The Three Loop Isotopy and Framed Isotopy Invariants of Virtual Knots

This paper introduces two virtual knot theory ``analogues'' of a well-known family of invariants for knots in thickened surfaces: the Grishanov-Vassiliev finite-type invariants of order two. The first, called the three loop isotopy invariant, is an invariant of virtual knots while the second, called the three loop framed isotopy invariant, is a regular isotopy invariant of framed virtual knots. The properties of these invariants are investigated at length. In addition, we make precise the informal notion of ``analogue''. Using this formal definition, it is proved that a generalized three loop invariant is a virtual knot theory analogue of a generalization of the Grishanov-Vassiliev invariants of order two

High-Intensity Interval Training in Well-trained Cyclists : Consecutive Days versus Alternating Days

Purpose: This study compared the effects of 3 weeks of high-intensity interval training (HIT) on well-trained cyclists when three weekly HIT sessions were performed on either consecutive or non-consecutive days. Methods: Fifteen well-trained cyclists volunteered to participate in the study. They performed a 5-km time-trial (TT5k) and an incremental test to assess peak oxygen consumption (VO2peak) and peak aerobic power output (PPOa), and were divided into two matched-pair groups based on TT5k performance. For 3 weeks, one group (N=9) performed three HIT sessions per week on consecutive days, while the other group (N=6) did so on non-consecutive days. Subjects trained lightly or not at all on the remaining 4 days. Sessions for both groups consisted of up to eight 2.5-minute intervals at 100% of PPOa, Pre- and post-training TT5k performance, VO2peak, and PPOa were compared using 2 x 2 (group x time) ANOVA with repeated measures on time. Results: Both groups significantly improved TT5k velocity (0.9 ± 0.8 km·hf -1) and average power output (17 ± 19 W), as well as VO2peak (0.2 ± 0.2 L·min-1), and PPOa (23 ± 15 W). Mean improvement (~7%) was similar for both groups, but varied widely among individuals. Conclusion: Neither the consecutive-day nor the non-consecutive day training design is definitively superior, although individual athletes may respond better to one design or the other

PERCUSSION INSTRUCTION IN BEGINNING BAND FOR PROGRAMS WITH A SINGLE TEACHER

PERCUSSION INSTRUCTION IN BEGINNING BAND FOR PROGRAMS WITH A SINGLE TEACHER An Abstract of the Thesis by Micah A. Martin The primary purpose of this study was to find the best methods for developing students into total percussionists in beginning band programs with only one band director on staff. A total percussionist is defined as one who is capable of playing keyboard percussion, snare drum, timpani, and the accessory instruments. The study consists of a survey to assess individual approaches to percussion instruction in beginning band. A questionnaire was developed using Google Forms and a link was emailed to band directors in Kansas, Missouri, and Arkansas. A link was also posted on the Facebook pages of the Southwest Missouri Music Educators Association and the Missouri Music Educators Association. Most of the respondents start percussion along with the other band students on both snare drum and keyboard percussion in the sixth grade. About four-fifths of them do not meet with percussionists for rehearsals or lessons outside of class. Around two-thirds indicated that their percussionists do not take lessons outside of school. Over half of them are able to meet class daily. Over half meet at least ninety minutes per week. However, many of the directors believe that they need more time for beginning band, and especially percussion

Screening for Pathogenic Escherichia Coli in the Chattahoochee River, Columbus, Georgia

Escherichia coli testing is frequently used to indicate the possible presence of harmful pathogens, but E. coli itself can be pathogenic. Serotype 0157:H7, enterohemorrhagic E. coli, is likely the most medically important pathogenic strain of E. coli in the United States. In this study, we surveyed for 0157:H7 and three strains of another pathogenic subtype: enterotoxigenic E. coli. We isolated E. coli colonies from samples taken from the Chattahoochee River in Columbus, Georgia at two different locations, above and below wastewater outputs. We used PCR to test for the individual subtypes and then used a nested PCR protocol for the human, bovine, and avian ETEC. Our results show that most isolated E. coli strains are not 0157:H7 or ETEC. However, nested PCR specific for human enterotoxigenic E. coli amplified target sequences in some tested colonies, which may indicate humans as a source of E. coli at our sample sites

Dawn of the Debt: The Increasing Problem of Creditors Infecting the Discharge Injunction with Zombie Debt

The discharge injunction is an integral aspect of the “fresh start” that bankruptcy affords to many debtors. But there has been a growing threat to the viability of the bankruptcy discharge: zombie debt! Just when honest but unfortunate debtors think they have finally laid their overdue financial obligations to rest and moved on with their lives, zombie debt comes back to life in form of outdated and misleading credit reports that some debt collectors have been using to coerce payment on debts that should have died years prior. This Article discusses the motivation behind these questionable collection tactics and potential remedies within the bankruptcy court through the lens of In re Haynes, a nationwide class action suit targeted at finally burying these undead debts