Mathematics Commons^™

Recent Advances In Energy-Efficient Sensor Networks, Sheikh Iqbal Ahamed, Wei Wang, Jiman Hong

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Concept Of Sub-Independence, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Limit theorems as well as other well-known results in probability and statistics are often based on the distributions of the sums of independent random variables. The concept of sub-independence, which is weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is stronger than uncorrelatedness.

Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann

Department of Math & Statistics Faculty Publications

The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that for all f∈H², the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that for all f∈H². The first type of inequality above was explored with H² replaced by one of the model spaces (Θ H²)^⊥ by Aleksandrov, Baranov, Cohn, Treil, and Vol'berg. In this paper, we discuss …

Characterizations Of Exponentiated Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the class of exponentiated distributions are presented. These characterizations are based on a simple relationship between two truncated moments and based on functions of the nth order statistic. The results are applied to certain well-known members of this class.

Robust Estimation Of The Correlation Matrix Of Longitudinal Data, Mehdi Maadooliat, Mohsen Pourahmadi, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ=DLL ^⊤ D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D, and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t-distributions with unknown degrees of freedom. We …

The Zografos-Balakrishnan Log-Logistic Distribution: Properties And Applications, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Cross‐Campus Collaboration: A Scientometric And Network Case Study Of Publication Activity Across Two Campuses Of A Single Institution, Jeremy Birnholtz, Shion Guha, Y. Connie Yuan, Geri Gay, Caren Heller

Mathematics, Statistics and Computer Science Faculty Research and Publications

Team science and collaboration have become crucial to addressing key research questions confronting society. Institutions that are spread across multiple geographic locations face additional challenges. To better understand the nature of cross‐campus collaboration within a single institution and the effects of institutional efforts to spark collaboration, we conducted a case study of collaboration at Cornell University using scientometric and network analyses. Results suggest that cross‐campus collaboration is increasingly common, but is accounted for primarily by a relatively small number of departments and individual researchers. Specific researchers involved in many collaborative projects are identified, and their unique characteristics are described. Institutional …

Knight's Tours On 3 X N Chessboards With A Single Square Removed, Amanda M. Miller, David L. Farnsworth

Articles

The following theorem is proved: A knight’s tour exists on all 3 x n chessboards with one square removed unless: n is even, the removed square is (i, j) with i + j odd, n = 3 when any square other than the center square is removed, n = 5, n = 7 when any square other than square (2, 2) or (2, 6) is removed, n = 9 when square (1, 3), (3, 3), (1, 7), (3, 7), (2, 4), (2, 6), (2, 2), or (2, 8) is removed, or n = 11 when square (1, 3), (2, 4), …

Analysis And Processing Of Irregularly Distributed Point Clouds, Kamala Hunt Diefenthaler

Theses and Dissertations

We address critical issues arising in the practical implementation of processing real point cloud data that exhibits irregularities. We develop an adaptive algorithm based on Learning Theory for processing point clouds from a stationary sensor that standard algorithms have difficulty approximating. Moreover, we build the theory of distribution-dependent subdivision schemes targeted at representing curves and surfaces with gaps in the data. The algorithms analyze aggregate quantities of the point cloud over subdomains and predict these quantities at the finer level from the ones at the coarser level.

On Continuously Defective Elastic Crystals, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

We analyze mathematical underpinnings of Davini's theory of defective crystals when the defectiveness of a kinematic state may be material point dependent. We show how the underlying space can be identified with a suitably chosen homogeneous space and how the uniformly defective structure is just a special case.

Study Of Dieldrin In Coralville Reservoir, Jeremy Smith

Undergraduate Journal of Mathematical Modeling: One + Two

Using existing experimental data taken over a period of roughly 12 years that documents the concentrations of dieldrin levels in the environment and fatty tissue of the fish, we construct a model of the total dieldrin concentration decline. Comparisons between the experimental data and speculative data can be made using calculus and elements of statistics in order to better understand the movement of dieldrin in the reservoir. Because of the potentially harmful exposure effects of dieldrin to humans as well as the environment, it is important to be able to predict when stability has been restored to the ecosystem.

