profiles were imposed to each of the overmentioned controllers –these are the so called smooth step, the saturated ramp and the sinusoidal reference- and good results, considering that the controlled variable is the velocity, were obtained. The last chapter corresponds to the conclusions of the performed research as well as to the future work.

Asymptotic Giant Branch (AGB) stars are stars with low- to intermediate mass in a late stage in their stellar evolution. An important feature of stellar evolution is the ongoing nucleosynthesis, the creation of heavier elements. Unlike main sequence stars, the AGB stars have a thick convective envelope which makes it possible to dredge-up the heavier fused elements from the stellar core to its surface. AGB stars are also pulsating variable stars, meaning the interior expands and contracts, causing the brightness to fluctuate. These pulsations will also play a major role in the mass loss observed in these stars. The mass loss is caused by stellar winds that accelerate gas and dust from the surface of these stars and thereby chemical enrich the interstellar medium. It is important to understand the properties of these pulsations since they play a key role in how stellar winds are produced and then enrich the galaxy with heavier synthesized elements. These pulsation periods can be observed with their corresponding Light-Curves, where the periodic motion of the brightness can be clearly seen. The main goal with this project is to calculate these pulsation periods for different AGB stars and compare these values with the periods listed in the General Catalogue of Variable Stars (GCVS). The comparison between these values gives a better understanding of methods of determining these periods and the uncertainties that follow. / Asymptotiska jättegrenen är en del av slutstadiet för låg- till medelmassiva stjärnor (AGB stjärnor). Ett viktigt kännetecken hos stjärnutvecklingen är den pågående nukleosyntesen, sammanslagningen av tyngre ämnen i stjärnans inre. Till skillnad mot stjärnor på huvudserien har AGB stjärnor ett tjockt konvektivt lager som gör det möjligt att dra upp dessa nybildade ämnen till stjärnans yta. AGB stjärnor är pulserande variabla stjärnor där variationer i stjärnans radie gör att ljusstyrkan varierar. Dessa pulsationer kommer även att spela en viktig roll för den massförlust som observeras hos dessa stjärnor. Massförlusten orsakas av stjärnvindar som accelererar gas och stoft från stjärnans yta och därmed kemiskt berikar det interstellära mediet. Det är viktigt att förstå dessa pulsationer eftersom de är en viktig komponent för hur stjärnvindar uppstår och sedan berikar galaxer med tyngre ämnen. Dessa pulsationsperioder kan studeras genom att observera stjärnornas ljuskurvor, där man tydligt ser det periodiska beteendet hos ljusstyrkan. Det huvudsakliga målet med detta projekt är att beräkna dessa perioder för olika AGB stjärnor och att sedan jämföra dem med värden från General Catalogue of Variable Stars (GCVS). Jämförelsen mellan dessa värden ger en bättre förståelse för metoderna som används för att bestämma dessa perioder och hur osäkra dessa värden är.

O aumento da demanda por sistemas computacionais mais eficientes para obter alto desempenho impôs novos desafios à comunidade de pesquisa, que precisou buscar por novas plataformas heterogêneas para grandes aplicações. Para utilizar todo o potencial dessas plataformas, podese agrupar a aplicação em grupos menores de modo que cada grupo seja executado em uma unidade de processamento específica, para reduzir o gargalo de comunicação, de acordo com o comportamento de comunicação durante a execução da aplicação. Com o propósito de oferecer um agrupamento mais eficiente, este projeto propõe a análise de agrupamento de uma aplicação levando em consideração não só o volume total de dados, mas também a distribuição desse volume durante o tempo de execução associado à restrição da banda e da taxa de transmissão. Embora alguns trabalhos considerem o volume total de dados para o agrupamento, não é evidenciado como esse volume é distribuído e como a restrição de banda afeta o agrupamento. Assim, neste projeto foi implementado um framework para sugerir um agrupamento considerando a distribuição do volume de comunicação e restrições de banda. Além disso, foi desenvolvido um módulo de extensão para a ferramenta externa MCProf (Memory and Communication Profiler) com o objetivo de obter a distribuição do volume de comunicação. A validação do framework foi realizada por meios de testes de agrupamentos de aplicações nos quais foram comparados o tempo de comunicação do agrupamento gerado pela execução do framework em relação aos resultado dos agrupamentos considerando os trabalhos da literatura. O uso desta abordagem apresentou um aumento no desempenho que variou de 1,117X a 2,621X para as aplicações usadas nos experimentos. / The increased demand for more efficient computing systems to achieve high performance proposed new challenges to the research community, which needed to search for new heterogeneous platforms for large applications. To utilize the full potential of these platforms, the application can be grouped into small groups that runs on a specific processing unit to reduce the communication bottleneck according to the communication behavior during application execution . With the purpose of offering a more efficient clustering, this project proposes the analysis of clustering of an application taking into account not only the total volume of data, but also the distribution of that volume during the execution time associated to the band and restriction of rate transmission. Although some studies consider the total volume of data for the cluster, it is not clear how this volume is distributed and how the band constraint affects clustering. Thus, in this project was implemented a framework to suggest a cluster considering the distribution of the volume of communication and band restrictions. In addition, an extension module was developed for the external tool MCProf (Memory and Communication Profiler) in order to obtain the distribution of the communication. The validation of the framework was performed by clsutering tests which used applications in which the communication time of the cluster generated by the execution of framework was compared to the results of the clusters considering the literature. The use of this approach showed an increase in performance ranging from 1.117X to 2.621X for the applications used in the experiments.

