Physical Sciences and Mathematics Commons^™

A New Approach For Solving Of Linear Time Varying Control Systems, Ali Vahidian Kamyad, Mehran Mazandarani

Mehran Mazandarani

This paper is concerned with the solution of Linear Time Varying [LTV] control systems. The concept of a solution for LTV systems is defined on the basis of finding the fundamental matrix corresponding to LTV control systems. There are some numerical methods such as Euler method and Taylor method for obtaining approximate solution of LTV system [LTVs], each of them has some limitations. In the recent years, other kinds of constructive approaches for the solution of LTVs are presented limited to the particular cases of it. In this paper, we introduced a new approach that we call it AVK approach …

Applications Of Variational Analysis To A Generalized Heron Problem, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr

Mathematics Research Reports

This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both qualitative and numerical viewpoints, the following optimal location problem as well as its further extensions: on a given nonempty subset of a Banach space, find a point such that the sum of the distances from it to n given nonempty subsets of this space is minimal. This is a generalized version of the classical Heron problem: on a given straight line, find a point …

Improving The Accuracy Of The Generalized Fdtd-Q Scheme For Solving The Linear Time-Dependent Schrödinger Equation, James John Elliot Iii

Doctoral Dissertations

This dissertation improves the accuracy of the Generalized Finite Difference Time Domain (FDTD) scheme by determining a differential operator that is capable of achieving reasonable accuracy when used to obtain even-order derivatives up to order fourteen. The Generalized FDTD scheme is an explicit, scheme used to solve the time-dependent Schrödinger equation, and being an explicit scheme, it must utilize a carefully devised ratio of the temporal step to the spatial step to maintain numerical stability. This ratio is called the mesh ratio, and the Generalized FDTD scheme allows this ratio to be significantly relaxed. As the mesh ratio increases, the …

A Study On Facility Planning Using Discrete Event Simulation: Case Study Of A Grain Delivery Terminal., Sarah M. Asio

Department of Industrial and Management Systems Engineering: Dissertations, Theses, and Student Research

The application of traditional approaches to the design of efficient facilities can be tedious and time consuming when uncertainty and a number of constraints exist. Queuing models and mathematical programming techniques are not able to capture the complex interaction between resources, the environment and space constraints for dynamic stochastic processes. In the following study discrete event simulation is applied to the facility planning process for a grain delivery terminal. The discrete event simulation approach has been applied to studies such as capacity planning and facility layout for a gasoline station and evaluating the resource requirements for a manufacturing facility. To …

Perfectly Matched Layer Absorbing Boundary Conditions For The Discrete Velocity Boltzmann-Bgk Equation, Elena Craig

Mathematics & Statistics Theses & Dissertations

Perfectly Matched Layer (PML) absorbing boundary conditions were first proposed by Berenger in 1994 for the Maxwell's equations of electromagnetics. Since Hu first applied the method to Euler's equations in 1996, progress made in the application of PML to Computational Aeroacoustics (CAA) includes linearized Euler equations with non-uniform mean flow, non-linear Euler equations, flows with an arbitrary mean flow direction, and non-linear clavier-Stokes equations. Although Boltzmann-BGK methods have appeared in the literature and have been shown capable of simulating aeroacoustics phenomena, very little has been done to develop absorbing boundary conditions for these methods. The purpose of this work was …

Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn

Doctoral Dissertations

In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.

In …

A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, Runzhou Liu

Doctoral Dissertations

Micro heat transfer induced by Ultrashort-pulsed lasers is an important research topic in mechanical engineering and material science. In order to apply ultrashort-pulsed lasers successfully, studying the thermal deformation in double-layered thin films with imperfect thermal interfacial contact induced by ultrashort-pulsed lasers is important for preventing thermal damage. For the ultrashort-pulsed laser, the thermal damage is different from that caused by the long-pulsed lasers, and ultrafast cracks occur after heating.

