The geometry in geometric algebra

Thesis (M.S.) University of Alaska Fairbanks, 2014We present an axiomatic development of geometric algebra. One may think of a geometric algebra as allowing one to add and multiply subspaces of a vector space. Properties of the geometric product are proven and derived products called the wedge and contraction product are introduced. Linear algebraic and geometric concepts such as linear independence and orthogonality may be expressed through the above derived products. Some examples with geometric algebra are then given.Chapter 1: Preliminaries -- Chapter 2: The geometry of blades -- Chapter 3: Examples with geometric algebra -- Chapter 4: Appendix -- 4.1. Construction of a geometric algebra -- References

Orthogonal Arrays and Legendre Pairs

Well-designed experiments greatly improve test and evaluation. Efficient experiments reduce the cost and time of running tests while improving the quality of the information obtained. Orthogonal Arrays (OAs) and Hadamard matrices are used as designed experiments to glean as much information as possible about a process with limited resources. However, constructing OAs and Hadamard matrices in general is a very difficult problem. Finding Legendre pairs (LPs) results in the construction of Hadamard matrices. This research studies the classification problem of OAs and the existence problem of LPs. In doing so, it makes two contributions to the discipline. First, it improves upon previous classification results of 2-symbol OAs of even-strength t and t+2 columns. Second, it presents previously unknown impossible values for the dimension of the convex hull of all feasible points to the LP problem improving our understanding of its feasible set

INDIRECT EFFECTS IN THE PEER VICTIMIZATION-ACADEMIC ACHIEVEMENT RELATION: THE ROLE OF ACADEMIC SELF-CONCEPT AND GENDER

Peer victimization is a concern because victimized youth are more likely to have social, emotional, and academic difficulties. The current study examined the link between peer victimization and academic achievement by exploring the indirect effect of academic self-concept on two variables. The sample consisted of 140 middle school students (40% male, 60% female). Using structural equation modeling, a mediation model revealed a significant indirect effect of victimization on academic achievement through academic self-concept; however, when tested for gender differences, the indirect effect was only significant for girls. Interpretation of these results and suggestions for future studies are discussed

AN INVESTIGATION OF RELATIONS AMONG ACADEMIC ENABLERS AND READING OUTCOMES

The current study examined the link between academic enablers and different types of reading achievement measures. Academic enablers are skills and behaviors that support, or enable, students to perform well academically, such as engagement, interpersonal skills, motivation, and study skills. The sample in this study consisted of 61 third-, fourth-, and fifth-grade students (54% male). Academic enablers were rated by classroom teachers via the Academic Competence Evaluation Scales (ACES; DiPerna & Elliott, 2000). Four different measures of reading achievement were included: classroom grades, global ratings of reading skills, standardized test scores, and Reading CBM scores. Results indicated that academic enablers were significantly related to each type of reading outcome. Academic enablers accounted for the greatest amount of variance for classroom grades (45%) and the least amount of variance in standardized test scores (11%). Results suggest that academic enablers are an important part of academic success in reading, particularly classroom grades, but when considering the variance accounted for by academic enablers, they alone are not likely to improve Reading CBM scores or standardized test scores

Efficacy and tolerance of oral versus parenteral cyanocobalamin supplement in hypocobalaminaemic dogs with chronic enteropathy: a controlled randomised open-label trial

Objectives: Determine comparative tolerance of daily oral and weekly parenteral cobalamin supplementation, in hypocobalaminaemic dogs with chronic enteropathy. Determine whether oral is as effective as parenteral supplementation at achieving eucobalaminaemia, in hypocobalaminaemic dogs with protein-losing enteropathy, severe hypocobalaminaemia or high canine inflammatory bowel disease activity index at inclusion. Materials and Methods: Thirty-seven client-owned dogs with hypocobalaminaemia and clinical signs of chronic enteropathy were prospectively enrolled in three UK referral centres. Dogs were randomly allocated to daily oral for 12 weeks or weekly parenteral cobalamin supplementation for 6 weeks and one additional dose 4 weeks later. Serum cobalamin, body condition score, canine inflammatory bowel disease activity index and bodyweight were assessed at inclusion, weeks 7 and 13. Serum methylmalonic acid concentration was evaluated at inclusion and at week 13. Owners completed treatment adherence, palatability, tolerance and satisfaction questionnaires at week 13. Results: Nineteen dogs completed the study. All dogs orally supplemented achieved normal or increased cobalaminaemia at weeks 7 and 13. There was no statistical difference in cobalamin concentration at week 13 in dogs treated with oral or parenteral supplementation, regardless of presence of protein-losing enteropathy, severity of hypocobalaminaemia or canine inflammatory bowel disease activity index at inclusion. Serum methylmalonic acid concentration was not significantly different between oral and parenteral groups, neither were treatment adherence, satisfaction, and tolerance scores at week 13. Clinical Significance: Oral is as effective and as well-tolerated as parenteral cobalamin supplementation in hypocobalaminaemic dogs with chronic enteropathy and severe clinical or biochemical phenotypes, and should be considered as a suitable treatment option regardless of disease severity.</p

