The 3x+1 Semigroup

The 3x+1 semigroup is the multiplicative semigroup generated by the rational numbers of form (2k+1)/(3k+2) for non-negative k, together with 2. This semigroup encodes backward iteration under the 3x+1 map, and the 3x+1 conjecture implies that it contains every positive integer. We prove this is the case, and show that this semigroup consists of all positive rational numbers a/b such that 3 does not divide b.Comment: 16 pages, latex; minor change

Providing True Opportunity for Opportunity Youth: Promising Practices and Principles for Helping Youth Facing Barriers to Employment

Many "opportunity youth" -- youth who are not working or in school -- would benefit substantially from gaining work experience but need help overcoming barriers to employment and accessing the labor market.Those opportunity youth facing the most significant challenges, such as extreme poverty, homelessness, and justice system involvement, often need even more intensive assistance in entering and keeping employment, and are at risk of being left behind even by employment programs that are specifically designed to serve opportunity youth.This paper builds on the research literature with extensive interviews with employment program providers who have had success in helping the most vulnerable opportunity youth succeed in the workforce. Six principles for effectively serving these youth are identified

A Recent Occurrence of Thermal Stratification and Low Dissolved Oxygen in Western Lake Erie

Author Institution: United States Department of the Interior, Bureau of Commercial Fisheries, Ann Arbor, Michigan, and Sandusky, Ohio and Ohio Department of Natural Resources, Division of Wildlife, Sandusky, OhioInstances of thermal stratification have been detected only occasionally in western Lake Erie during the past 40 years, but when it does occur it is of considerable importance because of associated dissolved oxygen (DO) depletion in the hypolimnion. Data collected in June of 1963 give an indication of the meteorological conditions necessary to produce this thermal stratification. These conditions are: daily wind speed of less than 3.1 m/sec (7 mph); highest wind speed of less than 6.7 m/sec (15 mph); and an average daily temperature of more than 18.5 C for approximately 5 consecutive days. Weather records for Sandusky, Ohio, show these conditions to have occurred on 33 separate occasions between 1953 and 1963. These data suggest stable thermal stratification occurs more frequently than heretofore suspected. The 1963 data also show that in only 5 days of stratification DO in the hypolimnion was reduced to less than 3 ppm, whereas 28 days were required in 1953. This increased rate of DO depletion is probably due to an increase in the oxygen demand of the bottom sediments in recent years

A New Sub-Period-Minimum Cataclysmic Variable With Partial Hydrogen Depletion And Evidence Of Spiral Disk Structure

We present time-resolved spectroscopy and photometry of CSS 120422:111127+571239 (=SBS 1108+574), a recently discovered SU UMa-type dwarf nova whose 55 minute orbital period is well below the cataclysmic variable (CV) period minimum of similar to 78 minutes. In contrast with most other known CVs, its spectrum features He I emission of comparable strength to the Balmer lines, implying a hydrogen abundance less than 0.1 of long-period CVs-but still at least 10 times higher than that in AM CVn stars. Together, the short orbital period and remarkable helium-to-hydrogen ratio suggest that mass transfer in CSS 120422 began near the end of the donor star's main-sequence lifetime, meaning that this CV is a strong candidate progenitor of an AM CVn system as described by Podsiadlowski et al. Moreover, a Doppler tomogram of the Ha line reveals two distinct regions of enhanced emission. While one is the result of the stream-disk impact, the other is probably attributable to spiral disk structure generated when material in the outer disk achieves a 2:1 orbital resonance with respect to the donor.NSF AST-1211196, AST-9987045Department of Physics at the University of Notre DameNSF Telescope System Instrumentation Program (TSIP)Ohio Board of RegentsOhio State University Office of ResearchAstronom

Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems

Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel time. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. In order to solve the problems, we provide a pre-processing scheme as well as exact and approximate mixed integer programming (MIP) solutions. Our experimental results show the effectiveness of the MIP solutions and in particular point out that the approximate MIP approach often leads to near optimal results within far less computation time than the exact approach

In-Process Radiography of ARC Weld

In-process nondestructive evaluation of welds is of major importance for automated weld processing. Real-time evaluation of defect formation makes possible on-line rewelding and adjustment of process parameters. Measurements of physical parameters related to weld quality may also give information important for understanding the weld process and for improvements of weld quality. In this study we implement industrial radiography for real-time weld process monitoring and testing. X-ray penetrating radiation is used for volume observation in the welding pool and the heat-affected zone during the weld process. The advantages of such a technique are on-line testing of defect formation in the weld and the study of metal fusion and filler metal-base metal interaction, metal transfer and mass flow in the welding pool. This technique may also be used for post-service real-time remote testing of weld quality. By integrating automatic nondestructive inspection with an automatic process control system, unified manufacturing control and testing procedures can be developed. In this unit approach, the nondestructive system may be included as a part of the sensing system in the feedback loop of the process control. Research and development of such general concepts for remote weld process control using real-time radiography as a vision system was initiated in our laboratory under the sponsorship of the Edison Welding Institute