scholarly journals Student interactions during class activities: a mathematical model

2018 ◽  
Vol 9 (2) ◽  
pp. 91-105
Author(s):  
D. Brunetto ◽  
C. Andrà ◽  
N. Parolini ◽  
M. Verani
Keyword(s):  
Mathematical Model ◽  
Small Groups ◽  
Numerical Experiments ◽  
Opinion Dynamics ◽  
Mathematical Education ◽  
Student Interactions ◽  
Mathematics Classrooms ◽  
Proposed Model ◽  
And Mathematics ◽  
Different Levels

Abstract This paper aims at bridging Mathematical Modelling and Mathematics Education by studying the opinion dynamics of students who work in small groups during mathematics classrooms. In particular, we propose a model which hinges upon the pioneering work of Hegselmann and Krause on opinion dynamics and integrates recent results of interactionist research in Mathematical Education. More precisely, the proposed model incorporates the following features: 1) the feelings of each student towards the classmates (building upon the so-called \I can" -\you can" framework); 2) the different levels of preparation of the students; 3) the presence of the teacher, who may or may not intervene to drive the students towards the correct solution of the problem. Several numerical experiments are presented to assess the capability of the model in reproducing typical realistic scenarios.

Mathematical Simulation of Concrete Fatigue Strength under Cyclic Loading

2014 ◽  
Vol 1061-1062 ◽  
pp. 751-756
Author(s):  
Galina G. Kashevarova ◽  
Yuri E. Kurbatov ◽  
Roman V. Sevastyanov
Keyword(s):  
Mathematical Model ◽  
Physical Modeling ◽  
Numerical Experiments ◽  
Damage Accumulation ◽  
Applied Load ◽  
Concrete Material ◽  
Fatigue Characteristics ◽  
Mathematical And Physical Modeling ◽  
Building Designs ◽  
Different Levels

The problem of forecasting the durability of structures, buildings and constructions is one of the most urgent and important tasks in building sphere. In this paper, the authors propose a mathematical model of damage accumulation for the numerical simulation of the fatigue life of concrete. The results of numerical experiments with different levels of the applied load to the model are given, the fatigue characteristics of concrete material - Wohler curve - is built. On the basis of the developed method, the algorithm for research building designs using mathematical and physical modeling is formulated.

Numerical Simulation of the Coffee-ring Effect Inside Containers with Time-dependent Evaporation Rate

2021 ◽  
Author(s):  
Hyundong Kim ◽  
Junxiang Yang ◽  
Sangkwon Kim ◽  
Chaeyoung Lee ◽  
Sungha Yoon ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Numerical Experiments ◽  
Evaporation Rate ◽  
Gravitational Force ◽  
Time Dependent ◽  
Coffee Ring ◽  
Proposed Model ◽  
Coffee Ring Effect ◽  
Ring Effect

Abstract In this work, using a mathematical model and numerical simulation, we investigate the effect of time-dependent evaporation rates on stripe formation inside containers, which is driven by the coffee-ring effect. The coffee particles inside a container move according to random walk and under the gravitational force. Because of the non-uniform evaporation rate, we can observe stripe formation inside a container filled with liquid carrying coffee particles. We perform various numerical experiments to demonstrate the proposed model can simulate the stripe formation in a container.

Mathematical Model for the Tree Leaf Shape and Estimation of Leaf Mass

2012 ◽  
Vol 557-559 ◽  
pp. 2015-2020
Author(s):  
Yang Liu ◽  
Zhao Liu ◽  
Yu Zhang ◽  
Qian Yao Duan
Keyword(s):  
Mathematical Model ◽  
Numerical Experiments ◽  
Growth Regulation ◽  
Mass Density ◽  
Leaf Shape ◽  
Fibonacci Sequence ◽  
Leaf Mass ◽  
Proposed Model ◽  
Tree Leaf ◽  
The Relationship

The relationship between leaf shape and tree profile is discussed in this paper at first. Through analysis of Leonardo’s rule, Fibonacci sequence and growth regulation, we conclude that leaf shape is related to sunlight, tree profile, and the distribution of leaves. Then by constructing an integral equation of the leaf-mass density, a mathematical model is established to estimate leaf mass of a tree when the density nearly obeys gamma distribution. At last, some numerical experiments are presented to confirm the proposed model.

