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Coefficients de Laurent de la série HilbertElmahdaoui, Aziz Raymond January 2006 (has links)
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
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Simulation dynamique du flottement d'un pont élancé à l'aide de coefficients instationnaires temporelsMaheux, Sébastien January 2017 (has links)
L'utilisation, par les ingénieurs, de portées principales de plus en plus grandes pour les ponts suspendus ou haubanés fait de l'interaction vent-structure un phénomène d'importance lors de la conception de ces ponts. Effectivement, des portées plus grandes amènent une augmentation de la flexibilité de leur tablier, ce qui les rend plus vulnérables aux instabilités aérodynamiques telles que le flottement, un phénomène auto-excité causant de grands mouvements du tablier et pouvant mener à la ruine du pont. C'est la formulation de Scanlan qui est la plus utilisée pour représenter les forces auto-excitées dans l'étude du flottement des ponts. Cette formulation ne permet pas la réalisation d'une étude du flottement en tenant compte des non-linéarités structurales et aérodynamiques. Par contre, les ponts élancés sont des structures qui ont un comportement structural non linéaire. De plus, plusieurs études ont démontré la non-linéarité des forces auto-excitées. Pour des prédictions du flottement plus réalistes, ces non-linéarités devraient être incluses dans des simulations temporelles notamment en utilisant des formulations temporelles des forces auto-excitées. Les formulations temporelles existantes comme les fonctions indicielles et les fonctions rationnelles sont difficiles à mettre en œuvre. Ce projet a donc pour but de développer une nouvelle représentation des forces auto-excitées dans le domaine temporel.
Pour mieux comprendre le comportement non linéaire des forces auto-excitées, des essais sectionnels en soufflerie en régime forcé harmonique ont été réalisés pour le pont est du Grand Belt, un pont suspendu, dans le but d'étudier l'effet de l'échelle, de la vitesse du tablier et de l'amplitude du mouvement sur les coefficients instationnaires de la formulation de Scanlan. Il est montré que l'adimensionnalisation utilisée dans la formulation de Scanlan est valide par rapport à la dimension du tablier. Par contre, il a été trouvé que les coefficients instationnaires montrent un comportement non linéaire par rapport à ces deux paramètres, mais plus particulièrement pour la vitesse du tablier. Puisque les coefficients instationnaires ont un comportement non linéaire par rapport à un paramètre temporel comme la vitesse du tablier, un nouveau modèle temporel des forces auto-excitées basé sur des coefficients instationnaires temporels qui sont fonction de la vitesse et de l'accélération du tablier a été développé. Ces coefficients instationnaires temporels ont été obtenus à partir d'essais en régime forcé cyclique à vitesse absolue constante et à accélération absolue constante. Ce modèle a été utilisé pour réaliser des simulations temporelles du flottement à échelle réelle. La vitesse de flottement prédite avec l'approche des coefficients instationnaires temporels concorde bien avec la vitesse de flottement expérimentale et celle prédite en utilisant la formulation de Scanlan.
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Estimation of Aerodynamic Parameters in Real-Time : Implementation and Comparison of a Sequential Frequency Domain Method and a Batch MethodNyman, Lina January 2016 (has links)
The flight testing and evaluation of collected data must be efficient during intensive flight-test programs such as the ones conducted during development of new aircraft. The aim of this thesis has thus been to produce a first version of an aerodynamic derivative estimation program that is to be used during real-time flight tests. The program is to give a first estimate of the aerodynamic derivatives as well as check the quality of the data collected and thus serve as a decision support during tests. The work that has been performed includes processing of data in order to use it in computations, comparing a batch and a sequential estimation method using real-time data and programming a user interface. All computations and programming has been done in Matlab. The estimation methods that have been compared are both built on transforming data to the frequency domain using a Chirp z-transform and then estimating the aerodynamic derivatives using complex least squares with instrumental variables.The sequential frequency domain method performs estimates at a given interval while the batch method performs one estimation at the end of the maneuver. Both methods compared in this thesis produce equal results. The continuous updates of the sequential method was however found to be better suited for a real-time application than the single estimation of the batch method. The telemetric data received from the aircraft must be synchronized to a common frequency of 60 Hz. Missing samples of the data stream must be linearly interpolated and different units of measured parameters must be corrected in order to be able to perform these estimations in the real-time test environment.
