Mathematics Commons^™

Reversibility Checking For Markov Chains, P. H. Brill, Chi Ho Cheung, Myron Hlynka, Q. Jiang

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Integral By A Near-Martingale, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Calculus Iii (Fvsu), Patcharin Marion, Dawit Aberra

Mathematics Grants Collections

This Grants Collection for Calculus III was created under a Round Ten ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

College Algebra (Asu), Zephyrinus Okonkwo, Anilkumar Deverapu, Anthony Smith, Vijay Kunwar, Laxmi Paudel

Mathematics Grants Collections

This Grants Collection for College Algebra was created under a Round Ten ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Non-Locality, Precognition & Spirit From The Physics Point Of View, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

There are various supernatural phenomena which can hardly be explained by the existing mainstream science, for instance non-local interactions (e.g. ESP) and also precognitive interdictions. And there are other problems such as how to include the Spirit in the framework of physics. For example, it has been known for long time that intuition plays significant role in many professions and human life, including entrepreneurship, government, and also in detective or law enforcement activities. Despite these examples, such a precognitive interdiction is hardly accepted in mainstream science. In this paper, we discuss non-local interactions and advanced solutions of Maxwell equations, and …

How Many Points Are There In A Line Segment? A New Answer From Discrete Cellular Space Viewpoint, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate our propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: …

Calculus I For Engineers (Ga Southern), Scott Kersey, Rami Haddad

Mathematics Grants Collections

This Grants Collection for Calculus I for Engineers was created under a Round Eleven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

College Algebra (Abac), April Abbott, Gary Dicks, Jan Gregus, Buddhi Pantha, Melanie Partlow, Lori Pearman, Amanda Urquhart, Eunkyung You

Mathematics Grants Collections

This Grants Collection for College Algebra was created under a Round Ten ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Character Sums Of Lee And Weintraub, Brad Isaacson

Publications and Research

We prove two conjectures of Lee and Weintraub and one conjecture of Ibukiyama and Kaneko about character sums arising as fixed point contributions in the Atiyah–Singer holomorphic Lefshetz formula applied to finite group actions on the space of certain Siegel cusp forms.

An Accurate Method For Solving Higher Order Differential Equations Based On The Implicit Hybrid Method, Ahlam Mohammed S Almokhmari

Mathematical Sciences Theses

In this thesis, we present numerical techniques to solve higher order differential equations based on the implicit Hybrid method. In these methods, we use the collocation and interpolating methods. Then, we derive the main schemes and their block methods. We investigate some theoretical results such as the order of the method, consistency, convergence, and region of absolute stability. Some numerical results and simulations are provided to show the efficiency of the proposed methods using Mathematica.

Numerical Ruin Probability In The Dual Risk Model With Risk-Free Investments, Sooie-Hoe Loke, Enrique Thomann

Mathematics Faculty Scholarship

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.

Time Sensitive Functionals Of Marked Random Measures In Real Time, Kizza M. Nandyose Frisbee

Theses and Dissertations

In this dissertation, we study marked random measures that model stochastic networks (under attacks), status of queueing systems during vacation modes, responses to cancer treatments (such as chemotherapy and radiation), hostile actions in economics and warfare. We extend the recently developed time sensitivity technique for investigating the processes’ behavior about a fixed threshold to a novel time sensitive technique in three important directions: (1) real-time monotone stochastic processes; (2) two-dimensional signed random measures; and (3) antagonistic stochastic games with two active players and one passive player. The need for the time sensitive feature in our study (i.e., an analytical association …

Using Magic In Computing Education And Outreach, Ronald I. Greenberg, Dale F. Reed

Computer Science: Faculty Publications and Other Works

This special session explores the use of magic tricks based on computer science ideas; magic tricks help grab students' attention and can motivate them to invest more deeply in underlying CS concepts. Error detection ideas long used by computer scientists provide a particularly rich basis for working such "magic'', with a CS Unplugged parity check activity being a notable example. Prior work has shown that one can perform much more sophisticated tricks than the relatively well-known CS Unplugged activity, and these tricks can motivate analyses across a wide variety of computer science concepts and are relevant to learning objectives across …

Thermodynamically Consistent Hydrodynamic Phase Field Models And Numerical Approximation For Multi-Component Compressible Viscous Fluid Mixtures, Xueping Zhao

Theses and Dissertations

Material systems comprising of multi-component, some of which are compressible, are ubiquitous in nature and industrial applications. In the compressible fluid flow, the material compressibility comes from two sources. One is the material compressibility itself and another is the mass-generating source. For example, the compressibility in the binary fluid flows of non-hydrocarbon (e.g. Carbon dioxide) and hydrocarbons encountered in the enhanced oil recovery (EOR) process, comes from the compressibility of the gas-liquid mixture itself. Another example of the mixture of compressible fluids is growing tissue, in which cell proliferation and cell migration make the material volume changes so that it …

