AJUR Volume 18 Issue 2 (September 2021)

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Links to individual manuscripts, abstracts, and keywords are provided below.

p.3. On Packing Thirteen Points in an Equilateral Triangle
Natalie Tedeschi
ABSTRACT: The conversation of how to maximize the minimum distance between points – or, equivalently, pack congruent circles- in an equilateral triangle began by Oler in the 1960s. In a 1993 paper, Melissen proved the optimal placements of 4 through 12 points in an equilateral triangle using only partitions and direct applications of Dirichlet’s pigeon-hole principle. In the same paper, he proposed his conjectured optimal arrangements for 13, 14, 17, and 19 points in an equilateral triangle. In 1997, Payan proved Melissen’s conjecture for the arrangement of fourteen points; and, in September 2020, Joos proved Melissen’s conjecture for the optimal arrangement of thirteen points. These proofs completed the optimal arrangements of up to and including fifteen points in an equilateral triangle. Unlike Melissen’s proofs, however, Joos’s proof for the optimal arrangement of thirteen points in an equilateral triangle requires continuous functions and calculus. I propose that it is possible to continue Melissen’s line of reasoning, and complete an entirely discrete proof of Joos’s Theorem for the optimal arrangement of thirteen points in an equilateral triangle. In this paper, we make progress towards such a proof. We prove discretely that if either of two points is fixed, Joos’s Theorem optimally places the remaining twelve.
KEYWORDS: optimization; packing; equilateral triangle; distance; circles; points; thirteen; maximize

p.13. An Unbiased Mineral Compositional Analysis Technique for Circumstellar Disks
Yung Kipreos & Inseok Song
ABSTRACT: A circumstellar disk that surrounds a star is composed of gas, dust, and rocky objects that are in orbit around it. Around infant stars, this disk can act as a source of material that can be used to form planetesimals, which can then accrete more material and form into planets. Studying the mineral composition of these disks can provide insight into the processes that created our solar system. The purpose of this paper is to analyze the mineral composition of these disks by using a newly created python package, Min-CaLM. This package determines the relative mineral abundance within a disk by using a linear regression technique called non-negative least square minimization. The circumstellar disks that are capable of undergoing compositional analysis must have a spectrum with both a detectable mid-infrared excess and prominent silicate features. From our sample, there are only eight debris disks that qualify to be candidates for the Min-CaLM program. The mineral compositions calculated by Min-CaLM are then compared to the Tholen asteroid classification scheme. HD 23514, HD 105234, HD 15407A, BD+20 307, HD 69830, and HD 172555 are found to have a compositions similar to that expected for C-type asteroids, TYC 9410-532-1 resembles the composition of S-type asteroids, and HD 100546 resembles D-type asteroids. Min-CaLM also calculates the mineral compositions of the comets Tempel 1 and Hale-Bopp, and they are used as a comparison between the material in our early solar system and the debris disk compositions.
KEYWORDS: Debris disk; Mineral; Composition; Analysis; Asteroid; Circumstellar; Spectroscopy; Python

p.29. Do Warmups Predict Pole Vault Competition Performance?
Alex Peskin
ABSTRACT: The aim of this research was to determine the relationship between pole vault warmup and competition performance in a sample of 16 collegiate vaulters over 60 observations. Pole vault athletes are given time to warm up in the same area that the competition will take place. This prompted investigation into whether better warmup performance could indicate better familiarity with the performance environment, and whether this could translate to the competition. The number of warmup vaults taken was also considered. Participants were observed during multiple warmup periods and data was collected on warmup performance. The findings indicate a significant correlation between instances in which participants displayed their best warmup scores and their best competition performances, likewise with their worst. Also, participants who took more warmup vaults performed significantly better on average. Athletes and coaches should consider implementing warmup practices that emphasize familiarizing oneself with their performance environment.
KEYWORDS: Pole Vault; Track and Field; Warmups; Warmup Performance; Competition Performance; Performance Environment; Nested Task; Task Constraints

p.35. A Narrative Literature Review of the Psychological Hindrances Affecting Return to Sport After Injuries
Ashley Sweeney, Stephanie M. Swanberg, & Suzan Kamel-ElSayed
ABSTRACT: After different sports injuries, athletes may experience various psychological emotions in response to such injuries, which could lead an athlete to feel stressed. These emotions include anger, fear, frustration, anxiety, and depression which may lead to lack of confidence in returning to their sport and/or fear of sustaining a new injury. This narrative review aims to determine the possible psychological hindrances present when an athlete is planning on returning to sport after injury to an anterior cruciate ligament (ACL) or after sustaining a concussion. The synthesized information for this review has been collected from researching the databases PubMed, SportDiscus, PsycInfo, and Google Scholar using search terms including “return to sport”, “ACL injury”, “concussion”, and “psychology”. Journal articles needed to be in English and published in the years 2009-2019; books and unpublished abstracts were excluded. A total of 42studies were included and analyzed using deductive coding to organize and synthesize relevant articles into themes. The review summarizes the shared common and the different psychological hindrances that may be found in athletes after an ACL injury or concussion. Shared psychological characteristics for returning to sport following either an ACL injury or concussion included fear, self-esteem, control, anxiety, stress, recovery, and social support. Discovering the common and unique psychological barriers which may affect the injured athletes from returning to sport can help educate athletes’ families, coaches, and healthcare professionals, as well as promote discussions for the future to help athletes feel more secure in their return to their respective sport.
KEYWORDS: ACL Injuries; Concussions; Sport Injuries; Athletes; Narrative Literature Review; Psychological Hindrances; Psychological Characteristics; Return to Sport; Psychology