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Articles 301 - 330 of 626
Full-Text Articles in Mathematics
Periodic Q-Difference Equations, Rotchana Chieochan
Periodic Q-Difference Equations, Rotchana Chieochan
Doctoral Dissertations
"The concept of periodic functions defined on the real numbers or on the integers is a classical topic and has been studied intensively, yielding numerous applications in every kind of science. It is of importance that the real numbers and the integers are closed with respect to addition. However, for a number q > 1, the so-called q-time scale, i.e., the set of nonnegative integer powers of q, is not closed with respect to addition, and therefore it was not possible to define periodic functions on the q-time scale in an obvious way. In this thesis, this important open problem has …
Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe
Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe
Doctoral Dissertations
"The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for …
Economics And Finance On Time Scales, Julius Severin Heim
Economics And Finance On Time Scales, Julius Severin Heim
Doctoral Dissertations
"This thesis consists of 6 papers that investigate models in economics and finance based on so-called dynamic equations on time scales. The first paper covers multiplier-accelerator models that can be described by linear second-order dynamic equations. The possibility of taxes as well as the possibility of foreign trade is taken into consideration. The second paper discusses cobweb models, which describe cyclical supply and demand in markets, where the supply is determined before the observation of the price. Cobweb models that can be formulated with first-order linear, second-order linear, and nonlinear dynamic equations are being considered. The third and fourth papers …
Small Sample Inference For Exponential Survival Times With Heavy Right-Censoring, Noroharivelo Volaniaina Randrianampy
Small Sample Inference For Exponential Survival Times With Heavy Right-Censoring, Noroharivelo Volaniaina Randrianampy
Doctoral Dissertations
"We develop a saddlepoint-based method and several generalized Bartholomew methods for generating confidence intervals about the rate parameter of an exponential distribution in the presence of heavy random right-censoring. Butler's conditional moment generating function formula is used to derive the relevant moment generating function for the rate parameter score function which provides access to a saddlepoint-based bootstrap method. Moment generating functions also play a key role in the generalized Bartholomew methods we develop. Since heavy censoring is assumed, the possible non-existence of the rate parameter maximum likelihood estimate (MLE) is nonignorable. The overwhelming majority of existing methods condition upon the …
Equivalent Circuit Model Of Coaxial Probes For Patch Antennas, Y. S. Hu, Yanzhi Zhang, Jun Fan
Equivalent Circuit Model Of Coaxial Probes For Patch Antennas, Y. S. Hu, Yanzhi Zhang, Jun Fan
Mathematics and Statistics Faculty Research & Creative Works
An equivalent circuit model of coaxial probes is derived directly from the intrinsic via circuit model. as all the higher-order evanescent modes have been included analytically in the parasitic circuit elements, only the propagating mode needs to be considered by the simplest uniform-current model of a coaxial probe in numerical solvers such as -nite element method (FEM) or -nite divergence time domain (FDTD). This avoids dense meshes or sub-gridding techniques and greatly reduces the computational efforts for accurate calculation of the probe input impedance. the derived equivalent circuit model and the new feeding technique have been validated by both analytical …
Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert
Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert
Masters Theses
"In this work, we study Abel dynamic equations of the first and the second kind. After a brief introduction to time scales, we introduce the Abel differential equations of the first and the second kind, as well as the canonical Abel form in the continuous case. Using the existing information, we derive novel results for time scales. We provide formulas for the Abel dynamic equations of the second kind and present a solution method. We furthermore achieve a special class of Abel equations of the first kind and discuss the canonical Abel equation. We get relations between common dynamic equations …
Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić
Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić
Mathematics and Statistics Faculty Research & Creative Works
We apply the theory of isotonic linear functionals to derive a series of known inequalities, extensions of known inequalities, and new inequalities in the theory of dynamic equations on time scales. © 2011 Matloob Anwar et al.
Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang
Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. the mathematical well-posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two-dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc.
A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang
A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We propose a new parallel Robin-Robin domain decomposition method for the coupled Stokes-Darcy system with Beavers-Joseph-Saffman-Jones interface boundary condition. in particular, we prove that, with an appropriate choice of parameters, the scheme converges geometrically independent of the mesh size. © 2011 Society for Industrial and Applied Mathematics.
A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le
A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.
Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler
Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We consider convergence analysis for a model reduction algorithm for a class of linear infinite dimensional systems. The algorithm computes an approximate balanced truncation of the system using solution snapshots of specific linear infinite dimensional differential equations. The algorithm is related to the proper orthogonal decomposition, and it was first proposed for systems of ordinary differential equations by Rowley (Int. J. Bifurc. Chaos Appl. Sci. Eng. 15(3), 997-1013, 2005). For the convergence analysis, we consider the algorithm in terms of the Hankel operator of the system, rather than the product of the system Gramians as originally proposed by Rowley. For …
Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten
Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale nite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented …
A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten
A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present a model for a rubber plate with piezoceramic actuators to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute a linear quadratic based tracking control for piezoelectric actuators placed along both leading and trailing edges. Using these piezoceramic devices, we demonstrate the effectiveness of model based feedback control in achieving a desired wing tip position; this modified shape is analogous to aircraft roll moment generation via wing twist.
Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler
Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We consider two algorithms to approximate the solution Z of a class of stable operator Lyapunov equations of the form AZ + ZA* + BB* = 0. The algorithms utilize time snapshots of solutions of certain linear infinite-dimensional differential equations to construct the approximations. Matrix approximations of the operators a and B are not required and the algorithms are applicable as long as the rank of B is relatively small. The first algorithm produces an optimal low-rank approximate solution using proper orthogonal decomposition. The second algorithm approximates the product of the solution with a few vectors and can be implemented …
Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le
Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal
Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal
Mathematics and Statistics Faculty Research & Creative Works
In this paper, activation dynamics of complex-valued neural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results. © 2011 Foundation for Scientific Research and Technological Innovation.
Robustness Analysis Of Slow Learning In Iterative Learning Control Systems, John R. Singler, Douglas A. Bristow
Robustness Analysis Of Slow Learning In Iterative Learning Control Systems, John R. Singler, Douglas A. Bristow
Mechanical and Aerospace Engineering Faculty Research & Creative Works
This paper examines robust stability and robust transient growth in Iterative Learning Control (ILC). It is well known that small perturbations in system dynamics can result in very large transient growth of some ILC systems. Even larger perturbations can result in instability. One ad hoc technique commonly employed to improve robustness is to slow the learning rate by reducing the learning filter gain or lowpass filtering the error signal. Here, pseudospectra analysis is used to analyze the robustness of ILC algorithms with slow learning. It is found that robustness bounds can be increased and transient growth decreased with decreasing learning …
Towards Transient Growth Analysis And Design In Iterative Learning Control, Douglas A. Bristow, John R. Singler
Towards Transient Growth Analysis And Design In Iterative Learning Control, Douglas A. Bristow, John R. Singler
Mechanical and Aerospace Engineering Faculty Research & Creative Works
In this article the problem of bounding transient growth in iterative learning control (ILC) is examined. While transient growth is not a desirable property, the alternative, robust monotonic convergence, leads to fundamental performance limitations. to circumvent these limitations, this article considers the possibility that some transient growth, if properly limited, is a viable and practical option. Towards this end, this article proposes tools for analysing worst-case transient growth in ILC. the proposed tools are based on pseudospectra analysis, which is extended to apply to ILC of uncertain systems. Two practical problems in norm-optimal ILC weighting parameter design are considered. Using …
Modeling Hourly Electricity Prices: A Structural Time Series Approach Incorporating Modified Garch Innovations, Edirisinghe Mudiyanselage Asitha Edirisinghe
Modeling Hourly Electricity Prices: A Structural Time Series Approach Incorporating Modified Garch Innovations, Edirisinghe Mudiyanselage Asitha Edirisinghe
Doctoral Dissertations
"The main objective of this research is to develop time series based procedures for modeling day-ahead and real-time hourly electricity prices. Such empirical processes exhibit features that make the direct application of standard time series models infeasible. Four years of hourly day-ahead and real-time electricity price data from the region supplied by the American Electric Power (AEP) company through the PJM Regional Transmission Organization (RTO) and one half years of real-time electricity prices from the MISO RTO are utilized as an empirical basis for developing such procedures. The price data show several features, such as irregular seasonal behavior, weekly and …
Minimal And Near Minimal Congruence Lattice Representations Of Finite Lattices By Finite Algebras On Sets Of Integers, Roger Lee Bunn
Minimal And Near Minimal Congruence Lattice Representations Of Finite Lattices By Finite Algebras On Sets Of Integers, Roger Lee Bunn
Doctoral Dissertations
"We give finite congruence lattice representations of some finite distributive, modular and nonmodular lattices by means of finite algebras on sets of integers. These representations are minimal or near minimal as determined by ρ, a mapping from the class R of finitely representable lattices into the natural numbers N"--Abstract, page iii.