Swope Supernova Survey 2017a (SSS17a), the Optical Counterpart to a Gravitational Wave Source

On 2017 August 17, the Laser Interferometer Gravitational-wave Observatory (LIGO) and the Virgo interferometer detected gravitational waves emanating from a binary neutron star merger, GW170817. Nearly simultaneously, the Fermi and INTEGRAL telescopes detected a gamma-ray transient, GRB 170817A. 10.9 hours after the gravitational wave trigger, we discovered a transient and fading optical source, Swope Supernova Survey 2017a (SSS17a), coincident with GW170817. SSS17a is located in NGC 4993, an S0 galaxy at a distance of 40 megaparsecs. The precise location of GW170817 provides an opportunity to probe the nature of these cataclysmic events by combining electromagnetic and gravitational-wave observations.Comment: 25 pages, 10 figures, 2 tables, published today in Scienc

The Old Host-Galaxy Environment of SSS17a, the First Electromagnetic Counterpart to a Gravitational Wave Source

We present an analysis of the host-galaxy environment of Swope Supernova Survey 2017a (SSS17a), the discovery of an electromagnetic counterpart to a gravitational wave source, GW170817. SSS17a occurred 1.9 kpc (in projection; 10.2") from the nucleus of NGC 4993, an S0 galaxy at a distance of 40 Mpc. We present a Hubble Space Telescope (HST) pre-trigger image of NGC 4993, Magellan optical spectroscopy of the nucleus of NGC 4993 and the location of SSS17a, and broad-band UV through IR photometry of NGC 4993. The spectrum and broad-band spectral-energy distribution indicate that NGC 4993 has a stellar mass of log (M/M_solar) = 10.49^{+0.08}_{-0.20} and star formation rate of 0.003 M_solar/yr, and the progenitor system of SSS17a likely had an age of >2.8 Gyr. There is no counterpart at the position of SSS17a in the HST pre-trigger image, indicating that the progenitor system had an absolute magnitude M_V > -5.8 mag. We detect dust lanes extending out to almost the position of SSS17a and >100 likely globular clusters associated with NGC 4993. The offset of SSS17a is similar to many short gamma-ray burst offsets, and its progenitor system was likely bound to NGC 4993. The environment of SSS17a is consistent with an old progenitor system such as a binary neutron star system.Comment: ApJL in pres

Safeguarding children in dentistry: 1. Child protection training, experience and practice of dental professionals with an interest in paediatric dentistry

* Few dental professionals with child protection training have experience of making referrals. * There is a wide gap in practice between recognising signs of child abuse and neglect and responding effectively. * This may indicate missed opportunities to save children from continuing abuse. * There is a need for improved child protection information, support and training for dental professionals. Abstract Following several highly publicised inquiries into the deaths of children from abuse and neglect, there has been much recent interest in the role and responsibility of all health professionals to protect children at risk of maltreatment. The findings of a postal questionnaire, sent in March 2005 to 789 dentists and dental care professionals with an interest in paediatric dentistry working in varied settings in the UK, are presented in a two-part report and discussed in the context of current multi-agency good practice in safeguarding and promoting the welfare of children. This first part explores reported child protection training, experience and practice. There was a significant gap between recognising signs of abuse and responding effectively: 67% of respondents had suspected abuse or neglect of a child patient at some time in their career but only 29% had ever made a child protection referral. The dental profession is alerted to the need to ensure necessary appropriate action to safeguard children is always taken when child abuse or neglect are suspected