scholarly journals Analysis of a Mathematical Model. Opportunities for the Training of Food Engineering Students

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1339
Author(s):  
Edwin Sepúlveda ◽  
Difariney González-Gómez ◽  
Jhony Alexander Villa-Ochoa
Keyword(s):  
Mathematical Model ◽  
Qualitative Study ◽  
Mathematical Models ◽  
Mathematics Teaching ◽  
Engineering Students ◽  
Teaching Experiment ◽  
Model Function ◽  
Pedagogical Approach ◽  
Food Engineering ◽  
Food Dryer

International research has revealed different roles of mathematics in the practices of engineers and some implications of mathematics teaching for engineering students. Modeling and mathematical models have proven to be valuable tools for their professional work and for their teaching process. This study identifies opportunities offered by a process of analysis of a mathematical model in the training of engineers. For this analysis, an interpretation of mathematical models as an object–user–representation triad was used; mathematical models were also considered a pedagogical approach to mathematics teaching. Based on this approach, a qualitative study was developed. A teaching experiment was designed, in which, through a set of tasks, the analysis of a model describing the percentage of moisture removed in a radial airflow food dryer is considered. Results show that students evidenced a comprehension of the model function as a covariation relationship and implemented strategies for understanding it through the graphs in the model. The situated character of students’ reasoning and their experience with professional practices of engineers are also highlighted.

scholarly journals Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3013
Author(s):  
Leonid Shaikhet
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Wide Class ◽  
Asymptotic Properties ◽  
Nonlinear Mathematical Model ◽  
Simple Criterion ◽  
Stochastic Perturbations ◽  
Food Engineering ◽  
Nonlinear Mathematical Models

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

Rapid determination of glomerular filtration rate by single-bolus inulin: a comparison of estimation analyses

1998 ◽  
Vol 84 (6) ◽  
pp. 2154-2162 ◽  
Author(s):  
Cord Sturgeon ◽  
Albert D. Sam ◽  
William R. Law
Keyword(s):  
Mathematical Model ◽  
Glomerular Filtration Rate ◽  
Mathematical Models ◽  
Glomerular Filtration ◽  
Filtration Rate ◽  
Rapid Determination ◽  
Constant Infusion ◽  
Sprague Dawley ◽  
Single Bolus ◽  
Sprague Dawley Rats

Rapid measurement of glomerular filtration rate (GFR) by an inulin single-bolus technique would be useful, but its accuracy has been questioned. We hypothesized that reported inaccuracies reflect the use of inappropriate mathematical models. GFR was measured in 14 intact and 5 unilaterally nephrectomized conscious male Sprague-Dawley rats (mean weight 368 ± 12 g) by both single-bolus (25 mg/kg) and constant-infusion techniques (0.693 mg ⋅ kg−1 ⋅ min−1). The temporal decline in plasma inulin concentration was analyzed through biexponential curve fitting, which accounted for renal inulin loss before complete vascular and interstitial mixing. We compared our mathematical model based on empirical rationale with those of other investigators whose studies suggest inaccuracy of single-bolus methods. Our mathematical model yielded GFR values by single bolus that agreed with those obtained by constant infusion [slope = 0.94 ± 0.16 (SE); y intercept = 0.23 ± 0.64; r = 0.82]. In comparison to the data obtained by constant inulin infusion, this method yielded a very small bias of −0.0041 ± 0.19 ml/min. Two previously reported models yielded unsatisfactory values (slope = 1.46 ± 0.34, y intercept = 0.47 ± 1.5, r = 0.72; and slope = 0.17 ± 1.26, y intercept = 17.15 ± 5.14, r = 0.03). The biases obtained by using these methods were −2.21 ± 0.42 and −13.90 ± 1.44 ml/min, respectively. The data indicate that when appropriate mathematical models are used, inulin clearance after single-bolus delivery can be used to measure GFR equivalent to that obtained by constant infusion of inulin. Attempts to use methods of analysis for simplicity or expediency can result in unacceptable measurements relative to the clinical range of values seen.

Twin Models

1970 ◽  
Vol 19 (1-2) ◽  
pp. 141-141
Author(s):  
L. Gedda ◽  
G. Brenci ◽  
M. T. Lun
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Genetic Parameters ◽  
Simultaneous Recording ◽  
Theoretical Relationship ◽  
Twin Models

The theoretical relationship between the distribution of a given trait in a population of twin pairs and several genetic parameters has been examined. In particular, a series of mathematical models has been worked out, that, when applied to a twin population, nonselected for the occurrence of a given trait and nondiagnosed as to zygosity, leads to an estimate of:1) The MZ: DZ ratio in the population;2) The frequency of the genotype responsible for a given trait;3) The probability of manifestation of the trait;4) The value of epistatic factors.A further mathematical model affords the estimate of linkage in the hypothesis of simultaneous recording of more than one trait.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

scholarly journals World Experience in Creating Mathematical Models of Air Springs: Advantages and Disadvantages

2021 ◽  
pp. 25-42
Author(s):  
A. Y Kuzyshyn ◽  
S. A Kostritsia ◽  
Yu. H Sobolevska ◽  
А. V Batih
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
High Speed ◽  
Vertical Direction ◽  
Rolling Stock ◽  
Air Spring ◽  
Advantages And Disadvantages ◽  
Mechanical Models

