907 resultados para General Linear Methods
Resumo:
In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.
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In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.
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The aim of this thesis research was to gain a better understanding of the emplacement of rapakivi granite intrusions, as well as the emplacement of gold-bearing hydrothermal fluids in structurally controlled mineralizations. Based on investigations of the magnetic fabric, the internal structures could be analysed and the intrusion mechanisms for rapakivi granite intrusions and respectively different deformation stages within gold-bearing shear and fault zones identified. Aeromagnetic images revealed circular structures within the rapakivi granite batholiths of Wiborg, Vehmaa and Åland. These circular structures represent intrusions that eventually build up these large batholiths. The rapakivi granite intrusions of Vehmaa, Ruotsinpyhtää within the Wiborg batholith and Saltvik intrusions within the Åland batholith all show bimodal magnetic susceptibilities with paramagnetic and ferromagnetic components. The distribution of the bimodality is related to different magma batches of the studied intrusions. The anisotropy of magnetic susceptibility (AMS) reveals internal structures that cannot be studied macroscopically or by microscope. The Ruotsinpyhtää and Vehmaa intrusions represent similar intrusion geometries, with gently to moderately outward dipping magnetic foliations. In the case of Vehmaa, the magnetic lineations are gently plunging and trend in the directions of the slightly elongated intrusion. The magnetic lineations represent magma flow. The shapes of the AMS ellipsoids are also more planar (oblate) in the central part of the intrusion, whereas they become more linear (prolate) near the margin. These AMS results, together with field observations, indicate that the main intrusion mechanism has involved the subsidence of older blocks with successive intrusion of fractionated magma during repeated cauldron subsidence. The Saltvik area within the Åland batholith consists of a number of smaller elliptical intrusions of different rapakivi types forming a multiple intrusive complex. The magnetic fabric shows a general westward dipping of the pyterlite and eastward dipping of the contiguous even-grained rapakivi granite, which indicates a central inflow of magma batches towards the east and west resulting from a laccolitic emplacement of magma batches, while the main mechanism for space creation was derived from subsidence. The magnetic fabric of structurally controlled gold potential shear and fault zones in Jokisivu, Satulinmäki and Koijärvi was investigated in order to describe the internal structures and define the deformation history and emplacement of hydrothermal fluids. A further aim of the research was to combine AMS studies with palaeomagnetic methods to constrain the timing for the shearing event relative to the precipitation of ferromagnetic minerals and gold. All of the studied formations are dominated by monoclinic pyrrhotite. The AMS directions generally follow the tectonic structures within the formations. However, internal variations in the AMS direction as well as the shapes of the AMS ellipsoids are observed within the shear zones. In Jokisivu and Satulinmäki in particular, the magnetic signatures of the shear zone core differ from the margins. Furthermore, the shape of the magnetic fabric in the shear zone core of Jokisivu is dominated by oblate shapes, whereas the margins exhibit prolate shapes. These variations indicate a later effect of the hydrothermal fluids on the general shear event. The palaeo-magnetic results reveal a deflection from the original Svecofennian age geomagnetic direction. These results, coupled with correlations between the orientation of the NRM vectors and the magnetic and rock fabrics, imply that the gold-rich hydrothermal fluids were emplaced pre/syntectonically during the late stages of the Svecofennian orogeny.
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A linear prediction procedure is one of the approved numerical methods of signal processing. In the field of optical spectroscopy it is used mainly for extrapolation known parts of an optical signal in order to obtain a longer one or deduce missing signal samples. The first is needed particularly when narrowing spectral lines for the purpose of spectral information extraction. In the present paper the coherent anti-Stokes Raman scattering (CARS) spectra were under investigation. The spectra were significantly distorted by the presence of nonlinear nonresonant background. In addition, line shapes were far from Gaussian/Lorentz profiles. To overcome these disadvantages the maximum entropy method (MEM) for phase spectrum retrieval was used. The obtained broad MEM spectra were further underwent the linear prediction analysis in order to be narrowed.
