Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.

Mathematical modeling of dehydration of 'Fuji' and 'Gala' apples slices using infrared

The objective of this work was to determine and model the infrared dehydration curves of apple slices - Fuji and Gala varieties. The slices were dehydrated until constant mass, in a prototype dryer with infrared heating source. The applied temperatures ranged from 50 to 100 °C. Due to the physical characteristics of the product, the dehydration curve was divided in two periods, constant and falling, separated by the critical moisture content. A linear model was used to describe the constant dehydration period. Empirical models traditionally used to model the drying behavior of agricultural products were fitted to the experimental data of the falling dehydration period. Critical moisture contents of 2.811 and 3.103 kgw kgs-1 were observed for the Fuji and Gala varieties, respectively. Based on the results, it was concluded that the constant dehydration rates presented a direct relationship with the temperature; thus, it was possible to fit a model that describes the moisture content variation in function of time and temperature. Among the tested models, which describe the falling dehydration period, the model proposed by Midilli presented the best fit for all studied conditions.

Mathematical modeling of microbial growth in milk

A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

Evaluation of a new mathematical model to describe Clostridium perfringens growth during the cooling of cooked ground beef

A mathematical model previously developed to study microbial growth in food products under an isothermal environment was adapted to a time-varying temperature regime. The resulting model was applied to study the growth of Clostridium perfringens in meat products. This micro-organism is of particular relevance to public health and economy due to the loss of productivity caused by it. Results showed a similar performance of the model used compared to the Baranyi model under an isothermal situation and a slightly better performance under a non-isothermal temperature profile.

Mathematical modeling of microwave dried celery leaves and determination of the effective moisture diffusivities and activation energy

Celery (Apium graveolens L. var. secalinum Alef) leaves with 50±0.07 g weight and 91.75±0.15% humidity (~11.21 db) were dried using 8 different microwave power densities ranging between 1.8-20 W g-1, until the humidity fell down to 8.95±0.23% (~0.1 db). Microwave drying processes were completed between 5.5 and 77 min depending on the microwave power densities. In this study, measured values were compared with predicted values obtained from twenty thin layer drying theoretical, semi-empirical and empirical equations with a new thin layer drying equation. Within applied microwave power density; models whose coefficient and correlation (R²) values are highest were chosen as the best models. Weibull distribution model gave the most suitable predictions at all power density. At increasing microwave power densities, the effective moisture diffusivity values ranged from 1.595 10-10 to 6.377 10-12 m2 s-1. The activation energy was calculated using an exponential expression based on Arrhenius equation. The linear relationship between the drying rate constant and effective moisture diffusivity gave the best fit.

Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

This infinite, unanimous dissonance : a study in mathematical existentialism through the work of Jean-Paul Sartre and Alain Badiou

This thesis seeks to elucidate a motif common to the work both of Jean-Paul Sartre and Alain Badiou (with special attention being given to Being and Nothingness and Being and Event respectively): the thesis that the subject 's existence precedes and determines its essence. To this end, the author aims to explicate the structural invariances, common to both philosophies, that allow this thesis to take shape. Their explication requires the construction of an overarching conceptual framework within which it may be possible to embed both the phenomenological ontology elaborated in Being and Event and the mathematical ontology outlined in Being and Event. Within this framework, whose axial concept is that of multiplicity, the precedence of essence by existence becomes intelligible in terms of a priority of extensional over intensional determination. A series of familiar existentialist concepts are reconstructed on this basis, such as lack and value, and these are set to work in the task of fleshing out the more or less skeletal theory of the subject presented in Being and Event.

Factors affecting performance proficiency : a case study involving intermediate piano students

The goal of this study was to determine the effect of a number of factors on the performance proficiency of three intermediate piano students having different learning styles, all of whom shared the same teacher. Four sets of data were collected in this investigation: the methodology of the teacher; the practice behaviour of the participants; the effect of intrinsic factors, such as participant attitude, motivation, and ownership of learning; and the effect of extrinsic factors that included parental influence, and participants' school- and employment-related responsibilities. Performance proficiency and assessment of practice behaviour were measured by three external, professionallyqualified music examiners. Performance proficiency varied to some extent between participants, but they shared similar practice behaviours. Learning style does not, therefore, affect practice behaviour. Although they planned their practice time, participants did not show much evidence of monitoring the quality of their practice. On the other hand, participants showed positive attitude; they were motivated to learn; and they were observed to plan their practice time, all indicators of, among other things, positive influence of the teacher and parents. Participants showed evidence that these constructive habits were a denominator common to both their schoolwork and piano practice. It was apparent that, except for learning style, all factors examined had an effect on performance proficiency. Performance proficiency is, therefore, influenced by a large web of factors, a finding that is instructive for classroom teachers. Teachers need to avoid the temptation to teach toward performance expectations. Emphasis should be placed instead on teaching and assessing formative learning strategies.

