The Relationship between Students’ Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

2015 ◽  
Vol 2 (1) ◽  
pp. 239 ◽  
Author(s):  
Ozgul Kartal ◽  
Beyza Aksu Dunya ◽  
Heidi A. Diefes-Dux ◽  
Judith S. Zawojewski
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Assessments ◽  
The Relationship

Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision

2017 ◽  
Author(s):  
Terrence Fine
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Theory Of Measurement ◽  
Belief Functions ◽  
Standard Practice ◽  
Mathematical Probability ◽  
Comparative Probability ◽  
The Relationship ◽  
Standard Probability

This chapter challenges the nearly universal reliance upon standard mathematical probability for mathematical modeling of chance and uncertain phenomena, and offers four alternatives. In standard practice, precise assignments are made inappropriately, even to the occurrences of events that may be unobservable in principle. Four familiar examples of chance or uncertain phenomena are discussed, about which this is true. The theory of measurement provides an understanding of the relationship between the accuracy of information and the precision with which the phenomenon under examination should be modeled mathematically. The model of modal or classificatory probability offers the least precision. Comparative probability, plausibility/belief functions and upper/lower probabilities are carefully considered. The selectable precision of these alternative mathematical models of chance and uncertainty makes for an improved range of levels of accuracy in modeling the empirical domain phenomena of chance, uncertainty, and indeterminacy. Knowledge of such models encourages further thought in this direction.

scholarly journals Applying Methods of Mathematical Modeling in Cattle Breeding

2019 ◽  
Vol 8 (12) ◽  
pp. 185-187 ◽  
Keyword(s):  
Mathematical Modeling ◽  
Animal Husbandry ◽  
The Body ◽  
Body Parts ◽  
Method Of Least Squares ◽  
Linear Measurements ◽  
Cattle Breeding ◽  
Modern Methods ◽  
Meat Productivity ◽  
The Relationship

In this manuscript has presented the results of applying modern methods of mathematical modeling in animal husbandry. To conduct the research has used the method of least squares, which has reflected in the work by approximation probabilistic non-linear relations, making it possible to establish the relationship between different measurements the body parts of animal and meat productivity, and linear measurements of the udder.

scholarly journals Mathematical Modelling and Optimization of Risk Analysis in Emergencies

2018 ◽  
Vol 7 (4.7) ◽  
pp. 209
Author(s):  
Korneev A.M ◽  
Salfetnikov M.V
Keyword(s):  
Mathematical Modeling ◽  
Decision Making ◽  
Mathematical Modelling ◽  
Systematic Approach ◽  
Natural Properties ◽  
Multi Level ◽  
Constituent Elements ◽  
State Of The Environment ◽  
The Relationship ◽  
Modelling And Optimization

In current work methods of intellectual support of acceptance of administrative decisions on risks of occurrence of extreme situations are considered. The relationship between human activity, the emergence emergencies and the state of the environment is systemic. An important role is given to the analysis of the causes of incidents and emergencies of technogenic nature. Emergencies refers to complex multi-level systems, so a systematic approach is needed to model them. When choosing models of complex systems, factors related to the natural properties of the constituent elements and subsystems, and the patterns of the functioning of the system as a whole are investigated. Various methods of mathematical modeling are used to determine the risks of emergencies. The problem of optimization of decision-making algorithms in the event of emergencies is solved.  

scholarly journals A Mathematical Modeling Approach to the Cort-Fitness Hypothesis

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
F El Moustaid ◽  
S J Lane ◽  
I T Moore ◽  
L R Johnson
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Reproductive Strategies ◽  
Evolutionary Biology ◽  
Positive Relationship ◽  
Negative Relationship ◽  
Environmental Challenges ◽  
Field Endocrinology ◽  
Empirical Tests ◽  
The Relationship

Abstract The Cort-Fitness Hypothesis has generated much interest from investigators integrating field endocrinology with evolutionary biology, ecology, and conservation. The hypothesis was developed to test the assumption that if glucocorticoid levels increase with environmental challenges and fitness decreases with environmental challenges, then there should be a negative relationship between baseline glucocorticoid levels and fitness. Indeed, studies across diverse taxa have found that the relationship between baseline glucocorticoid levels and fitness are not consistent: some studies show a positive relationship, others negative, and some show no correlation. Hence, a deeper understanding of the mechanisms underlying the relationship between baseline glucocorticoid levels, environmental challenges, and fitness is needed. We propose a mathematical model representing the links between baseline glucocorticoid levels, environmental challenges, and fitness. Our model describes how variation in the predictability and intensity of environmental challenges, reproductive strategies, and fitness metrics can all contribute to the variability observed in empirical tests of the Cort-Fitness Hypothesis. We provide qualitative results showing that much of the inconsistency in previous studies can be explained and we discuss how the model can be used to inform future Cort-Fitness studies.

