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Full-Text Articles in Applied Mathematics

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon Dec 2024

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon

Mechanical Engineering

This report aims to allow our sponsor, to review our design process of the Hitch Cart Landing Gear Prototype. In the design overview section of this report, we discuss the primary design modifications we made to the wheel mechanism of the existing hitch cart prototype, including the addition of the ACME screws and the folding brackets. This allows our sponsor to see the intended improvements made to the past prototype and understand the primary goal of our project. Then, in the implementation section, we cover the entire manufacturing process to allow our sponsor to understand what manufacturing steps must be …


(R2070) Poisson-Exponentiated Weibull Distribution: Properties, Applications And Extension, Alphonsa George, Dais George Jun 2024

(R2070) Poisson-Exponentiated Weibull Distribution: Properties, Applications And Extension, Alphonsa George, Dais George

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we introduce a new member of the Poisson-X family namely, the Poisson-exponentiated Weibull distribution. The statistical as well as the distributional properties of the new distribution are studied, and the performance of the maximum likelihood method of estimation is verified by a simulation study. The flexibility of the distribution is illustrated by a real data set. We develop and study a reliability test plan for the acceptance or rejection of a lot of products submitted for inspection when their lifetimes follow the new distribution. A real data example is also given to illustrate the feasibility of the …


Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, Prashant Shekhar Feb 2024

Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, Prashant Shekhar

Math Department Colloquium Series

Problems with current synovitis grading procedures

  • There has been a lack of reliability in grading these images in the medical community due to a lack of universally accepted diagnostic criteria [Momtazmanesh et al., 2022]
  • The human/machine variability creates an additional challenge in an efficient automated scoring system [Ranganath et al., 2022]
  • There is a lack of consistency between doctors in grading these images [Momtazmanesh et al., 2022]


On A Generator Of Copulas Method Based On A Duplication-Parameter Technique, Christophe Chesneau Feb 2024

On A Generator Of Copulas Method Based On A Duplication-Parameter Technique, Christophe Chesneau

International Journal of Emerging Multidisciplinaries: Mathematics

A two-dimensional copula is a function that accurately depicts the pattern of dependence between two quantitative variables. The demand for new two-dimensional copulas is as strong as ever, driven by the emergence of contemporary data from various sources. This paper makes a contribution to this area by presenting a novel modification of the well-known convex sums of copulas method. This modification is based on a thorough duplication-parameter technique: we transform one parameter into two, and we apply the classical convex sums method to only one of these parameters in the unit distribution setting. The main goals are (i) to solve …


Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich Jan 2024

Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich

Undergraduate Research Symposium

In this project, we explore radial solutions to the Total Variation Flow (TVF) equation with the help of the Sign Fast Diffusion Equation (SFDE) and prior results in the 1-dimensional case. Specifically for radial solutions, we derive equations and explicit solutions relating to the n-dimensional case. Lastly, we look at how level sets and (time) profiles change.


Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince Jan 2024

Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince

Numeracy

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of …


Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown Jan 2024

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

The Journal of Purdue Undergraduate Research

No abstract provided.


Machine Learning Of Big Data: A Gaussian Regression Model To Predict The Spatiotemporal Distribution Of Ground Ozone, Jerry Gu Jan 2024

Machine Learning Of Big Data: A Gaussian Regression Model To Predict The Spatiotemporal Distribution Of Ground Ozone, Jerry Gu

The Journal of Purdue Undergraduate Research

Tracking pollution levels on the ground is important to the environment and public health. One of the pollutants of concern is ozone, which, at high concentrations, can cause respiratory and cardiovascular problems. The National Center for Atmospheric Research (NCAR) has published valuable ozone data obtained from ground-based sensors installed at selected locations. Because it is unfeasible to measure the exact ozone levels everywhere at any time, it would be valuable to predict the temporal-spatial distributions of ozone concentration based on existing data. This would help us better understand the patterns and trends in the data and make better decisions to …


Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw Jan 2024

Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw

Faculty Publications and Other Works -- Mathematics

In this second progress report we expand upon our previous report and preliminary work. Specifically, we review some work on the numerical solution of single- and multi-species BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for each species for accurate simulation. …