The influence of physical activity behaviour on the relationship between motor proficiency and body composition in children

There is an emerging awareness that children with poor motor abilities are at particular risk for overweight. This cross-sectional study examined the influence of physical activity behaviour on the relationship between motor proficiency and body composition. Participants were 1287 (646 males, 641 females) Grade 6 students in the Physical Health Activity Study project. Height, weight, waist girth, and motor proficiency (Bruininks-Oseretsky Test of Motor Performance BOTMP-SF) were assessed. Physical activity behaviours were also evaluated with a multifaceted approach and reported for school-based, non-school based physical activity, free-time play, and sedentary activities (Participation Questionnaire), and leisure time exercise (Godin-Shephard Leisure Time Exercise Questionnaire GS). Overweight was defined by BMI scores: boys :::20.6-21.2 and <25.1-26.0; girls: ::: 20.7-21.7and <25.4-26.7 and obesity was defined as: boys:::: 25.1-26.0; girls: :::25.4-26.7. Children were classified as case group (CG,::; 10% on BOTMP-SF), borderline case group (BC, > 10% to ::; 20% on BOTMP-SF) or non-case group. Analyses of variance (ANOVAs) uncovered a significant difference in overweight and obesity between the case group and non-case group. Normal-weight children reported higher participation in organized school-sports (intra-mural and inter-school teams). The CG reported significantly lower participation in school sports teams and lower GS results, with a trend towards lower participation in all active pursuits. They also reported a significantly higher duration of television watching and book reading. There were no significant differences between motor proficiency groups by gender, age, nonschool sports, or free-time activity. Multivariate ordinal logistic regression analysis showed that the case group was 10.9 times more likely to be overweight/obese than their peers. No single aspect of physical activity was able to explain the difference in odds ratios for the motor proficiency groups. However, for the entire cohort, children who participated in more organized school sports were less likely to be overweight/obese. These findings confirm that children with low motor proficiency are at significant risk of developing overweight. It is evident that these children have generally attenuated activity levels and heightened levels of sedentary pursuits. School-based activities appear particularly limited, and are the one area where children have near autonomy in their decision to pursue active opportunities. The promotion of school-based programs, specifically intramural sports may be an important aspect in increasing children's overall activity levels. It is also essential to consider the needs of those children with low motor proficiency when designing activity promotion programs. Future research should further explore motor proficiency and overweight/obesity.

Investigating the association between motor proficiency and body satisfaction in grade 5 children

The inverse relationships between motor proficiency and overweight, and between overweight and body satisfaction have been well documented. However, the association between motor proficiency and body satisfaction has been largely neglected in the literature. Knowledge of the influence that low motor proficiency may have on body satisfaction is essential if the full burden that those children with poor motor abilities face is to be fully recognized, as low body satisfaction has been linked to an increased risk for low self-esteem, depression, and disordered eating. The cohort investigated in this report included 1907 (971 males, 936 female) Grade 5 students from the Physical Health Activity Study Team (PHAST) project in the Niagara Region of Southern Ontario. Children were grouped as overweight or healthy weight (using BMI cut offs for age and gender), and as low motor proficiency or normal motor proficiency (cut-off set at lowest 10% Bruininks Oseretsky Test of Motor Proficiency-short form (BOTMPsf). It was apparent from analyses of variance (ANOVAs) by gender that boys demonstrated significantly higher motor proficiency scores. As a result separate multiple logistic regressions by gender were used to determine the relationship between body satisfaction, BMI, and motor proficiency. There was a significant relationship between BMI and body satisfaction for both genders (p<0.01) and for males a significant relationship between motor proficiency and body satisfaction (p<0.03). Overweight females were less likely to be satisfied with their bodies with an odds ratio (OR) of 0.33 (CI: 0.23-0.47). The same trend was found in overweight males (OR: 0.42, CI: 0.29-0.59). Males with low motor proficiency were significantly less satisfied with their bodies (OR: 0.53, CI: 0.29-0.97). Males with poor motor proficiency were at greater risk for low body satisfaction regardless of their overweight status. Overweight is known to be prevalent among children with low motor proficiency and, these results indicate that low body satisfaction is also a significant concern. These findings confirm that attention needs to be paid to perceptions of body satisfaction among children with low motor proficiency. This is particularly true for boys, as their bodies may fail them in two common societal expectations, shape and skill and for whom their risk of low body satisfaction is heightened by their poor motor proficiency.

Mediating Influence of Physical Fitness on the Relationship between Academic Performance and Motor Proficiency

We explored the potential mediating influence of physical fitness on the relationship between academic performance and motor proficiency in children. 1864 students (F:926, M:938, age 11.91 (SD:0.34). Academic achievement was derived from an average of standardized tests of reading, writing, and math. The Bruininks-Oseretsky Test of Motor Performance (short-form) determined motor proficiency. Fitness (peak oxygen uptake) was established with the Léger 20-m Shuttle Run Test. OLS regression identified several significant predictors of academic performance. After controlling for age (p=0.0135), gender (p<0.0001), and parental education (p<0.0001), motor proficiency (p<0.0001), was significant. After adding physical fitness (p=0.0030) to the model the effect of motor proficiency remained significant however the point estimate was reduced from 0.0034 (p<0.0001) to 0.0026 (p<0.0001). These results suggest that physical fitness plays a mediating role on the relationship between academic performance and motor proficiency although both aerobic fitness and motor proficiency have independent roles.

Undergraduate Students' Experiences of Their Mathematical Identity

This research study explored how undergraduate mathematics students perceive themselves as capable mathematics learners and whether gender differences exist in the undergraduates students' perceptions. The research was framed by three approaches of understanding identity: self-efficacy, environment, and four faces of learner's identity. A mixed methods approach to the study was used where data were collected from interviews and an online questionnaire. Data analysis revealed that undergraduate mathematics students' perceptions of their mathematical identity as capable mathematics learners are influenced by their perceptions of their experiences such as: (a) perceptions of having previous knowledge of the course, (b) being able teach others and others understand it, (c) being recognized by their professors, (d) contributing and fitting in, (e) having opportunities to interact with their peers, and (f) being able to fit in with their image of a capable mathematics learner.

Elementos of geometry and trigonometry : from the works of A.M. Legendre, adapted to the course of mathematical instruction in the United State

UANL

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.