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Magmatisme, métasomatisme et recyclage à l'aplomb d'une zone de subduction : apports des xénolithes mantelliques du volcan andésitique Avachinsky (Kamchatka, Russie) / Magmatism, metasomatism and recycling underneath a subduction zone : insights from mantle xenoliths from andesitic volcano Avachinsky (Kamchatka, Russie)Bénard, Antoine 29 November 2011 (has links)
Nous avons étudié des harzburgites à spinelles échantillonnées au volcan andésitique Avachinsky (Sud du Kamchatka, Russie). Ces roches contiennent des inclusions vitreuses dans des spinelles et sont recoupées par des veines pyroxénitiques. L’étude des inclusions vitreuses dans les spinelles révèle deux générations de liquides: (1) un liquide formé à haute température (>1200°C) dans l’asthénosphère et (2) un liquide formé à plus basse température (>900°C) dans la lithosphère mantellique. Ce travail permet de mesurer directement la composition en éléments majeurs et en trace des liquides produits par fusion partielle dans le manteau sous-arc. Les veines webstéritiques recoupant les xénolithes sont formées par des boninites riches en Ca. Ces liquides peuvent être issus de la fusion partielle d’une harzburgite hybridisée par des fluides alumino-silicatés dérivant de la plaque Pacifique plongeante. Les boninites riches en Ca peuvent être produites dans un arc mature et ne pas être des indicateurs géodynamiques fiables mais des précurseurs de certains produits éruptifs du volcanisme andésitique. L’étude des veines orthopyroxénitiques recoupant les xénolithes révèle les processus de modification des liquides produits et percolants dans le manteau sous-arc. Ces processus se caractérisent par une combinaison de fractionnement et ré-équilibration partielle du liquide percolant avec l’encaissant péridotitique. Le processus global affecte des liquides avec des signatures géochimiques variées et se caractérise par la formation de spectres de terres rares en forme de U coexistant avec des anomalies positives en Zr-Hf. La signature en éléments en trace des boninites pauvres en Ca peut être le résultat de ce processus. Le développement méthodologique de l’imagerie tridimensionnelle par microscopie multiphotonique, appliquée aux sulfures disséminés dans les xénolithes, montre que cette technique permet d’obtenir une résolution sub-micronique avec un minimum de mise en oeuvre. L’étude de la signature en éléments du groupe du platine des sulfures des veines orthopyroxénitiques montre que cette signature est aussi fortement modifiée lors de l’interaction du liquide percolant avec un liquide sulfuré interstitiel, résidant dans la roche encaissante. L’étude du F et du Cl dans les minéraux des xénolithes nous permet d’établir les premiers coefficients de partage pour ces deux éléments, applicables à la fusion et à la cristallisation dans le manteau sous-arc. Les mesures de H2O, CO2, S et halogènes dans les inclusions vitreuses montrent qu’une part importante du recyclage de ces éléments est réalisé au travers des liquides de relative basse température (>900°C) dans le manteau lithosphérique sous-arc / We have studied spinel harzburgites sampled at the andesitic volcano Avachinsky (South of Kamchatka, Russia). These rocks contain spinel-hosted glassy inclusions and are crosscut by pyroxenitic veins. The study of glassy inclusions in spinels reveals two types of liquids: (1) one formed at high temperature (>1200°C) in the asthenosphere and (2) one formed at lower temperature (>900°C) in the lithospheric sub-arc mantle. This work allows to measure directly the composition in major and trace elements of liquids produced by partial melting in the sub-arc mantle. Websteritic veins crosscutting the xenoliths are formed by Ca-rich boninites. These liquids can be produced by partial melting of an harzburgite, hybridized by alumino-silicated fluids deriving from the sinking Pacific plate. Ca-rich boninites can be produced in a mature arc, may not be reliable geodynamic indicators and rather precursors of some eruptive products of the andesitic volcanism. The study of orthopyroxenitic