Mathematics Commons^™

Rank-Based Two Sample Tests Under A General Alternative, Jamye Curry

Electronic Theses and Dissertations

The problem of testing whether two samples come from the same or different population is a classical one in statistics. In this dissertation, I first study rank based formulation of univariate two-sample distribution-free tests. One form of the test statistic is the average of between-group distances of ranks. The other form of the test statistic is the difference between the average of between-group distances of ranks and the average of within-group distances of ranks. Although they are different in formulation, they are closely related to the two-sample Cramer-von Mises criterion. The first one is a linear transformation of Cramer-von Mises …

New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

For the first time authors have ventured to study, analyse and investigate the properties of the fuzzy models, the experts opinion and so on. Here the concept of merged Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps are carried out, which are based on merged graphs and merged matrices. This concept is better than the usual combined Fuzzy Cognitive Maps. Further by this new technique we are able to give equal importance to all the experts who work with the problem. Here the new concept of New Average Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps is defined and described. This new …

Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.

Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does …

Smooth Peano Functions For Perfect Subsets Of The Real Line, Krzysztof Ciesielski

Faculty & Staff Scholarship

In this paper we investigate for which closed subsets P of the real line R there exists a continuous map from P onto P 2 and, if such a function exists, how smooth can it be. We show that there exists an infinitely many times differentiable function f : R → R 2 which maps an unbounded perfect set P onto P 2 . At the same time, no continuously differentiable function f : R → R 2 can map a compact perfect set onto its square. Finally, we show that a disconnected compact perfect set P admits a continuous …

Length Effects Of A Built-In Flapping Flat Plate On The Flow Over A Traveling Wavy Foil, Nansheng Liu, Yan Peng, Xiyun Lu

Mathematics & Statistics Faculty Publications

Flow over the traveling wavy foil with a built-in rigid flapping plate at its trailing edge has been numerically studied using the multi-relaxation-time Lattice Boltzmann method and immersed boundary method. The effect of the plate length on the propulsive performance such as the thrust force, energy consumption, and propeller efficiency has been investigated. Three modes (body force dominated, body and tail force competing and tail force dominated modes) have been identified that are associated with different hydrodynamics and flow structures. It is revealed that there exists a better performance plate length region and, within this region, a high propeller efficiency …

Network-Based Assessments Of Percolation-Induced Current Distributions In Sheared Rod Macromolecular Dispersions, Feng Shi, Simi Wang, M. Gregory Forest, Peter J. Mucha, Ruhai Zhou

Mathematics & Statistics Faculty Publications

Conducting high-aspect-ratio rods with 1-10 nm-scale diameters dispersed in poorly conducting matrices at extremely low, O(1%), volume fractions induce dramatic gains in bulk conductivity at rod percolation threshold. Experimentally [Nan, Shen, and Ma, Annu. Rev. Mater. Res., 40 (2010), pp. 131-151], bulk conductivity abandons the prepercolation, linear scaling with volume fraction that follows from homogenization theory [Zheng et al., Adv. Funct. Mater., 15 (2005), pp. 627-638], and then postpercolation jumps orders of magnitude to approach that of the pure rod macromolecular phase as predicted by classical percolation theory [Stauffer and Aharony, Introduction to Percolation Theory, CRC …

Comparison Of Second Order Conformal Symplectic Schemes With Linear Stability Analysis, Dwayne Floyd

Electronic Theses and Dissertations

Numerical methods for solving linearly damped Hamiltonian ordinary differential equations are analyzed and compared. The methods are constructed from the well-known Störmer-Verlet and implicit midpoint methods. The structure preservation properties of each method are shown analytically and numerically. Each method is shown to preserve a symplectic form up to a constant and are therefore conformal symplectic integrators, with each method shown to accurately preserve the rate of momentum dissipation. An analytical linear stability analysis is completed for each method, establishing thresholds between the value of the damping coefficient and the step-size that ensure stability. The methods are all second order …

Hamiltonicity And Sigma-Hypergraphs, Christina Zarb

Theory & Applications of Graphs

We define and study a special type of hypergraph. A σ-hypergraph Η= Η(n,r,q |σ), where σ is a partition of r, is an r-uniform hypergraph having nq vertices partitioned into n classes of q vertices each. If the classes are denoted by V1, V2,...,Vn, then a subset Κ of V(Η) of size r is an edge if the partition of r formed by the non-zero cardinalities |Κ ∩ Vi |, 1 ≤ i ≤ n, is σ. The non-empty intersections Κ ∩ Vi are called the parts of Κ, and s(σ) …

Not All Traces On The Circle Come From Functions Of Least Gradient In The Disk, Gregory S. Spradlin, Alexandru Tamasan

Publications

We provide an example of an L¹ function on the circle, which cannot be the trace of a function of bounded variation of least gradient in the disk.

