Mathematical Modeling Research Papers - Academia.edu (original) (raw)

Several components shows that the process of algebraic thinking on students in solving problems. One of these components is the process of using algebra as a tool for doing mathematical modelling. This study aims to reveal how the... more

Several components shows that the process of algebraic thinking on students in solving problems. One of these components is the process of using algebra as a tool for doing mathematical modelling. This study aims to reveal how the students' competency in making mathematical modelling for solving an algebraic problem. The descriptive qualitative study design was used to obtain an overview of the mathematical modelling competencies of nine students (15-16 years old) in Pekanbaru, Riau Province. Each participant received a test that contains an algebraic problem. The results of this study show that when students do mathematical modelling there are several errors as follows: (1) failure in making suppositions for the problem and simplifying the given situation; (2) failure in recognizing quantities that influence the given situation, to identify the key variable; (3) failure in construct relation between variable; and (4) failure in solving question within mathematical modelling.

Considering the undeniable importance of petroleum prices in making decisions with regard to politics and economy, Artificial Neural Networks as one of the most reliable methods in solving nonlinear problems was used in the present... more

Considering the undeniable importance of petroleum prices in making decisions with regard to politics and economy, Artificial Neural Networks as one of the most reliable methods in solving nonlinear problems was used in the present research to forecast petroleum prices. As for the training of the neural network, three consecutive years of data were used. Identifying first the most effective factors on the petroleum price, efforts were made to forecast the next-day as well as the next-week prices. Using these factors for three consecutive past days as the neural network inputs, the petroleum price for the following day was predicted. The data for the same day past three consecutive weeks were then used as inputs to the network to predict the price for the same day of the following week. On the daily time basis, the trained network provided an acceptable response with about 80% accuracy. Using a weekly time basis then, it was found that the network was able to predict with a 60%, accuracy. Noting that a higher risk is associated with the weekly than the daily time interval, such a performance in forecasting the petroleum price one week ahead of time can be considered acceptable indeed. These predicted prices are presented, indicating a quite acceptable set of results when compared with the actual values.

This paper analyses the current progression of the coronavirus pandemic, with the help of a mathematical model based on differential equations. The model has been inspired by the standard SIR (Susceptible-Infected-Recovered) model in... more

This paper analyses the current progression of the coronavirus pandemic, with the help of a mathematical model based on differential equations. The model has been inspired by the standard SIR (Susceptible-Infected-Recovered) model in epidemiology. The model takes the effect of co-morbidities and vaccination into account. The susceptible population is split into healthy and co-morbid sub-compartments. A series of graphs is presented for the visual depiction of the situation at hand in the Indian context. Finally, a survey (carried out through an online questionnaire) based analysis of the perception of vaccination in the masses in general, and the medical community in particular, has also been presented.

Owing to the wide utilization of heat exchangers in industrial processes, their cost minimization is an important target for both designers and users. Traditional design approaches are based on iterative procedures which gradually change... more

Owing to the wide utilization of heat exchangers in industrial processes, their cost minimization is an important target for both designers and users. Traditional design approaches are based on iterative procedures which gradually change the design and geometric parameters to satisfy a given heat duty and constraints. Although well proven, this kind of approach is time consuming and may not lead to cost effective design as no cost criteria are explicitly accounted for. The present study explores the use of nontraditional optimization technique: called simulated annealing (SA), for design optimization of shell and tube heat exchangers from economic point of view. The optimization procedure involves the selection of the major geometric parameters such as tube diameters, tube length, baffle spacing, number of tube passes, tube layout, type of head, baffle cut etc and minimization of total annual cost is considered as design target. The presented simulated annealing technique is simple ...

Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual's blood glucose levels, and its main regulator, insulin. These... more

Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual's blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine''. From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient's current physiological state. We developed a simple mathematical model that accurately simulates the dynamics between glucose, insulin, and pancreatic beta\betabeta-cells throughout disease progression with constraints to maintain biological relevance. The current framework is clearly capable of tracking the patient's current progress through the disease, dependent on factors such as latent insulin resistance or an attrite beta\betabeta-cell population. Further interests would be to develop tools that allow the direct and feasible testing of how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.

We discuss a model illustrating how the outcome of repeated endotoxin administration experiments can emerge as a natural consequence of the tightly regulated signaling pathways and also highlight the importance of a dual negative feedback... more

We discuss a model illustrating how the outcome of repeated endotoxin administration experiments can emerge as a natural consequence of the tightly regulated signaling pathways and also highlight the importance of a dual negative feedback regulation including PI3K/Akt and IRAK-M (IRAK3). We identify the relative time scales of the onset and the magnitude of the stimulus as key determinants of outcome in repeated administration experiments. The results of our simulations involve potentiated response, tolerance, and protective tolerance. Moreover, the knockout of negative regulators shows that IRAK-M is a necessary and sufficient factor for generation of endotoxin tolerance (ET). The effects of the knockout of IRAK-M gene or administration of PI3K inhibitor do yield predictions that have been verified experimentally. Finally, the pretreatment with PI3K inhibitor reveals the interaction between these two negative regulations.