veins crosscutting the xenoliths reveals the processes of modification of liquids produced and percolating in the sub-arc mantle. These processes are characterized by a combination of fractionnation and partial re-equilibration of the percolating liquid with the host peridotite. The overall process affects liquids with various geochemical signatures and is characterized by the formation of U-shaped rare-earth elements spectra coexisting with Zr-Hf spykes. The trace element signature of Ca-poor boninites can result from this process. The methodological development of three-dimensional imaging by multiphoton microscopy applied to disseminated sulfides in xenoliths shows that this technique allows to obtain a sub-micronic resolution with a minimum of implementation. The study of the platinum group elements signature of sulphides in orthopyroxenitic veins reveals that this signature is also strongly modified during the interaction of the percolating liquid with an interstitial sulfide liquid located in the host harzburgite. The study of F and Cl in minerals from the xenoliths allows us to establish the first partitioning coefficients for these two elements, suitable for partial melting and crystallization in the sub-arc mantle. H2O, CO2, S and halogens measurements in the glassy inclusions reveal that an important part of the recycling of these elements is made through the relative lowtemperature (>900°C) liquids in the lithospheric sub-arc mantle
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Heat transfer and flow characteristics of sonic nozzleMadamadakala, Ganapathi Reddy January 1900 (has links)
Master of Science / Department of Mechanical and Nuclear Engineering / Steven Eckels / The current research presents the experimental investigation of heat transfer and flow characteristics of sonic multiphase flow in a converging-diverging nozzle. R134a and R123 are used in this study. Four different nozzle assemblies with two different throat sizes (2.43mm and 1.5 mm with 1° growth angle with the centerline of the nozzle in the diverging section) and two different heater lengths (200 mm and 125 mm) were tested. Each test section was an assembly of aluminum nozzle sections. The experimental facility design allowed controlling three variables: throat velocity, inlet temperature, back pressure saturation temperature.
The analysis used to find the average heat transfer of the fluid to each nozzle section. This was achieved by measuring the nozzle wall temperature and fluid pressure in a steady state condition. Two methods for finding the average heat flux in sonic nozzle were included in the data analysis: infinite contact resistance and zero contact resistance between nozzle sections.
The input variables ranges were 25 °C and 30 °C for inlet temperature and back pressure saturation temperatures, 1100-60,000 kg/m[superscript]2s for mass flux, and 1.4-700 kW/m[superscript]2 heat flux. The effect of the mass flux and heat flux on the average two-phase heat transfer coefficients was investigated. The flow quality, Mach number(M), and Nusselt number ratio ([phi]) were also calculated for each section of the nozzle.
As the fluid flowed through the nozzle, the pressure of the liquid dropped below the inlet saturation pressure of the liquid due to sonic expansion in the nozzle. This temperature drop was significantly lower in the case of R134a than R123. The results showed that the two-phase heat transfer coefficients were above of 30000 W/m^2 K in the first 75 mm of the nozzle, and they decreased along the nozzle. The Mach number profile appeared similar to the temperature profile, and the fluid was in the sonic region as long as temperature of the fluid dropped in the nozzle. Nusselt number ratios were compared with the Mach numbers and showed that the Nusselt number ratio were increased in the sonic region. The results showed that the length of the sonic region was larger for R123 than for R134a, and the Mach numbers were higher for R123. The Nusselt ratios of R123 were low compared to the R134a cases, and the trend in the Nusselt ratios was notably different as well.