A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine Jan 2024

A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine

Spora: A Journal of Biomathematics

The smallpox and poliomyelitis (polio) viruses were, at a time, one of the largest threats to global public health killing millions until global eradication campaigns were put into effect. Vaccination led to the eradication of smallpox and the elimination of polio for most of the world. However, polio continues to persist at endemic levels in Pakistan and Afghanistan. We developed ODE models of smallpox and polio to explore differences in transmission dynamics and determine if the underlying biology has made poliomyelitis more difficult to eradicate. Our model analysis shows there are multiple factors which should allow polio to have a …


A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry Jan 2024

A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry

Spora: A Journal of Biomathematics

Rhinoceros populations in Africa are in peril largely due to the high value of their horns and the poaching that ensues. The strategy of legalizing the international trade of rhino horn is receiving increased support among both the people and government officials in Africa. Many in the international conservation community remain opposed to the idea. The legalization strategy is straightforward in theory: legalizing the trade of rhino horn will introduce a large quantity of horn to the market, the increased supply will lead to lower prices for rhino horn, and lower prices will reduce the overall poaching pressure these animals …


The Influence Of Green Building Design On Tourists' Intention To Stay In Eco-Friendly Hotels: A Study On Perceptions And Preferences, Enas Al Sayed Salama Dr., Gehad Nasr Abdelsalam Dr. Jan 2024

The Influence Of Green Building Design On Tourists' Intention To Stay In Eco-Friendly Hotels: A Study On Perceptions And Preferences, Enas Al Sayed Salama Dr., Gehad Nasr Abdelsalam Dr.

Journal of Engineering Research

Green building design involves integrating sustainable and environmentally friendly practices into the construction and operation of buildings, including hotels, with the goal of minimizing the adverse impact on the environment. This paper delves into the pivotal role of green building design and eco-service provision within the context of green hotels. The aim is to investigate the interconnections among tourists' environmental concerns, their perceived significance of green building design, and their intention to choose green hotels.

To enhance the understanding of tourist behavior and its implications for tourism in Egypt, a questionnaire was administered in Sharm El Sheikh, a prominent Egyptian …


Experimental Study Of Bent Glass Curtain Walls., Sarah Said Abd El Kariem, Moustafa El Shami, Mahmoud El Nagar Jan 2024

Experimental Study Of Bent Glass Curtain Walls., Sarah Said Abd El Kariem, Moustafa El Shami, Mahmoud El Nagar

Journal of Engineering Research

A Bent Laminated Glass is commonly used in the residential and commercial structures, its methodology is not present in the curves and tables at the ASTM E1300. Therefore, it has become a need for architects to use basis for this type of glass. To the best of authors ‘knowledge, no one study the bent laminated glass in details. A variety of safety glass that has lately gained popularity in the construction sector is modern laminated glass. Given that it offers a safe failover capability, it is perfect for the automotive industry. Double-lite glass is produced using two or more …


Market Analysis And Bidding Strategy Of Hybrid Renewable Energy Systems Considering Emissions, Fatma Elzahraa, Mohamed Elnemr, Samir Dawoud Jan 2024

Market Analysis And Bidding Strategy Of Hybrid Renewable Energy Systems Considering Emissions, Fatma Elzahraa, Mohamed Elnemr, Samir Dawoud

Journal of Engineering Research

The competition in the electricity markets makes it difficult to choose a suitable strategy for maximizing profit while reducing harmful emissions. To have an adequate energy price for consumers while minimizing the harmful emissions to the atmosphere and maximizing profits of all participants in the electricity market needs an aggressive bidding strategy. Developing these bidding strategies with the integration of renewable energy (RE) in the electricity market became important. This research studies various bidding strategies for maximizing profits in the deregulated energy market since participants are keen on developing bidding strategies considering emissions. These bidding strategies will consider the integration …


Effects Of Fuel Equivalence Ratio And Swirl Vane Angles On Premixed Burner Turbulent Flame Combustion Characteristics, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng. Jan 2024

