Applied Mathematics Commons^™

Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy

Applications and Applied Mathematics: An International Journal (AAM)

A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented …

Classification Of Some First Order Functional Differential Equations With Constant Coefficients To Solvable Lie Algebras, J. Z. Lobo, Y. S. Valaulikar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we shall apply symmetry analysis to some first order functional differential equations with constant coefficients. The approach used in this paper accounts for obtaining the inverse of the classification. We define the standard Lie bracket and make a complete classification of some first order linear functional differential equations with constant coefficients to solvable Lie algebras.We also classify some nonlinear functional differential equations with constant coefficients to solvable Lie algebras.

The Binomial Transform Of P-Recursive Sequences And The Dilogarithm Function, Stephanie L. Harshbarger, Barton L. Willis

Applications and Applied Mathematics: An International Journal (AAM)

Using a generalized binomial transform and a novel binomial coefficient identity, we will show that the set of p-recursive sequences is closed under the binomial transform. Using these results, we will derive a new series representation for the dilogarithm function that converges on its domain of analyticity. Finally, we will show that this series representation results in a scheme for numerical evaluation of the dilogarithm function that is accurate, efficient, and stable.

Dynamical Behavior Of An Eco-Epidemiological Model Incorporating Prey Refuge And Prey Harvesting, Dawit Melese, Ousman Muhye, Subrata K. Sahu

Applications and Applied Mathematics: An International Journal (AAM)

In this paper an eco-epidemiological model incorporating a prey refuge and prey harvesting with disease in the prey-population is considered. Predators are assumed to consume both the susceptible and infected prey at different rates. The positivity and boundedness of the solution of the system are discussed. The existence and stability of the biologically feasible equilibrium points are investigated. Numerical simulations are performed to support our analytical findings.

Multilayer Security Of Rgb Image In Discrete Hartley Domain, Umar H. Mir, Deep Singh, D. C. Mishra, Parveiz N. Lone

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we present RGB image encryption and decryption using random matrix affine cipher (RMAC) associated with discrete Hartley transform (DHT) and random matrix shift cipher (RMSC). The parameters in RMAC and RMSC phases act as two series of secret keys whose arrangement is imperative in the proposed algorithm. The computer simulations with results and examples are given to analyze the efficiency of the proposed approach. Further, security analysis and comparison with the prior techniques successfully supports the robustness and validation of the proposed technique.

Explicit Formulas For Solutions Of Maxwell’S Equations In Conducting Media, Valery Yakhno

Applications and Applied Mathematics: An International Journal (AAM)

A new explicit presentation of the fundamental solution of the time-dependent Maxwell’s equations in conducting isotropic media is derived by Hadamard techniques through the fundamental solution of the telegraph operator. This presentation is used to obtain explicit formulas for generalized solutions of the initial value problem for Maxwell’s equations. A new explicit Kirchhoff’s formula for the classical solution of the initial value problem for the Maxwell equations in conducting media is derived. The obtained explicit formulas can be used in the boundary integral method, Green’s functions method and for computation of electric and magnetic fields in conducting media and materials.

Approximate Solutions For The Nonlinear Systems Of Algebraic Equations Using The Power Series Method, M. M. Khader, M. Adel

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the approximate solutions for systems of nonlinear algebraic equations by the power series method (PSM) are presented. Illustrative examples have been presented to demonstrate the efficiency of the proposed method. In addition, the obtained results are compared with those obtained from the standard Adomian decomposition method. It turns out that the convergence of the proposed algorithm is rapid.

On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulated two types of higher-order dual models for such optimization problem.Weak, strong and strict converse duality theorems are derived under higherorder generalized invexity.

On An Ecological Model Of Mutualisim Between Two Species With A Mortal Predator, Srinivasarao Thota

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study an ecological model of a three-space food chain consists of two logically growing mutual species and third species acts as a predator to second mutual species with Holling type II functional response. This model is constituted by a system of nonlinear decoupled ordinary differential equations. By using perturbed method, we identify the nature of the system at each equilibrium point and also global stability is investigated for this model using Lypanov function at the possible equilibrium points.

