Applied Mathematics Commons^™

The Multivariate Statistical Analysis Of Abiotic Parameters Of The Lake Tanganyika Sub Catchment, Hudson Nkotagu

Tanzania Journal of Engineering and Technology (TJET)

Results from multivariate statistical analysis of abiotic parameters conducted during the dry season at 20 accessible sites on 8 rivers, 2 lakes and a dam covering the Lake Tanganyika sub catchment are discussed. Standard methods were used to determine the levels of abiotic parameters from water samples. Physical parameters including DO, EC, Eh, turbidity, temperature, pH and secchi transparency were measured in situ while chlorophyll a was determined in the laboratory. Nutrients such as NO3-, SiO2, PO4 3- and Fe2+ were determined along with HCO3-. Factor analysis resulted in four factors including increased primary productivity, redox conditions, dissolution, and reduction …

An Equation For Estimating The (R) Usle Slope Steepness Factors, Mathew Mulemgera

Tanzania Journal of Engineering and Technology (TJET)

Abstract Currently three equations are used for calculating slope steepness factor for the Revised Universal Soil Loss Equation (RUSLE); one for slopes less than nine percent, the second for slopes equal or greater than nine percent, and the third equation that has been proposed for use in China for slopes equal or greater than 17 %. The three equations have linear relationships between slope steepness factor, S and the sine of the slope angle, θ. The three equations under predict the factor, S when used on slope steepness beyond the data sets used to develop them. In addressing this problem …

Confidence Intervals For A Common Mean With Missing Data With Applications In An Aids Study, Hua Liang, Haiyan Su, Guohua Zou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In practical data analysis, nonresponse phenomenon frequently occurs. In this paper, we propose an empirical likelihood based confidence interval for a common mean by combining the imputed data, assuming that data are missing completely at random. Simulation studies show that such confidence intervals perform well, even when the missing proportion is high. Our method is applied to an analysis of a real data set from an AIDS clinic trial study.

Greedy Signal Recovery Review, Deanna Needell, Joel A. Tropp, Roman Vershynin

CMC Faculty Publications and Research

The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees.

Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This …

Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling

Mathematical Sciences Technical Reports (MSTR)

Developing methods for the nondestructive testing of materials is an important area of research for industry. Situations often arise in which the integrity of an object is questioned, but testing it is very difficult. For example, a support bar may be embedded in a larger structure so that testing the bar’s integrity directly would require the impractical task of breaking down the larger structure. Instead, the ends of the bar might be accessible without dismantling the enclosing structure. The goal of nondestructive testing is to use methods that require taking measurements at the ends of the bar alone to give …

Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones

Mathematical Sciences Technical Reports (MSTR)

Impedance imaging has received a lot of attention in the past two decades, as a means for non-destructively imaging the interior of a conductive object. One injects a known electrical current pattern into an object at the exterior boundary, then measures the induced potential (voltage) on some portion of the boundary. The goal is to recover information about the interior conductivity of the object, which (we hope) influences the voltages we measure. Of course one can also use multiple input currents and measured voltages. A variation on this problem is that of "boundary identification," in which some portion of the …

Transient Analysis Of Heat And Mass Transfer By Natural Convection In Power-Law Fluid Past A Vertical Plate Immersed In A Porous Medium (Numerical Study), Nasser S. Elgazery

Applications and Applied Mathematics: An International Journal (AAM)

This paper attempted a numerical examination of the problem of unsteady free convection with heat and mass transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium. The flow in the porous medium was described via the Darcy-Brinkman-Forchheimer model. The simultaneous development of the problem of boundary layers was obtained numerically by finite difference method. Boundary layer and Boussinesq approximations had been incorporated. Numerical calculations were carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles were shown graphically and the physical quantities of the problem were given in tables. It …

Soliton Perturbation Theory For The Modified Kawahara Equation, Anjan Biswas

Applications and Applied Mathematics: An International Journal (AAM)

The modified Kawahara equation is studied along with its perturbation terms. The adiabatic dynamics of the soliton amplitude and the velocity of the soliton are obtained by the aid of soliton perturbation theory.

