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Articles 6151 - 6180 of 7997
Full-Text Articles in Physical Sciences and Mathematics
Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din
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.
A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din
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.
Remarks On The Stability Of Some Size-Structured Population Models Iii: The Case Of Constant Inflow Of Newborns, Mohammed El-Doma
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).
Numerical Modeling Of A Stenosed Artery Using Mathematical Model Of Variable Shape, S. Mukhopadhyay, G. C. Layek
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 …
The Möbius Geometry Of Hypersurfaces, Michael Bolt
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
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.
An Optimal Principle In Fluid-Structure Interaction, Bong Jae Chung, Ashuwin Vaidya
An Optimal Principle In Fluid-Structure Interaction, Bong Jae Chung, Ashuwin Vaidya
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We study the steady terminal orientation of a fore-aft symmetric body as it settles in a viscous fluid. An optimal principle for the settling behavior is discussed based upon entropy production in the system, both in the Stokes limit and the case of near equilibrium states when inertial effects emerge. We show that in the Stokes limit, the entropy production in the system is zero allowing any possible terminal orientation while in the presence of inertia, the particle assumes a horizontal position which coincides with the state of maximum entropy production. Our results are seen to agree well with experimental …
Metric Regularity Of Mappings And Generalized Normals To Set Images, Boris S. Mordukhovich, Nguyen Mau Nam, Bingwu Wang
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
Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li
Yi Li
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.
Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li
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.
All-Optical Suppression Of Relativistic Self-Focusing Of Laser Beams In Plasmas, Serguei Y. Kalmykov, Sunghwan A. Yi, Gennady Shvets
All-Optical Suppression Of Relativistic Self-Focusing Of Laser Beams In Plasmas, Serguei Y. Kalmykov, Sunghwan A. Yi, Gennady Shvets
Serge Youri Kalmykov
It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bi-envelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly …
Numerical Simulation Of Thermo-Elasticity, Inelasticity And Rupture Inmembrane Theory, Michael Taylor
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
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
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.
Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd
Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd
Chris J. Lloyd
The exact null distribution of a P-value typically depends on nuisance parameters unspecified under the null. For discrete models and standard approximate P-values, this dependence can be quite strong. The estimated (or bootstrap) P-value is the exact probability of the P-value being no larger than its observed value, with the null estimate of the nuisance parameter substituted. For continuous models, it is known that such `bootstrap' P-values deviate from uniformity by terms of order m^{-3/2}, where m is a measure of sample size. The main difficulty with discrete models is the breakdown of asymptotics near the boundary. The aim of …
Oscillating Regime In Carbonylation Reaction Of Propargyl Alcohol (In Russian), Sergey N. Gorodsky, Anatoly V. Kurdiukov, Oleg N. Temkin
Oscillating Regime In Carbonylation Reaction Of Propargyl Alcohol (In Russian), Sergey N. Gorodsky, Anatoly V. Kurdiukov, Oleg N. Temkin
Sergey N. Gorodsky
No abstract provided.
Limiting Subgradients Of Minimal Time Functions In Banach Spaces, Boris S. Mordukhovich, Nguyen Mau Nam
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
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
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 …
Oscillation Regularity In Noise-Driven Excitable Systems With Multi-Time-Scale Adaptation, William H. Nesse, Christopher A. Del Negro, Paul C. Bressloff
Oscillation Regularity In Noise-Driven Excitable Systems With Multi-Time-Scale Adaptation, William H. Nesse, Christopher A. Del Negro, Paul C. Bressloff
Arts & Sciences Articles
We investigate oscillation regularity of a noise-driven system modeled with a slow after-hyperpolarizing adaptation current (AHP) composed of multiple-exponential relaxation time scales. Sufficiently separated slow and fast AHP time scales (biphasic decay) cause a peak in oscillation irregularity for intermediate input currents I, with relatively regular oscillations for small and large currents. An analytic formulation of the system as a stochastic escape problem establishes that the phenomena is distinct from standard forms of coherence resonance. Our results explain data on the oscillation regularity of the pre-Bötzinger complex, a neural oscillator responsible for inspiratory breathing rhythm generation in mammals.
Fast Fourier Transform Algorithms With Applications, Todd Mateer
Fast Fourier Transform Algorithms With Applications, Todd Mateer
All Dissertations
This manuscript describes a number of algorithms that can be used to quickly evaluate a polynomial over a collection of points and interpolate these evaluations back into a polynomial. Engineers define the 'Fast Fourier Transform' as a method of solving the interpolation problem where the coefficient ring used to construct the polynomials has a special multiplicative structure. Mathematicians define the 'Fast Fourier Transform' as a method of solving the evaluation problem. One purpose of the document is to provide a mathematical treatment of the topic of the 'Fast Fourier Transform' that can also be understood by someone who has an …
Portfolio Selection Under Various Risk Measures, Hariharan Kandasamy
Portfolio Selection Under Various Risk Measures, Hariharan Kandasamy
All Dissertations
Portfolio selection has been a major area of study after Markowitz's ground-breaking paper. Risk quantification for portfolio selection is studied in the literature extensively and many risk measures have been proposed.