Probability Theory On Time Scales And Applications To Finance And Inequalities, Thomas Matthews
Probability Theory On Time Scales And Applications To Finance And Inequalities, Thomas Matthews
Doctoral Dissertations
"In this dissertation, the recently discovered concept of time scales is applied to probability theory, thus unifying discrete, continuous and many other cases. A short introduction to the theory of time scales is provided. Following this preliminary overview, the moment generating function is derived using a Laplace transformation on time scales. Various unifications of statements and new theorems in statistics are shown. Next, distributions on time scales are defined and their properties are studied. Most of the derived formulas and statements correspond exactly to those from discrete and continuous calculus and extend the applicability to many other cases. Some theorems …
Feedback Control Of A Bioinspired Plate-Beam System, Cody W. Ray, Belinda A. Batten, John R. Singler
Feedback Control Of A Bioinspired Plate-Beam System, Cody W. Ray, Belinda A. Batten, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present a model for a plate-beam system to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute functional gains that can be used for sensor placement and show that a piezoceramic actuator on the beam can be used for camber control
Analysis Of Nonlinear Spectral Eddy-Viscosity Models Of Turbulence, Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang
Analysis Of Nonlinear Spectral Eddy-Viscosity Models Of Turbulence, Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability. © 2009 Springer …
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Partial And Spectral-Viscosity Models For Geophysical Flows, Qingshan Chen, Max Gunzburger, Xiaoming Wang
Partial And Spectral-Viscosity Models For Geophysical Flows, Qingshan Chen, Max Gunzburger, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
Two models based on the hydrostatic primitive equations are proposed. the first model is the primitive equations with partial viscosity only and is oriented towards large-scale wave structures in the ocean and atmosphere. the second model is the viscous primitive equations with spectral eddy viscosity and is oriented towards turbulent geophysical flows. for both models, the existence and uniqueness of global strong solutions are established. for the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established. © 2010 Editorial Office of CAM (Fudan University) …
Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang
Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by …
Structural Measurements For Enhanced Mav Flight, John R. Singler, Gregg Abate, Benjamin T. Dickinson
Structural Measurements For Enhanced Mav Flight, John R. Singler, Gregg Abate, Benjamin T. Dickinson
Mathematics and Statistics Faculty Research & Creative Works
Our sense of touch allows us to feel the forces in our limbs when we walk, swim, or hold our arms out the window of a moving car. We anticipate this sense is key in the locomotion of natural flyers. Inspired by the sense of touch, the overall goal of this research is to develop techniques for the estimation of aerodynamic loads from structural measurements for flight control applications. We submit a general algorithm for the direct estimation of distributed steady loads over bodies from embedded noisy deformation-based measurements. The estimation algorithm is applied to a linearly elastic membrane test …
Asymptotic Analysis Of The Differences Between The Stokes-Darcy System With Different Interface Conditions And The Stokes-Brinkman System, Nan Chen, Max Gunzburger, Xiaoming Wang
Asymptotic Analysis Of The Differences Between The Stokes-Darcy System With Different Interface Conditions And The Stokes-Brinkman System, Nan Chen, Max Gunzburger, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We consider the coupling of the Stokes and Darcy systems with different choices for the interface conditions. We show that, comparing results with those for the Stokes-Brinkman equations, the solutions of Stokes-Darcy equations with the Beavers-Joseph interface condition in the one-dimensional and quasi-two-dimensional (periodic) cases are more accurate than are those obtained using the Beavers-Joseph-Saffman-Jones interface condition and that both of these are more accurate than solutions obtained using a zero tangential velocity interface condition. the zero tangential velocity interface condition is in turn more accurate than the free-slip interface boundary condition. We also prove that the summation of the …
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang
Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We consider temporal approximation of stationary statistical properties of dissipative infinite-dimensional dynamical systems. We demonstrate that stationary statistical properties of the time discrete approximations, i.e., numerical scheme, converge to those of the underlying continuous dissipative infinite-dimensional dynamical system under three very natural assumptions as the time step approaches zero. the three conditions that are sufficient for the convergence of the stationary statistical properties are: (1) uniform dissipativity of the scheme in the sense that the union of the global attractors for the numerical approximations is pre-compact in the phase space; (2) convergence of the solutions of the numerical scheme to …