(k+1)-sums versus k-sums

A $k$-sum of a set $A\subseteq \mathbb{Z}$ is an integer that may be expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of the number of $(k+1)$-sums to the number of $k$-sums be? Writing $k\wedge A$ for the set of $k$-sums of $A$ we prove that $$\frac{|(k+1)\wedge A|}{|k\wedge A|}\, \le \, \frac{|A|-k}{k+1}$$ whenever $|A|\ge (k^{2}+7k)/2$. The inequality is tight -- the above ratio being attained when $A$ is a geometric progression. This answers a question of Ruzsa.Comment: 5 page

This Rock Is My Rock, This Rock Is Your Rock

In this activity, students use their observational skills to explore the makeup of various samples of rocks. They will recognize that the rocks are made up of one or more minerals. Educational levels: Intermediate elementary, Middle school

Adaptation: A Way of Life, Plant and Animal Desert Adaptations

This document provides several activities that show how desert plants and animals are well-adapted to life in the desert and thrive on little moisture and high temperatures. There are extension lessons as well as a drawing activity. Educational levels: Intermediate elementary, Primary elementary

Search for exotics in the rare decay B→J/ψKKKB \rightarrow J/\psi K K K at BABARBABAR

One of the most intriguing puzzles in hadron spectroscopy are the numerous charmonium-like states observed in the last decade, including charged states that are manifestly exotic. Over the years, the experiment $BABAR$ has extensively studied those in B meson decays, initial state radiation processes and two photon reactions. We report in this paper a new study on some of those states, performed using the entire data sample collected by $BABAR$ in $e^+e^-$ collisions, at center of mass energies near 10.58 GeV/c$^2$. The study of the process $B \rightarrow J/\psi \phi K$ will be presented, and the search for the resonant states X(4140) and X(4270) in their decays to $J/\psi \phi$, will be highlighted.Comment: 5 pages, 16 figures; Proceedings written for a poster at the International Conference of New Frontiers in Physics, ICNFP 2014; submitted at EPJ Web of Conference

Lawrence K. Williams

[Excerpt] In 1952, Professor Williams graduated cum laude from Tufts University. He received his Masters Degree in 1954 from the University Illinois. In 1960, he earned a PhD in psychology from the University of Michigan. Professor Williams served in the U.S. Army from 1954-56, and worked as a research psychologist. In 1961 he came to Cornell University as an assistant professor, and became a full professor in 1969. When he retired in 1999, his colleagues awarded him an emeritus professorship. During his long career, Professor Williams served for a period as chairman of the Department of Organizational Behavior and for 25 years was the director of graduate studies for the school of Industrial and Labor Relations. He served on the committees of over 250 graduate students and was chairman for more than 70 students. He was also one of the founders and directors of GOALS, a foundation to support under represented minority graduate students in Human Resources and Industrial Relations. Professor Williams was also a Fulbright scholar in Peru during 1967-72

Monochromatic Progressions in Random Colorings

Let N^{+}(k)= 2^{k/2} k^{3/2} f(k) and N^{-}(k)= 2^{k/2} k^{1/2} g(k) where 1=o(f(k)) and g(k)=o(1). We show that the probability of a random 2-coloring of {1,2,...,N^{+}(k)} containing a monochromatic k-term arithmetic progression approaches 1, and the probability of a random 2-coloring of {1,2,...,N^{-}(k)} containing a monochromatic k-term arithmetic progression approaches 0, for large k. This improves an upper bound due to Brown, who had established an analogous result for N^{+}(k)= 2^k log k f(k).Comment: 5 page

K-Space Interactive Search

In this paper we will present the K-Space1 Interactive Search system for content-based video information retrieval to be demonstrated in the VideOlympics. This system is an exten-sion of the system we developed as part of our participation in TRECVID 2007 [1]. In TRECVID 2007 we created two interfaces, known as the ‘Shot’ based and ‘Broadcast’ based interfaces. Our VideOlympics submission takes these two in-terfaces and the lessons learned from our user experiments, to create a single user interface which attempts to leverage the best aspects of both