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Articles 149971 - 150000 of 294521

Full-Text Articles in Physical Sciences and Mathematics

The Relationships Between Cg, Bfgs, And Two Limited-Memory Algorithms, Zhiwei (Tony) Qin Jun 2016

The Relationships Between Cg, Bfgs, And Two Limited-Memory Algorithms, Zhiwei (Tony) Qin

Furman University Electronic Journal of Undergraduate Mathematics

For the solution of linear systems, the conjugate gradient (CG) and BFGS are among the most popular and successful algorithms with their respective advantages. The limited-memory methods have been developed to combine the best of the two. We describe and examine CG, BFGS, and two limited-memory methods (L-BFGS and VSCG) in the context of linear systems. We focus on the relationships between each of the four algorithms, and we present numerical results to illustrate those relationships.

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Finding Prime Numbers: Miller Rabin And Beyond, Christina Mcintosh Jun 2016

Finding Prime Numbers: Miller Rabin And Beyond, Christina Mcintosh

Furman University Electronic Journal of Undergraduate Mathematics

This expository paper motivates and explains the Miller Rabin test and gives some generalizations of it. The Miller Rabin test is a standard probabilistic test used to find large prime numbers quickly.

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Carolinas Mathematics Undergraduate Research Conference Abstracts, John Harris Jun 2016

Carolinas Mathematics Undergraduate Research Conference Abstracts, John Harris

Furman University Electronic Journal of Undergraduate Mathematics

On Friday, March 24, 2006, Furman University hosted the Carolinas Mathematics Undergraduate Research Conference. The conference was supported by the Mathematical Association of America (NSF Grant DMS-0241090). These are the abstracts for the eight undergraduate talks given on that day.

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Notes On Gabriel's Horn, Joseph Krenicky, Jan Rychtář Jun 2016

Notes On Gabriel's Horn, Joseph Krenicky, Jan Rychtář

Furman University Electronic Journal of Undergraduate Mathematics

A smooth bounded solid of finite volume and infinite surface is constructed. It is a variant of the classical Gabriel’s horn that is often taught in Calculus classes.

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Derham Cohomology Of The Rectangular Torus, Eric M. Katerman Jun 2016

Derham Cohomology Of The Rectangular Torus, Eric M. Katerman

Furman University Electronic Journal of Undergraduate Mathematics

For the special case of a rectangular at torus, we present and prove DeRham's Theorem, which says that cohomology is given by closed differential forms modulo exact forms.

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The University Of North Carolina At Greensboro Regional Undergraduate Mathematics Conference Abstracts, Jan Rychtář Jun 2016

The University Of North Carolina At Greensboro Regional Undergraduate Mathematics Conference Abstracts, Jan Rychtář

Furman University Electronic Journal of Undergraduate Mathematics

It was a very chaotic day, says Kathryn Sikes. Indeed, mutants spread everywhere, according to Brian Stadler. Bacterial wars raged all over the place, adds Dan MacMartin. Everybody was stealing, reported Christian Sykes. There were no limits to it, witnessed by Samuel Grundman. Only the fittest survived and got out of the prison, noted by Joseph Krenicky. The group was set free by Steven Piantadosi. We almost got lost in cyclic paths, said Heather Allmond. At least, our weight was a perfect number, smiles Michael Shiver, because we were not oversized thanks to Martha Shott. Finally, a picture was taken …

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On The Nonexistence Of Singular Equilibria In The Four-Vortex Problem, Marshall Hampton, Andrea Peterson, Heather Stoller, Albert Wang Jun 2016

On The Nonexistence Of Singular Equilibria In The Four-Vortex Problem, Marshall Hampton, Andrea Peterson, Heather Stoller, Albert Wang

Furman University Electronic Journal of Undergraduate Mathematics

In this paper we provide a partial answer to a question recently posed by Hassan Aref et. al. in their article Vortex Crystals, namely whether there are certain singular equilibria of point vortices. We prove that there are no such equilibria in the four-vortex case.

