Digital Commons Network^™

Properties Of Catlin’S Reduced Graphs And Supereulerian Graphs, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu

Scholarship and Professional Work - LAS

A graph G is called collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph H of G such that R is the set of vertices of odd degree in H. A graph is the reduction of G if it is obtained from G by contracting all the nontrivial collapsible subgraphs. A graph is reduced if it has no nontrivial collapsible subgraphs. In this paper, we first prove a few results on the properties of reduced graphs. As an application, for 3-edge-connected graphs G of order n with d(u) + d(v) ≥ 2(n/p − …

The Perpetuation Of Graffiti Art Subculture, Camille Lannert

Butler Journal of Undergraduate Research

Graffiti art and the subculture that supports it is a form of graffiti that differs from gang graffiti, immediate graffiti, and street art. This research is a qualitative analysis using partial participant observation of a graffiti art subculture in a Midwestern city. Six themes which characterize this subculture were individual identity, communication, competition, criminality, aesthetic criteria, and changing forms of communication. The implications of the findings for labeling theory and differential association theories are discussed.

Table Of Contents

Butler Journal of Undergraduate Research

Front cover, a list of the article contents in this issue, and editorial information.

Lai’S Conditions For Spanning And Dominating Closed Trails, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu

Scholarship and Professional Work - LAS

No abstract provided.

Universal Electric Current Of Interacting Resonant-Level Models With Asymmetric Interactions: An Extension Of The Landauer Formula, Akinori Nishino, Naomichi Hatano, Gonzalo Ordonez

Scholarship and Professional Work - LAS

We study the electron transport in open quantum-dot systems described by the interacting resonant-level models with Coulomb interactions. We consider the situation in which the quantum dot is connected to the left and right leads asymmetrically. We exactly construct many-electron scattering eigenstates for the two-lead system, where two-body bound states appear as a consequence of one-body resonances and the Coulomb interactions. By using an extension of the Landauer formula, we calculate the average electric current for the system under bias voltages in the first order of the interaction parameters. Through a renormalization-group technique, we arrive at the universal electric current, …

Near-Optimal Online Multiselection In Internal And External Memory, Jonathan P. Sorenson, Jérémy Barbay, Ankur Gupta, S. Srinivasa Rao

Scholarship and Professional Work - LAS

We introduce an online version of the multiselection problem, in which q selection queries are requested on an unsorted array of n elements. We provide the first online algorithm that is 1-competitive with online algorithm proposed by Kaligosi et al.[ICALP 2005] in terms of comparison complexity. Our algorithm also supports online search queries efficiently.

We then extend our algorithm to the dynamic setting, while retaining online functionality, by supporting arbitrary insertions and deletions on the array. Assuming that the insertion of an element is immediately preceded by a search for that element, we show that our dynamic online algorithm performs …

Four Color Observations Of 2501 Lohja, Bin Li, Haibin Zhao, Hao Lu, Xianming Han

Scholarship and Professional Work - LAS

Photometric studies of asteroid 2501 Lohja were made between 2014 June 24 and 25 using the Southeastern Association for Research in Astronomy (SARA) Kitt Peak telescope with Bessell B, V, R and I filters. We obtained a synodic period of 3.81 ± 0.01h, which is consistent with previous values.

Symmetries And Patterns In Non-Euclidean Settings, Sarah Elizabeth Stoops

Undergraduate Honors Thesis Collection

From the Megalithic Temples of Malta constructed over 5,500 years ago, to the Pyramid of Djoser in Egypt built some 4,700 years ago, to more recent works of architectural wonder such an the Taj Mahal, the testimonials to the innate human genius for creating beauty through symmetry, color, and patterns abound. Evidently, the mathematical underpinnings of many architectural marvels are mostly rooted in the Euclidean Geometry. Now, as marvelous as these monuments are, one may wonder what would be the concepts of beauty and symmetry in a non-Euclidean universe. It turns out that this is not a far-fetched thought. It …

Superstable Manifolds Of Invariant Circles And Codimension-One Böttcher Functions, Scott R. Kaschner, Roland K.W. Roeder

Scholarship and Professional Work - LAS

Let f:X ⇢ X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n>1. Suppose that there is an embedded copy of P1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose that f restricted to this line is given by z↦zb, with resulting invariant circle S. We prove that if a≥b, then the local stable manifold Wsloc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition …

Scrambled Squares, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

Jeremiah's puzzle "Scrambled Squares", which was exchanged at the 2015 Ottawa International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exchange them. This puzzle is also manufactured by Kate Jones as "Scrambled Squares".

Rational Maps Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder

Scholarship and Professional Work - LAS

We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.

Two Compact Incremental Prime Sieves, Jonathan P. Sorenson

Scholarship and Professional Work - LAS

A prime sieve is an algorithm that finds the primes up to a bound n. We say that a prime sieve is incremental, if it can quickly determine if n+1 is prime after having found all primes up to n. We say a sieve is compact if it uses roughly √n space or less. In this paper, we present two new results.

• We describe the rolling sieve, a practical, incremental prime sieve that takes O(n log log n) time and O(√n log n) bits of space.

• We also …

Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott R. Kaschner, Reaper Romero, David Simmons

Scholarship and Professional Work - LAS

We show that the geometric limit as n → ∞ of the Julia sets J(P_n,c) for the maps P_n,c(z) = zⁿ + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.