The explicit structure of the prolongation algebra of the hirota-satsuma system

For a coupled system of KdV equations the prolongation Lie algebra is explicitly determined. It turns out to be of Kac-Moody type

The Lie algebra of infinitesimal symmetries of nonlinear diffusion equations

By using developed software for solving overdetermined systems of partial differential equations, the authors establish the complete Lie algebra of infinitesimal symmetries of nonlinear diffusion equations

Lie algebra computations

In the context of prolongation theory, introduced by Wahlquist and Estabrook, computations of a lot of Jacobi identities in (infinite-dimensional) Lie algebras are necessary. These computations can be done (automatically) using ‘symbolic computations’. A package written in REDUCE is demonstrated to give an idea of the chosen approach

Solutions of WDVV Equations in Seiberg-Witten Theory from Root Systems

We present a complete proof that solutions of the WDVV equations in Seiberg-Witten theory may be constructed from root systems. A generalization to weight systems is proposed

Symbolic computations in applied differential geometry

The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and the calculation of invariance groups of exterior differential systems. A large number of worked examples have been included in the text to demonstrate the concrete manipulations in practice. In the appendix, a list of programs discussed in the paper is added

Software to compute infinitesimal symmetries of exterior differenial systems, with applications

A description is given of a software package to compute symmetries of partial differential equations, using computer algebra. As an application, the computation of higher-order symmetries of the classical Boussinesq equation is given leading to the recursion operator for symmetries in a straightforward way. Nonlocal symmetries for the Federbush model are obtained yielding the linearization of the model

Six-locus high resolution HLA haplotype frequencies derived from mixed-resolution DNA typing for the entire US donor registry

AbstractWe have calculated six-locus high resolution HLA A∼C∼B∼DRB3/4/5∼DRB1∼DQB1 haplotype frequencies using all Be The Match® Registry volunteer donors typed by DNA methods at recruitment. Mixed resolution HLA typing data was inputted to a modified expectation–maximization (EM) algorithm in the form of genotype lists generated by interpretation of primary genomic typing data to the IMGT/HLA v3.4.0 allele list. The full cohort consists of 6.59million subjects categorized at a broad race level. Overall 25.8% of the individuals were typed at the C locus, and 5.2% typed at the DQB1 locus, while all individuals were typed for A, B, DRB1. We also present a subset of 2.90million subjects with detailed race/ethnic information mapped to 21 population subgroups, 64.1% of which have primary DNA typing data across at least A, B, and DRB1 loci. Sample sizes at the detailed race level range from 1,242,890 for European Caucasian to 1,376 Alaskan Native or Aleut. Genetic distance measurements show high levels of HLA genetic divergence among the 21 detailed race categories, especially among the eight Asian–American populations. These haplotype frequencies will be used to improve match predictions for donor selection algorithms for hematopoietic stem cell transplantation and improve the accuracy in modeling registry match rates

Societal Spheres: Reconstructing Gender through Romance

For centuries, people have been captivated by tales of questing knights, fair ladies, and magical encounters. As someone who grew up immersed in the fantasy genre, transitioning from the Brian Jacques Redwall series as a child to George R.R. Martin's A Song of lce and Fire as an adult, I always wondered how such escapism into distant fantasy worlds could be so relatable to my life. When investigating the history of the source material, I found that chivalric romances have been crafted to suit various audiences and purposes, providing sociopolitical commentary throughout the literary eras. In this thesis, I investigate the impact of the chivalric romance on medieval, Victorian, and contemporary culture by exploring Chrétien de Troyes' twelfth-century romances Erec and Enide and Lancelot, Heldris de Comualle's thirteenth-century Le Roman de Silence, Matthew Arnold's nineteenth-century Tristram and Iseult, and George R.R. Martin's twenty-first-century A Song of lce and Fire. Using a feminist theoretical framework, I highlight how these authors interwove social commentary with gender expectations. What I found the most fascinating is that despite being separated by centuries, these authors (and their listening and reading audiences) grappled with similar philosophical questions on gender and the societal roles that still resonate today. The treatment of such topics in romance is one reason why the chivalric romance has endured from the twelfth into the twenty-first century

Validity of a Functional Obstacle Course as a Tool to Screen for Fall Risks in Older Adults

INTRODUCTION: There is currently no specific instrument or test to diagnose fall risks in older adults. A functional obstacle designed and based on current research and the components of falls has the potential to be an effective method of diagnosing fall risks in older adults. PURPOSE: The purpose of this study was to determine the construct validity and reliability of the Modified Functional Obstacle Course (MFOC) and to examine the instrument’s intra-obstacle measurement parameters. METHODS: Participants (N = 63) performed a single series of three common fall risk assessments: Activity Specific Balance Confidence Scale; Dynamic Gait Index and the Tinetti Balance Test (ABC, DGI, & TBT); and, the new Modified Functional Obstacle Course (MFOC). The order of tests, per series, was randomized between participants. Participants (N = 30) from the original sample returned for a single day of testing on the MFOC. DATA ANALYSIS: Construct validity and reliability was determined by measuring correlation (r) to the (ABC, DGI & TBT). Intra-obstacle analysis was performed by using principal component analysis. CONCLUSION: The Modified Functional Obstacle Course demonstrated a moderate to high construct validity, r(63) = .75 - .76, p \u3c .05, in correlation to the convergent measures and it demonstrated high test re-test reliability, r(30) = .99, p \u3c .05 and internal consistency. Principal component analysis demonstrated five distinct components within the MFOC, which accounted for 78% of the variability in scores