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Properties Of The Iterates Of The Weierstrass-℘ Function, Walter H. Chen, Michael S. Willis Jun 2016

Properties Of The Iterates Of The Weierstrass-℘ Function, Walter H. Chen, Michael S. Willis

Furman University Electronic Journal of Undergraduate Mathematics

This paper discusses several properties of the Weierstrass-℘ function, as defined on the fundamental parallelogram C/Γ, where C is the complex plane and Γ is the lattice generated by ω1 and ω2. Using the addition formula for ℘(z1 + z2), we develop a reccurence relation for ℘(nz) in terms of ℘(z). We then examine the degree of this expression, some coefficients, and patterns concerning the poles of this function. We also consider the geometric interpretation of taking an arbitrary z0 and adding it to itself, both in the fundamental parallelogram C/Γ and …

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A Dynamical Programming Solution For Shortest Path Itineraries In Robotics, Martin Talbot Jun 2016

A Dynamical Programming Solution For Shortest Path Itineraries In Robotics, Martin Talbot

Furman University Electronic Journal of Undergraduate Mathematics

In robotics, more precisely Autonomous Mobile Robotics (AMR), robots, much like human beings, are confronted regularly with the problem of finding the best path to take from a source location to a destination location. This is an optimization concern, since the robot wants to minimize its cost in time or in energy while achieving its goal. Different algorithms exist for shortest path computation; the famous Dijkstra’s Shortest Path Algorithm will solve single-source shortest path problems in near linear time (O(mn log n)). However, for certain complex optimization path-planning problems, this algorithm alone is insufficient. We will …

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Vertex Magic, Daisy Cunningham Jun 2016

Vertex Magic, Daisy Cunningham

Furman University Electronic Journal of Undergraduate Mathematics

This paper addresses labeling graphs in such a way that the sum of the vertex labels and incident edge labels are the same for every vertex. Bounds on this so-called magic number are found for cycle graphs. If a graph has an odd number of vertices, algorithms can be found to produce different magic-vertex graphs with the maximum and minimum magic number. Also, every cycle graph with an odd number of vertices can be made into a vertexmagic graph if the odd numbers or even numbers are placed on the vertices. Some interesting problems arise when one begins to look …

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Some Geometry Of H(RN), Christopher Frayer Jun 2016

Some Geometry Of H(RN), Christopher Frayer

Furman University Electronic Journal of Undergraduate Mathematics

If X is a complete metric space, the collection of all non-empty compact subsets of X forms a complete metric space (H(X), h), where h is the Hausdorff metric. In this paper we explore some of the geometry of the space H(Rn). Specifically, we concentrate on understanding lines in H(R). In particular, we show that for any two points A, B, ∈ H(Rn), there exist infinitely many points on the line joining A and B. We characterize some points on the lines formed using closed …

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Tiling By (K, N)-Crosses, Joanne Charlebois Jun 2016

Tiling By (K, N)-Crosses, Joanne Charlebois

Furman University Electronic Journal of Undergraduate Mathematics

We investigate lattice tilings of n-space by (k, n)-crosses, establishing necessary and sufficient conditions for tilings with certain small values of k. We give a necessary condition for tilings corresponding to nonsingular splittings with general values of k. We also prove one case of a conjecture made by Stein and Szabó in [4].

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Fourier And Wavelet Representations Of Functions, Nicholas G. Roland Jun 2016

Fourier And Wavelet Representations Of Functions, Nicholas G. Roland

Furman University Electronic Journal of Undergraduate Mathematics

Representations of functions are compared using the traditional technique of Fourier series with a more modern technique using wavelets. Under certain conditions, a function can be represented with a sum of sine and cosine functions. Such a representation is called a Fourier series. This classical method is used in applications such as storage of sound waves and visual images on a computer. One problem with this sum is that it is infinite. In use, only a finite number of terms can be used. More accuracy requires more terms in the series, but more terms require more time to compute and …

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A Lie Algebra Of Integrals For Keplerian Motion Restricted To The Plane, Jason Osborne Jun 2016

A Lie Algebra Of Integrals For Keplerian Motion Restricted To The Plane, Jason Osborne

Furman University Electronic Journal of Undergraduate Mathematics

In this paper we consider the slightly simpler problem of Keplerian motion restricted to the plane rather than Keplerian motion in three dimensions as done in [3, page 11]. We parallel the three-dimensional problem in that we use the same actions to find invariants (integrals) but rather than working in a six-dimensional phase space to find six independent integrals we restrict ourselves to a four-dimensional phase space. In doing this, we find that we have three independent integrals and thus we have a three-dimensional Lie algebra.

