»   home
        »   vol. 1, issue 1
        »   vol. 1, issue 2
        »   vol. 2, issue 1
        »   vol. 2, issue 2
        »   vol. 3, issue 1
        »   vol. 3, issue 2
        »   vol. 4, issue 1
        »   vol. 4, issue 2
        »   vol. 5, issue 1
        »   vol. 5, issue 2
        »   vol. 6, issue 1
        »   vol. 6, issue 2
        »   vol. 7, issue 1
        »   vol. 7, issue 2
        »   vol. 8, issue 1
        »   vol. 8, issue 2
        »   vol. 9, issue 1
        »   vol. 9, issue 2
        »   vol. 10, issue 1
        »   vol. 10, issue 2
        »   vol. 11, issue 1
        »   vol. 11, issue 2
        »   vol. 12, issue 1
        »   vol. 12, issue 2
        »   vol. 13, issue 1
        »   vol. 13, issue 2
        »   vol. 14, issue 1
        »   vol. 14, issue 2
        »   vol. 15, issue 1
        »   vol. 15, issue 2
        »   vol. 16, issue 1
        »   vol. 16, issue 2


» Vol. 15, Issue 2, 2014 «



Title: Efficiency of Lossless Compression of a Binary Tree via its Minimal Directed Acyclic Graph Representation
Author: Mayfawny Bergmann, Purdue University Author Bio    
Abstract: We consider the minimal directed acyclyc graph (DAG) lossless compression strategy introduced in Kieffer et. al., with the aim of testing its asymptotic effectiveness on binary trees of size n. We have four models for studying the compression strategy: two ways of measuring size (either the number of leaves or the depth of the tree), and two types of probability distributions (all planar trees are equally likely, or all nonplanar trees are equally likely). We calculate the average compression achieved by Kieffer et. al.'s strategy for some specific example classes of binary trees, and then more generally, averaging over all (either nonplanar, or planar) binary trees of a fixed size n. We use the results to draw conclusions about the kinds of trees for which the strategy is effective. An ultimate goal is to determine the extent to which the size of the DAG is correlated with the information embodied in the associated tree.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: Irreducibility and Factors of Polynomials in Noetherian Integral Domains
Author: Benjamin E. Anzis, University of Idaho Author Bio    
Abstract: Let R be a Noetherian integral domain, and let f be a polynomial with coefficients in R. A question of great importance is whether f is irreducible. In this paper, we give a sufficient condition for f to be irreducible by looking at the content ideal of f. This result is then extended to show a connection between the height of a polynomial's (proper) content ideal and the maximal number of irreducible factors it can possess.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: The Stability of a Semi-Implicit Numerical Scheme for a Competition Model Arising in Math Biology
Author: Brennon Bauer, Southern Utah University
Amy Gifford, Southern Utah University
Author Bio    
Author Bio    
Abstract: We study a Lotka-Volterra competition model. By using the nondimensionalization method, we analyze the stability of the steady state solutions for this system. Also, a stable numerical scheme is proposed to verify the theoretical results of the system. Using the Principle of Mathematical Induction, we prove the unconditional stability and convergence of the numerical scheme.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: Graphs with Minimal Well-Covered Dimension
Author: Gabriella Clemente, The City College of New York Author Bio    
Abstract: We generalize a theorem by Brown and Nowakowski on the well-covered dimension of chordal graphs. Furthermore, we prove that the well-covered dimension of any Sierpinski gasket graph of order at least 2 is equal to 3, the simplicial clique number.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: Notes on the Riemannian Geometry of Lie Groups
Author: Michael L. Geis, Rutgers University Author Bio    
Abstract: Lie groups occupy a central position in modern differential geometry and physics, as they are very useful for describing the continuous symmetries of a space. This paper is an expository article meant to introduce the theory of Lie groups, as well as survey some results related to the Riemannian geometry of groups admitting invariant metrics. In particular, a non-standard proof of the classification of invariant metrics is presented. For those unfamiliar with tensor calculus, a section devoted to tensors on manifolds and the Lie derivative is included.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: Continuously Diagonalizing the Shape Operator
Author: Matthew M. Lukac, University of Arkansas Author Bio    
Abstract: In this paper, we investigate the behavior of the curvature of non-developable surfaces around an umbilic point at the origin. The surfaces are of the form z = f(x,y) where f is a nonhomogeneous bivariate polynomial with cubic and quartic terms. We do this by looking at the continuity of the principal directions around the origin as well as the rate that the principal curvatures converge to zero as they approach the origin. This is done by considering the eigenvectors and eigenvalues of the shape operator. In our main result, we prove that a continuously diagonalizable shape operator implies the existence of a path through the origin with noncomparable principal curvatures.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: Isoperimetry in the Plane with Density e-1/r
Author: Paul Gallagher, University of Pennsylvania
David Hu, Georgetown University
Zane Martin, Williams College
Maggie Miller, University of Texas at Austin
Byron Perpetua, Williams College
Author Bio    
Author Bio    
Author Bio    
Author Bio    
Author Bio    
Abstract: We study the isoperimetric problem in the plane with weighting or density e-1/r. The isoperimetric problem seeks to enclose prescribed weighted area with minimum weighted perimeter. For density e-1/r, isoperimetric curves are conjectured to pass through the origin. We provide numerical and theoretical evidence that such curves have an angle at the origin approaching 1 radian from above as area approaches zero and provide further estimates.
Article: Downloadable PDF    
Additional Downloads:

» BACK TO TOP



Title: The Strong Symmetric Genus Spectrum of Abelian Groups
Author: Breanna Borror, Towson University
Allison Morris, Towson University
Michelle Tarr, Towson University
Author Bio    
Author Bio    
Author Bio    
Abstract: The strong symmetric genus of a group G is the minimum genus of any compact surface on which G acts faithfully while preserving orientation. We investigate the set of positive integers which occur as the strong symmetric genus of a finite abelian group. This is called the strong symmetric genus spectrum. We prove that there are an infinite number of gaps in the strong symmetric genus spectrum of finite abelian groups. We also determine an upper bound for the size of a finite abelian group that can act faithfully on a surface of a particular genus and then find the genus of abelian groups in particular families. These formulas produce a lower bound for the density of the strong symmetric genus spectrum.
Article: Downloadable PDF    
Additional Downloads: MAGMA Program     MAGMA Data    

» BACK TO TOP