Fearless: Kevin Lugo

This summer, recent graduate Kevin Lugo will bike over 4,000 miles across the country to benefit the Ulman Cancer Fund for Young Adults. His choice to bike for seventy days from Baltimore to Seattle makes him fearless! His goal is to raise $7,476 for the organization, and he reached that goal last night (although more donations are always welcome in support of fighting cancer)! Kevin explains that when he studied abroad in Denmark in the fall of 2011, he “fell in love with sustainable transportation, especially cycling.” Not only does his fearless endeavor raise money to fight cancer, but he is also supporting healthy environmental practices. [excerpt

Teaching and Learning by Analogy: Psychological Perspectives on the Parables of Jesus

Christian teachers are often encouraged to use Jesus’ teaching strategies as models for their own pedagogy. Jesus frequently utilized analogical comparisons, or parables, to help his learners understand elements of his Gospel message. Although teachers can use analogical models to facilitate comprehension, such models also can sow the seeds of confusion and misconception. Recent advances in cognitive psychology have provided new theoretical frameworks to help us understand how instructional analogies function in the teaching-learning process. The goal of this paper is to analyze Jesus’ analogical teaching from these psychological perspectives, with implications for all teachers who utilize instructional analogies. In addition to reviewing basic analogical learning processes, I explore a six-variable model to account systematically for potential analogical misconceptions

Irrational numbers associated to sequences without geometric progressions

Let s and k be integers with s \geq 2 and k \geq 2. Let g_k^{(s)}(n) denote the cardinality of the largest subset of the set {1,2,..., n} that contains no geometric progression of length k whose common ratio is a power of s. Let r_k(\ell) denote the cardinality of the largest subset of the set {0,1,2,\ldots, \ell -1\} that contains no arithmetric progression of length k. The limit $$\lim_{n\rightarrow \infty} \frac{g_k^{(s)}(n)}{n} = (s-1) \sum_{m=1}^{\infty} \left(\frac{1}{s} \right)^{\min \left(r_k^{-1}(m)\right)}$$ exists and converges to an irrational number.Comment: 7 page

On sequences without geometric progressions

An improved upper bound is obtained for the density of sequences of positive integers that contain no k-term geometric progression.Comment: 4 pages; minor correctio

Executive Compensation in American Unions

[Exerpt] Studying compensation in the nonprofit sector is difficult. In nonprofit organizations, it is not always clear what the objectives of the organization are and, therefore, perhaps even more difficult to consider how to compensate managers than in the for-profit sector. This paper investigates the determinants of executive compensation of leaders of American labor unions. We use panel data on more than 75,000 organization-years of unions from 2000 to 2007 which allows us to examine within union differences over time. We specifically concentrate on two issues of importance to unions – the level of membership and the wages of union members. Both measures are strongly related to the compensation of the leaders of American labor unions, even after controlling for organization size and individual organization fixed-effects. That is, within the same union, higher levels of membership size and average member wage over time are associated with higher levels of pay for union leaders. Additionally, the elasticity of pay with respect to membership for unions is very similar to the elasticity of pay with respect to employees in for-profit firms over the same period

A problem of Rankin on sets without geometric progressions

A geometric progression of length $k$ and integer ratio is a set of numbers of the form $\{a,ar,\dots,ar^{k-1}\}$ for some positive real number $a$ and integer $r\geq 2$. For each integer $k \geq 3$, a greedy algorithm is used to construct a strictly decreasing sequence $(a_i)_{i=1}^{\infty}$ of positive real numbers with $a_1 = 1$ such that the set $$G^{(k)} = \bigcup_{i=1}^{\infty} \left(a_{2i} , a_{2i-1} \right]$$ contains no geometric progression of length $k$ and integer ratio. Moreover, $G^{(k)}$ is a maximal subset of $(0,1]$ that contains no geometric progression of length $k$ and integer ratio. It is also proved that there is a strictly increasing sequence $(A_i)_{i=1}^{\infty}$ of positive integers with $A_1 = 1$ such that $a_i = 1/A_i$ for all $i = 1,2,3,\ldots$. The set $G^{(k)}$ gives a new lower bound for the maximum cardinality of a subset of the set of integers $\{1,2,\dots,n\}$ that contains no geometric progression of length $k$ and integer ratio.Comment: 15 page