Iteration With Stepsize Parameter And Condition Numbers For A Nonlinear Matrix Equation, 2018 Pusan National University

#### Iteration With Stepsize Parameter And Condition Numbers For A Nonlinear Matrix Equation, Syed M. Raza Shah Naqvi, Jie Meng, Hyun-Min Kim

*Electronic Journal of Linear Algebra*

In this paper, the nonlinear matrix equation $X^p+A^TXA=Q$, where $p$ is a positive integer, $A$ is an arbitrary $n\times n$ matrix, and $Q$ is a symmetric positive definite matrix, is considered. A fixed-point iteration with stepsize parameter for obtaining the symmetric positive definite solution of the matrix equation is proposed. The explicit expressions of the normwise, mixed and componentwise condition numbers are derived. Several numerical examples are presented to show the efficiency of the proposed iterative method with proper stepsize parameter and the sharpness of the three kinds of condition numbers.

Transport Phenomena In Field Effect Transistors, 2018 National Institute of Standards and Technology

#### Transport Phenomena In Field Effect Transistors, Ryan M. Evans, Arvind Balijepalli, Anthony Kearsley

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

United States Population Future Estimates And Long-Term Distribution, 2018 DePaul University

#### United States Population Future Estimates And Long-Term Distribution, Sean P. Brogan

*DePaul Discoveries*

The population of the United States has always increased year over year. Even now with decreasing birth rates, the overall population continues to grow when looking at conventional models. The present study specifically examines what would happen to the U.S. population if we were to maintain the current birth and survival rates into the future. By 2050, our research shows that the U.S. population will become much older and cease to grow at all.

Algorithmic Trading With Prior Information, 2018 Washington University in St. Louis

#### Algorithmic Trading With Prior Information, Xinyi Cai

*Arts & Sciences Electronic Theses and Dissertations*

Traders utilize strategies by using a mix of market and limit orders to generate profits. There are different types of traders in the market, some have prior information and can learn from changes in prices to tweak her trading strategy continuously(Informed Traders), some have no prior information but can learn(Uninformed Learners), and some have no prior information and cannot learn(Uninformed Traders). In this thesis. Alvaro C, Sebastian J and Damir K \cite{AL} proposed a model for algorithmic traders to access the impact of dynamic learning in profit and loss in 2014. The traders can employ the ...

Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, 2018 The University of Southern Mississippi

#### Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Montiforte

*Master's Theses*

Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.

Properties And Computation Of The Inverse Of The Gamma Function, 2018 The University of Western Ontario

#### Properties And Computation Of The Inverse Of The Gamma Function, Folitse Komla Amenyou

*Electronic Thesis and Dissertation Repository*

We explore the approximation formulas for the inverse function of Γ. The inverse function of Γ is a multivalued function and must be computed branch by branch. We compare three approximations for the principal branch Γ̌ 0 . Plots and numerical values show that the choice of the approximation depends on the domain of the arguments, specially for small arguments. We also investigate some iterative schemes and find that the Inverse Quadratic Interpolation scheme is better than Newton’s scheme for improving the initial approximation. We introduce the contours technique for extending a real-valued function into the complex plane using two ...

Math Behind Computer Graphics: Piecewise Smooth Interpolation, 2018 Carroll College

#### Math Behind Computer Graphics: Piecewise Smooth Interpolation, Jesica Bauer

*Carroll College Student Undergraduate Research Festival*

Modern computers are able to create complex imagery with only a small set of information. For example, the fonts on your computer are saved as a set of points and the computer is told how to connect them. Many 3D animations start the same way, where the animation starts as a grid before the rest of the shape is systematically filled in. But how does the computer know how to connect the dots into a mesh? Or know how to create the smooth surface so that it doesn’t look blocky? To solve these problems, we implement mathematical algorithms to ...

Analyzing Lagrangian Statistics Of Eddy-Permitting Models, 2018 University of Colorado, Boulder

#### Analyzing Lagrangian Statistics Of Eddy-Permitting Models, Amy Chen

*Applied Mathematics Graduate Theses & Dissertations*

Mesoscale eddies are the strongest currents in the world oceans and transport properties such as heat, dissolved nutrients, and carbon. The current inability to effectively diagnose and parameterize mesoscale eddy processes in oceanic turbulence is a critical limitation upon the ability to accurately model large-scale oceanic circulations. This investigation analyzes the Lagrangian statistics for four faster and less computationally expensive eddy-permitting models --- Biharmonic, Leith, Jansen & Held Deterministic, and Jansen & Held Stochastic --- and compares them against each other and an eddy-resolving quasigeostrophic Reference model. Results from single-particle climatology show that all models exhibit similar behaviour in large-scale movement over long times ...

The Devil You Don’T Know: A Spatial Analysis Of Crime At Newark’S Prudential Center On Hockey Game Days, 2018 Institute for Security and Crime Science - University of Waikato

#### The Devil You Don’T Know: A Spatial Analysis Of Crime At Newark’S Prudential Center On Hockey Game Days, Justin Kurland, Eric Piza

*Journal of Sport Safety and Security*

Inspired by empirical research on spatial crime patterns in and around sports venues in the United Kingdom, this paper sought to measure the criminogenic extent of 216 hockey games that took place at the Prudential Center in Newark, NJ between 2007-2016. Do games generate patterns of crime in the areas beyond the arena, and if so, for what type of crime and how far? Police-recorded data for Newark are examined using a variety of exploratory methods and non-parametric permutation tests to visualize differences in crime patterns between game and non-game days across all of Newark and the downtown area. Change ...

