Applied Mathematics Commons^™

Mitigation Impact Of Statewide Non-Pharmaceutical Policies On Covid-19: An Application Of Infectious Disease Transmission Model And Partially Observed Markov Process To New Mexico, Xingya Ma

Mathematics & Statistics ETDs

This thesis is an application of epidemiological models for infectious disease transmission and the use of partially observed Markov process (POMP) for model fitting. It focuses on COVID-19 pandemic in the state of New Mexico. The analysis covered March 2020 to June 2021. Daily data of COVID19 cases and deaths and a daily index of eleven statewide government non-pharmaceutical intervention (NPI) policies were collected from six public sources and were validated. These data were integrated through the Susceptible-Exposed-Infected-Removed (SEIR) model. Estimated daily transmission rates between the model compartments quantify the impact of the mitigation policies, and show that transmission rates …

Uniqueness Of Steady State Positive Solutions To A General Elliptic System With Dirichlet Boundary Conditions, Joon Hyuk Kang

Faculty Publications

The purpose of this paper is to give conditions for the uniqueness of positive solution to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rⁿ. Also considered are the effects of perturbations on the coexistence state and uniqueness.

Matemáticas Financieras Aplicadas, Odair Triana Calderón

Ciencias Administrativas, Económicas y Contables

Teniendo en cuenta que las matemáticas son una herramienta fundamental en las Ciencias Administrativas, especialmente en las finanzas. MATEMÁTICAS FINANCIERAS APLICADAS, busca dar solución a aquellos problemas de tipo económico y financiero que se presentan en una economía, organización o núcleo familiar, mediante la utilización de modelos matemáticos y la aplicación en Microsoft Excel.

El texto realiza un estudio de problemas de inversión y financiación, donde el cálculo de intereses con base en un capital y atendiendo a variables como el tiempo y las tasas de rendimiento, permite el desarrollo de casos utilizando el interés simple e interés compuesto.

Por …

Ambientes De Inclusión Para El Desarrollo Del Pensamiento Numérico Con Población Con Síndrome De Down, Luisa Valeria Escobar Buitrago, Ingry Yuliana Torres Garzón, Juan David Firigua Bejarano

Educación

La importancia de tratar sobre una educación inclusiva es hacer que la humanidad obtenga la aceptación hacia la diversidad, donde se encuentre un mundo lleno de posibilidades reconociendo todos los tipos de población entre ella las personas con Síndrome de Down, lo cual consiste en que la educación esté centrado en el respeto y la valoración de la diversidad, haciendo un enfoque general en las necesidades que esta población tiene, desarrollando habilidades para su desenvolvimiento tanto personal como laboral en determinada sociedad, por lo tanto el objetivo principal de este trabajo es desarrollar el pensamiento numérico de los estudiantes de …

(R1981) Evaluating The Mhd Non-Newtonian Fluid Motion Past A Stretching Sheet Under The Influence Of Non-Uniform Thickness With Dufour And Soret Effects Implementing Chebyshev Spectral Method, M. M. Khader, Ram Prakash Sharma

Applications and Applied Mathematics: An International Journal (AAM)

A study is made on the development of hydromagnetic non-Newtonian Casson and Williamson boundary layer flow in an electrically conducting fluid in the presence of heat flux, mass flux, and the uniform magnetic field. The governing non-linear system of PDEs is transformed into a set of non-linear coupled ODEs and then treated numerically by using the Chebyshev spectral method. The velocity, temperature, and concentration fields of the steady boundary layer flow, which are generated by the stretched sheet with non-uniform thickness are discussed. The simultaneous effects of the external magnetic field, Soret and Dufour phenomena with reference have been explored. …

(R1886) Effect Of Aggregation Function In Moma-Plus Method For Obtaining Pareto Optimal Solutions, Alexandre Som, Abdoulaye Compaoré, Kounhinir Somé, Blaise Somé

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we have proposed some variants of MOMA-Plus method that we have numerically tested for the resolution of nonlinear multiobjective optimization problems. This MOMA-Plus method and variants differ from each other by the choice of aggregation functions in order to reduce the number of objective functions. The theoretical results allowing us to use these aggregation functions to transform multiobjective optimization problems into single objective optimization problems are proved by two theorems. This study has highlighted the advantages of each aggregation function according to the type of Pareto front of the optimization problem. Six benchmarks test problems have been …

(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …

(R1894) Invariant Solution For Two-Dimensional And Axisymmetric Jet Of Power-Law Fluids, Bhavixa Bhagat, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An invariant solution is derived using the Lie symmetry technique for steady laminar two-dimensional and axisymmetric boundary layer jet flow of incompressible power-law fluids with appropriate boundary conditions. Using symmetry, the nonlinear partial differential equation of the jet flow problem is transformed into a nonlinear ordinary differential equation. The resultant nonlinear ordinary differential equation with boundary conditions is converted to an initial value problem using the Lie symmetry technique. A numerical solution for the resulting initial value problem is derived using Fehlberg’s fourth-fifth order Runge-Kutta method through Maple software. The graphical representation of the characteristics of the velocity field for …

(R1964) Solving Multi-Objective Linear Fractional Programming Problems Via Zero-Sum Game, Gizem Temelcan, Inci Albayrak, Mustafa Sivri

Applications and Applied Mathematics: An International Journal (AAM)

This study presents a hybrid algorithm consisting of game theory and the first order Taylor series approach to find compromise solutions to multi-objective linear fractional programming (MOLFP) problems. The proposed algorithm consists of three phases including different techniques: in the first phase, the optimal solution to each LFP problem is found using the simplex method; in the second phase, a zero-sum game is solved to determine the weights of the objective functions via the ratio matrix obtained from a payoff matrix; in the last phase, fractional objective functions of the MOLFP problem are linearized using the 1st order Taylor series. …

(R1971) Analysis Of Feedback Queueing Model With Differentiated Vacations Under Classical Retrial Policy, Poonam Gupta, Naveen Kumar, Rajni Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical …

(R1984) Analysis Of M^[X1], M^[X2]/G1, G_2^(A,B)/1 Queue With Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback, G. Ayyappan, S. Nithya, B. Somasundaram

Applications and Applied Mathematics: An International Journal (AAM)

In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to "a", else the server should not …

(R1985) Study The Effect Of Modified Newtonian Force On The Restricted 3-Body Configuration In Non-Linear Sense, Bhawna Singh, Kumari Shalini, Sada Nand Prasad, Abdullah A. Ansari

Applications and Applied Mathematics: An International Journal (AAM)

This paper aims to investigate the non-linear stability of the triangular libration point in the restricted three-body problem (R3BP). The model, we use for our problem consists of a primary body as a heterogeneous spheroid with N-layers having different densities of each layer and a secondary body as a point mass that is producing the modified Newtonian Potential. We determine the equation of motion of the smallest body which is under the influence of the above-mentioned perturbations and also influenced by Coriolis as well as Centrifugal forces and then evaluated the Lagrangian for the evaluated system of equations. Afterwards, we …

(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which …

(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a two-species amensalism model with a cover to protect the first species from the second species, with the assumption that the growth of the second species is governed by nonlinear harvesting. Analytical and numerical analyses have both been done on this suggested ecological model. Boundedness and positivity of the solutions of the model are examined. The existence of feasible equilibrium points and their local stability have been discussed. In addition, the parametric conditions under which the proposed system is globally stable have been determined. It has also been shown, using the Sotomayor theorem, that under certain parametric …

(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .

Applications and Applied Mathematics: An International Journal (AAM)

Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave …

Modeling Of Population Dynamics In Spatially Continuous And Heterogeneous Environments Using Partial Differential Equations, Ryan T. St. Clair

Masters Theses & Specialist Projects

This thesis provides an expansion of existing reaction diffusion population ecology models into patchy landscapes with greater spatial heterogeneity. The Sturm-Loiville eigenvalue problem for a heterogeneous 3 patch landscape is solved implicitly and the population growth rate and migration dynamics on such a landscape are thoroughly discussed. In addition a system of interface equations is found whose greatest solution is the dominant eigenvalue of an N-patch landscape. The results of this model agree well with previously published results and show the mathematical equivalence of two published approaches for incorporating organism behavior at habitat interfaces. Increased modeling capabilities in heterogeneous environments …

(R2022) Mathematical Modelling Of Tuberculosis And Covid-19 Co-Infection In India: A Real Data Analysis On Concomitant Diseases, Vijai Shanker Verma, Harshita Kaushik, Archana Singh Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have proposed an epidemiological model to study the dynamics of two concomitant diseases Tuberculosis (TB) and COVID-19. Here, we have formulated a deterministic compartmental model as an extended form of the classical SIS model. First, the basic reproduction number R₀ is derived and then stability analysis of the model is done. It is observed that the disease-free equilibrium is stable when R₀ is less than one and the endemic equilibrium is stable only when R₀ is greater than one. Numerical simulation is carried out to illustrate the theoretical findings and to study the …

(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong

Applications and Applied Mathematics: An International Journal (AAM)

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use …

Statistical Methods For Meta-Analysis In Large-Scale Genomic Experiments, Wimarsha Thathsarani Jayanetti

Mathematics & Statistics Theses & Dissertations

Recent developments in high throughput genomic assays have opened up the possibility of testing hundreds and thousands of genes simultaneously. With the availability of vast amounts of public databases, researchers tend to combine genomic analysis results from multiple studies in the form of a meta-analysis. Meta-analysis methods can be broadly classified into two main categories. The first approach is to combine the statistical significance (pvalues) of the genes from each individual study, and the second approach is to combine the statistical estimates (effect sizes) from the individual studies. In this dissertation, we will discuss how adherence to the standard null …

Kinetic Simulations Of Active Nematic Polymers In Channel Flow, Lacey Savoie Schenk

Mathematics & Statistics Theses & Dissertations

Suspensions of active nematic liquid crystalline polymers exhibit complex phenomena such as spontaneous flows, pattern formations, and defects. They have many applications in industry, commercial settings, and our daily lives. We employ the Kinetic Model for our research, an extensive model that couples the Smoluchowski Equation and the incompressible Navier-Stokes Equations to solve for the active nanorod number density function–a function dependent on the polymer’s physical orientation and space at a given time. Using this function, we can derive the polymer’s polarity and nematic orientations as well as other rheological properties. In this research, we conduct numerical simulations of active, …

Lyubeznik Numbers Of Unmixed Edge Ideals, Sara Rae Jones

Graduate Theses and Dissertations

Lyubeznik numbers, defined in terms of local cohomology, are invariants of local rings that are able to detect many algebraic and geometric properties. Notably they recognize topological behaviors of various structures associated to their rings. We will discuss computations of these numbers for unmixed edge ideals by giving a completely combinatorial construction which realizes the connectedness information captured by these numbers.

Improving Efficiency Of Rational Krylov Subspace Methods, Shengjie Xu

All Dissertations

This thesis studies two classes of numerical linear algebra problems, approximating the product of a function of a matrix with a vector, and solving the linear eigenvalue problem $Av=\lambda Bv$ for a small number of eigenvalues. These problems are solved by rational Krylov subspace methods (RKSM). We present several improvements in two directions: pole selection and applying inexact methods.