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Baroreflex sensitivity was studied in the same group of conscious rats using vasoactive drugs (phenylephrine and sodium nitroprusside) administered by three different approaches: 1) bolus injection, 2) steady-state (blood pressure (BP) changes produced in steps), 3) ramp infusion (30 s, brief infusion). The heart rate (HR) responses were evaluated by the mean index (mean ratio of all HR changes and mean arterial pressure (MAP) changes), by linear regression and by the logistic method (maximum gain of the sigmoid curve by a logistic function). The experiments were performed on three consecutive days. Basal MAP and resting HR were similar on all days of the study. Bradycardic responses evaluated by the mean index (-1.5 ± 0.2, -2.1 ± 0.2 and -1.6 ± 0.2 bpm/mmHg) and linear regression (-1.8 ± 0.3, -1.4 ± 0.3 and -1.7 ± 0.2 bpm/mmHg) were similar for all three approaches used to change blood pressure. The tachycardic responses to decreases of MAP were similar when evaluated by linear regression (-3.9 ± 0.8, -2.1 ± 0.7 and -3.8 ± 0.4 bpm/mmHg). However, the tachycardic mean index (-3.1 ± 0.4, -6.6 ± 1 and -3.6 ± 0.5 bpm/mmHg) was higher when assessed by the steady-state method. The average gain evaluated by logistic function (-3.5 ± 0.6, -7.6 ± 1.3 and -3.8 ± 0.4 bpm/mmHg) was similar to the reflex tachycardic values, but different from the bradycardic values. Since different ways to change BP may alter the afferent baroreceptor function, the MAP changes obtained during short periods of time (up to 30 s: bolus and ramp infusion) are more appropriate to prevent the acute resetting. Assessment of the baroreflex sensitivity by mean index and linear regression permits a separate analysis of gain for reflex bradycardia and reflex tachycardia. Although two values of baroreflex sensitivity cannot be evaluated by a single symmetric logistic function, this method has the advantage of better comparing the baroreflex sensitivity of animals with different basal blood pressures.
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Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.
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This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.
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Preparative liquid chromatography is one of the most selective separation techniques in the fine chemical, pharmaceutical, and food industries. Several process concepts have been developed and applied for improving the performance of classical batch chromatography. The most powerful approaches include various single-column recycling schemes, counter-current and cross-current multi-column setups, and hybrid processes where chromatography is coupled with other unit operations such as crystallization, chemical reactor, and/or solvent removal unit. To fully utilize the potential of stand-alone and integrated chromatographic processes, efficient methods for selecting the best process alternative as well as optimal operating conditions are needed. In this thesis, a unified method is developed for analysis and design of the following singlecolumn fixed bed processes and corresponding cross-current schemes: (1) batch chromatography, (2) batch chromatography with an integrated solvent removal unit, (3) mixed-recycle steady state recycling chromatography (SSR), and (4) mixed-recycle steady state recycling chromatography with solvent removal from fresh feed, recycle fraction, or column feed (SSR–SR). The method is based on the equilibrium theory of chromatography with an assumption of negligible mass transfer resistance and axial dispersion. The design criteria are given in general, dimensionless form that is formally analogous to that applied widely in the so called triangle theory of counter-current multi-column chromatography. Analytical design equations are derived for binary systems that follow competitive Langmuir adsorption isotherm model. For this purpose, the existing analytic solution of the ideal model of chromatography for binary Langmuir mixtures is completed by deriving missing explicit equations for the height and location of the pure first component shock in the case of a small feed pulse. It is thus shown that the entire chromatographic cycle at the column outlet can be expressed in closed-form. The developed design method allows predicting the feasible range of operating parameters that lead to desired product purities. It can be applied for the calculation of first estimates of optimal operating conditions, the analysis of process robustness, and the early-stage evaluation of different process alternatives. The design method is utilized to analyse the possibility to enhance the performance of conventional SSR chromatography by integrating it with a solvent removal unit. It is shown that the amount of fresh feed processed during a chromatographic cycle and thus the productivity of SSR process can be improved by removing solvent. The maximum solvent removal capacity depends on the location of the solvent removal unit and the physical solvent removal constraints, such as solubility, viscosity, and/or osmotic pressure limits. Usually, the most flexible option is to remove solvent from the column feed. Applicability of the equilibrium design for real, non-ideal separation problems is evaluated by means of numerical simulations. Due to assumption of infinite column efficiency, the developed design method is most applicable for high performance systems where thermodynamic effects are predominant, while significant deviations are observed under highly non-ideal conditions. The findings based on the equilibrium theory are applied to develop a shortcut approach for the design of chromatographic separation processes under strongly non-ideal conditions with significant dispersive effects. The method is based on a simple procedure applied to a single conventional chromatogram. Applicability of the approach for the design of batch and counter-current simulated moving bed processes is evaluated with case studies. It is shown that the shortcut approach works the better the higher the column efficiency and the lower the purity constraints are.