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Excellent Rings With Singleton Formal Fibers, Dan Lee, Leanne Leer, Shara A. Pilch, Yu Yasufuku Jun 2016

Excellent Rings With Singleton Formal Fibers, Dan Lee, Leanne Leer, Shara A. Pilch, Yu Yasufuku

Furman University Electronic Journal of Undergraduate Mathematics

In this paper we construct a non complete excellent local ring A such that the natural map Spec  → Spec A is bijective.

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Planar Double Bubbles On Flat Walls, G. Christopher Hruska, Dmitriy Leykekhman, Daniel Pinzon, Brian Shay Jun 2016

Planar Double Bubbles On Flat Walls, G. Christopher Hruska, Dmitriy Leykekhman, Daniel Pinzon, Brian Shay

Furman University Electronic Journal of Undergraduate Mathematics

In this paper, we investigate some properties of planar soap bubbles on a straight wall with a single corner. We show that when a wall has a single corner and a bubble consists of two connected regions, the perimeter minimizing bubble must be one of the types, two concentric circular arcs or a truncated standard double bubble, depending on the angle of the corner and areas of the regions.

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The Strong Shadowing Property On The Unit Interval, James O. Warren, Joseph H. Brown Jun 2016

The Strong Shadowing Property On The Unit Interval, James O. Warren, Joseph H. Brown

Furman University Electronic Journal of Undergraduate Mathematics

We study continuous maps of the unit interval into itself. We determine necessary and suffcient conditions so that all pseudo-orbits can be approximated by orbits with the same initial point.

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Quantifying Chaos In Dynamical Systems With Lyapunov Exponents, Michael Van Opstall Jun 2016

Quantifying Chaos In Dynamical Systems With Lyapunov Exponents, Michael Van Opstall

Furman University Electronic Journal of Undergraduate Mathematics

In this paper we analyze the dynamics of a four dimensional mechanical system which exhibits sensitive dependence on initial conditions. The aim of the paper is to introduce the basic ideas of chaos theory while assuming only a course in ordinary differential equations as a prerequisite.

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Divisability Tests, Apoorva Khare Jun 2016

Divisability Tests, Apoorva Khare

Furman University Electronic Journal of Undergraduate Mathematics

In this paper, we give a new method to test the divisibility of any positive integer by another. First, we outline the usual test, in which one proceeds from right to left, i.e. the direction opposite the one taken while carrying out long division. After pointing out some of the problems with this method, we give another method, which forms the core of this paper. This latter method works along the same lines as the earlier one, but here one proceeds from left to right. Examples of some well known divisibility tests for special divisors are given along with some …

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Maximum Matchings In Complete Multipartite Graphs, David Sitton Jun 2016

Maximum Matchings In Complete Multipartite Graphs, David Sitton

Furman University Electronic Journal of Undergraduate Mathematics

How many edges can there be in a maximum matching in a complete multipartite graph? Several cases where the answer is known are discussed, and then a new formula is given which answers this question.

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Compactifications Of Topological Spaces, Jay Blankespoor, John Krueger Jun 2016

Compactifications Of Topological Spaces, Jay Blankespoor, John Krueger

Furman University Electronic Journal of Undergraduate Mathematics

Given a locally compact, Hausdorff space, χ, there are several ways to compactify it. We examine two of these compactifications – the one-point compactification, X̌, and the Stone-Čech compactification, β(χ) – and give conditions which guarantee that X̌ ≠ β(χ). We also give new examples of topological spaces for which X̌ = β(χ).

