Physical Sciences and Mathematics Commons^™

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 …

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

(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 …

(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.

(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 …

(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 …

(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 …

Region Detection & Segmentation Of Nissl-Stained Rat Brain Tissue, Alexandro Arnal

Open Access Theses & Dissertations

People who analyze images of biological tissue rely on the segmentation of structures as a preliminary step. In particular, laboratories studying the rat brain delineate brain regions to position scientific findings on a brain atlas to propose hypotheses about the rat brain and, ultimately, the human brain. Our work intersects with the preliminary step of delineating regions in images of brain tissue via computational methods.

We investigate pixel-wise classification or segmentation of brain regions using ten histological images of brain tissue sections stained for Nissl substance. We present a deep learning approach that uses the fully convolutional neural network, U-Net, …

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 …

(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 …

(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 …

Automated Feature Extraction From Large Cardiac Electrophysiological Data Sets, And A Population Dynamics Approach To The Distribution Of Space Debris In Low-Earth Orbit, John Jurkiewicz

Theses and Dissertations

We present two applications of mathematics to relevant real-world situations.

In the first chapter, we discuss an automated method for the extraction of useful data from large file-size readings of cardiac data. We begin by describing the history of electrophysiology and the background of the work's setting, wherein a new multi-electrode array-based application for the long-term recording of action potentials from electrogenic cells makes large-scale readings of relevant data possible, opening the way for exciting cardiac electrophysiology studies in health and disease. With hundreds of simultaneous electrode recordings being acquired over a period of days, the main challenge becomes achieving …

(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 …

(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) …

Voting Rules And Properties, Zhuorong Mao

Undergraduate Honors Theses

This thesis composes of two chapters. Chapter one considers the higher order of Borda Rules (Bp) and the Perron Rule (P) as extensions of the classic Borda Rule. We study the properties of those vector-valued voting rules and compare them with Simple Majority Voting (SMV). Using simulation, we found that SMV can yield different results from B1, B2, and P even when it is transitive. We also give a new condition that forces SMV to be transitive, and then quantify the frequency of transitivity when it fails.

In chapter two, we study the `protocol paradox' of approval voting. In approval …

(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 …

(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 …

Gmres Convergence Of Block Preconditioners For Nonsymmetric Matrices, Miguel A. Mascorro

Theses and Dissertations

GMRES is an iterative method for solving linear systems that minimizes the residual over the k-dimensional Krylov subspace at iteration k. Murphy, Golub and Wathen in [11] show that saddle point type matrices can be preconditioned so that GMRES converges in two or three steps. Ipsen in [10] extends this work to matrixes where the (2,2) block is nonzero. However, the three step convergence result no longer holds in this case. In this thesis we investigate how many more steps are needed for convergence as a function of the size of that (2,2) block.

Towards Reduced-Order Model Accelerated Optimization For Aerodynamic Design, Andrew L. Kaminsky

Doctoral Dissertations

The adoption of mathematically formal simulation-based optimization approaches within aerodynamic design depends upon a delicate balance of affordability and accessibility. Techniques are needed to accelerate the simulation-based optimization process, but they must remain approachable enough for the implementation time to not eliminate the cost savings or act as a barrier to adoption.

This dissertation introduces a reduced-order model technique for accelerating fixed-point iterative solvers (e.g. such as those employed to solve primal equations, sensitivity equations, design equations, and their combination). The reduced-order model-based acceleration technique collects snapshots of early iteration (pre-convergent) solutions and residuals and then uses them to project …

On Variants Of Sliding And Frank-Wolfe Type Methods And Their Applications In Video Co-Localization, Seyed Hamid Nazari

All Dissertations

In this dissertation, our main focus is to design and analyze first-order methods for computing approximate solutions to convex, smooth optimization problems over certain feasible sets. Specifically, our goal in this dissertation is to explore some variants of sliding and Frank-Wolfe (FW) type algorithms, analyze their convergence complexity, and examine their performance in numerical experiments. We achieve three accomplishments in our research results throughout this dissertation. First, we incorporate a linesearch technique to a well-known projection-free sliding algorithm, namely the conditional gradient sliding (CGS) method. Our proposed algorithm, called the conditional gradient sliding with linesearch (CGSls), does not require the …