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, 2018 Nanjing University of Aeronautics and Astronautics

#### Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

*Mathematics and Statistics Faculty Publications*

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved ...

Fast Verified Computation For The Solvent Of The Quadratic Matrix Equation, 2018 Iwate University

#### Fast Verified Computation For The Solvent Of The Quadratic Matrix Equation, Shinya Miyajima

*Electronic Journal of Linear Algebra*

Two fast algorithms for numerically computing an interval matrix containing the solvent of the quadratic matrix equation $AX^2 + BX + C = 0$ with square matrices $A$, $B$, $C$ and $X$ are proposed. These algorithms require only cubic complexity, verify the uniqueness of the contained solvent, and do not involve iterative process. Let $\ap{X}$ be a numerical approximation to the solvent. The first and second algorithms are applicable when $A$ and $A\ap{X}+B$ are nonsingular and numerically computed eigenvector matrices of $\ap{X}^T$ and $\ap{X} + \inv{A}B$, and $\ap{X}^T$ and $\inv{(A\ap ...

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, 2018 Western Kentucky University

#### Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

*Masters Theses & Specialist Projects*

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of ...

Rapid Generation Of Jacobi Matrices For Measures Modified By Rational Factors, 2018 The University of Southern Mississippi

#### Rapid Generation Of Jacobi Matrices For Measures Modified By Rational Factors, Amber Sumner

*Dissertations*

Orthogonal polynomials are important throughout the fields of numerical analysis and numerical linear algebra. The Jacobi matrix J for a family of n orthogonal polynomials is an n x n tridiagonal symmetric matrix constructed from the recursion coefficients for the three-term recurrence satisfied by the family. Every family of polynomials orthogonal with respect to a measure on a real interval [a,b] satisfies such a recurrence. Given a measure that is modified by multiplying by a rational weight function r(t), an important problem is to compute the modified Jacobi matrix Jmod corresponding to the new measure from knowledge of ...

General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, 2018 Louisiana State University and Agricultural and Mechanical College

#### General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai

*LSU Doctoral Dissertations*

A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory ...

Numerical Simulation Of Energy Localization In Dynamic Materials, 2018 Tallinn University of Technology

#### Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski

*Publications*

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also ...

Numerical Studies Of Electrohydrodynamic Flow Induced By Corona And Dielectric Barrier Discharges, 2018 The University of Western Ontario

#### Numerical Studies Of Electrohydrodynamic Flow Induced By Corona And Dielectric Barrier Discharges, Chaoao Shi

*Electronic Thesis and Dissertation Repository*

Electrohyrodynamic (EHD) flow produced by gas discharges allows the control of airflow through electrostatic forces. Various promising applications of EHD can be considered, but this requires a deeper understanding of the physical mechanisms involved.

This thesis investigates the EHD flow generated by three forms of gas discharge. First, a multiple pin-plate EHD dryer associated with the positive corona discharge is studied using a stationary model. Second, the dynamics of a dielectric barrier discharge (DBD) plasma actuator is simulated with a time-dependent solver. Third, different configurations of the extended DBD are explored to enhance the EHD flow.

The results of the ...

Theoretical Analysis Of Nonlinear Differential Equations, 2018 Stephen F Austin State University

#### Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

*Electronic Theses and Dissertations*

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy ...

Truancy In High School, 2018 Northeastern Illinois University

#### Truancy In High School, Itzel Ruiz, Jason Mink, Xochitl Aleman

*SPACE: Student Perspectives About Civic Engagement*

The main focus of this project is to analyze students’ poor attendance in order to understand the applicable factors as to why upperclassmen tend to miss more school than students in younger grades. We will be focusing on how students relationships with parents and teachers affect upperclassmen attendance. An anonymous ten question survey was given to five Junior and Senior Civics and U.S. History classes at Steinmetz College Prep high school. The questions were geared towards the students days absent during the school year, and their relationship with teachers and parents. Majority of the students surveyed missed more than ...

An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, 2018 Washington University in St. Louis

#### An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen

*Ronald Greenberg*

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three sub-algorithms. The first is a Gauss-Seidel type step. The second is a real (non-interval) Newton iteration. The third solves the linearized equations by elimination. We explain why each sub-algorithm is desirable and how they fit together to provide solutions in as little as 1/3 to 1/4 the time required by a commonly used method due to Krawczyk.

Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, 2018 The University of Akron

#### Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans

*Honors Research Projects*

The spreading behavior of spherical and cylindrical water droplets between 30Å and 100Å in radius on a sapphire surface is investigated using all-atom molecular dynamics simulations for durations on the order of tens of nanoseconds. A monolayer film develops rapidly and wets the surface, while the bulk of the droplet spreads on top of the monolayer, maintaining the shape of a spherical cap. Unlike previous simulations in the literature, the bulk radius is found to increase to a maximum value and receed as the monolayer continues to expand. Simple time and droplet size dependence is observed for monolayer radius and ...