Applied Mathematics Commons^™

Dividend Maximization Under A Set Ruin Probability Target In The Presence Of Proportional And Excess-Of-Loss Reinsurance, Christian Kasumo, Juma Kasozi, Dmitry Kuznetsov

Applications and Applied Mathematics: An International Journal (AAM)

We study dividend maximization with set ruin probability targets for an insurance company whose surplus is modelled by a diffusion perturbed classical risk process. The company is permitted to enter into proportional or excess-of-loss reinsurance arrangements. By applying stochastic control theory, we derive Volterra integral equations and solve numerically using block-by-block methods. In each of the models, we have established the optimal barrier to use for paying dividends provided the ruin probability does not exceed a predetermined target. Numerical examples involving the use of both light- and heavy-tailed distributions are given. The results show that ruin probability targets result in …

Viral Dynamics Of Delayed Ctl-Inclusive Hiv-1 Infection Model With Both Virus-To-Cell And Cell-To-Cell Transmissions, M. L. Mann Manyombe, J. Mbang, L. Nkague Nkamba, D. F. Nkoa Onana

Applications and Applied Mathematics: An International Journal (AAM)

We consider a mathematical model that describes a viral infection of HIV-1 with both virus-tocell and cell-to-cell transmission, CTL response immune and four distributed delays, describing intracellular delays and immune response delay. One of the main features of the model is that it includes a constant production rate of CTLs export from thymus, and an immune response delay. We derive the basic reproduction number and show that if the basic reproduction number is less than one, then the infection free equilibrium is globally asymptotically stable; whereas, if the basic reproduction number is greater than one, then there exist a chronic …

The Impact Of Nonlinear Harvesting On A Ratio-Dependent Holling-Tanner Predator-Prey System And Optimum Harvesting, Manoj Kumar Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using …

Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal, Charanpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The Newton-Raphson basins of convergence, related to the equilibrium points, in the collinear restricted four-body problem with repulsive Manev potential are numerically investigated. We monitor the parametric evolution of the position as well as of the stability of the equilibrium points, as a function of the parameter e. The multivariate Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the parameter e affects the geometry as well as the basin entropy …

Mathematical Modeling Of Nonlinear Blood Glucose-Insulin Dynamics With Beta Cells Effect, Gabriela Urbina, Daniel N. Riahi, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

We consider mathematical modeling of blood glucose-insulin regulatory system with the additional effect of the secreted insulin by the pancreatic beta cells and in the presence of an external energy input to such system. Such modeling system is investigated to determine the time-dependent nonlinear dynamics that take place by the quantities, which represent the glucose and insulin concentrations in the blood, insulin action as well as in the absence or presence of secreted insulin due to the pancreatic beta cells. Using both analytical and numerical procedures, we determine such quantities versus time for both diabetes patients and normal human and …

Spherically Symmetric Charged Anisotropic Solution In Higher Dimensional Bimetric General Relativity, D. N. Pandya, A. H. Hasmani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have obtained a solution of field equations of Rosen’s bimetric general relativity (BGR) for the static spherically symmetric space-time with charged anisotropic fluid distribution in (n+2)-dimensions. An exact solution is obtained and a special case is considered. This work is an extension of our previous work where four-dimensional case was discussed.

A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. …

A Study Of Small Perturbations In The Coriolis And Centrifugal Forces In Rr3bp With Finite Straight Segment, Bhavneet Kaur, Dinesh Kumar, Shipra Chauhan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the effect of small perturbations in the Coriolis and centrifugal forces on the existence and stability of the equilibrium point in the Robe’s restricted three-body problem (RR3BP) by taking the smaller primary as a finite straight segment is introduced. In the present structure the density rho₁ of the fluid filled in the bigger primary of mass m₁^*and the density rho₃ of the infinitesimal body of mass m₃ are considered to be equal. It is worth mentioning that the location of the equilibrium point is affected by a small perturbation in the …

Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, B. Echeng Bassey

Applications and Applied Mathematics: An International Journal (AAM)

Following the rising cases of high hospitalization versa-vise incessant fatality rates and the close affinity of listeriosis with HIV/AIDS infection, which often emanates from food-borne pathogens associated with listeria monocytogenes infection, this present paper seek and formulated as penultimate model, an 8-Dimensional classical mathematical Equations which directly accounted for the biological interplay of dual listeriosis virions with dual set of population (human and animals). The model was studied under multiple chemotherapies (trimethoprim-sulphamethoxazole with a combination of penicillin or ampicillin and/or gentamicin). Using ODE’s, the positivity and boundedness of system solutions was investigated with model presented as an optimal control problem. …

Study On Solving Two-Dimensional Linear And Nonlinear Volterra Partial Integro-Differential Equations By Reduced Differential Transform Method, Seyyedeh Roodabeh Moosavi Noori, Nasir Taghizadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we study on the analytical and numerical solution of two-dimensional linear and nonlinear Volterra partial integro-differential equations with the appropriate initial condition by means of reduced differential transform method. The advantage of this method is its simplicity in using, it solves the problem directly without the need for linearization, perturbation, or any other transformation and gives the solution in the form of convergent power series with elegantly computed components. The validity and efficiency of this method are illustrated by considering five computational examples.

The Traveling Wave Solution Of The Fuzzy Linear Partial Differential Equation, Zahra Shahsavari, Tofigh Allahviranloo, Saeid Abbasbandy, Mohsen Rostamy-Malkhalifeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we are going to obtain fuzzy traveling wave solutions for fuzzy linear partial differential equations by considering the type of generalized Hukuhara differentiability. In particular, the fuzzy traveling wave solutions for fuzzy Advection equation, fuzzy linear Diffusion equation, fuzzy Convection-Diffusion-Reaction equation, and fuzzy Klein-Gordon equation are obtained.

On The Asymptotic Stability Of A Nonlinear Fractional-Order System With Multiple Variable Delays, Yener Altun, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink.

On The Qualitative Analysis Of Volterra Iddes With Infinite Delay, Osman Tunç, Erdal Korkmaz, Özkan Atan

Applications and Applied Mathematics: An International Journal (AAM)

This investigation deals with a nonlinear Volterra integro-differential equation with infinite retardation (IDDE).We will prove three new results on the stability, uniformly stability (US) and square integrability (SI) of solutions of that IDDE. The proofs of theorems rely on the use of an appropriate Lyapunov-Krasovskii functional (LKF). By the outcomes of this paper, we generalize and obtain some former results in mathematical literature under weaker conditions.

Some Contiguous Relation On K-Generalised Hypergeometric Function, Ekta Mittal, Sunil Joshi, Sona Kumari

Applications and Applied Mathematics: An International Journal (AAM)

In this research work our aim is to determine some contiguous relations and some integral transform of the k-generalised hypergeometric functions, by using the concept of “k-Gamma and k-Beta function”. “Obviously if k approaches 1”, then the contiguous function relations become Gauss contiguous relations.

Modeling And Analysis Of The Impact Of Vocational Education On The Unemployment Rate In Nigeria, Abayomi Ayoade, Opeyemi Odetunde, Bidemi Falodun

Applications and Applied Mathematics: An International Journal (AAM)

Unemployment is a major determinant of a weak economy and a good measure of living standard in a country. Nigeria is faced with the problem of unemployment at present. By that, a mathematical model is formulated to investigate the effect of vocational education on the unemployment challenges in Nigeria. The model is tested for the basic requirements of a good mathematical model. The equilibrium analysis of the model is conducted and both the unemployment-free and the unemployment endemic equilibria are obtained. The threshold for the implementation success of the vocational education program is also derived following the approach of epidemic …

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan

Electronic Theses, Projects, and Dissertations

DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is …

Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan

Department of Mathematics: Faculty Publications

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.

Inventory Models For Deteriorating Items With Power Pattern Demand Rate, Olalekan Adaraniwon Amos

Student Works (2020-2029)

Inventory management has become a prevalent topic in the field of operational research over some decades now. It cuts across many areas like management sciences, statistics and engineering. However, research focusing on inventory model with power demand pattern is quite limited. Demand patterns are defined as different ways by which products are removed out of inventory to supply customers demand during the schedule period. Power demand pattern permits suiting the demand to a more practical situation. In this research, four deterministic inventory model for deteriorating items with power demand pattern has been developed. We considered in the first models an …

Coding Against Stragglers In Distributed Computation Scenarios, Malihe Aliasgari

Dissertations

Data and analytics capabilities have made a leap forward in recent years. The volume of available data has grown exponentially. The huge amount of data needs to be transferred and stored with extremely high reliability. The concept of "coded computing", or a distributed computing paradigm that utilizes coding theory to smartly inject and leverage data/computation redundancy into distributed computing systems, mitigates the fundamental performance bottlenecks for running large-scale data analytics.

In this dissertation, a distributed computing framework, first for input files distributedly stored on the uplink of a cloud radio access network architecture, is studied. It focuses on that decoding …

Evaluating Driving Performance Of A Novel Behavior Planning Model On Connected Autonomous Vehicles, Keyur Shah

Honors Scholar Theses

Many current algorithms and approaches in autonomous driving attempt to solve the "trajectory generation" or "trajectory following” problems: given a target behavior (e.g. stay in the current lane at the speed limit or change lane), what trajectory should the vehicle follow, and what inputs should the driving agent apply to the throttle and brake to achieve this trajectory? In this work, we instead focus on the “behavior planning” problem—specifically, should an autonomous vehicle change lane or keep lane given the current state of the system?

In addition, current theory mainly focuses on single-vehicle systems, where vehicles do not communicate with …

Computational Study Of The Time Relaxation Model With High Order Deconvolution Operator, Jeffrey Belding, Monika Neda, Fran Pahlevani

Mathematical Sciences Faculty Research

This paper presents a computational investigation for a time relaxation regularization of Navier–Stokes equations known as Time Relaxation Model, TRM, and its corresponding sensitivity equations. The model generates a regularization based on both filtering and deconvolution. We discretize the equations of TRM and the corresponding sensitivity equations using finite element in space and Crank–Nicolson in time. The step problem and the shear layer roll-up benchmark is used to computationally test the performance of TRM across different orders of deconvolution operator as well as the sensitivity of the shear layer computations of the model with respect to the variation of time …

Glucose Regulation Using An Intelligent Pid Controller, Parker Willmon

Mathematics Senior Capstone Papers

Type 1 diabetes is a condition characterized by a lack of insulin production. This lack of insulin causes glucose concentration in the blood to increase after meals. In order to maintain blood glucose levels, diabetics must inject insulin using needles or an insulin pump. Additionally, the lack of insulin can cause glucose levels to decrease overnight. This project uses a proportional integral derivative (PID) controller to modify the rate of insulin and glucagon infusion when glucose levels are increasing or decreasing, respectively. A system of 13 differential equations were used to anticipate changes in glucose concentration as insulin and glucagon …

The Boundary Element Method For Parabolic Equation And Its Implementation In Bem++, Sihao Wang

Mathematics Theses and Dissertations

The goal of this work is to develop a fast method for solving Galerkin discretizations of boundary integral formulations of the heat equation. The main contribution of this work is to devise a new fast algorithm for evaluating the dense matrices of the discretized integral equations.

Similar to the parabolic FMM, this method is based on a subdivision of the matrices into an appropriate hierarchical block structure. However, instead of an expansion of the kernel in both space and time we interpolate kernel in the temporal variables and use of the adaptive cross approximation (ACA) in the spatial variables.

The …

A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang

Mathematics Theses and Dissertations

Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating …

Spreading Mechanics And Differentiation Of Astrocytes During Retinal Development, Tracy Stepien, Timothy W. Secomb

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Role Of Diversity Amplification For Personal Protection Control Strategies In Vector-Borne Disease Models, Jeffery Demers, Sharon Bewick, Justin M. Calabrese, William F. Fagan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parallel-In-Time Simulation Of Biofluids, Weifan Liu, Minghao Rostami

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Model-Based Investigation Of The Role Of Density Dependence In Juvenile Mosquito Development And Survival, Melody Walker Ms, Lauren M. Childs, Michael A. Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.