Esta tese teve por objetivo verificar o impacto da influência familiar na discricionariedade da determinação da remuneração dos executivos em empresas brasileiras. Assume-se que a visão tradicional da relação principal x agente é fundamentalmente distinta nas empresas familiares, nas quais a propriedade e a gestão se confundem, se não totalmente, pelo menos em parte. Nesse caso, questionam-se o uso e função da remuneração por incentivo como mecanismo de alinhamento de interesses. Existem evidências de que as empresas familiares tendem a estruturar planos de incentivo com menor uso de remuneração variável, parte pelo controle natural e implícito da presença familiar na empresa, parte, por não ser compatível com preservação da riqueza socioemocional. Essas evidências influenciam nas relações esperadas: (a) quanto maior a influência familiar menor a tendência para fornecer remuneração variável aos executivos; (b) quanto maior a influência familiar maior a propensão para uso de flexibilidade na avaliação de desempenho para a determinação da remuneração variável dos executivos; (c) quanto maior a propensão para uso de flexibilidade na avaliação de desempenho menor a tendência para fornecer remuneração variável aos executivos. Para analisar essas relações, a pesquisa foi desenvolvida por meio de um levantamento realizado em 128 empresas familiares brasileiras de capital fechado. Os dados foram analisados por meio de modelagem de equações estruturais. Os resultados indicaram que a influência familiar captada pelo modelo F-PEC (poder, experiência e cultura) não tem relação direta com a proporção de remuneração variável fornecida aos executivos. Entretanto, a influência familiar impacta positivamente na propensão sobre a flexibilização da avaliação de desempenho para a determinação da remuneração variável dos executivos. Os achados evidenciaram que quanto maior é a propensão para uso de flexibilidade na avaliação de desempenho, maior a tendência para fornecer remuneração variável aos executivos. Esse resultado contradiz a relação esperada na pesquisa, todavia, pode ser interpretado como propício do ambiente familiar, em que a confiança, a preocupação com a reputação e a percepção de justiça são tidos como características fundamentais, indicando que quanto maior é a influência familiar, maior é a propensão ao uso de discricionariedade na determinação dos incentivos, o que resulta em maior proporção de remuneração variável em relação a remuneração total do executivo. Entretanto, a relação entre influência familiar e remuneração variável só foi constatada quando a flexibilidade tem papel de mediadora. Do ponto de vista organizacional, essa flexibilização para mudança pode trazer diferentes consequências sobre a empresa. Quando proporcionar mudança tal que o executivo perceba sua meta como inatingível, o fato pode gerar desinteresse dos executivos sobre o plano de remuneração e destruir a estratégia de motivação. Da mesma forma, se a mudança for feita e o executivo entender que foi favorável, pode ocorrer, como consequência, o descrédito perante o sistema de avaliação, sendo considerado que ele não será utilizado de fato. Todavia, a possibilidade de descrédito perante o sistema de avaliação e remuneração pode não ocorrer em ambientes nos quais a confiança, a preocupação com a reputação e a percepção de justiça são tidos como características fundamentais, o que é mais comum em empresas familiares. / The main goal of this thesis was to verify the impact of family influence in the discretionary choice of the remuneration of executives in Brazilian companies. This research assumed that the traditional view of the principal versus agent relationship is fundamentally different in family firms, where ownership and management are, at least in part, confused. In this case scenario, we question the use and function of the incentive compensation as interests alignment mechanism. Theoretical evidences support that family businesses tend to structure incentive plans with less use of variable compensation. This could be explained in part by the natural control and implicit family presence in the company, and in part by it\'s incompatibility with the preservation of socioemotional wealth. Those evidences are related with the expected relationships: (a) greater the family influence in the company, higher is the probability that the company provide variable remuneration to their executives; (b) higher family influence increase the propensity for flexibility in the use of performance assessment for determining the variable remuneration of the executives; (c) bigger propensity for flexibility in the use of lower performance evaluation tend to provide variable remuneration to the executives. To analyze these relationships, this research conducted a survey with 128 Brazilian family companies that are privately held. Data were analyzed using structural equation modeling. The results indicated that family influence captured by the F-PEC model (power, experience and culture) are not directly related to the proportion of variable compensation provided to executives. However, the family influence positively impacts the propensity on the relaxation of performance evaluation for determining the variable remuneration of executives. The results also showed that higher propensity for flexibility in the evaluation of performance, is associated with a higher tendency to provide variable remuneration to the executives. This finding contradicts the expected theoretical relationship, however, they can be interpreted as a consequence of a unique family environment, where trust, concern for the reputation and the perception of fairness are considered fundamental characteristics, indicating that the larger the family influence, greater is the propensity to use discretion in determining the remuneration incentives, which results in a higher proportion of variable remuneration in relation to total executive remuneration. However, the relationship between family influence and variable compensation was only found when flexibility works as a mediator factor. From an organizational point of view, this higher flexibility to change can bring different consequences for the company. If the change makes the executive realizes its goal as unattainable, for example, that can generate disinterest of business on the compensation plan and destroy the motivation strategy of the company. Similarly, if the change is made and the executive view this change as favorable, they tend to discredit the system of evaluation, and considered that it will not actually be used. However, the possibility of disbelief before the evaluation and remuneration system, cannot occur in environments where trust, concern with the reputation and the perception of fairness are considered fundamental characteristics, which is more common in families companies