On The Mixed Sum Of Doubly Infinite And Finite Independent Random Variables, Mridula Garg

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the present paper is to study the distribution of the mixed sum of two random variables. Here we establish a theorem which gives the probability density function (pdf) of sum of doubly infinite and finite independent random variables. The distribution of the infinite and finite independent random variables is given in the form of corollary. As an application of these results we have obtained a distribution of sum of bilateral exponential variate with triangular, Rayleigh with uniform and Weibull with triangular variate. Some graphs of these distributions have also been given.

Establishment Of A Chebyshev-Dependent Inhomogeneous Second Order Differential Equation For The Applied Physics-Related Boubaker-Turki Polynomials, Micahel Dada, O. Bamidele Awojoyogbe, Maximilian Hasler, Karem B. Ben Mahmoud, Amine Bannour

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes Chebyshev-dependent inhomogeneous second order differential equation for the m-Boubaker polynomials (or Boubaker-Turki polynomials). This differential equation is also presented as a guide to applied physics studies. A concrete example is given through an attempt to solve the Bloch NMR flow equation inside blood vessels.

Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable combination of homotopy perturbation method and Padé approximants to investigate the Flierl-Petviashivili (FP) equation. The approach introduces a new transformation necessary for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed homotopy perturbation method is applied to the reformulated first order initial value problem which leads the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm may …

Numerical Modeling Of A Stenosed Artery Using Mathematical Model Of Variable Shape, S. Mukhopadhyay, G. C. Layek

Applications and Applied Mathematics: An International Journal (AAM)

The intention of the present work is to carry out a systematic analysis of flow behavior in a two-dimensional tube (modeled as artery) with a locally variable shaped constrictions. The simulated artery, containing a viscous incompressible fluid representing the flowing blood, is treated to be complaint as well as rigid tube. The shape of the stenosis in the arterial lumen is chosen to be symmetric as well as asymmetric about the middle cross section perpendicular to the axis of the tube in order to improve resemblance to the in-vivo situation. The constricted tube is transformed into a straight tube and …

On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

The a-ary 3-point and 5-point interpolatery subdivision schemes for curve design are introduced for arbitrary odd integer a greater than or equal to 3. These new schemes further extend the family of the classical 4- and 6-point interpolatory schemes.

A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the variational iteration method (VIM) for solving higher-order integro differential equations by converting the problems into system of integral equations. The proposed technique is applied to the re-formulated system of integro-differential equations. Numerical results show the accuracy and efficiency of the suggested algorithm. The fact that the VIM solves nonlinear problems without calculating Adomian’s polynomials is a clear advantage of this technique over the decomposition method.

On Existence And Uniqueness Theorem Concerning Time–Dependent Heat Transfer Model, Naji A. Qatanani, Qasem M. Heeh

Applications and Applied Mathematics: An International Journal (AAM)

In this article we consider a physical model describing time-dependent heat transfer by conduction and radiation. This model contains two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-grey surfaces. The aim of this work is to present a reliable framework to prove the existence and the uniqueness of a weak solution for this problem. The existence of the solution can be proved by solving an auxiliary problem by the Galerkin-based approximation method and Moser-type arguments which implies the existence of solution to the original problem. The uniqueness of the solution will …

Robust Stability And Optimality Conditions For Parametric Infinite And Semi-Infinite Programs, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper primarily concerns the study of parametric problems of infinite and semi-infinite programming, where functional constraints are given by systems of infinitely many linear inequalities indexed by an arbitrary set T, where decision variables run over Banach (infinite programming) or finite-dimensional (semi-infinite case) spaces, and where objectives are generally described by nonsmooth and nonconvex cost functions. The parameter space of admissible perturbations in such problems is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the l(infinity)-type. By using …

Remarks On The Stability Of Some Size-Structured Population Models Iii: The Case Of Constant Inflow Of Newborns, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El- Doma (2006) and El-Doma (2008).

Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a relatively new technique which is called the variational iteration decomposition method (VIDM) by combining the traditional variational iteration and the decomposition methods for solving higher dimensional initial boundary value problems. The proposed method is an elegant combination of variational iteration and the decomposition methods. The analytical results of the problems have been obtained in terms of convergent series with easily computable components. The method is quite efficient and is practically well suited for use in these problems. Several examples are given to verify the accuracy and efficiency of the proposed technique.

