Applied Mathematics Commons^™

Analysis Of Heart Rate Variability Signal Using State Space Based Methods, Mihails Tihonciks

Theses and Dissertations

In this study, we try to determine validity of the several different measures applied to the nonlinear HRV data. There were many studies done using traditional methods of Approximate Entropy, Correlation Dimension, Lyapunov exponents and recurrence plots. While employing some of these methods, we also decided to use Support Vector Machines. This method of analysis is quite new to the world of nonlinear data. We obtained data from five different groups of young healthy adults: spontaneous breathing group (Normal), metronomic breathing group (Metron) and elite athletes (Ironman), as well as two groups of people participating in specific traditional forms of …

Socio-Economic Impacts Of Computer Viruses In Tanzania, M Victor

Tanzania Journal of Engineering and Technology (TJET)

This paper reports on a research project conducted with an objective of identifying and assessing various approaches used by different computer users (Management, System Administrators and end users) in Tanzania to combat computer viruses (CVs), and to assess users' awareness level on CVs. Specifically, the study aimed at assessing the awareness level on CVs to the Tanzanian business community; analyze the socio -economic impact caused by CVs in Tanzania and; assess existing methods, capacity and limitations on controlling CVs in Tanzania. Data was collected using both questionnaires and interview from financial institutions such as NBC and BOT, and telecommunications sector …

A Remark On Conservative Diffeomorphisms, Jairo Bochi, Bassam R. Fayad, Enrique Pujals

Publications and Research

Abstract:

We show that a stably ergodic diffeomorphism can be C¹ approximated by a diffeomorphism having stably non-zero Lyapunov exponents.

Résumé:

On montre qu'un difféomorphisme stablement ergodique peut être C¹ approché par un difféomorphisme ayant des exposants de Lyapunov stablement non-nuls.

Inverse Scattering Transform For The Camassa-Holm Equation, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.

Hamiltonian Formulation And Integrability Of A Complex Symmetric Nonlinear System, Rossen Ivanov

Articles

The integrability of a complex generalisation of the ’elegant’ system, proposed by D. Fairlie and its relation to the Nahm equation and the Manakov top is discussed.

A System Equivalence Related To Dulac's Extension Of Bendixson's Negative Theorem For Planar Dynamical Systems, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

Bendixson's Theorem [H. Ricardo, A Modem Introduction to Differential Equations, Houghton-Mifflin, New York, Boston, 2003] is useful in proving the non-existence of periodic orbits for planar systems

dx/dt = F(x, y), dy/dt = G (x, y)

in a simply connected domain D, where F, G are continuously differentiable. From the work of Dulac [M. Kot, Elements of Mathematical Ecology, 2nd printing, University Press, Cambridge, 2003] one suspects that system (1) has periodic solutions if and only if the more general system

dx/d tau = B(x, y)F(x, y), dy/d tau = B(x, y)G(x, y)

does, which makes the subcase (1) more …

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by …

Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov

Articles

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.

An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov

Articles

Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system and are universal for a given system. The anharmonic oscillator is chosen as an example and is discussed for different choices of its physical parameters. It is shown that the typical approach for the determination of the Volterra Series representation is not valid for the important case when the nonlinear system exhibits oscillatory behaviour and the input has a pole …

Of Parts And Wholes: Self-Similarity And Synecdoche In Science, Culture And Literature, Dirk Vanderbeke

Reconstruction: Studies in Contemporary Culture

[Editors' Introduction]

The discussion here centers on how self-similarity, or parts resembling a whole, has been a recurring aspect in the most diverse fields of human thinking from antiquity to the present. Primary examples are drawn from physics, biology, cybernetics, alchemy, philosophy, myth and, of course, language and literature. The author argues that self-similar patterns are one of the persistent ways in which the human mind structures its experience and knowledge of the world, and then examines some of the questions that arise when an almost ubiquitous concept, structure or linguistic and literary phenomenon resurfaces in a new guise in …

Is Chaos Theory Postmodern Science?, J. Linn Mackey

Reconstruction: Studies in Contemporary Culture

[Editors' Introduction]

Based on a comparison between the theories of N. Katherine Hayles (Chaos Bound: Orderly Disorder in Contemporary Literature and Science) and Vladimir Tasic (Mathematics and the Roots of Postmodern Thought), J. Linn Mackey asks the question Is Chaos Theory Postmodern Science and looks at parallels between the literature dubbed as postmodern and the scientific branch more properly termed complex dynamics. His conclusions are surprising: both Hayles and Tasic miss important connective elements of both the science and the practice of postmodernism. Postmodern science does, in fact, exist, and literature just may be it.

Review Of The Product Development Process And Information Flow In The Manufacturing Industry: Problems And A Possible Wav Forward, E Opiyo

Tanzania Journal of Engineering and Technology (TJET)

No abstract provided.