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …

Controlling And Synchronizing Combined Effect Of Chaos Generated In Generalized Lotka-Volterra Three Species Biological Model Using Active Control Design, Taqseer Khan, Harindri Chaudhary

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we study hybrid projective combination synchronization scheme among identical chaotic generalized Lotka-Volterra three species biological systems using active control design. We consider here generalized Lotka-Volterra system containing two predators and one prey population existing in nature. An active control design is investigated which is essentially based on Lyapunov stability theory. The considered technique derives the global asymptotic stability using hybrid projective combination synchronization technique. In addition, the presented simulation outcomes and graphical results illustrate the validation of our proposed scheme. Prominently, both the analytical and computational results agree excellently. Comparisons versus others strategies exhibiting our proposed technique …

An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit

Applications and Applied Mathematics: An International Journal (AAM)

In this article a direct method is introduced, which is based on orthonormal Bernstein polynomials, to present an efficient and stable algorithm for numerical inversion of the system of singular integral equations of Abel type. The appropriateness of earlier numerical inversion methods was restricted to the one portion of singular integral equations of Abel type. The proposed method is absolutely accurate, and numerical illustrations are given to show the convergence and utilization of the suggested method and comparisons are made with some other existing numerical solution.

Integrated Farm Model For Optimal Allocation Of Resources- A Linear Programming Approach, Mahak Bhatia, Anil Rana

Applications and Applied Mathematics: An International Journal (AAM)

The mathematical model for optimal allocation of farm resources, especially land and water are proposed to optimize the resources that contribute to increase farm revenues. A study is being carried out, to analyze the cropping practice adopted by growers, depending on availability and accessibility of resources. Different crop-combinations and cropping patterns are being analyzed in districts of Rajasthan. Rajasthan has arid topography with varying weather conditions. Thus, a diverse crop variety is being cultivated in a region. Being a state with inadequate water resources, the formulated model proposed different crop combinations alternatives. A crop-mix model is developed to reduce the …

On The Unsolvability Conditions For Quasilinear Pseudohyperbolic Equations, Birilew Tsegaw

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the nonexistence of global weak solutions to the Cauchy problem of quasilinear pseudohyperbolic equations with damping term. The sufficient conditions for nonexistence of nontrivial global weak solutions is obtained in terms of exponents, singularities order and other parameters in the problem. The nonlinear capacity method is applied to prove nonexistence theorems. The proofs of our nonexistence theorems are based on deriving apriori estimates for the possible solutions to the problem by an algebraic analysis of the integral form of inequalities with an optimal choice of test functions. The result is extended to the case of …

Analysis Of Map/Ph/1 Queueing Model With Breakdown, Instantaneous Feedback And Server Vacation, G. Ayyappan, K. Thilagavathy

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we analyze a single server queueing model with feedback, a single vacation under Bernoulli schedule, breakdown and repair. The arriving customers follow the Markovian Arrival Process (MAP) and service follow the phase-type distribution. When the server returns from vacation, if there is no one present in the system, the server will wait until the customer’s arrival. When the service completion epoch if the customer is not satisfied then that customer will get the service immediately. Under the steady-state probability vector that the total number of customers are present in the system is probed by the Matrix-analytic method. …

Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum …

Stability Analysis Of Circular Robe’S R3bp With Finite Straight Segment And Viscosity, Bhavneet Kaur, Sumit Kumar, Shipra Chauhan, Dinesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the effect of viscous force on the linear stability of equilibrium points of the circular Robe’s restricted three-body problem (CRR3BP) with smaller primary as a finite straight segment is studied. The present model comprises of a bigger primary m^*₁ which is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ₁ and the smaller primary m₂ lies outside the shell. The infinitesimal mass m₃ is a small solid sphere of density ρ₃ moving inside m^*₁. The pertinent equations of motion of m₃ are derived …

Stability Of Modified Host-Parasitoid Model With Allee Effect, Özlem A. Gümüs, A. G. Maria Selvam, R. Janagaraj

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with a host-parasitoid model subject to Allee effect and its dynamical behavior. Steady state points of the proposed host-parasitoid model are computed. Stability properties are analyzed with eigen values of Jacobian matrix which are determined at the steady states. Theoretical findings are supported by numerical illustrations and enhanced by pictorial representations such as bifurcation diagrams, phase portraits and local amplifications for different parameter values. Existence of chaotic behavior in the system is established via bifurcation and sensitivity analysis of the system at the initial conditions. Various phase portraits are simulated for a better understanding of the qualitative …

Bivariate Markov Chain Model Of Irritable Bowel Syndrome (Ibs) Subtypes And Abdominal Pain, Ricardo Reyna Jr.