In Chapter 3, a flexible extended Krylov subspace method ($\mathcal{F}$-EKSM) is considered for numerical approximation of the action of a matrix function $f(A)$ to a vector $b$, where the function $f$ is of Markov type. $\mathcal{F}$-EKSM has the same framework as …

Efficient Hierarchical Space-Time Models For Large Areal Datasets With Application To Forest Inventory Mapping Using Remote Sensing Imagery, Md Kamrul Hasan Khan

Graduate Theses and Dissertations

The focus of this dissertation is development of a novel hierarchical framework, that can be used for predictive modeling of Forest Inventory and Analysis (FIA) data over large regions. This dissertation has two significant contributions. Based on a study region in north-central Wisconsin, we analyze satellite imagery, along with a sample of national forest inventory field plots, to monitor and predict changes in forest conditions over time. The auxiliary data from the satellite imagery of this region are relatively dense in space and time, and can be used to learn how forest conditions changed over that decade. However, these records …

(R1884) Motion Of Variable Mass Body In The Seventh-Degree Henon-Heiles System, Shiv K. Sahdev, Abdullah A. Ansari

Applications and Applied Mathematics: An International Journal (AAM)

The goal of this paper is to reveal numerically the generalized Henon-Heiles system, that is, in the seventh-degree potential function where the smallest body mass varies. Utilizing the seventh degree potential function, we determine the equations of motion for the variable mass generalized Henon-Heiles system. Then we perform the graphical works such as locations of parking points, allowed regions of motion, and attracting domain basins. Lastly, using the Meshcherskii space transformations, we investigate stability states for these parking points.

(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted …

(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah

Applications and Applied Mathematics: An International Journal (AAM)

In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …

(R1995) Weighted Block-Wise Burst Error Correcting Codes, Amita Sethi, Arpana Sharma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we construct new types of codes, called Weighted Block-wise Burst Error Correcting Codes (Weighted BBEC Codes), which are an improvement on the previously known block wise burst error correcting codes in the sense of their weight, i.e., (n = n₁ + n₂, k) linear codes that correct all the bursts of length b₁ (fixed) with the weight w₁ (w₁ ≤ b₁) or more (less) in the first sub-block of length n₁ and all the bursts of length b₂ (fixed) with the weight w₂ or more (less) …

(R1895) On Refinements And Generalizations Of Hadamard Inequalities For Riemann-Liouville (R-L) Integrals, Ghulam Farid, Sidra Bibi

Applications and Applied Mathematics: An International Journal (AAM)

The Hadamard inequality is a graphical interpretation of convex functions in the coordinate plane. We give its different variants for (R-L) fractional integrals of strongly exponentially (α, h − m)- convex functions. These inequalities are generalizations and refinements of Hadamard inequalities for Riemann-Liouville fractional integrals of exponentially; convex, m-convex, (α,m)-convex, (h − m)-convex, (s,m)-convex functions in combined forms. The error bounds of established inequalities are also obtained. Special cases of main results are mentioned, which have been already published by different authors.

(R1989) Mixed Convection Slippery Cross Fluid Flow Due To A Stratified Sheet Under The Effect Of Radiation Phenomenon, Nourhan I. Ghoneim, Ahmed M. Megahed

Applications and Applied Mathematics: An International Journal (AAM)

In view of the meaning of a two dimensional laminar Cross liquid in depicting an exhaustive assortment of experimental information, an assessment is done for a numerical and mathematical arrangement over a stratified extensible sheet. The non-dimensionality technique is brought into the controlling equations within the sight of the slip phenomenon and to make the solution more thorough. The data have been taken at a steady, viscous and laminar ow. Heat transfer across fluid is employed as a non-Newtonian fluid, where the fluid has a affected by radiation. Additionally, thermal radiation and heat generation are considered with the basic influence …

(R1976) A Novel Approach To Solve Fuzzy Rough Matrix Game With Two Players, Vinod Jangid, Ganesh Kumar, Gaurav Sharama, Vishnu Narayan Mishra

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems for the first player in the form of upper approximation intervals and lower approximation intervals. Two problems for the second player can be created in the same way. These problems have been split into five sub-crisp problems for the player first and five sub-crisp problems for the …