Mathematics Commons^™

Programmatic Assessment Of Mathematical Content Knowledge For Teaching, Shannon Driskell, G. Keen

Shannon O.S. Driskell

Driskell, S. (Co-PI), & Keen, G. (Co-PI), WeEXCEL (West Ohio Center of Excellence for Science and Mathematics Education) Mini-Grant, $9,000 Year: 2008

Enumeration Schemes For Words Avoiding Patterns With Repeated Letters, Lara Pudwell

Lara K. Pudwell

No abstract provided.

Intrinsic Linking And Knotting Are Arbitrarily Complex, Ramin Naimi, Erica Flapan, Blake Mellor

Ramin Naimi

We show that, given any $n$ and $\alpha$, every embedding of any sufficiently large complete graph in $\mathbb{R}^3$ contains an oriented link with components $Q_1$, ..., $Q_n$ such that for every $i\not =j$, $|\lk(Q_i,Q_j)|\geq\alpha$ and $|a_2(Q_i)|\geq\alpha$, where $a_{2}(Q_i)$ denotes the second coefficient of the Conway polynomial of $Q_i$.

Highly Connected Multicoloured Subgraphs Of Multicoloured Graphs, H. Liu, R. Morris, N. Prince

Noah Prince

Suppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; how large a k-connected subgraph are we guaranteed to find, which uses only at most s of the colours? This question is due to Bollobás, and the case s=1 was considered in Liu et al. [Highly connected monochromatic subgraphs of multicoloured graphs, J. Graph Theory, to appear]. Here we shall consider the case s is greater than or equal to 2, proving in particular that when s=2 and r+1 is a power of 2 then the answer lies between 4n/(r+1)-17kr(r+2k+1) and 4n/(r+1)+4 and that …

On KS,T-Minors In Graphs With Given Average Degree, A. V. Kostochka, N. Prince

Noah Prince

Let D(H) be the minimum d such that every graph G with average degree d has an H-minor. Myers and Thomason found good bounds on D(H) for almost all graphs H and proved that for 'balanced' H random graphs provide extremal examples and determine the extremal function. Examples of 'unbalanced graphs' are complete bipartite graphs K_s,t for a fixed s and large t. Myers proved upper bounds on D(K_s,t ) and made a conjecture on the order of magnitude of D(K_s,t ) for a fixed s and …

Padé Spline Functions, Tian-Xiao He

Tian-Xiao He

We present here the definition of Pad´e spline functions, their expressions, and the estimate of the remainders of pad´e spline expansions. Some algorithms are also given.

Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench

William F. Trench

No abstract provided.

Tuberculosis Screening For International Students At A Midwestern Liberal Arts College, Grace Goetzke, Victor Addona, Chad M. Topaz

Chad M. Topaz

Participants: 318 international students at Macalester College screened for latent tuberculosis infection via tuberculin skin tests (TST) from 2004-2008. Objective: To estimate positive TST probability based on countries of residency and history of BCG vaccination. Methods and Results: 52% of students had a positive TST. Logistic regression modeling shows that a positive TST is insignificantly correlated with history of BCG vaccination (p=0.910) but is significantly negatively correlated with residence in the European Union (p=0.00502) and the Middle East (p=0.00451), and positively correlated with residence in North America (p=0.00151). Conclusions: There is a significant relationship between TST result and residence in …

Thermal Roots Of Correlation-Based Complexity, Philip Fraundorf

Phil Fraundorf