Combinatorics of Link Diagrams and Volume

We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in an A-adequate diagram. We then restrict our attention to plat closures of certain braids, a rich family of links whose volumes can be bounded in terms of the twist number alone. Furthermore, in the absence of special tangles, our volume bounds can be expressed in terms of a single stable coefficient of the colored Jones polynomial. Consequently, we are able to provide a new collection of links that satisfy a Coarse Volume Conjecture.Comment: 17 pages. 15 figure

MS-108: Louise Ramer ’29 Chi Omega Collection

This collection contains a number of different materials, including a scrapbook and photographs, newspaper clippings, letters, publications, and programs from both Tau Delta chapter and the national sorority. A majority of these materials are from the 1930’s and 1940’s, when Gamma Phi became Chi Omega. They focus on a number of events, including the installation banquet, a national conference, and an anniversary dinner, and many are associated with the Alumnae Chapter Ramer helped to establish in Gettysburg. Ramer was a national officer in Chi Omega at the time, and involved in planning a number of these events, and her scrapbook includes photographs, programs and menus from the Chi Omega National Convention in 1938. This collection would be useful to anyone interested in the history of Greek life on campus, the Chi Omega sisterhood, or how sororities operated in the early to mid 20th century. Special Collections and College Archives Finding Aids are discovery tools used to describe and provide access to our holdings. Finding aids include historical and biographical information about each collection in addition to inventories of their content. More information about our collections can be found on our website http://www.gettysburg.edu/special_collections/collections/.https://cupola.gettysburg.edu/findingaidsall/1097/thumbnail.jp

Gentzen systems and decision procedures for relevant logics

This dissertation is primarily a proof theoretic investigation of the positive fragments and boolean extensions of two of the principal relevant logics T and R, with and without contraction, and of the corresponding positive semilattice relevant logics. In addition to motivational and syntactic preliminaries, Chapter 1 contains some new semantic results which are useful in the later chapters. In Chapter 2 we develop subscripted Gentzen systems for four positive semilattice logics. Appropriate Cut Theorems are proved, and one system is shown to be equivalent to uR+ Decision procedures are then given for the two contractionless systems. In Chapter 3 Gentzen systems are given for TW+, T+, RW+ and R+, Cut Theorems and equivalences are proved, and TW+ and RW+ are shown to be decidable. The sequent calculi that are used are multiply structured as required for relevant logics. Chapter 4 begins by collecting decision procedures for fragments of TW+ and RW+. We then discuss and make some progress toward solving some open problems, viz., the decision questions for EW+, TW and RW, and the question of equivalence between RW+ and its semilattice counterpart uRW+

Influence of Placement on the Validity of RunScribe™

Due to the high incidence of running-related injury, biomechanical flaws of the running stride must be investigated.¹ RunScribe™ footpods are light-weight devices that clip onto the shoe and record kinematic variables with each step.² PURPOSE: This study will investigate the influence of footpod placement on the validity of RunScribe™ output compared to hi-speed video analysis. METHOD: Ten collegiate distance runners (6 female, 4 male, 20.9yo ± 0.7yo; 170.2cm ± 6.9cm; 61.4kg ± 7.9 kg) volunteered to participate and granted informed consent. Participants were fit with left-sided body-markers along the line of the achilles tendon and superior-inferior axis of the shoe’s heel-counter, a RunScribe™ on both the left laces and heel, and ran for two, 5-min sessions on a treadmill (Woodway, Desmo). High-speed cameras (Casio EX-10, 210 Hz) recorded in the sagittal and frontal planes. The last 21 strides were analyzed using Kinovea computer software and compared to data downloaded from RunScribe™ for stride-length, stride-rate, ground-contact-time (GCT), pronation-excursion, and max pronation-velocity. Validity and reliability of measurements between RunScribe™ and video were assessed with SPSS and intraclass correlation coefficients, respectively. RESULTS: There was a strong correlation between data from both footpod locations and Kinovea for all sagittal plane variables tested, specifically GCT and stride-rate. There is a much stronger relationship between the heel and Kinovea (r=0.905) than the laces and Kinovea (r=0.204) for max pronation-velocity. CONCLUSION: RunScribe™ is an accurate tool in assessing GCT, stride-rate, and stride-length. Heel-placement will likely output more accurate frontal plane data than the laces

The effectiveness of close reading strategies on the expository text comprehension of students with learning disabilities

The purpose of this study was to examine the effect of close reading using Achieve3000 on the text comprehension and use of text evidence by students with learning disabilities in grades 4-5. In addition, student satisfaction with close reading was evaluated for social validity. Two fourth grade students and one fifth grade student, both female, participated in the study. Two students were classified with specific learning disability, and one was classified as communication impaired. A single-subject methodology with an ABAB design was used. During the Baseline phase, students independently read the expository text. They answered comprehension questions, and wrote their responses using text evidence on lined paper. During the Intervention phase, expository texts were identified by Achieve300 at individual student lexile levels. As students read the passages, they used comprehension strategies provided by Achieve3000 on a computer. Results show that after instruction in close reading using Achieve3000 students increased comprehension and use of text evidence. Results from student surveys given after instruction suggest that the Intervention was socially accepted. Further research is needed to examine possible long-term benefits of close reading for students with disabilities

By the Noble Daring of Her Sons: The Florida Brigade of the Army of the Tennessee

Shining a Light on the Little Known Roll of Floridians During the War The service of Florida’s sons in the Civil War, in particular those men who served in the Army of Tennessee, has received scant attention from historians over the years. This oversight has been ably corrected by Jonat...

Vacua of Marginal Deformations in Gauged Supergravity Models

L'abstract è presente nell'allegato / the abstract is in the attachmen