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Conjugacy Classes Of Triple Products In Finite Groups, Emily Salvo, Kevin Hutson Jun 2016

Conjugacy Classes Of Triple Products In Finite Groups, Emily Salvo, Kevin Hutson

Furman University Electronic Journal of Undergraduate Mathematics

Let G be a finite group and let T1 be the number of times a triple (x, y, z) ∈ G3 binds X, where X = {xyz, xzy, yxz, yzx, zxy, zyx}, to one conjugacy class. Let T2 denote the number of times a triple G3 breaks X into two conjugacy classes. We have established the following results: i) the probability that a triple (x, y, z) ∈ D3n binds X to one contingency class is ≥ 5/8. ii) for groups such …

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The N-Extent Of S3(P,M), Paul Jung, Tucker Mcelroy, Jason Samuels Jun 2016

The N-Extent Of S3(P,M), Paul Jung, Tucker Mcelroy, Jason Samuels

Furman University Electronic Journal of Undergraduate Mathematics

In this paper we estimate xtn (S3 (p, m)), the n-extent of various lens spaces. We give numerical evidence for extending certain results of D. G. Yang [Duke Math. J., 74 (1994), 531-545.] to primes p between 11 and 37. We explain the implication of our results for the topology of 4-dimensional manifolds of positive sectional curvature with nontrivial isometric Zp-actions.

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Structure And Geochronology Of The White Fork Pluton, Southern Sierra Nevada, Ian Richard Mahaffey Jun 2016

Structure And Geochronology Of The White Fork Pluton, Southern Sierra Nevada, Ian Richard Mahaffey

Natural Resources Management and Environmental Sciences

The Sierra Nevada batholith represents an archetypal continental arc, although the style of deformation throughout the history of the arc is only poorly understood, in part due to the voluminous nature of Late Cretaceous magmatism that has overprinted earlier structures. The purpose of this study is to gain a better understanding of pre-Late Cretaceous deformation in the Sierra Nevada batholith through a structural and geochronological study of the Jurassic White Fork pluton. A Jurassic age for the White Fork pluton is indicated by its inclusion of numerous 148 Ma Independence dikes, and geochronology on the White Fork pluton is limited …

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An Example Of Persistent Microstructure In A Long Rain Event, A. R. Jameson, M. L. Larsen, A. B. Kostinski Jun 2016

An Example Of Persistent Microstructure In A Long Rain Event, A. R. Jameson, M. L. Larsen, A. B. Kostinski

Department of Physics Publications

A 2D video disdrometer (2DVD) probe was used to gather detailed drop measurements over a 770-min rain event. Accumulated totals of the rainfall and of the number of drops for each square centimeter showed persistent, significant correlated structures across the approximately 11 cm × 11 cm grid of the 2DVD. This is surprising because larger-scale studies suggest that the values in each square centimeter should be highly correlated with very little variation. Nevertheless, this correlation remains strikingly similar to what is observed at a coarser resolution, suggesting that it somehow scales with spatial resolution. However, because the correlation functions are …

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Ecosystem-Based Fisheries Management (Ebfm) Risk Assessment Of The Western Australian Silver-Lipped Pearl Oyster (Pinctada Maxima) Industry, K. L. Travaille, R. Jones, B Wise Jun 2016

Ecosystem-Based Fisheries Management (Ebfm) Risk Assessment Of The Western Australian Silver-Lipped Pearl Oyster (Pinctada Maxima) Industry, K. L. Travaille, R. Jones, B Wise

WA Marine Stewardship Council report series

This report provides a comprehensive overview of the Western Australian silver-lipped pearling (Pinctada maxima) industry and the outcomes from the 2015 ecological risk assessment of this industry. The P. maxima pearling industry has been operating in Western Australia since the 1880s, initially harvesting pearl oysters for mother-of-pearl production.