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The aim of this study was to examine community and individual approaches in responses to mass violence after the school shooting incidents in Jokela (November 2007) and Kauhajoki (September 2008), Finland. In considering the community approach, responses to any shocking criminal event may have integrative, as well as disintegrative effects, within the neighborhood. The integration perspective argues that a heinous criminal event within one’s community is a matter of offence to collectively held feelings and beliefs, and increases perceived solidarity; whereas the disintegration perspective suggests that a criminal event weakens the social fabric of community life by increasing fear of crime and mistrust among locals. In considering the individual approach, socio-demographic factors, such as one’s gender, are typically significant indicators, which explain variation in fear of crime. Beyond this, people are not equally exposed to violent crime and therefore prior victimization and event related experiences may further explain why people differ in their sensitivity to risk from mass violence. Finally, factors related to subjective mental health, such as depressed mood, are also likely to moderate individual differences in responses to mass violence. This study is based on the correlational design of four independent cross-sectional postal surveys. The sampling frames (N=700) for the surveys were the Finnish speaking adult population aged 18–74-years. The first mail survey in Jokela (n=330) was conducted between May and June 2008, approximately six months from the shooting incident at the local high-school. The second Jokela survey (n=278) was conducted in May–June of 2009, 18 months removed from the incident. The first survey in Kauhajoki (n=319) was collected six months after the incident at the local University of Applied Sciences, March– April 2009, and the second (n=339) in March–April 2010, approximately 18 months after the event. Linear and ordinal regression and path analysis are used as methods of analyses. The school shootings in Jokela and Kauhajoki were extremely disturbing events, which deeply affected the communities involved. However, based on the results collected, community responses to mass violence between the two localities were different. An increase in social solidarity appears to apply in the case of the Jokela community, but not in the case of the Kauhajoki community. Thus a criminal event does not necessarily impact the wider community. Every empirical finding is most likely related to different contextual and event-specific factors. Beyond this, community responses to mass violence in Jokela also indicated that the incident was related to a more general sense of insecurity and was also associating with perceived community deterioration and further suggests that responses to mass violence may have both integrating and disintegrating effects. Moreover, community responses to mass violence should also be examined in relation to broader social anxieties and as a proxy for generalized insecurity. Community response is an emotive process and incident related feelings are perhaps projected onto other identifiable concerns. However, this may open the door for social errors and, despite integrative effects, this may also have negative consequences within the neighborhood. The individual approach suggests that women are more fearful than men when a threat refers to violent crime. Young women (aged 18–34) were the most worried age and gender group as concerns perception of threat from mass violence at schools compared to young men (aged 18–34), who were also the least worried age and gender group when compared to older men. It was also found that concerns about mass violence were stronger among respondents with the lowest level of monthly household income compared to financially better-off respondents. Perhaps more importantly, responses to mass violence were affected by the emotional proximity to the event; and worry about the recurrence of school shootings was stronger among respondents who either were a parent of a school-aged child, or knew a victim. Finally, results indicate that psychological wellbeing is an important individual level factor. Respondents who expressed depressed mood consistently expressed their concerns about mass violence and community deterioration. Systematic assessments of the impact of school shooting events on communities are therefore needed. This requires the consolidation of community and individual approaches. Comparative study designs would further benefit from international collaboration across disciplines. Extreme school violence has also become a national concern and deeper understanding of crime related anxieties in contemporary Finland also requires community-based surveys.