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Určení teploty vodní hladiny z družicových dat. / Skin surface water temperatures determination in selected lakes and reservoirs from satellite dataFormánek, Tomáš January 2018 (has links)
LAKE SURFACE TEMPERATURE DETERMINED BY SATELLITE IMAGES Abstract The aim of this master thesis is to create a method to determine surface temperature of water in lake Osoyoos (LSWT - Lake Surface Water Temperature). It is necessary to know this temperature in order to make easier decisions in a paradigm of global warming processes. Thanks to LSWT it is possible to make a timeline visualisation of temperature development in years. The first chapter deals with a physical definition of how to get thermal information - the basis of remote thermal sensing is measuring of radiance intensity and it's transformation to brightness temperature. This radiation is not only influenced by atmospheric properties but also by local climatic and meteorological conditions, but it is also influenced by the relief. The thesis seeks to create a method for calculating surface temperature of lake Osoyoos located at Canadian-American border. This calculation is based on data provided by ASTER using a split-window method. The method works with the differences in bands of sensing in order to remove atmospheric influences. This thesis contains several charts, graphs and pictures. The final result of this paper is a map of distribution of lake surface water temperatures. Keywords: Thermal remote sensing, land surface temperature, ASTER, TIR
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Perda localizada de carga em conexões utilizadas em sistemas de microirrigação / Minor losses caused by fittings used in microirrigation systemsBombardelli, Wagner Wilson Ávila 05 February 2018 (has links)
Há pouca disponibilidade de informações de perda localizada de carga sobre conexões utilizadas em microirrigação. Diante disso, objetivou-se desenvolver e validar uma bancada automatizada para ensaios e determinar experimentalmente as perdas localizadas provocadas por conexões utilizadas em sistemas de microirrigação. Desenvolveu-se uma bancada automatizada utilizando um circuito eletrônico microcontrolado que dispõe de funcionalidades para aquisição e condicionamento de sinais de sensores; controle de inversor de frequência e válvula proporcional; controle Proporcional-Integral-Derivativo (PID); e, comunicação Modbus RTU com outros dispositivos através de rede RS-485. O firmware implementado no microcontrolador foi desenvolvido na linguagem C, enquanto que a interface gráfica do usuário (GUI) foi desenvolvida em C#. A metodologia de ensaios foi elaborada combinando recomendações de normas técnicas internacionais. Os ensaios foram conduzidos sob pressão de entrada controlada em 150 kPa, sendo ensaiadas entre cinco e dez peças para cada modelo de conexão. As curvas relacionando vazão e perda localizada de carga foram construídas com, pelo menos, 15 valores de vazão, submetidos sob condição de incremento e decréscimo para incluir eventuais efeitos de histerese do sistema de medição. Foram coletados 30 pontos por condição de vazão, tendo sido realizado uma aquisição de 900 pontos por ensaio. Para cada modelo avaliado foram apresentados as seguintes informações: curva de perda localizada de carga em função de vazão, coeficiente de perda localizada de carga (KL) e comprimento equivalente (Leq). A bancada de ensaios automatizada permitiu a condução dos ensaios onde os sistemas de medição e controle operaram adequadamente, sendo capazes de atender a requisitos estabelecidos em normas técnicas. Os valores aproximados de KL se apresentaram entre 2,70 a 24,08. Em muitos dos casos, o coeficiente tendeu a uma constância após um número de Reynolds de 10000. Pôde-se verificar também a sensibilidade do coeficiente relacionada com a razão das seções internas nas conexões. Os expoentes da vazão assumem valores próximos do que é aplicado pela equação de Darcy-Weisbach (m=2). / Information about minor losses caused by fittings employed in microirrigation systems are hard to be found in literature. The objective of this research was to develop and validate an automated bench for determine experimentally minor losses caused by fittings commonly installed in microirrigation. An automated bench was developed using a microcontrolled electronic circuit that has functionalities for data acquisition and signal conditioning; control of variable frequency drive and proportional valve; Proportional-Integral-Derivative Control (PID); and, Modbus RTU communication with other devices through a RS-485 network. The firmware implemented for the microcontroller was programmed in the C language, while the graphical user interface (GUI) was developed in C#. The methodology of tests was based on international standards. The tests were carried out under controlled inlet pressure, at 150 kPa, and five to ten units were tested for each fitting model. The curves relating flow and minor losses were drawn based on minimum of 15 flow values, obtained under conditions of increase and decrease of flow rate in order to take into account possible effects of hysteresis related to the measurement system. In each flow rate, 30 points were collected resulting in a sample size of 900 points in each test. For each model of fitting evaluated, the following information was presented: curves of minor losses as a function of flow rate, minor loss coefficient (KL) and minor losses expressed as an equivalent length (Leq). The automated test bench enabled to carry out the experiments properly, being able to meet the requirements established by technical standards. The values of KL presented ranged from 2.70 to 24.08. Usually, that coefficient tended to become constant for Reynolds number higher than 10000. The sensitivity of the coefficient related to a ratio of the internal sections in the connections was also verified. The flow exponents presented values close to what is applied by the Darcy-Weisbach equation (m = 2).