Purpose. Taking into account the production and commissioning of modern high-speed rolling stock, the authors are aimed to analyze the currently created mathematical models describing the dynamic behavior of the air spring, systematize them and consider the advantages and disadvantages of each model type. Methodology. For the analysis, a comparative chronological method was used, which makes it possible to trace the development of several points of view, concepts, theories. In accordance with the adopted decision equations, the existing models of air springs were divided into three groups: mechanical, thermodynamic and finite-elements. When analyzing mathematical models, the influence of a number of parameters on the dynamic behavior of the air spring, such as disturbing force frequency, heat transfer, nonlinear characteristics of materials, the shape of the membrane, etc., was considered. Findings. A feature of mechanical models is the determination of input parameters based on the analysis of experimental results, requires access to complex measuring equipment and must be performed for each new model of an air spring separately. Unlike mechanical models, which allow taking into account the damping effect of an air spring in the horizontal and vertical direction, thermodynamic models are mainly focused on studying the dynamic behavior of an air spring in the vertical direction. The use of the finite element method makes it possible to most accurately reproduce the dynamic behavior of an air spring, however, it requires significant expenditures of time and effort to create a finite element model and perform calculations. Originality. Mathematical models of the dynamic behavior of an air spring are systematized, and the importance of their study in conjunction with a spatial mathematical model of high-speed rolling stock is emphasized. Practical value. The analysis of the mathematical models of the dynamic behavior of the air spring shows the ways of their further improvement, indicates the possibility of their use in the spatial mathematical model of the rolling stock in accordance with the tasks set. It will allow, even at the design stage of high-speed rolling stock, to evaluate its dynamic characteristic and traffic safety indicators when interacting with a railway track.

scholarly journals Starting generator driving torque modeling in the studies of synchronous starting of synchronous machines

2002 ◽  
Vol 15 (3) ◽  
pp. 399-408
Author(s):  
Zoran Stajic ◽  
Dragan Petrovic ◽  
Dusan Arnautovic
Keyword(s):  
Mathematical Model ◽  
Linear Function ◽  
Polynomial Approximation ◽  
System Model ◽  
Synchronous Machines ◽  
Model Function ◽  
Detailed Model ◽  
Pumped Storage ◽  
Driving Torque ◽  
Time Linear

The paper deals with significance of the starting generator (SG) driving torque modeling in the studies of synchronous starting of synchronous machines (SSSM). The detailed mathematical model of SSSM in reversible pumped storage plant (RPSP) "Bajina Basta" is derived. Because it is very difficult to include the detailed model of the SG turbine in the system model, function of SG driving torque is modeled approximately. The most frequent case in SSSM studies is its approximation with a time linear function, until it reaches the value that should provide rotating of both machine rotors with synchronous velocities, which is also used in the paper Afterwards, three different cases are considered: constant, linear and polynomial approximation in terms of SG rotor velocity. Numerical results obtained by applying developed models to a particular case of synchronous starting are compared with the corresponding experimental results. In this way, it is shown that the application of the most frequently used SG driving torque modeling leads to the erroneous results. The advantages of the polynomial approximation suggested in the paper and its validity is demonstrated.

scholarly journals Interdisciplinary Pedagogical Actions to Optimize Engineering Undergraduate Written Production

10.29007/6434 ◽  
2018 ◽  
Author(s):  
Alicia Noceti
Keyword(s):  
Engineering Students ◽  
Time Window ◽  
Mother Tongue ◽  
Linguistic Features ◽  
Generic Structure ◽  
Food Engineering ◽  
Final Project ◽  
Written Production ◽  
Academic Genres ◽  
Audience Awareness

Writing is extremely challenging for engineering students. Navarro (2012) asserts that academic literacy in the mother tongue is similar to learning a foreign language as it involves immersion in a new culture. Food Engineering undergraduates (School of Food Science, University of Entre Ríos) face this difficulty when they have to write their Final Project. As a consequence, interdisciplinary actions were implemented by engineers and linguists (both in English and Spanish) in order to raise students´ awareness of this genre characteristics, to facilitate its production and to write relevant titles and abstracts. The importance of both title and abstract is paramount once the Final Projects are uploaded to the university website in order to attract readers. The objective of this study was to explore whether interdisciplinary actions could optimize undergraduates´ written production. All titles produced since the first Food Engineer graduated were collected. This corpus analysis revealed that titles were extremely short and provided very little information. Consequently, pedagogical activities were designed and implemented as from 2012. An exploration of antecedent or prior genre knowledge (Artemeva, N. & Fox., J., 2010) was carried out in different workshops. Generic structure, audience awareness, rhetorical functions and linguistic features studied in the English courses were activated. Writing seminars in Spanish were implemented in 5º year. In addition, undergraduates attended tutorials with the engineers and then and then interviews with the linguists. In several meetings students discussed titles and abstracts (in Spanish and English), designed their slides for the oral defense and rehearsed their oral presentations. The analysis of the corpus including all projects´ titles defended within the time window that included our actions indicated that students had activated their previous generic knowledge. Feedback from students, after graduation, demonstrated that interdisciplinary activities included language as an across the curriculum content and contributed to the adequate production of academic genres. Results may affect curricular design and decisions at the macro level since implementation of writing seminars along undergraduates´ trajectories has been positioned as a top priority.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

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