Theses and Dissertations

Researchers use stochastic models like continuous-time Markov chains (CTMC) to model progression of morbidities of public health impact, like HIV and Hepatitis C. Most of the research in that area is done for a single disease. In this research, we use a bivariate continuous-time Markov chain (CTMC) to model progression of co-morbidities. In particular, we use a bivariate CTMC to model the joint progression of Irritable Bowel Syndrome (IBS) and abdominal pain. Symptoms of IBS are known to change throughout the duration of the disorder. Hence, patients are normally asked to make a journal of the stool type, symptoms, and …

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

A Collection Of Fast Algorithms For Scalar And Vector-Valued Data On Irregular Domains: Spherical Harmonic Analysis, Divergence-Free/Curl-Free Radial Basis Functions, And Implicit Surface Reconstruction, Kathryn Primrose Drake

Boise State University Theses and Dissertations

This dissertation addresses problems that arise in a diverse group of fields including cosmology, electromagnetism, and graphic design. While these topics may seem disparate, they share a commonality in their need for fast and accurate algorithms which can handle large datasets collected on irregular domains. An important issue in cosmology is the calculation of the angular power spectrum of the cosmic microwave background (CMB) radiation. CMB photons offer a direct insight into the early stages of the universe's development and give the strongest evidence for the Big Bang theory to date. The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) grid is …

Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, Cian Anthony Branco

Mechanical & Aerospace Engineering Theses & Dissertations

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in a novel …

Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

Mathematics & Statistics Theses & Dissertations

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change …

Under Frequency Load Shedding Scheme For Islanded Distribution System Based On Mixed Integer Linear Programming, Sohail Sarwar

Student Works (2020-2029)

In recent years, significant climate changes have pivoted the distribution system towards utilization of renewable energy, particularly through distributed generators (DGs). Although DGs offer many benefits, its integration affects the stability of the system, which could lead to blackout, when the grid is disconnected. The system frequency will drop drastically if DG’s generation capacity is less than the total load demand in the network. In order to sustain the system stability, Under Frequency Load Shedding (UFLS) is a commonly used technique to minimize the difference in load demand and power generation. However, existing load shedding techniques are lack in accurate …

Fredholm-Regularity Of Holomorphic Discs In Plane Bundles Over Compact Surfaces, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with a single complex point has C2,α-close sections such that any (non-multiply covered) holomorphic disc with boundary in these sections are Fredholm regular. Fredholm regularity is also established when the complex surface is neutral K¨ahler, the action is both holomorphic and symplectic, and the section is Lagrangian with a single complex point.

Energy-Efficient Communications In Wireless Powered Cognitive Radio Networks Based On Game Theory, Fadhil Mukhlif Aswad Al-Obaidy

Student Works (2020-2029)

There are challenging and prevalent problems related to spectrum resources with the interference of battery-based devices in future wireless networks. To address such challenges, this thesis proposes a theoretical framework for designing and analyzing the distributed power control algorithms in modern 5G cognitive networks. Previous experiments have shown that game theory tools can be used as a suitable and efficient technique to build scalable, balanced, and energy efficient for the distributed power control schemes in order to use it practically in battery-based devices in wireless networks. In reality, the power control issue is constructed as a non-cooperative game for which …

Preludes To Mathematical Biology Education, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Reactions To A Pandemic: The Coronavirus Brings Mathematicians To The Front Line, Ami Radunskaya

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Asymptotic Analysis Of Radial Point Rupture Solutions For Elliptic Equations, Attou Miloua

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Personalized Immunotherapy Treatment Strategies For A System Of Chronic Myelogenous Leukemia, Paul Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.