Chebyshev Collocation Method For The Effect Of Variable Thermal Conductivity On Micropolar Fluid Flow Over Vertical Cylinder With Variable Surface Temperature, Nasser S. Elgazery, Nader Y. Abd Elazem

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is performed to study the role of a variable thermal conductivity on unsteady free convection in a micro-polar fluid past a semi-infinite vertical cylinder with variable surface temperature in the presence of magnetic filed and radiation. The surface temperature is measured to vary as a power of the axial coordinate measured from the leading edge of the cylinder. The governing non-linear partial differential equations are transformed into a linear algebraic system utilizing Chebyshev collocation method in spatial and Crank-Nicolson method in time. Numerical results for the velocity, angular velocity and temperature profiles as well as for the local …

The Möbius Geometry Of Hypersurfaces, Michael Bolt

University Faculty Publications and Creative Works

No abstract provided.

The Möbius Geometry Of Hypersurfaces, Michael Bolt

University Faculty Publications and Creative Works

No abstract provided.

Global Existence Of Some Infinite Energy Solutions For A Perfect Incompressible Fluid, Ralph A. Saxton, Feride Tiğlay

Mathematics Faculty Publications

This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we obtain an initial value problem for a nonlocal equation. We establish local well-posedness in all dimensions and persistence in time of these solutions for three and higher dimensions. We also examine a weaker class of global solutions.

Metric Regularity Of Mappings And Generalized Normals To Set Images, Boris S. Mordukhovich, Nguyen Mau Nam, Bingwu Wang

Mathematics Research Reports

The primary goal of this paper is to study some notions of normals to nonconvex sets in finite-dimensional and infinite-dimensional spaces and their images under single-valued and set-valued mappings. The main motivation for our study comes from variational analysis and optimization, where the problems under consideration play a crucial role in many important aspects of generalized differential calculus and applications. Our major results provide precise equality formulas (sometimes just efficient upper estimates) allowing us to compute generalized normals in various senses to direct and inverse images of nonconvex sets under single-valued and set-valued mappings between Banach spaces. The main tools …

Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li

Mathematics and Statistics Faculty Publications

In this article, we provide some asymptotic behaviors of linearized viscoelastic flows in a general two-dimensional domain with certain parameters small and the time variable large.

Numerical Simulation Of Thermo-Elasticity, Inelasticity And Rupture Inmembrane Theory, Michael Taylor

Mechanical Engineering

Two distinct two-dimensional theories for the modeling of thin elastic bodies are developed. These are demonstrated through numerical simulation of various types of membrane deformation. The work includes a continuum thermomechanics-based theory for wrinkled thin films. The theory takes into account single-layer sheets as well as composite membranes made of multiple lamina. The resulting model is applied to the study of entropic elastic elastomers as well as Mylar/aluminum composite films. The latter has direct application in the area of solar sails. Several equilibrium deformations are illustrated numerically by applying the theory of dynamic relaxation to a finite difference discretization based …

Optimization Of Delay-Differential Inclusions Of Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang

Mathematics Research Reports

No abstract provided.

Topological Dynamics Of Two-Piece Eventually Expanding Maps, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this work we show that two-piece eventually expanding maps have the same topological dynamics as two-piece expanding maps. A two-piece eventually expanding map possesses an invariant set that is either a topological attractor or can be perturbed to become one.

Limiting Subgradients Of Minimal Time Functions In Banach Spaces, Boris S. Mordukhovich, Nguyen Mau Nam

Mathematics Research Reports

The paper mostly concerns the study of generalized differential properties of the so-called minimal time functions associated, in particular, with constant dynamics and arbitrary closed target sets in control theory. Functions of this type play a significant role in many aspects of optimization, control theory: and Hamilton-Jacobi partial differential equations. We pay the main attention to computing and estimating limiting subgradients of the minimal value functions and to deriving the corresponding relations for Frechet type epsilon-subgradients in arbitrary Banach spaces.

Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall

Miscellaneous (presentations, translations, interviews, etc)

We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow …

The Roc Curves Of Fused Independent Classification Systems, Michael B. Walsh

Theses and Dissertations

The need for optimal target detection arises in many different fields. Due to the complexity of many targets, it is thought that the combination of multiple classification systems, which can be tuned to several individual target attributes or features, might lead to more optimal target detection performance. The ROC curves of fused independent two-label classification systems may be generated by the mathematical combination of their ROC curves to achieve optimal classifier performance without the need to test every Boolean combination. The monotonic combination of two-label independent classification systems which assign labels to the same target types results in a lattice …