In this dissertation we study portfolio selection under various risk measures. After exploring important risk measures currently available we propose a new risk measure, Unequal Prioritized Downside Risk (UPDR). We illustrate the formulation of UPDR for portfolio selection as a mixed-integer program. We establish conditions under which UPDR can be formulated as a linear program.
We study single-period portfolio selection using two risk measures simultaneously. We propose four alternate …
Numerical Analysis Of A Fractional Step Theta-Method For Fluid Flow Problems, John Chrispell
Numerical Analysis Of A Fractional Step Theta-Method For Fluid Flow Problems, John Chrispell
All Dissertations
The accurate numerical approximation of viscoelastic fluid flow poses two difficulties: the large number of unknowns in the approximating algebraic system (corresponding to velocity, pressure, and stress), and the different mathematical types of the modeling equations. Specifically, the viscoelastic modeling equations have a hyperbolic constitutive equation coupled to a parabolic conservation of momentum equation. An appealing approximation approach is to use a fractional step $\theta$-method. The $\theta$-method is an operator splitting technique that may be used to decouple mathematical equations of different types as well as separate the updates of distinct modeling equation variables when modeling mixed systems of partial …
Homomorphisms Of Graphs, Samuel Lyle
Homomorphisms Of Graphs, Samuel Lyle
All Dissertations
Understanding the structure of graphs is fundamental to advances in many areas of graph theory, as well as in many applications. In many cases, an analysis of the structure of graphs follows one of two approaches; either many structural properties are considered over a restricted class of graphs, or a particular structural property is considered over many classes of graphs. Both approaches will be considered in this dissertation.
Graphs which do not contain a clique of size r, i.e., Kr-free graphs, are of fundamental importance in the area of extremal graph theory. Many results have been obtained …
On Graph Isomorphism And The Pagerank Algorithm, Christopher J. Augeri
On Graph Isomorphism And The Pagerank Algorithm, Christopher J. Augeri
Theses and Dissertations
A graph is a key construct for expressing relationships among objects, such as the radio connectivity between nodes contained in an unmanned vehicle swarm. The study of such networks may include ranking nodes based on importance, for example, by applying the PageRank algorithm used in some search engines to order their query responses. The PageRank values correspond to a unique eigenvector typically computed by applying the power method, an iterative technique based on matrix multiplication. The first new result described herein is a lower bound on the execution time of the PageRank algorithm that is derived by applying standard assumptions …
The Dependence Of Measured Modulation Error Ratio On Phase Noise, Ron D. Katznelson
The Dependence Of Measured Modulation Error Ratio On Phase Noise, Ron D. Katznelson
Ron D. Katznelson
This paper reviews the algorithms used by Vector Signal Analyzers to measure Modulation Error Ratio (MER) and derives the explicit functional dependence of measured MER on phase noise of digital transmitters. The modulation error model is introduced and the analytical expression for key estimated parameters required to obtain MER measure are derived. The essential elements of algorithms employed by MER measurement instruments to estimate amplitude scale, frequency offset, and initial phase intercept and the resulting MER are identified. The frequency response of the effective phase-noise rejection filtering action associated with a given measurement epoch is derived. It is shown that …
Understanding Similarity: Bridging Geometric And Numeric Contexts For Proportional Reasoning, Dana Christine Cox
Understanding Similarity: Bridging Geometric And Numeric Contexts For Proportional Reasoning, Dana Christine Cox
Dissertations
The concept of similarity is uniquely situated at the crossroads of geometric and numerical proportional reasoning. Although studies have documented the existence and nature of student difficulties with this topic, there exists a gap between documented visual insights of younger children and the quantitative inadequacies of older ones. Using a revised version of the Similarity Perception Test followed by 21 clinical interviews, this study investigated the visual and analytical strategies that are used by middle-school students to differentiate and construct similar figures.
New strategies for construction and differentiation were identified, and three overarching conclusions were drawn from the work. First, …
Optimization In The Undergraduate Curriculum, Allen Holder
Optimization In The Undergraduate Curriculum, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
A discussion of how an optimization course fits into the undergraduate mathematics curriculum
Modeling Of Fermentation Processes Using Online Kernel Learning Algorithm, Yi Liu
Modeling Of Fermentation Processes Using Online Kernel Learning Algorithm, Yi Liu
Dr. Yi Liu
No abstract provided.
Adaptive Control Of A Class Of Nonlinear Discrete-Time Systems With Online Kernel Learning, Yi Liu
Adaptive Control Of A Class Of Nonlinear Discrete-Time Systems With Online Kernel Learning, Yi Liu
Dr. Yi Liu
No abstract provided.