The present paper describes the development of a monitoring, analysis and diagnosis system of power plant equipments based on strain measurements. The objective is to help companies increase availability and reduce maintenance costs.... more

The present paper describes the development of a
monitoring, analysis and diagnosis system of power plant
equipments based on strain measurements. The objective
is to help companies increase availability and reduce
maintenance costs. The aim is the integrity evaluation of
a main steam and a hot reheat steam piping through
inspection, strain monitoring and computational
diagnosis.
The benefits are, among others, reduction in the
uncertainty of the remaining life prediction and reduction
of work, through process automation and integration and
real time monitoring (through the Internet) of the
operational condition of the equipment. Thus, greater
confidence and availability of the monitored generating
unit is sought as well as cost reduction as a consequence
of reduced frequency of unnecessary unit stops and
greater speed in decision making due to more precise
follow up of the operational condition of the targetequipment
and of its remaining life.

"Formal methods aim to apply mathematically-based techniques to the development of computer-based systems, especially at the specification level, but also down to the implementation level. This aids early detection and avoidance of errors... more

"Formal methods aim to apply mathematically-based techniques to the development of computer-based systems, especially at the specification level, but also down to the implementation level. This aids early detection and avoidance of errors through increased understanding. It is also beneficial for more rigorous testing coverage. This talk presents the use of formal methods on a real project. The Z notation has been used to specify a large-scale high integrity system to aid in air traffic control. The system has been implemented directly from the Z specification using SPARK Ada, an annotated subset of the Ada programming language that includes assertions and tool support for proofs. The Z specification has been used to direct the testing of the software through additional test design documents using tables and fragments of Z. In addition, Mathematica has been used as a test oracle for algorithmic aspects of the system. In summary, formal methods can be used successfully in all phases of the lifecycle for a large software project with suitably trained engineers, despite limited tool support.
"

Mathematical modeling is an important step for developing many advanced technologies in various domains such as network security, data mining and etc… This lecture introduces a process that the speaker summarizes from his past practice... more

Mathematical modeling is an important step for developing many advanced technologies in various domains such as network security, data mining and etc… This lecture introduces a process that the speaker summarizes from his past practice of mathematical modeling and algorithmic solutions in IT industry, as an applied mathematician, algorithm specialist or software engineer , and even as an entrepreneur. A practical problem from DLP system will be used as an example for creating math models and providing algorithmic solutions.

In this paper we have established a mathematical model on diabetes mellitus under the influence of ingested glucose where glucose and insulin both are affected by the externally ingested glucose. The ingested glucose is the external... more

In this paper we have established a mathematical model on diabetes mellitus under the influence of ingested glucose where glucose and insulin both are affected by the externally ingested glucose. The ingested glucose is the external source of glucose that is coming from the source of food and assumed to follow the logistic growth. With the introduction of ingested glucose and its impact on the glucose as well as on insulin, a three variable mathematical model is established. The stability of the model is discussed under various equilibrium conditions. Numerical simulations are used to validate and describe the stability of the proposed model.

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph... more

Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based on í µí»¼-cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.

In this project, we have developed the basic codes of the Kalman filter by applying to a linear system and we have validated that by the Sequential Importance Sampling (SIS)algorithm of Particle filter using Monte Carlo simulations. The... more

In this project, we have developed the basic codes of the Kalman filter by applying to a linear system and we have validated that by the Sequential Importance Sampling (SIS)algorithm of Particle filter using Monte Carlo simulations. The problem of degeneracy in the SIS Algorithm has also been explored in the project.

Abstract-this paper presents a study of the approaches taken to model and simulate power systems of an industrial plant. Even the best-designed electric systems occasionally experience short-circuits resulting in abnormally high currents.... more

Abstract-this paper presents a study of the approaches taken to model and simulate power systems of an industrial plant. Even the best-designed electric systems occasionally experience short-circuits resulting in abnormally high currents. To predict the behavior of these short ...

Разработана математическая модель для расчета температуры полосы при горячей прокатке на стане 2000 ПАО «Северсталь», основанная на методе конечных разностей. Созданный компьютерный модуль, реализующий эту модель, включен в интегральную... more

Разработана математическая модель для расчета температуры полосы при горячей прокатке на стане 2000 ПАО «Северсталь», основанная на методе конечных разностей. Созданный компьютерный модуль, реализующий эту модель, включен в интегральную компьютерную модель горячей прокатки на стане 2000 (STAN 2000), с помощью которой проведены расчеты температуры в середине поверхности 164 полос 30 марок стали (с широким диапазоном изменения химического состава) после второй, пятой и 12-й клетей, а также перед смоткой в рулон. Полученные результаты хорошо согласуются с показаниями соответствующих пирометров. Средние абсолютные погрешности расчета отмеченных температур соответственно: 8,4; 10,6; 14,1 и 16,4 °C.