Solitary Waves In Layered Nonlinear Media, Randall J. Leveque, Darryl H. Yong

All HMC Faculty Publications and Research

We study longitudinal elastic strain waves in a one-dimensional periodically layered medium, alternating between two materials with different densities and stress-strain relations. If the impedances are different, dispersive effects are seen due to reflection at the interfaces. When the stress-strain relations are nonlinear, the combination of dispersion and nonlinearity leads to the appearance of solitary waves that interact like solitons. We study the scaling properties of these solitary waves and derive a homogenized system of equations that includes dispersive terms. We show that pseudospectral solutions to these equations agree well with direct solutions of the hyperbolic conservation laws in the …

Observations And Modelling Of The Near Equatorial Tropical Atmospheric Boundary Layer, Aiman Abdalla Soleiman

Student Works (2000-2009)

Existing models developed to simulate the evolution of the atmospheric boundary layer (ABL) have focused on the conditions prevalent in mid-latitude regions. The problem for these models in terms of their application to tropical conditions is that the mid-latitude ABL is, in many respects, physically quite different from that of the tropical ABL. Because of this, and due also to the relative lack of relevant atmospheric observations in tropical areas, the tropical ABL is incorrectly represented in such models, and also in various applications that use the mid-latitude ABL representation (for example, air pollution dispersion models). A recent review of …

Real-Time Travel Time Estimation Using Macroscopic Traffic Flow Models, Pushkin Kachroo, Kaan Ozbay, Antoine G. Hobeika

Electrical & Computer Engineering Faculty Research

This paper presents the estimation of travel time on highways based on macroscopic modelling. The focus is on real-time values as compared to average or static values. The macroscopic models are used for distributed and time/space lumped settings and corresponding travel time estimation functions and algorithms are developed. The implications of these algorithms for the implementation of various incident management and traffic control strategies are also discussed.

Equilibrium Spells Death : Applying Chaos Theory To Organisations, Saurav Mukherji

IIMB Management Review

Organisations have long been viewed as open systems consisting of inter-connected components having multiple levels of interdependencies that work together by exchanging resources within themselves and with the environment. Treating organisations as complex systems, organisational designers tried to match the structural complexity of organisations with a complex
environment and technology. However, in the light of some important discoveries in other fields regarding the nature of complex systems, it may be worthwhile to re-examine some of the basic assumptions made.

Application Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Arton Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Art, Silas Kajuna

Tanzania Journal of Engineering and Technology (TJET)

Vibration is one of the techniques employed in the determination of dynamic properties of fruits and vegetables. It entails generation of a mechanical or acoustic vibrational signal which is propagated through the flesh of the agricultural material. A transducer is either attached or held close to the specimen to monitor the propagation of the signal through the specimen. The manner in which the signal is transmitted through the material is analyzed, and the dynamic properties of the specimen which relate to its firmness or its internal being are derived. The technique has been around for the past 30 years or …

Marketing Strategy And Game Theory, Nagasimha Balakrishna Kanagal

IIMB Management Review

Management Update establishes the links between Management Strategy and Game Theory and develops the theme with apt illustrations.

Dynamical Systems: Predictability And Chaos, Blane Hollingsworth

Honors Capstone Projects and Theses

No abstract provided.

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Global Attractors From The Explosion Of Singular Cycles, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Résumé:

Nous présentons dans cette Note des résultats récents concernant l’existence et les bifurcations d’un nouvel attracteur global chaotique.

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke

Mechanical & Aerospace Engineering Theses & Dissertations

The control of payload swing in industrial gantry cranes is a topic of widespread interest. In this thesis, the control of the swing of a payload idealized by a point mass assumption is investigated utilizing s, compact robotics matrix/vector representation of the dynamical model. In this form, this particular system can be viewed as sn underactuated manipulator with equal numbers of active and passive degrees of freedom. The full three dimensional model is developed and linearized by modelling the cable as a single thread of fiexible wire and the degree of dynamic coupling between the active and passive coordinates is …

A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order pre­dictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

Generalized Linear Inversion Using Tau-P Forward Modeling, Stephen Dade Walker

Graduate Theses

The Generalized Linear Inversion (GLI) method is used in conjunction with a tau-p forward model to successfully perform inversions of test and real-data examples. All data examples used are one-dimensional velocity profiles that represent several different cases. The stability of the technique is demonstrated in all the test-data sets. The use of simple models and wel1-control 1ed test data results in a minimum of iterations of the inversion process. Different levels of perturbation of the model and test-data examples are used to reveal insight into the robust nature of the inversion.

Additive Control Of Stochastic Linear Systems With Finite Horizon, Pao-Liu Chow, José-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be …

Entropy Measures In Input-Output Analysis, Martin Zwick, Abbas Heiat

Complex Systems Faculty Publications and Presentations

Applications of Shannon's entropy measure to the matrices of technical and interdependence coefficients, to the final demand vector, and to other aspects of input- output tables are proposed. These entropy measures serve as indices of different types of economic diversity. The relevance of such indices for economic planning and for analyses of economic structural complexity and development is discussed.