Effects Of Fuel Equivalence Ratio And Swirl Vane Angles On Premixed Burner Turbulent Flame Combustion Characteristics, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

A turbulent flow field has a major effect on the premixed flame structure and temperature distribution that specifically determines the effectiveness of the burned fuel and the amounts of produced emissions. However, the premixed flame tangential and axial velocity distribution through the flame length help to predict the combustion and emissions attributes of the burned fuel. In this regard, an experimental and analytical investigation on premixed turbulent burners at different equivalence fuel-air ratios with different swirl vane angles has been achieved in the present work to assess the combustion performance and emissions characteristics. A theoretical methodology was carried out to …


Enhancing The Performance Of Conventional Solar Still Using The Nano-Doped Paint (Ndp) Coating, Hagar Alm-Eldin Bastawissi Prof.Dr, Nermin Elgendy Engineer, Ayman R. El-Tohamy Jan 2024

Enhancing The Performance Of Conventional Solar Still Using The Nano-Doped Paint (Ndp) Coating, Hagar Alm-Eldin Bastawissi Prof.Dr, Nermin Elgendy Engineer, Ayman R. El-Tohamy

Journal of Engineering Research

Nations are throughout the entire globe continuously confronting the problem of potable water shortage. Recently, it has been thought that using solar energy to desalinate brackish water offers a practical answer to the world's water crises. The output of these stills, is meager, and academics haven't done much to boost it in any way. Solar distillers have been proposed as an efficient method to produce potable water. In recent years, saltwater has produced drinking water by various ways. The efficiency of a solar distiller is significantly influenced by various factors, most important factor of them is the absorber surface. In …


Engine Performance And Emissions Improvement Study On Direct Injection Of Diesel/Ammonia Dual Fuel By Adding Cng As Partially Premixed Charge, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi Prof. Dr., Mohammed Osama Elsamadony Dr. Eng., Abdallah Salem Abdalhadi Eng. Jan 2024

Engine Performance And Emissions Improvement Study On Direct Injection Of Diesel/Ammonia Dual Fuel By Adding Cng As Partially Premixed Charge, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi Prof. Dr., Mohammed Osama Elsamadony Dr. Eng., Abdallah Salem Abdalhadi Eng.

Journal of Engineering Research

Researchers have recently moved on in their studies to find a solution to prevent or reduce this problem. There have been directions taken by researchers to solve the problem, including, replacing fossil fuels with environmentally friendly types or by combining two or more types of fuel. This is by modifying fuel injection systems as appears in the PCCI, RCCI, or HCCI systems, or working to integrate the two trends by using new injection systems and burning alternative fuels with fossil fuels. Therefore, the trend has good results on the specific consumption of fuel, raising thermal efficiency, and working to reduce …


Experimental Study On The Impact Of Secondary Air Injection And Different Swirl Van Angles On Premixed Turbulent Flame Propagation And Emission Behaviors, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng. Jan 2024

Experimental Study On The Impact Of Secondary Air Injection And Different Swirl Van Angles On Premixed Turbulent Flame Propagation And Emission Behaviors, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

The objective of the present paper is to investigate experimentally the flame characteristics utilizing different secondary air inlet direction for different primary air swirl numbers and equivalence fuel-air ratios. In this study, an experimental test rig was carried out to investigate the flame temperature and emission behavior with flame length at the equivalence fuel-air ratios taken0.96, 0.80, 0.70, and 0.60, and swirl vane angles were varied as 20, 30, 45, and 60° to generate different swirl numbers of 0.26, 0.416, 0.71 and 1.23, respectively. In addition to the introduction of secondary air in test combustor, whereas the primary air and …


The Effect Of An Existing Tunnel And A Newly Excavated Tunnel On Ground Loss Beneath Sand Slope-3d Numerical Study, Ashraf Nazir, Ahmed Nasr, Asmaa Saeed Jan 2024

The Effect Of An Existing Tunnel And A Newly Excavated Tunnel On Ground Loss Beneath Sand Slope-3d Numerical Study, Ashraf Nazir, Ahmed Nasr, Asmaa Saeed