Algorithms For Solving The Discrete Logarithm Problem, Ryan Edward Whaley

Online Theses and Dissertations

In mathematics, there are often many procedures to solve or prove the same problem. The discrete logarithm is one of these problems. The baby step, giant step algorithm and Pollard's kangaroo algorithm are two algorithms that attempt to solve discrete logarithm problems. Explanations on what these two algorithms are will be discussed as well as examples of each algorithm. In addition to these two algorithms, a modified form of Pollard's kangaroo algorithm will be provided with results. Throughout the text, Mathematica programs will be presented that simulate each of the three algorithms above.

The Effectiveness Of Manipulatives In A High School Algebra Ii Class, Brooke Elizabeth Bruins

Online Theses and Dissertations

This study explores the use of manipulatives in high school Algebra II. The effectiveness of the Concrete-Representational-Abstract (CRA) Model is compared to explicit instruction. The participants in this study are students from six high school Algebra II classes -two honors classes, and four standard classes. One honors class and two standard classes were randomly selected as the treatment groups receiving CRA instruction. The other three classes learned through abstract explicit instruction. Each class learned two new mathematical concepts, domain and range of quadratic functions and transformations of quadratic functions, through the selected method of instruction. At the end of instruction, …

An Incremental Reseeding Strategy For Clustering, Xavier Bresson, Huiyi Hu, Thomas Laurent, Arthur Szlam, James Von Brecht

Mathematics, Statistics and Data Science Faculty Works

In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then randomly reseeding the thresholded clusters. We demonstrate experimentally that the proper combination of these ingredients leads to an algorithm that achieves state-of-the-art performance in terms of cluster purity on standard benchmarks datasets. Moreover, the algorithm runs an order of magnitude faster than the other algorithms that achieve comparable results in terms of accuracy. We also describe a coarsen, cluster and refine approach similar to GRACLUS and …

Crossed Modules Of Racks, Alissa S. Crans, Friedrich Wagemann

Mathematics, Statistics and Data Science Faculty Works

We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the relation between crossed modules of groups and strict 2-groups. Then we explore topological applications. We show that by applying the rack-space functor, a crossed module of racks gives rise to a covering. Our main result shows how the fundamental racks associated to links upstairs and downstairs in a covering fit together to form a crossed module of racks.

Complete Bipartite Graphs Whose Topological Symmetry Groups Are Polyhedral, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We determine for which n, the complete bipartite graph K_n,n has an embedding in S³ whose topological symmetry group is isomorphic to one of the polyhedral groups: A₄, A₅, or S₄.

Robust Noise Attenuation Under Stochastic Noises And Worst-Case Unmodelled Dynamics, Araz Hashemi, Ben G. Fitzpatrick, Le Yi Wang, George Yin

Mathematics, Statistics and Data Science Faculty Works

This paper investigates noise attenuation problems for systems with unmodelled dynamics and unknown noise characteristics. A unique methodology is introduced that employs signal estimation in one phase, followed by control design for noise rejection. The methodology enjoys certain advantages in its simple control design process, accommodation of unmodelled dynamics, and non-conservative noise rejection performance. Under mild information on unmodelled dynamics, we first derive robust performance bounds on noise attenuation with respect to unmodelled dynamics without noise estimation errors. Then more general results are presented for systems that are subject to both stochastic signal estimation errors and unmodelled dynamics. Examples are …

Hom Quandles, Alissa S. Crans, Sam Nelson

Mathematics, Statistics and Data Science Faculty Works

If A is an abelian quandle and Q is a quandle, the hom set Hom(Q,A) of quandle homomorphisms from Q to A has a natural quandle structure. We exploit this fact to enhance the quandle counting invariant, providing an example of links with the same counting invariant values but distinguished by the hom quandle structure. We generalize the result to the case of biquandles, collect observations and results about abelian quandles and the hom quandle, and show that the category of abelian quandles is symmetric monoidal closed.

Simulation Of The Sampling Distribution Of The Mean Can Mislead, Ann E. Watkins, Anna E. Bargagliotti, Christine Franklin

Mathematics, Statistics and Data Science Faculty Works

Although the use of simulation to teach the sampling distribution of the mean is meant to provide students with sound conceptual understanding, it may lead them astray. We discuss a misunderstanding that can be introduced or reinforced when students who intuitively understand that “bigger samples are better” conduct a simulation to explore the effect of sample size on the properties of the sampling distribution of the mean. From observing the patterns in a typical series of simulated sampling distributions constructed with increasing sample sizes, students reasonably—but incorrectly—conclude that, as the sample size, n, increases, the mean of the (exact) sampling …