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Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.
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Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 ± 2.63 years old) and 16 postmenopausal (57 ± 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg-1 min-1), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg-1 min-1) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (r s = 0.75) and VCO2 (r s = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.
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Both epidural and general anesthesia can impair thermoregulatory mechanisms during surgery. However, there is lack of information about the effects of different methods of anesthesia on newborn temperature. The purpose of this study was to determine whether there are differences in newborn rectal temperature related to type of anesthesia. Sixty-three pregnant women were randomly assigned to receive general or epidural anesthesia. Maternal core temperature was measured three times with a rectal probe just before anesthesia, at the beginning of surgery and at delivery. In addition, umbilical vein blood was sampled for pH. The rectal temperatures of the babies were recorded immediately after delivery, and Apgar scores were determined 1, 5, and 10 min after birth. The duration of anesthesia and the volume of intravenous fluid given during the procedure (833 ± 144 vs 420 ± 215 mL) were significantly higher in the epidural group than in the general anesthesia group (P < 0.0001). Maternal rectal temperatures were not different in both groups at all measurements. In contrast, newborn rectal temperatures were lower in the epidural anesthesia group than in the general anesthesia group (37.4 ± 0.3 vs 37.6 ± 0.3°C; P < 0.05) immediately after birth. Furthermore, the umbilical vein pH value (7.31 ± 0.05 vs 7.33 ± 0.01; P < 0.05) and Apgar scores at the 1st-min measurement (8.0 ± 0.9 vs 8.5 ± 0.7; P < 0.05) were lower in the epidural anesthesia group than in the general anesthesia group. Since epidural anesthesia requires more iv fluid infusion and a longer time for cesarean section, it involves a risk of a mild temperature reduction for the baby which, however, did not reach the limits of hypothermia.
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The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.
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Rice cooking quality is usually evaluated by texture and stickiness characteristics using many different methods. Gelatinization temperature, amylose content, viscosity (Brookfield viscometer and Rapid Visco Analyzer), and sensory analysis were performed to characterize culinary quality of rice grains produced under two cropping systems and submitted to different technologies. All samples from the upland cropping system and two from the irrigated cropping system presented intermediate amylose content. Regarding stickiness, BRS Primavera, BRS Sertaneja, and BRS Tropical showed loose cooked grains. Irrigated cultivars presented less viscosity and were softer than upland cultivars. Upland grain samples had similar profile on the viscoamylografic curve, but the highest viscosity peaks were observed for BRS Alvorada, IRGA 417, and SCS BRS Piracema among the irrigated cropping system samples. In general, distinct grain characteristics were observed between upland and irrigated samples by cluster analysis. The majority of the upland cultivars showed soft and loose grains with adequate cooking quality confirmed by sensory tests. Most of the irrigated cultivars, however, presented soft and sticky grains. Different methodologies allowed to improve the construction of the culinary profile of the varieties studied.
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The DNA extraction is a critical step in Genetically Modified Organisms analysis based on real-time PCR. In this study, the CTAB and DNeasy methods provided good quality and quantity of DNA from the texturized soy protein, infant formula, and soy milk samples. Concerning the Certified Reference Material consisting of 5% Roundup Ready® soybean, neither method yielded DNA of good quality. However, the dilution test applied in the CTAB extracts showed no interference of inhibitory substances. The PCR efficiencies of lectin target amplification were not statistically different, and the coefficients of correlation (R²) demonstrated high degree of correlation between the copy numbers and the threshold cycle (Ct) values. ANOVA showed suitable adjustment of the regression and absence of significant linear deviations. The efficiencies of the p35S amplification were not statistically different, and all R² values using DNeasy extracts were above 0.98 with no significant linear deviations. Two out of three R² values using CTAB extracts were lower than 0.98, corresponding to lower degree of correlation, and the lack-of-fit test showed significant linear deviation in one run. The comparative analysis of the Ct values for the p35S and lectin targets demonstrated no statistical significant differences between the analytical curves of each target.