This dissertation presents a new finite difference method for investigating the thermal deformation in a 3D gold-chromium thin film with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers. The method …

Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov

Articles

The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann- Hilbert problem. The momentum map from the action-angle scattering variables T^∗(T^N) to the flow momentum (X^∗) provides the Eulerian representation of the N-soliton solution of CH in terms of the scattering data and squared eigenfunctions of its isospectral eigenvalue problem. The …

Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis

Mathematics Faculty Publications

During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …

Models, Techniques, And Metrics For Managing Risk In Software Engineering, Andriy Miranskyy

Electronic Thesis and Dissertation Repository

The field of Software Engineering (SE) is the study of systematic and quantifiable approaches to software development, operation, and maintenance. This thesis presents a set of scalable and easily implemented techniques for quantifying and mitigating risks associated with the SE process. The thesis comprises six papers corresponding to SE knowledge areas such as software requirements, testing, and management. The techniques for risk management are drawn from stochastic modeling and operational research.

The first two papers relate to software testing and maintenance. The first paper describes and validates novel iterative-unfolding technique for filtering a set of execution traces relevant to a …

Applications Of Local Fractional Calculus To Engineering In Fractal Time-Space: Local Fractional Differential Equations With Local Fractional Derivative, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.

A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent’s series of complex functions in complex fractal space, and generalized residue theorems are investigated.

Cavitation Modelling Based On Eulerian-Eulerian Multiphase Flow, Rachid Bannari Ph.D

Rachid BANNARI

Cavitation is a physical phenomenon encountered in the normal operation of hydraulic turbines. It can lead to loss in efficiency, vibrations and blade erosion damages. It is crucial to accurately predict cavitation development and evolution to make confident predictive results for hydraulic turbines in a cavitating regime. The cavity closure is a critical region that is characterized by its unsteady and unstable behavior. In this region, liquid and vapor are highly mixed and experienced a strong interaction between the cavity and the outer flow. Most of the published work is based on the mixture multiphase model. An important limitation of …

Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.

A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun

Xiao-Jun Yang

It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.

The Search For Hamilton, Eric Gossett

ACMS Conference Proceedings 2011

In July and August of 2009 my wife and I went on a four-week trip to Scotland and Ireland. We would be visiting Dublin, so I decided that we should visit the famous bridge where William Rowan Hamilton carved the equations for the quaternions. The task was not as simple as I had assumed. This paper gives some details of the search.

Thinking Philosophically About Mathematics, Robert L. Brabenec

ACMS Conference Proceedings 2011

In my early years as a teacher of mathematics, the history of mathematics was seldom mentioned in the classroom. It was viewed as an unworthy topic that would detract from the presentation of mathematics itself. This opinion has dramatically changed over the years, and the history of mathematics is now embraced and used by many mathematicians in their teaching and even research. We might choose to ask a related question. How much philosophy is necessary or helpful for a mathematics teacher to know, and to use in his or her teaching? We see a growing interest in the philosophy of …

Bringing Undergraduate Research Into The Classroom, Stephen Lovett

ACMS Conference Proceedings 2011

Mathematics graduate programs and companies that employ math majors often want to ascertain an applicant’s potential for research. However, in many undergraduate courses, assessments consist only of regular exercise sets, quizzes, and in-class tests. Without doing a senior research thesis or landing an official REUs, students do not regularly gain experience in or an appreciation for research. Courses in the humanities regularly require students to write in the discipline, progressively preparing them methodologically for “writing in the field.” This begs the question: could math departments do a little more to prepare our students to use mathematics beyond college?

In this …

Calculus Communication Circle, Judith Palagallo

ACMS Conference Proceedings 2011

Calculus Communication Circle is a network for the professional development of Advanced Placement Calculus teachers. In Northeast Ohio the Circle provides a forum where teachers meet to share ideas about mathematics and the teaching of calculus. This article describes the creation of the Circle and the progress it has made over its three year existence.

The Need For A Graphics Programming Course, Nathan Gossett

ACMS Conference Proceedings 2011

A discussion of the benefits of offering a course on programming Computer Graphics in an undergraduate Computer Science curriculum. A sample course outline is provided, as well as a discussion of ways to conduct lectures, labs and a list of suggested assignments. A discussion of “dos and don’t s will also be presented, including a list of required prerequisite courses and skills that students would need in order for the course to be a success.