On Improvement In Estimating Population Parameter(S) Using Auxiliary Information, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers, written by eight coauthors (listed in the order of the papers): Manoj K. Chaudhary, Sachin Malik, Rajesh Singh, Florentin Smarandache, Hemant Verma, Prayas Sharma, Olufadi Yunusa, and Viplav Kumar Singh, from India, Nigeria, and USA. The following problems have been discussed in the book: In chapter one an estimator in systematic sampling using auxiliary information is studied in the presence of non-response. In second chapter some improved …

Proceedings Of The First International Conference On Smarandache Multispace & Multistructures, Florentin Smarandache, Linfan Mao

Branch Mathematics and Statistics Faculty and Staff Publications

In recent decades, Smarandache’s notions of multispace and multistructure were widely spread and have shown much importance in sciences around the world. Organizedby Prof.Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.

Control, Stability, And Qualitative Theory Of Dynamical Systems, Nazim Idrisoglu Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren

Mathematics Faculty Publications

No abstract provided.

Modified Pal Interpolation And Sampling Bilevel Signals With Finite Rate Of Innovation, Gayatri Ramesh

Electronic Theses and Dissertations

Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified Pal´ Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified Pal interpolation, based on papers by P ´ al, J ´ oo´ and Szabo, and we establish the existence and …

Partially Integrable Pt-Symmetric Hierarchies Of Some Canonical Nonlinear Partial Differential Equations, Keri Pecora

Electronic Theses and Dissertations

In this dissertation, we generalize the work of Bender and co-workers to derive new partially-integrable hierarchies of various PT -symmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev´e Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev´e expansion for the solution. For the PT -symmetric Korteweg-de Vries (KdV) equation, as with some other hierarchies, the first or n = 1 equation fails the test, the n = 2 member corresponds to …

Extremal Values Of Ratios: Distance Problems Vs. Subtree Problems In Trees, László A. Székely, Hua Wang

Mathematical Sciences: Faculty Publications

The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems [Discrete Appl. Math. 155 (3) 2006, 374-385; Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80 (1997), 37-56] determined extremal values of σT(w)/σT(u), σT(w)/σT(v), σ(T)/σT(v), and σ(T)/σT(w), where T is a tree on n vertices, v is in the centroid of …

Essays On Rethinking African Development: Contextual And Methodological Advances, Olumayokun Soremekun

2013

This research study sets out to provide analytical answers to the questions of African development and inequality. We examine various aspects of development from the issue of inequality among African countries to unravelling the synergies among the MDG goals and finally to investigating the progress if any that African countries have made towards attaining the MDG goals.

This research is broken down into three main studies: measuring inequality of opportunity, examining the synergies between the Millennium development goals at a particular point in time and lastly assessing the progress that has been made towards attaining the MDG goals in Africa. …

Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems, Ibrahim Oumar Diakite

Mathematics Dissertations - Archive

To understand the effects of discrete time delays and of parameters variation on certain biological system models, we first consider a Delay Differential Equation model of human immunodeficiency virus (HIV). We investigate the effects of the discrete time on the virulence of the HIV strain, and present sufficient and necessary condition for the virulence of the pathogen to change as the time delay changes. We also consider the same delay differential model for HIV infection, and we investigate analytically and numerically the stability of the endemically infected equilibrium. Our analysis shows that certain key parameters, such as the rate of …

Haplotype-Based Statistical Inference For Case-Control Genetic Association Studies With Complex Sampling, Daoying Lin

Mathematics Dissertations - Archive

With the advances in human genome research, it is now believed that the risks of many complex diseases are triggered by the interplay of genetic susceptibilities and environmental exposures. The population-based case-control study (PBCCS) is widely used to investigate the role of genetic variants and environmental exposures in the etiology of complex diseases. There are numerous ways to implement the selection process of cases and controls. In its simplest form, a simple random sampling (SRS) design is used to choose cases and controls from diseased and disease-free population, respectively. Though SRS is easy to conduct and relevant statistical methodologies are …