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Uncertainty Quantification and Assimilation for Efficient Coastal Ocean ForecastingSiripatana, Adil 21 April 2019 (has links)
Bayesian inference is commonly used to quantify and reduce modeling uncertainties in coastal ocean models by computing the posterior probability distribution function (pdf) of some uncertain quantities to be estimated conditioned on available observations. The posterior can be computed either directly, using a Markov Chain Monte Carlo (MCMC) approach, or by sequentially processing the data following a data assimilation (DA) approach. The advantage of data assimilation schemes over MCMC-type methods arises from the ability to algorithmically accommodate a large number of uncertain quantities without a significant increase in the computational requirements. However, only approximate estimates are generally obtained by this approach often due to restricted Gaussian prior and noise assumptions.
This thesis aims to develop, implement and test novel efficient Bayesian inference techniques to quantify and reduce modeling and parameter uncertainties of coastal ocean models. Both state and parameter estimations will be addressed within the framework of a state of-the-art coastal ocean model, the Advanced Circulation (ADCIRC) model. The first part of the thesis proposes efficient Bayesian inference techniques for uncertainty quantification (UQ) and state-parameters estimation. Based on a realistic framework of observation system simulation experiments (OSSEs), an ensemble Kalman filter (EnKF) is first evaluated against a Polynomial Chaos (PC)-surrogate MCMC method under identical scenarios. After demonstrating the relevance of the EnKF for parameters estimation, an iterative EnKF is introduced and validated for the estimation of a spatially varying Manning’s n coefficients field. Karhunen-Lo`eve (KL) expansion is also tested for dimensionality reduction and conditioning of the parameter search space. To further enhance the performance of PC-MCMC for estimating spatially varying parameters, a coordinate transformation of a Gaussian process with parameterized prior covariance function is next incorporated into the Bayesian inference framework to account for the uncertainty in covariance model hyperparameters. The second part of the thesis focuses on the use of UQ and DA on adaptive mesh models. We developed new approaches combining EnKF and multiresolution analysis, and demonstrated significant reduction in the cost of data assimilation compared to the traditional EnKF implemented on a non-adaptive mesh.
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Essays in Econometrics and Dynamic Kidney ExchangeBaisi Hadad, Vitor January 2018 (has links)
Thesis advisor: Stefan Hoderlein / This dissertation is divided into two parts. Part I - Dynamic Kidney Exchange In recent years, kidney paired donation (KPD) has an emerged as an attractive alternative for end-stage renal disease patients with incompatible living donors. However, we argue that the matching algorithm currently used by organ clearinghouses is inefficient, in the sense that a larger number of patients may be reached if kidney transplant centers take into consideration how their pool of patients and donors will evolve over time. In our work Two Novel Algorithms for Dynamic Kidney Exchange, we explore this claim and propose new computational algorithms to increase the cardinality of matchings in a discrete-time dynamic kidney exchange model with Poisson entries and Geometric deaths. Our algorithms are classified into direct prediction methods and multi-armed bandit methods. In the direct prediction method, we use machine learning estimator to produce a probability that each patient-donor pair should be matched today, as op- posed to being left for a future matching. The estimators are trained on offline optimal solutions. In contrast, in multi-armed bandit methods, we use simulations to evaluate the desirability of different matchings. Since the amount of different matchings is enormous, multi-armed bandits (MAB) are employed to decrease order to decrease the computational burden. Our methods are evaluated using simulations in a variety of simulation configurations. We find that the performance of at least one of our methods, based on multi-armed bandit algorithms, is able to uniformly dominate the myopic method that is used by kidney transplants in practice. We restrict our experiments to pairwise kidney exchange, but the methods described here are easily extensible, computational constraints permitting. Part II - Econometrics In our econometric paper Heterogenous Production Functions, Panel Data, and Productivity, we present methods for identification of moments and nonparametric marginal distributions of endogenous random coefficient models in fixed-T linear panel data models. Our identification strategy is constructive, immediately leading to relatively simple estimators that can be shown to be consistent and asymptotically normal. Because our strategy makes use of special properties of “small” (measure-zero) subpopulations, our estimators are irregularly identified: they can be shown to be consistent and asymptotically Normal, but converge at rates slower than root-n. We provide an illustration of our methods by estimating first and second moments of random Cobb-Douglas coefficients in production functions, using Indian plant-level microdata. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.