Lesson’S Learned: A Journey In Computational Science, Ryan Botts, Lori Carter

ACMS Conference Proceedings 2011

Inspired by work on building a computational science program and student questions about modeling, we aim to discuss some of our experiences with computational science. We will first clarify what computational science is, why it is a legitimate science, why it is worth our students’ time and what makes it a challenging field. We will also discuss how computer scientists, mathematicians and laboratory scientists each have something different to contribute to the field.

Google And The Mathematics Of Web Search, Michael Rempe

ACMS Conference Proceedings 2011

This article examines the algorithms used by Google to rank search engine results, called PageRank.

Real Simulations And Simulated Reality, Wayne Iba

ACMS Conference Proceedings 2011

Movies such as The Matrix have stimulated popular interest in “brain in a vat” scenarios. Amidst the traditional questions of the mind, we tend to overlook an integral enabling component—the world simulation—which merits consideration in its own right. When facing the simulations in these imagined scenarios, we struggle with conceptual muddles regarding what is real and not. In this paper, I argue that simulated worlds are every bit as real as the one we inhabit. This turns out to be important when considering the possibility, as suggested by Nick Bostrom, that the world we experience as “real” is actually a …

History Of Mathematics: An Exercise In Strengths, Mary Walkins

ACMS Conference Proceedings 2011

As a leader in strengths-based education, Lee University encourages each new student, since fall of 2003, to take the Gallup StrengthsFinder to determine their top 5 signature themes (out of a possible 34). At Lee, the syllabus for the History of Mathematics course calls for students to write a paper on a mathematician. In the fall of 2009, as an added dimension, students were asked to critically think about and incorporate the strengths they believe that mathematician may have. Each student was required to compare and contrast his or her strengths with those of the mathematician. This was done with …

Pascal’S Thoughts Seen In The Light Of Scripture, Loredana Ciurariu

ACMS Conference Proceedings 2011

In this paper we study Pascal’s character via his writings. There are indications that his health might have deteriorated following the experiments he had done using mercury. He talks in his Pensées about faith, grace and purity of the heart, about the peoples and the way in which God leads them, about wisdom, dreams and hopes and that which lies in the human heart. If a statistics was done concerning the most used books and verses from the Bible in Pensées, these would be: Ecclesiastes, Proverbs, Matthew, Mark, Jeremiah, Hebrews, Romans, Luke, Isaiah, Psalms. But those which occupy a central …

The History Of The Area Between A Line And A Parabola, Gordon A. Swain

ACMS Conference Proceedings 2011

This is a review of various methods used by many mathematicians to determine the area of the segment bounded by a parabola and a line. We include descriptions of proofs from the Greek period (Archimedes), the Arabic period (ibn Qurra and ibn Sinan), and the 1600's in European (Galileo, Roberval, Fermat and Wallis, among others), in order to display the changing nature of mathematics.

Pk Mathematics, Jeremy Case

ACMS Conference Proceedings 2011

An examination of the historical development of mathematics and how mathematical history has changed by looking at mathematicians who were also PKs (Preacher’s Kids).

The Mathematics Of Cubic Sudoku, Nicholas Zoller

ACMS Conference Proceedings 2011

In the last decade the Sudoku puzzle has fixed itself in America’s puzzle consciousness. Sudoku puzzles share space with crossword puzzles and word finds in newspaper puzzle sections, and several books have been written for the Sudoku playing community. Mathematicians are among the most dedicated Sudoku players. Although some are content with simply solving puzzle after puzzle, others have used tools from combinatorics and algebra to study its important properties.

We investigate a variant of Sudoku called Cubic Sudoku, as well as Cubic Sudoku’s simpler relative, Cubic Shidoku. We successfully count the number of Cubic Shidoku puzzles in two different …

What We Can Learn From Process Theology: Integrating Faith And Mathematics, Josh Wilkerson

ACMS Conference Proceedings 2011

In the inaugural issue of The Journal of the Association of Christians in the Mathematical Sciences, James Bradley, the founding editor, suggests fourteen areas that need to be addressed by Christian mathematicians who are series about integrating their faith and their work. One of those areas is the topic of this paper. Bradly frames the question: “Some thinkers (perhaps influenced by process theology) have asserted the idea that God’s creation is not a finished work but that he creates new mathematical objects through mathematicians. Is this idea theologically sound? Is it helpful for our understanding of mathematics?” I copy …