Measures Of Tactical Efficiency In Water Polo, James Graham, John Mayberry

College of the Pacific Faculty Articles

We present a notational analysis of offensive tactics commonly employed in elite men's water polo and address three questions related to this objective: which tactics are most effective?, which tactical performance indicators best classify the winning team?, and how accurate are predictive models based on these performance indicators? We define a new statistic, Efficiency Rating, which quantifies the importance of a tactic via a weighted average of direct and indirect goals generated by its use. By this measure, direct shot is the most efficient even strategy despite being employed far less frequently than centre or perimeter tactics. We address our …

Central Configurations In The Collinear 5-Body Problem, Muhammad Shoaib, Anoop Sivasankaran, Abdulrehman Kashif

Turkish Journal of Mathematics

We study the inverse problem of central configuration of collinear general 4- and 5-body problems. A central configuration for n-body problems is formed if the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration. In the 3-body problem, it is always possible to find 3 positive masses for any given 3 collinear positions given that they are central. This is not possible for more than 4-body problems in general. We consider a collinear 5-body problem and identify regions in the phase space where it is possible to choose positive …

Hausdorff Dimension Of The Graph Of The Error-Sum Function Of \Alpha-Lüroth Series, Haibo Chen, Wenbo Wang, Min Yu

Turkish Journal of Mathematics

Let \alpha be a countable partition of the unit interval [0,1]. In this paper, we will introduce the error-sum function of \alpha-Lüroth series and determine the Hausdorff dimension of its graph when the partition \alpha is eventually decreasing. Some other properties of the error-sum function are also investigated.

Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, Shinya Fujita, Colton Magnant, Yaping Mao, Kenta Ozeki

Theory & Applications of Graphs

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.

Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani

Theory & Applications of Graphs

In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter 2. For a tournament Τ of diameter 2, we show 2 ≤ → rc (Τ) ≤ 3. Furthermore, we provide a general upper bound on the rainbow κ-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of κ^thdiameter 2 has rainbow κ-connection number at most approximately κ².

Prospect Theory Preferences In Noncooperative Game Theory, Philip Leclerc

Theses and Dissertations

The present work seeks to incorporate a popular descriptive, empirically grounded model of human preference under risk, prospect theory, into the equilibrium theory of noncooperative games. Three primary, candidate definitions are systematically identified on the basis of classical characterizations of Nash Equilibrium; in addition, three equilibrium subtypes are defined for each primary definition, in order to enable modeling of players' reference points as exogenous and fixed, slowly and myopically adaptive, highly flexible and non-myopically adaptive. Each primary equilibrium concept was analyzed both theoretically and empirically; for the theoretical analyses, prospect theory, game theory, and computational complexity theory were all summoned …

Comparing Skew Schur Functions: A Quasisymmetric Perspective, Peter R. W. Mcnamara

Faculty Journal Articles

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that s_A and s_B have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true.

In fact, we work in terms of inequalities, showing that if the F-support of s_{A …}

On Groups With A Class-Preserving Outer Automorphism, Peter A. Brooksbank

Faculty Journal Articles

Four infinite families of 2-groups are presented, all of whose members possess an outer automorphism that preserves conjugacy classes. The groups in these families are central extensions of their predecessors by a cyclic group of order 2. For each integer r>1, there is precisely one 2-group of nilpotency class r in each of the four families. All other known families of 2-groups possessing a class-preserving outer automorphism consist entirely of groups of nilpotency class 2.

Groups Acting On Tensor Products, Peter A. Brooksbank

Faculty Journal Articles

Groups preserving a distributive product are encountered often in mathematics. Examples include automorphism groups of associative and non associative rings, classical groups, and automorphisms of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving such tensor products over semisimple and semi primary rings, and present effective algorithms to construct generators for these groups. We also discuss …

Ramp Loss Svm With L1-Norm Regularizaion, Eric Hess

Theses and Dissertations

The Support Vector Machine (SVM) classification method has recently gained popularity due to the ease of implementing non-linear separating surfaces. SVM is an optimization problem with the two competing goals, minimizing misclassification on training data and maximizing a margin defined by the normal vector of a learned separating surface. We develop and implement new SVM models based on previously conceived SVM with L_1-Norm regularization with ramp loss error terms. The goal being a new SVM model that is both robust to outliers due to ramp loss, while also easy to implement in open source and off the shelf mathematical programming …

Maximal Arcs, Above And Beyond, Diego Domenzain-Gonzale

Dissertations, Master's Theses and Master's Reports - Open

This report explores combinatorial structures in Finite Geometries by giving known constructions of maximal arcs; using maximal arcs to construct two-weight codes, partial geometries, strongly regular graphs and LDPC codes; a review on how to generalize maximal arcs to higher dimensions through Perp-Systems; and an effort in finding constructions of new Perp-Systems.

High Performance, Low Cost Subspace Decomposition And Polynomial Rooting For Real Time Direction Of Arrival Estimation: Analysis And Implementation, Mrudula V. Athi

Dissertations, Master's Theses and Master's Reports - Open

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna …