Physical Sciences and Mathematics Commons^™

Discrete Grüss Type Inequality On Fractional Calculus, Elvan Akin, Serkan Asliyuce, Ayse Feza Guvenilir, Billur Kaymakcalan

Mathematics and Statistics Faculty Research & Creative Works

We give a discrete Grüss type inequality on fractional calculus.

Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. as a consequence, the convergence of the attractors and longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.

Global Attractor Of Solutions Of A Rational System In The Plane, Miron B. Bekker, Martin Bohner, Hristo D. Voulov

Mathematics and Statistics Faculty Research & Creative Works

We consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured that every positive solution of this system converges to a finite limit. Here we confirm this conjecture, subject to an additional assumption.

Steam Flooding Screening And Eor Prediction By Using Clustering Algorithm And Data Visualization, Na Zhang

Masters Theses

"Enhanced Oil Recovery (EOR) techniques are vitally important in the oil industry because these techniques could not only extend the life of wells, but also produce 10% to 30% additional oil from the reservoir. However, selecting the most suitable EOR techniques for unknown reservoirs is not easy for decision making. Based on literature, EOR screening criteria could help to find the best candidates for unknown projects, which is classified into two categories: conventional EOR screening and advanced EOR screening. In this research, an artificial intelligent (AI) method, hierarchical clustering algorithm, is adapted to analyze both steam flooding projects and worldwide …

Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin

Masters Theses

"In this thesis, we presented in detail different aspects of Verrall's chain ladder method and their advantages and disadvantages. Insurance companies must ensure there are enough reserves to cover future claims. To that end, it is useful to estimate mean expected losses. The chain ladder technique under a general linear model is the most widely used method for such estimation in property and casualty insurance. Verrall's chain ladder technique develops estimators for loss development ratios, mean expected ultimate claims, Bayesian premiums, and Bühlmann credibility premiums. The chain ladder technique can be used to estimate loss development in cases where data …

Day Of The Week Effect In Returns And Volatility Of The S&P 500 Sector Indices, Juan Liu

Masters Theses

"Previous studies have shown that returns associated with the stock market or foreign exchange's futures show variations across the day of the week. On such study, that employs a modified GARCH model for estimation, shows that returns associated with the S&P 500 stock index is highest on Wednesday and lowest returns on Monday. The same study shows that volatility is highest on Fridays and lowest on Wednesdays. In this study we investigate if this day-of-the-week effect on returns and volatility is present in the different sectors that constitute the S&P 500 index. The data set used provides daily returns from …

Essays On Unit Root Testing In Time Series, Xiao Zhong

Doctoral Dissertations

"Unit root tests are frequently employed by applied time series analysts to determine if the underlying model that generates an empirical process has a component that can be well-described by a random walk. More specifically, when the time series can be modeled using an autoregressive moving average (ARMA) process, such tests aim to determine if the autoregressive (AR) polynomial has one or more unit roots. The effect of economic shocks do not diminish with time when there is one or more unit roots in the AR polynomial, whereas the contribution of shocks decay geometrically when all the roots are outside …

Small Sample Saddlepoint Confidence Intervals In Epidemiology, Pasan Manuranga Edirisinghe

Doctoral Dissertations

"In section 1, we develop a novel method of confidence interval construction for directly standardized rates. These intervals involve saddlepoint approximations to the intractable distribution of a weighted sum of Poisson random variables and the determination of hypothetical Poisson mean values for each of the age groups. Simulation studies show that, in terms of coverage probability and length, the saddlepoint confidence interval (SP) outperforms four competing confidence intervals obtained from the moment matching (M8), gamma-based (G1,G4) and ABC bootstrap (ABC) methods.

In section 2, we first consider Brillinger's classical model for a vital rate estimate with a random denominator. We …

Small Sample Umpu Equivalence Testing Based On Saddlepoint Approximations, Renren Zhao

Doctoral Dissertations

"In the first section, we consider small sample equivalence tests for exponentiality. Statistical inference in this setting is particularly challenging since equivalence testing procedures typically require a much larger sample size, in comparison to classical "difference tests", to perform well. We make use of Butler's marginal likelihood for the shape parameter of a gamma distribution in our development of equivalence tests for exponentiality. We consider two procedures using the principle of confidence interval inclusion, four Bayesian methods, and the uniformly most powerful unbiased (UMPU) test where a saddlepoint approximation to the intractable distribution of a canonical sufficient statistic is used. …

Space-Based Relative Multitarget Tracking, Keith Allen Legrand

Masters Theses

"Access to space has expanded dramatically over the past decade. The growing popularity of small satellites, specifically cubesats, and the following launch initiatives have resulted in exponentially growing launch numbers into low Earth orbit. This growing congestion in space has punctuated the need for local space monitoring and autonomous satellite inspection. This work describes the development of a framework for monitoring local space and tracking multiple objects concurrently in a satellite's neighborhood. The development of this multitarget tracking systems has produced collateral developments in numerical methods, relative orbital mechanics, and initial relative orbit determination.

This work belongs to a class …

Uncertainty Quantification Of Turbulence Model Closure Coefficients For Transonic Wall-Bounded Flows, John Anthony Schaefer

Masters Theses

"The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-ω Model, and the …

Computational Intelligence Based Complex Adaptive System-Of-Systems Architecture Evolution Strategy, Siddharth Agarwal

Doctoral Dissertations

The dynamic planning for a system-of-systems (SoS) is a challenging endeavor. Large scale organizations and operations constantly face challenges to incorporate new systems and upgrade existing systems over a period of time under threats, constrained budget and uncertainty. It is therefore necessary for the program managers to be able to look at the future scenarios and critically assess the impact of technology and stakeholder changes. Managers and engineers are always looking for options that signify affordable acquisition selections and lessen the cycle time for early acquisition and new technology addition. This research helps in analyzing sequential decisions in an evolving …

Investigation Of Robust Optimization And Evidence Theory With Stochastic Expansions For Aerospace Applications Under Mixed Uncertainty, Harsheel R. Shah

Doctoral Dissertations

One of the primary objectives of this research is to develop a method to model and propagate mixed (aleatory and epistemic) uncertainty in aerospace simulations using DSTE. In order to avoid excessive computational cost associated with large scale applications and the evaluation of Dempster Shafer structures, stochastic expansions are implemented for efficient UQ. The mixed UQ with DSTE approach was demonstrated on an analytical example and high fidelity computational fluid dynamics (CFD) study of transonic flow over a RAE 2822 airfoil.

Another objective is to devise a DSTE based performance assessment framework through the use of quantification of margins and …

A Domain Decomposition Method For The Steady-State Navier-Stokes-Darcy Model With Beavers-Joseph Interface Condition, Xiaoming He, Jian Li, Yanping Lin, Ju Ming

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the two regular interface conditions for the mass conservation and the force balance, the Beavers-Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers-Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system [Y. Cao et al., Comm. Math. Sci., 8 (2010), pp. 1-25; Y. Cao et al., SIAM J. Numer. Anal., 47 (2010), pp. 4239-4256]. In …