Mathematics Commons^™

Productivity Formulae Of An Infinite-Conductivity Hydraulically Fractured Well Producing At Constant Wellbore Pressure Based On Numerical Solutions Of A Weakly Singular Integral Equation Of The First Kind, Chaolang Hu, Jing Lu, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In order to increase productivity, it is important to study the performance of a hydraulically fractured well producing at constant wellbore pressure. This paper constructs a new productivity formula, which is obtained by solving a weakly singular integral equation of the first kind, for an infinite-conductivity hydraulically fractured well producing at constant pressure. And the two key components of this paper are a weakly singular integral equation of the first kind and a steady-state productivity formula. A new midrectangle algorithm and a Galerkin method are presented in order to solve the weakly singular integral equation. The numerical results of these …

Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence

Mathematics and Statistics Faculty Research & Creative Works

In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic systems.

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman

Mathematics Faculty Publications

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.

Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin

Pomona Faculty Publications and Research

[This piece is a series of interviews with giants in the field of medicine on their views of how statistics is changing medicine. I interviewed the editor of the New England Journal of Medicine, a preeminent doctor/researcher of lung cancer, the director of the LA County Department of Public Health, and a Harvard statistician who sits on the editorial board of the New England Journal of Medicine.]

Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

Absolute Differentiation In Metric Spaces, W. J. Charatonik, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

In this article, we introduce a new notion of (strong) absolute derivative, for functions derived between metric spaces, and we investigate various properties and uses of this concept, especially regarding the geometry of abstract metric spaces carrying no other structure.

Various Characterizations Of Modified Weibull And Log Modified Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the well-known modified Weibull and log-modified Weibull distributions are presented. These characterizations are based on a simple relationship between two truncated moments; on the hazard function and on functions of the order statistics.

Characterizations Of Certain Continuous Univariate Distributions Based On The Conditional Distribution Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing probability distributions is an interesting problem which has recently attracted the attention of many researchers. Various characterization results have been established in different directions as reported in the literature. We present here, various characterizations of certain univariate continuous distributions based on the conditional distribution of generalized order statistics.

A Direct D-Bar Reconstruction Algorithm For Recovering A Complex Conductivity In 2d, Sarah J. Hamilton, C. N. L. Herrera, J. L. Mueller, A. Von Herrmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

A direct reconstruction algorithm for complex conductivities in W^{2, ∞}(Ω), where Ω is a bounded, simply connected Lipschitz domain in R² , is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107–19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Modeling Temporal Pattern And Event Detection Using Hidden Markov Model With Application To A Sludge Bulking Data, Naveen K. Bansal, Xin Feng, Wenjing Zhang, Wutao Wi, Yuanhao Zhao

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper discusses a method of modeling temporal pattern and event detection based on Hidden Markov Model (HMM) for a continuous time series data. We also provide methods for checking model adequacy and predicting future events. These methods are applied to a real example of sludge bulking data for detecting sludge bulking for a water plant in Chicago.

Protection By 20-5,14-Hedge Against Surgically-Induced Ischemia Reperfusion Lung Injury In Rats, Irshad Ali, Stephanie Gruenloh, Ying Gao, Anne V. Clough, John R. Falck, Meetha Medhora, Elizabeth R. Jacobs

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

We previously reported that the cytochrome P450 product 20-hydroxyeicosatetraenoic acid has prosurvival effects in pulmonary artery endothelial cells and ex vivo pulmonary arteries. We tested the potential of a 20-hydroxyeicosatetraenoic acid analog N-[20-hydroxyeicosa-5(Z),14(Z)-dienoyl]glycine (20-5,14-HEDGE) to protect against lung ischemic reperfusion injury in rats. Furthermore, we examined activation of innate immune system components, high mobility group box 1 (HMGB1) and toll-like receptor 4 (TLR4), in this model as well as the effect of 20-5,14-HEDGE on this signaling pathway.

Methods

Sprague-Dawley rats treated with 20-5,14-HEDGE or vehicle were subjected to surgically induced, unilateral lung ischemia for 60 minutes followed by reperfusion …

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 …

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Mathematics Faculty Publications

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.

Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.

Generalizing Amdahl’S Law For Power And Energy, Rong Ge, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Extending Amdahl's law to identify optimal power-performance configurations requires considering the interactive effects of power, performance, and parallel overhead.

Categoricity And Topological Graphs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let X be a topological graph, with arcs joined only at end points. If Y is any locally connected metrizable compactum that is co-elementarily equivalent to X, then Y is homeomorphic to X. In particular, X and Y are homeomorphic if some lattice base for one is elementarily equivalent to some lattice base for the other.

Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu

USF Tampa Graduate Theses and Dissertations

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, …

Stochastic Hybrid Dynamic Systems: Modeling, Estimation And Simulation, Daniel Siu

USF Tampa Graduate Theses and Dissertations

Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems.

The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described …

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 …

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 …

Mathematical Analysis Of The Problems Faced By The People With Disabilities (Pwds), Florentin Smarandache, W.B. Vasantha Kandasamy, A. Praveen Prakash

Branch Mathematics and Statistics Faculty and Staff Publications

The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire / by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu. Now any reader would be interested to know whether the Tamils (natives of Tamil Nadu) had ever spoken about people with disability. Even before 2000 years tamils had heroic poetry Purananuru (28th poem) about the war fare methods. In …

Design And Implementation Of An Open Framework For Ubiquitous Carbon Footprint Calculator Applications, Farzana Rahman, Casey O'Brien, Sheikh Iqbal Ahamed, He Zhang, Lin Liu

Mathematics, Statistics and Computer Science Faculty Research and Publications

As climate change is becoming an important global issue, more and more people are beginning to pay attention to reducing greenhouse gas emissions. To measure personal or household carbon dioxide emission, there are already plenty of carbon footprint calculators available on the web. Most of these calculators use quantitative models to estimate carbon emission caused by a user's activities. Although these calculators can promote public awareness regarding carbon emission due to an individual's behavior, there are concerns about the consistency and transparency of these existing CO₂ calculators. Apart from a small group of smart phone based carbon footprint calculator …

Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.

A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz

Masters Theses & Specialist Projects

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …

Interactive Real-Time Embedded Systems Education Infused With Applied Internet Telephony, Kyle Persohn, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The transition from traditional circuit-switched phone systems to modern packet-based Internet telephony networks demands tools to support Voice over Internet Protocol (VoIP) development. In this paper, we introduce the XinuPhone, an integrated hardware/software approach for educating users about VoIP technology on a real-time embedded platform. We propose modular course topics for design-oriented, hands-on laboratory exercises: filter design, timing, serial communications, interrupts and resource budgeting, network transmission, and system benchmarking. Our open-source software platform encourages development and testing of new CODECs alongside existing standards, unlike similar commercial solutions. Furthermore, the supporting hardware features inexpensive, readily available components designed specifically for educational …

An Experimental Nexos Laboratory Using Virtual Xinu, Paul Ruth, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Nexos Project is a joint effort between Marquette University, the University of Buffalo, and the University of Mississippi to build curriculum materials and a supporting experimental laboratory for hands-on projects in computer systems courses. The approach focuses on inexpensive, flexible, commodity embedded hardware, freely available development and debugging tools, and a fresh implementation of a classic operating system, Embedded Xinu, that is ideal for student exploration. This paper describes an extension to the Nexos laboratory that includes a new target platform composed of Qemu virtual machines. Virtual Xinu addresses two challenges that limit the effectiveness of Nexos. First, potential …

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

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.