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Analysis Of A Parallel Machine Scheduling Problem With Sequence Dependent Setup Times And Job Availability Intervals, Ridvan Gedik, Chase Rainwater, Heather Nachtmann, Edward A. Pohl Jun 2016

Analysis Of A Parallel Machine Scheduling Problem With Sequence Dependent Setup Times And Job Availability Intervals, Ridvan Gedik, Chase Rainwater, Heather Nachtmann, Edward A. Pohl

Mechanical and Industrial Engineering Faculty Publications

In this study, we propose constraint programming (CP) model and logic-based Benders algorithms in order to make the best decisions for scheduling non-identical jobs with availability intervals and sequence dependent setup times on unrelated parallel machines in a fixed planning horizon. In this problem, each job has a profit, cost and must be assigned to at most one machine in such a way that total profit is maximized. In addition, the total cost has to be less than or equal to a budget level. Computational tests are performed on a real-life case study prepared in collaboration with the U.S. Army …

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Development And Implementation Of Problem-Based Chemistry Experiments For Engineering Students In A Multi-Disciplinary Course, Tiffany Hesser, Stephanie R. Bunyea Jun 2016

Development And Implementation Of Problem-Based Chemistry Experiments For Engineering Students In A Multi-Disciplinary Course, Tiffany Hesser, Stephanie R. Bunyea

Chemistry and Chemical Engineering Faculty Publications

This paper will describe the implementation and continuing development of five problem based laboratory experiments in a general chemistry course designed specifically for multiple disciplines of engineering students at the University of New Haven. The Problem Based Laboratory Experiments (PBLE) were developed to provide students with the opportunity to perform and develop experimental procedures working in interdisciplinary teams, while achieving a greater understanding of the role of chemistry in engineering fields. In each PBLE, students first complete a traditional chemistry experiment to gain an understanding of the chemical concepts and to become familiar with executing a written procedure with a …

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Comparing Local Constants Of Ordinary Elliptic Curves In Dihedral Extensions, Sunil Chetty Jun 2016

Comparing Local Constants Of Ordinary Elliptic Curves In Dihedral Extensions, Sunil Chetty

Mathematics Faculty Publications

We establish, for a substantial class of elliptic curves, that the arithmetic local constants introduced by Mazur and Rubin agree with quotients of analytic root numbers.

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Carbon And Energy Fluxes In Cropland Ecosystems: A Model-Data Comparison, Erandathie Lokupitiya, A. S. Denning, K. Schaefer, D. Ricciuto, R. Anderson, M. A. Arain, Colorado State University, A. G. Barr, G. Chen, J. M. Chen, P. Ciais, D. R. Cook, M. Dietze, M. El Maayar, M. Fischer, University Of Alberta, D. Hollinger, C. Izaurralde, A. Jain, C. Kucharik, Z. Li, S. Liu, L. Li, R. Matamala, P. Peylin, D. Price, S. W. Running, A. Sahoo, M. Sprintsin, Andrew Suyker, H. Tian, C. Tonitto, M. Torn, Hans Verbeeck, Shashi Verma, Y. Xue Jun 2016

Carbon And Energy Fluxes In Cropland Ecosystems: A Model-Data Comparison, Erandathie Lokupitiya, A. S. Denning, K. Schaefer, D. Ricciuto, R. Anderson, M. A. Arain, Colorado State University, A. G. Barr, G. Chen, J. M. Chen, P. Ciais, D. R. Cook, M. Dietze, M. El Maayar, M. Fischer, University Of Alberta, D. Hollinger, C. Izaurralde, A. Jain, C. Kucharik, Z. Li, S. Liu, L. Li, R. Matamala, P. Peylin, D. Price, S. W. Running, A. Sahoo, M. Sprintsin, Andrew Suyker, H. Tian, C. Tonitto, M. Torn, Hans Verbeeck, Shashi Verma, Y. Xue

School of Natural Resources: Faculty Publications

Croplands are highly productive ecosystems that contribute to land–atmosphere exchange of carbon, energy, and water during their short growing seasons. We evaluated and compared net ecosystem exchange (NEE), latent heat flux (LE), and sensible heat flux (H) simulated by a suite of ecosystem models at five agricultural eddy covariance flux tower sites in the central United States as part of the North American Carbon Program Site Synthesis project. Most of the models overestimated H and underestimated LE during the growing season, leading to overall higher Bowen ratios compared to the observations. Most models systematically under predicted NEE, especially at rain-fed …

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