Numerical Analysis and Computation Commons^™

A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

This paper introduces a generalization of the Fractional Optimal Control Problem (GFOCP). Proposed generalizations differ in terms of explaining the constraint involved in the dynamical system of the control problem. We assume the constraint as an arbitrary function of fractional derivatives and fractional integrals. By this assumption the restriction on constraint, to be of some prescribed function of fractional operators, is removed. Deduction of necessary optimality conditions followed by particular cases and examples has been provided. Additionally, we construct a solution scheme for the suggested class of (GFOCP)’s. The formulation of this scheme is done by implementing the Adomian decomposition …

On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.

Implementation Of The Matrix Differential Transform Method For Obtaining An Approximate Solution Of Some Nonlinear Matrix Evolution Equations, M. M. Khader, A. Borhanifar

Applications and Applied Mathematics: An International Journal (AAM)

This article introduces the matrix differential transform method (MDTM) to apply to matrix partial differential equations (MPDEs) and employs it for solving matrix Fisher equations, matrix Burgers equations and matrix KdV equations. We show how the MDTM applies to the linear part and nonlinear part of any MPDE and give various examples of MPDEs to illustrate the efficiency of the method. The results obtained are in excellent agreement with the exact solution and show that the proposed method is powerful, accurate, and easy.

Non Markovian Queue With Two Types Service Optional Re-Service And General Vacation Distribution, K. Sathiya, G. Ayyappan

Applications and Applied Mathematics: An International Journal (AAM)

We consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with …

Some Results On F-Simultaneous Chebyshev Approximation, Sh. Al-Sharif, Kh. Qaraman

Applications and Applied Mathematics: An International Journal (AAM)

Let X be Hausdorff topological vector space and f be a real valued continuous function on X: In this paper we introduce and study the concept of f-simultaneous approximation of a nonempty subset K of X as a generalization to the problem of simultaneous approximation. Further we present some results regarding f-simultaneous approximation in the quotient space.

Modern Fair-Weather And Storm Sediment Transport Around Ship Island, Mississippi: Implications For Coastal Habitats And Restoration Efforts, Eve Rettew Eisemann

Master's Theses

The Mississippi – Alabama barrier island chain is experiencing accelerated sea level rise, decreased sediment supply, and frequent hurricane impacts. These three factors drive unprecedented rates of morphology change and ecosystem reduction. All islands in the chain have experienced land loss on the order of hectares per year since records began in the 1840s. In 1969, Hurricane Camille impacted as a Category 5, breaching Ship Island, and significantly reduced viable seagrass habitat. Hurricane Katrina impacted as a Category 3 in 2005, further widening Camille Cut. To better understand the sustainability of these important islands and the ecosystems they support, sediment …

Fast Method Of Particular Solutions For Solving Partial Differential Equations, Anup Raja Lamichhane

Dissertations

Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the large-scale problems are some of the challenges which need to overcome. In this dissertation, we have used several techniques to overcome such challenges.

The closed-form particular solutions for the Matérn and Gaussian RBFs were not known yet. With the help of the symbolic computational tools, we have derived the closed-form particular solutions of the Matérn and Gaussian RBFs for the Laplace and biharmonic …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

A 10-Point Approximating Subdivision Scheme Based On Least Squares Technique, Ghulam Mustafa, Muhammad T. Iqbal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a 10-point approximating subdivision scheme is presented. Least squares technique for fitting the polynomial of degree 9 to data is used to develop this scheme. The proposed strategy can be used to generate a family of schemes. The important characteristics of the scheme are also discussed. Graphical efficiency of the scheme is shown by applying it on different types of data.

Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene

Publications and Research

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …

Stability Analysis Of A Prey Refuge Predator-Prey Model With Allee Effects, Unal Ufuktepe Prof

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Influence Of Preventive Measures To Eradicate The Spread Of The Zika Arbovirus, Pradyuta Padmanabhan, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

How Steep Is Steep? Learning Curves In Training Undergraduates To Do Fluid-Structure Interaction Modeling, Nicholas A. Battista

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A 2-D Compartmental Model For Multi-Capillary Supply, Liang Sun, Junkoo Park, Alessandra L. Barrera

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Interdisciplinary Undergraduate Research In Biofluids, Eva M. Strawbridge

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling, Analysis And Computation Of The Interaction Between Human Sub Populations And Vector-Borne Zika Transmission During The Summer 2016 Olympics, Pradyuta Padmanabhan, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multi-Dome Forming Of A Ti–Al–Mn Alloy, Sergey Aksenov, Aleksey Kolesnikov, Ivan Zakhariev

The 8th International Conference on Physical and Numerical Simulation of Materials Processing

No abstract provided.

Numerical Simulation Of Residual Stress In Low-Temperature Colossal Carburized Layer On Austenitic Stainless Steel, Dongsong Rong, Yong Jiang, Jianming Gong, Yawei Peng

The 8th International Conference on Physical and Numerical Simulation of Materials Processing

No abstract provided.

On Some Optimal Stopping Problems With Constraint, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

We consider the optimal stopping problem of a Markov process {x_t : t ≤ 0} when the controller is allowed to stop only at the arrival times of a signal, that is, at a sequence of instants {τ_n : n ≤ 1} independent of {x_t : t ≤ 0}. We solve in detail this problem for general Markov–Feller processes with compact state space when the interarrival times of the signal are independent identically distributed random variables. In addition, we discuss several extensions to other signals and to other cases of state spaces. These results …

Breakdown Of Itcz-Like Pv Patterns, Ajay Raghavendra, Thomas A. Guinn

Beyond: Undergraduate Research Journal

The Inter-Tropical Convergence Zone (ITCZ) is a zonal belt of intense convection, responsible for the genesis of over 80% of all tropical cyclones. This region of intense diabatic heating and shear results in a maximum of Ertel's potential vorticity (PV) meeting Rayleigh's necessary condition for barotropic instability. A fundamental issue is understanding the necessary precursor events leading to the breakdown of the ITCZ and subsequent formation of tropical cyclones. Our research examines the non-linear PV dynamics of the breakdown of both finite-length and infinite-length vorticity strips of varying widths and shapes, simulating the ITCZ found near the tropical eastern Pacific …

Multi-Objective Optimization Under Uncertainty Using The Hyper-Volume Expected Improvement, Martin Figura, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

The Summer Undergraduate Research Fellowship (SURF) Symposium

The design of real engineering systems requires the optimization of multiple quantities of interest. In the electric motor design, one wants to maximize the average torque and minimize the torque variation. A study has shown that these attributes vary for different geometries of the rotor teeth. However, simulations of a large number of designs cannot be performed due to their high cost. In many problems, design optimization of multi-objective functions is a very challenging task due to the difficulty to evaluate the expectation of the objectives. Current multi-objective optimization (MOO) techniques, e.g., evolutionary algorithms cannot solve such problems because they …

A Fast Model For The Simulation Of External Gear Pumps, Zechao Lu, Xinran Zhao, Andrea Vacca

The Summer Undergraduate Research Fellowship (SURF) Symposium

External gear pump is an important category of positive displacement fluid machines used to perform the mechanical–hydraulic energy conversions in many fluid power applications. An efficient numerical simulation program is needed to simulate the system in order to provide a direction for design purpose. The model consists of a lumped parameter fluid dynamic model and a model that simulates the radial micro-motions of the gear’s axes of rotation. The system consists of a set of ordinary differential equations related to the conservation on mass of the internal control volumes of the pump, which are given by the tooth space volumes …

Design Optimization Of A Stochastic Multi-Objective Problem: Gaussian Process Regressions For Objective Surrogates, Juan Sebastian Martinez, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

The Summer Undergraduate Research Fellowship (SURF) Symposium

Multi-objective optimization (MOO) problems arise frequently in science and engineering situations. In an optimization problem, we want to find the set of input parameters that generate the set of optimal outputs, mathematically known as the Pareto frontier (PF). Solving the MOO problem is a challenge since expensive experiments can be performed only a constrained number of times and there is a limited set of data to work with, e.g. a roll-to-roll microwave plasma chemical vapor deposition (MPCVD) reactor for manufacturing high quality graphene. State-of-the-art techniques, e.g. evolutionary algorithms; particle swarm optimization, require a large amount of observations and do not …

Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, Haley Renee Dozier

Master's Theses

Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.

This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.

Numerical Computing With Functions On The Sphere And Disk, Heather Denise Wilber

Boise State University Theses and Dissertations

A new low rank approximation method for computing with functions in polar and spherical geometries is developed. By synthesizing a classic procedure known as the double Fourier sphere (DFS) method with a structure-preserving variant of Gaussian elimination, approximants to functions on the sphere and disk can be constructed that (1) preserve the bi-periodicity of the sphere, (2) are smooth over the poles of the sphere (and origin of the disk), (3) allow for the use of FFT-based algorithms, and (4) are near-optimal in their underlying discretizations. This method is used to develop a suite of fast, scalable algorithms that exploit …

An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

Electronic Theses and Dissertations

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R³, but also to the general case of finding minimal functionals on hypersurfaces in Rⁿ associated with an arbitrary metric.

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model …