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Balanço de nutrientes, uso aparente da energia e digestibilidade ileal aparente e estandardizada dos aminoácidos do farelo do trigo, farelo de arroz, sorgo, farelo de canola, farelo de girassol, milho, farelo de soja e soja integral extrusada, com inclusão isolada e combinada de multi-carboidrase e fitase, em frangos de corte dos 14 aos 21 dias de idade / Nutrient balance, energy apparent use and apparent andstandardized ileal amino acid digestibility from wheat bran, rice bran, sorghum, canola meal, sunflower meal, corn, soybean meal and extruded soybean meal with individual or combined multi-carbohydrase and phytse supplementation from broiler chickens from 14 to 21 days oldVela, Connie Gallardo 21 October 2016 (has links)
O objetivo do presente estudo foi determinar, em presença de multi-carboidrase (MC: galactomananase, xilanase, beta-glucanase, e alfa-galactosidase) e fitase (10.000 FTU/g) o balanço nutricional, uso aparente da energia (EMA), a digestibilidade ileal aparente e estandardizada dos aminoácidos em diferentes ingredientes usados na alimentação de frangos de corte. Sob o delineamento inteiramente casualizado 1960 frangos machos (Cobb 500) foram distribuídos do 1 aos 21 dias de idade para receberem cinco tratamentos, em sete repetições com sete aves cada. A adaptação das aves às gaiolas, sob níveis nutricionais dietéticos recomendados à fase, se deu do 1º ao 10º dia de idade. A seguir, receberam as dietas experimentais dos 11 aos 18 dias, quando se procedeu a coleta de excretas, período esse, definido como Ensaio 1. A partir do 19º dia as aves receberam nova dieta até os 21 dias de idade, quando se deu o abate para amostragens do conteúdo ileal, período definido como Ensaio 2. As dietas do período experimental foram: dieta de referência e quatro dietas a base de milho (Ensaio 1) e quatro dietas a base de amido de milho (Ensaio 2). As dietas experimentais tinham como única fonte de proteína 30% do ingrediente testado, sendo fornecidas sob arranjo fatorial 2 MC (0 ou 200 mg/kg) x 2 fitase (0 ou 50 mg/kg). Os ingredientes testados foram: farelo de trigo, farelo de arroz, sorgo, farelo de canola, farelo de girassol, milho, farelo de soja e soja integral extrusada. Os dados foram submetidos à análise de variância utilizando o PROC GLM do SAS 9.2. As enzimas melhoraram (P < 0,05) o balanço de nutrientes, a EMA, digestibilidade ileal aparente e estandardizada dos aminoácidos nos diferentes ingredientes testados. Separada ou combinada a multi-carboidrase e fitase tiveram eficiência diferenciada para cada ingrediente estudado e utilizado na formulação das rações de frangos de corte na fase inicial, correspondente ao período de 14 aos 21 dias de idade / The aim of this study was to determine the effects of multi-carbohydrase (MC, that consist in: galactomannanase, xylanase, beta-glucanase and alpha-galactosidase) and phytase (10000 FTU/g of activity) the nutrients balance, apparent energy use (AME), apparent and standardized ileal amino acids digestibility in some feedstuffs fed to young chickens. Under a completely randomized design 1960 male broilers (Cobb 500) were allotted from 1 to 21 days old to receive five treatments in seven replicates with seven birds each. Birds cages adaptation under dietary nutritional levels recommended to the stage occurred from the 1st to 10th day of age. Then, the birds received the experimental diet from 11 to 18 days when was realized the excreta collection, period defined as Assay 1. From the 19th day the birds received the new diet until 21 days old when birds were slaughter for ileal digesta collection, this period was defined like Assay 2. The experimental diets were: one reference diet and four corn-based diets (Assay 1) and four corn-starch-based diets (Assay 2). The experimental diets containing 30% of ingredient test as a sole protein source in 2 MC (0 or 200 mg/kg) x 2 phytase (0 or 50 mg/kg) factorial arrangement. The ingredients tested were: wheat bran, rice bran, sorghum, canola meal, sunflower meal, corn, soybean meal and extruded soybean meal. Data were subjected to variance analysis using the PROC GLM of SAS 9.2. Enzymes improved (P < 0.05) the nutrients balance, AME use, apparent and standardized ileal amino acids digestibility on different tested ingredients. Isolated or combined the multi-carbohydrase and phytase have different efficiency for each studied ingredient and used on feed formulation for broiler chickens in initial phase, that corresponding from 14 to 21 days old
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