Modeling of braiding parameter impact on pore size and porosity in a tubular braiding fabric

e-Polymers ◽  
2017 ◽  
Vol 17 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Chaojing Li ◽  
Xiaoming Wang ◽  
Fan Zhao ◽  
Fujun Wang ◽  
Zou Ting ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Pore Size ◽  
Connective Tissues ◽  
Technical Parameters ◽  
Structure Control ◽  
Yarn Diameter ◽  
Model Pore ◽  
The Relationship ◽  
Pore Structure Control ◽  
Cell Adhesion And Proliferation

AbstractTubular braiding fabric is widely used in developing tissue-engineered scaffolds, and is especially suitable for connective tissues like ligaments and tendons. The pore size and porosity of braiding structure scaffolds not only highly affect cell adhesion and proliferation, but also influence the mechanical behavior of those scaffolds. It is important to develop braiding scaffolds with controllable pore size and distribution. The purpose of this work is to add insight to the mechanics of this passive pore structure control system. Thus, some constitutive equations were established to reveal the relationship between braiding technical parameters (including the number of spindles, braiding structure, cylindrical mandrel radius, and yarn diameter) and the pore size, the porosity of tubular braiding fabric by the mathematical modeling method. Through this model, pore size and the porosity of the tubular braiding scaffold can be precisely controlled by quantitatively adjusting braiding technical parameters. Furthermore, the reliability and accuracy of this model were verified by the experimental data.

scholarly journals Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells

2021 ◽  
Vol 12 ◽  
Author(s):  
Isabella Marinelli ◽  
Patrick A. Fletcher ◽  
Arthur S. Sherman ◽  
Leslie S. Satin ◽  
Richard Bertram
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Β Cells ◽  
Pancreatic Β Cells ◽  
Intracellular Ca ◽  
Metabolic Oscillations ◽  
Insulin Exocytosis ◽  
The Relationship ◽  
Contradictory Data ◽  
Oscillatory Processes

Insulin is secreted in a pulsatile pattern, with important physiological ramifications. In pancreatic β-cells, which are the cells that synthesize insulin, insulin exocytosis is elicited by pulses of elevated intracellular Ca2+ initiated by bursts of electrical activity. In parallel with these electrical and Ca2+ oscillations are oscillations in metabolism, and the periods of all of these oscillatory processes are similar. A key question that remains unresolved is whether the electrical oscillations are responsible for the metabolic oscillations via the effects of Ca2+, or whether the metabolic oscillations are responsible for the electrical oscillations due to the effects of ATP on ATP-sensitive ion channels? Mathematical modeling is a useful tool for addressing this and related questions as modeling can aid in the design of well-focused experiments that can test the predictions of particular models and subsequently be used to improve the models in an iterative fashion. In this article, we discuss a recent mathematical model, the Integrated Oscillator Model (IOM), that was the product of many years of development. We use the model to demonstrate that the relationship between calcium and metabolism in beta cells is symbiotic: in some contexts, the electrical oscillations drive the metabolic oscillations, while in other contexts it is the opposite. We provide new insights regarding these results and illustrate that what might at first appear to be contradictory data are actually compatible when viewed holistically with the IOM.

Mathematical Modeling Of Air Distribution In Ventilation Systems Of Residential Buildings

2019 ◽  
pp. 72-80
Keyword(s):  
Mathematical Modeling ◽  
Residential Buildings ◽  
Air Distribution ◽  
Airflow Rate ◽  
Calculation Algorithm ◽  
Pressure Losses ◽  
Relationship Of ◽  
Exhaust Valves ◽  
The Relationship ◽  
Ventilation Systems

The main provisions of mathematical modeling of air regime of residential buildings are considered; the solution of this problem on the basis of the theory of hydraulic circuits is also offered. The dependences describing the relationship of pressure losses and airflow rate for individual elements of ventilation systems are given. The formulas making it possible to take into account with higher accuracy the characteristics of fans, supply and exhaust valves, window and door units included in the aerodynamic network of ventilation systems are proposed. The influence of the method of setting the dependence of airflow on the pressure drop on the results of mathematical modeling is evaluated. Examples of calculation schemes and graphs of some ventilation systems, calculation algorithm, and simulation results of air conditions of buildings with due regard for changes in the characteristics of ventilation elements at the operation stage are presented.

USE OF MATHEMATICAL MODELING UNIT FOR SOLVING PROBLEMS IN ELECTRICAL ENGINEERING

2020 ◽  
Author(s):  
R.M. Turaev ◽  
Keyword(s):  
Mathematical Modeling ◽  
Electrical Engineering ◽  
Charging Time ◽  
Sinusoidal Current ◽  
The Relationship

The article is devoted to the simulation of the processes of charging the capacitor in the chain of the single-half straightener. Using the Mathcad package will simulate the process of charging the capacitor in the sinusoidal current chain. The created model will take data to understand the relationship between different parameters and charging time of the capacitor.

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