How Design Features In Digital Math Games Support Learning And Mathematics Connections, Patricia S. Moyer-Packenham, Christina W. Lommatsch, Kristy Litster, Jill Ashby, Emma P. Bullock, Allison L. Roxburgh, Jessica F. Shumway, Emily Speed, Benjamin Covington, Christine Hartmann, Jody Clarke-Midura, Joel Skaria, Arla Westenskow, Beth L. Macdonald, Jurgen Symanzik, Kerry Jordan

Teacher Education and Leadership Faculty Publications

Current research shows that digital games can significantly enhance children’s learning. The purpose of this study was to examine how design features in 12 digital math games influenced children’s learning. The participants in this study were 193 children in Grades 2 through 6 (ages 8-12). During clinical interviews, children in the study completed pre-tests, interacted with digital math games, responded to questions about the digital math games, and completed post-tests. We recorded the interactions using two video perspectives that recorded children’s gameplay and responses to interviewers. We employed mixed methods to analyze the data and identify salient patterns in children’s …

The Effects Of Metacognitive Training On Algebra Students’ Calibration Accuracy, Achievement, And Mathematical Literacy, Deana J. Ford

Teaching & Learning Theses & Dissertations

This dissertation describes an empirical study that investigated how metacognitive training influenced lower achieving Algebra students’ calibration accuracy, achievement, and development of mathematics literacy. Multiple methods were used to collect and analyze the data. Close analysis of students’ work and classroom observations revealed that students that were exposed to the metacognitive training had significantly higher prediction accuracy and made gains in their understanding of the mathematics word problems than did students who did not receive the metacognitive training. Overall, however, both the intervention and comparison groups improved in their academic performance and became more mathematically literate and accurate in their …

A Deterministic-Stochastic Method For Computing The Boltzmann Collision Integral In O(Mn) Operations, Alexander Alekseenko, Truong Nguyen, Aihua W. Wood

Faculty Publications

We developed and implemented a numerical algorithm for evaluating the Boltzmann collision integral with O(MN) operations, where N is the number of the discrete velocity points and M < N. At the base of the algorithm are nodal-discontinuous Galerkin discretizations of the collision operator on uniform grids and a bilinear convolution form of the Galerkin projection of the collision operator. Efficiency of the algorithm is achieved by applying singular value decomposition compression of the discrete collision kernel and by approximating the kinetic solution by a sum of Maxwellian streams using a stochastic likelihood maximization algorithm. Accuracy of the method is …

Non-Stationary Platform Inverse Synthetic Aperture Radar Maneuvering Target Imaging Based On Phase Retrieval, Hongyin Shi, Saixue Xia, Qi Qin, Ting Yang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

As a powerful signal processing tool for imaging moving targets, placing radar on a non-stationary platform (such as an aerostat) is a future direction of Inverse Synthetic Aperture Radar (ISAR) systems. However, more phase errors are introduced into the received signal due to the instability of the radar platform, making it difficult for popular algorithms to accurately perform motion compensation, which leads to severe effects in the resultant ISAR images. Moreover, maneuvering targets may have complex motion whose motion parameters are unknown to radar systems. To overcome the issue of non-stationary platform ISAR autofocus imaging, a high-resolution imaging method based …

Evaluating Annual Fixed Wing Maintenance Costs, Kirsten Bunecke, Edward D. White, Jonathan D. Ritschel, Brett A. Bush

Faculty Publications

This article serves two purposes: first, to empirically model the annual percentage increase of operations and support (O&S) costs for fixed wing aircraft; and second, to place into the archival realm another reference for other researchers to consider when investigating other O&S topics. For this study of 21 different airframes grouped together at the Mission- Design Series (MDS), maintenance subcategories 3.1 Consumable Materials and Repair Parts, 3.2 Depot Level Repairables (DLR), and 3.4 Depot Maintenance accounted for an average 91.5% of annual organic maintenance costs. For contractor-maintained MDS, subcategory 3.7, Contractor Logistics Support (CLS) accounted for 96.6% of annual maintenance …

A Spacetime Dpg Method For The Wave Equation In Multiple Dimensions, Jay Gopalakrishnan, Paulina Sepulveda

Portland Institute for Computational Science Publications

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in detail for a simple domain in arbitrary dimensions. The DPG method based on the weak formulation is then studied theoretically and numerically. Error estimates and numerical results are presented for triangular, rectangular, tetrahedral, and hexahedral meshes of …