Task-Related Verbal Interaction and Mathematics Learning in Small Groups

1991 ◽  
Vol 22 (5) ◽  
pp. 366-389 ◽  
Author(s):  
Noreen M. Webb
Keyword(s):  
Small Group ◽  
Small Groups ◽  
Mathematics Learning ◽  
Group Interaction ◽  
Verbal Interaction ◽  
Mathematics Classrooms ◽  
Directed Learning ◽  
And Gender ◽  
And Mathematics ◽  
Group Compositions

The past fifteen years have shown a resurgence of interest in small-group, peer-directed learning in the classroom. This article reviews and analyzes the research linking task-related verbal interaction to learning in small groups in mathematics classrooms, as well as factors that have been shown to predict peer interaction in mathematics groups, and discusses strategies for shaping group interaction. Critical features of group interaction include the level of elaboration of help given and received and the responsiveness of help to the needs of students. Important predictors of group interaction included student ability, gender and personality, and group composition on ability and gender. Possible strategies for promoting effective small-group interaction include using certain group compositions, altering the reward structure, providing training in desirable verbal behavior, and structuring the group activity to require students to give explanations to each other.

scholarly journals Long-Time Analysis of a Time-Dependent SUC Epidemic Model for the COVID-19 Pandemic

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Youngjin Hwang ◽  
Soobin Kwak ◽  
Junseok Kim
Keyword(s):  
Mathematical Model ◽  
Epidemic Model ◽  
Numerical Experiments ◽  
Time Dependent ◽  
Test Results ◽  
Time Analysis ◽  
Transmission Parameter ◽  
Proposed Model ◽  
Long Time ◽  
Dependent Parameter

In this study, we propose a time-dependent susceptible-unidentified infected-confirmed (tSUC) epidemic mathematical model for the COVID-19 pandemic, which has a time-dependent transmission parameter. Using the tSUC model with real confirmed data, we can estimate the number of unidentified infected cases. We can perform a long-time epidemic analysis from the beginning to the current pandemic of COVID-19 using the time-dependent parameter. To verify the performance of the proposed model, we present several numerical experiments. The computational test results confirm the usefulness of the proposed model in the analysis of the COVID-19 pandemic.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

A model to account for the consequences of host nutrition on the outcome of gastrointestinal parasitism in sheep: model evaluation

Parasitology ◽  
2007 ◽  
Vol 134 (9) ◽  
pp. 1279-1289 ◽  
Author(s):  
D. VAGENAS ◽  
S. C. BISHOP ◽  
I. KYRIAZAKIS
Keyword(s):  
Mathematical Model ◽  
Worm Burden ◽  
Management Strategies ◽  
Sensitivity Analyses ◽  
Sheep Model ◽  
Host Nutrition ◽  
Gastrointestinal Parasitism ◽  
Different Characteristics ◽  
Nutritional Strategies ◽  
Different Levels

SUMMARYThis paper describes sensitivity analyses and expectations obtained from a mathematical model developed to account for the effects of host nutrition on the consequences of gastrointestinal parasitism in sheep. The scenarios explored included different levels of parasitic challenge at different planes of nutrition, for hosts differing only in their characteristics for growth. The model was able to predict the consequences of host nutrition on the outcome of parasitism, in terms of worm burden, number of eggs excreted per gram faeces and animal performance. The model outputs predict that conclusions on the ability of hosts of different characteristics for growth to cope with parasitism (i.e. resistance) depend on the plane of nutrition. Furthermore, differences in the growth rate of sheep, on their own, are not sufficient to account for differences in the observed resistance of animals. The model forms the basis for evaluating the consequences of differing management strategies and environments, such as breeding for certain traits associated with resistance and nutritional strategies, on the consequences of gastrointestinal parasitism on sheep.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

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