Journal of Engineering Research

Abstract- Most researchers perform their numerical models for tunnels by modeling perfectly horizontal ground surfaces above the tunnels. The prediction of surface settlement of a sandy slope due to the interaction mechanism between the slope and the tunnels is one of the critical problems in urban areas. As a result, in this work, a numerical analysis using PLAXIS 3D TUNNEL has been performed to investigate the effect of tunnel excavation on the deformation of a shallow sandy slope, and empirically by the Herzog method. The study also assesses the influence of parameters on slope deformation that have not been …


Utilization Of Adomain Decomposition Method And Laplace Transform To Study Fractional Kdv And Fractional Benjamin Models Via Caputo Fractional Operator, Muhammad Sohail, Hina Younis Jan 2024

Utilization Of Adomain Decomposition Method And Laplace Transform To Study Fractional Kdv And Fractional Benjamin Models Via Caputo Fractional Operator, Muhammad Sohail, Hina Younis

International Journal of Emerging Multidisciplinaries: Mathematics

In the present study, we implement Adomian decomposition method (ADM) to solve fractional potential Korteweg-de Vries (p-KdV) and Benjamin models. The investigated approach is a hybrid of the Adomian decomposition method and the Laplace transform, and the fractional operator developed by Caputo has been utilized in the present research. In a vast accessible domain, the proposed solution tackle impacts and regulates the gained conclusions. Additionally, it provides a simple technique for determining the point of convergence region of the derived result. To ensure that the LADM is realistic and dependable, mathematical simulations for each equation were run, and the results …


Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans Jan 2024

Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans

Spora: A Journal of Biomathematics

Compartmental modeling serves as a necessary framework in many fields, especially biomathematics and ecology. This article introduces readers to a user-friendly approach to constructing compartmental models and solving the resulting systems of differential equations to simulate real-world applications. The platform used is Berkeley Madonna, a software package that has an intuitive graphical interface which empowers users—even those with limited mathematical and programming backgrounds—to focus on modeling concepts rather than mathematical or programming intricacies. This makes Berkeley Madonna an ideal platform for students, educators, and researchers.


Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr Jan 2024

Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr

CODEE Journal

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …


Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum Jan 2024

Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum

CODEE Journal

Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …


Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist Jan 2024

Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist

CODEE Journal

In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.


Modeling Aircraft Takeoffs, Catherine Cavagnaro Jan 2024

Modeling Aircraft Takeoffs, Catherine Cavagnaro

CODEE Journal

Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …


Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier Jan 2024

Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier

CODEE Journal

A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.


Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), Marguerite R. Butler, Jana Hrncirova, Meredith Clark, Sucharita Dutta, John B. Cooper Jan 2024

Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), Marguerite R. Butler, Jana Hrncirova, Meredith Clark, Sucharita Dutta, John B. Cooper

Chemistry & Biochemistry Faculty Publications

Surface-enhanced Raman spectroscopy (SERS) is an ultrasensitive spectroscopic technique that generates signal-enhanced fingerprint vibrational spectra of small molecules. However, without rigorous control of SERS substrate active sites, geometry, surface area, or surface functionality, SERS is notoriously irreproducible, complicating the consistent quantitative analysis of small molecules. While evaporatively prepared samples yield significant SERS enhancement resulting in lower detection limits, the distribution of these enhancements along the SERS surface is inherently stochastic. Acquiring spatially resolved SERS spectra of these dried surfaces, we have shown that this enhancement is governed by a power law as a function of analyte concentration. Consequently, by definition, …


Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen Jan 2024

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …


Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage Dec 2023

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …


Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, Miraziz Vorisovich Sagatov Dec 2023

Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

In this work, based on the theory of barycentric coordinates and simplexes, a linear interpolation method is proposed for modeling and controlling the operation of multiparameter converters. It has been determined that the linear interpolation method minimizes the structural diagram of a computing device, which makes it possible to more accurately determine the metrological characteristics of multiparameter measuring transducers and offer effective methods and means for processing primary measurement information. A theorem has been proven about a linear interpolating polynomial of a function of many variables, which will allow us to judge the property of linearization of multidimensional quantities from …