Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

A brief educational intervention using acceptance and commitment therapy: Four injured athletes' experiences

The purpose of this study was to research the experiences of four injured athletes during their rehabilitation from ACL injuries and to examine the potential usefulness of an adapted ACT intervention in addressing individuals' adherence to rehabilitation protocols and their general psychological well-being. We investigated the usefulness of a brief, 4-session ACT program adapted for educational purposes and presented data as case studies. The case studies suggested that (a) the injured athletes experienced a multitude of private events immediately following injury, throughout their recovery, and when approaching a full return to sport; (b) the injured athletes typically avoided these private events and engaged in emotion-driven behaviors; (c) an adapted ACT approach for educational purposes could be useful on at least a basic level to help injured athletes accept private events, commit to rehabilitation behaviors, and have some certainty about returning to sport; and (d) more could be done to address the needs of injured athletes beyond the structure of our 4-session educational intervention. We concluded that the ACT-based intervention, to a certain extent, educated injured athletes about how to meet the challenges of their recoveries and how to commit to their rehabilitations, as well as to exhibit behaviors that would potentially permit their successful reentries to sport

Evaluation of a Subject-Specific, Torque-Driven Computer Simulation Model of One-Handed Tennis Backhand Ground Strokes

This article was published in the serial, Journal of Applied Biomechanics [© Human Kinetics].A torque-driven, subject-specific 3-D computer simulation model of the impact phase of one-handed tennis backhand strokes was evaluated by comparing performance and simulation results. Backhand strokes of an elite subject were recorded on an artificial tennis court. Over the 50-ms period after impact, good agreement was found with an overall RMS difference of 3.3° between matching simulation and performance in terms of joint and racket angles. Consistent with previous experimental research, the evaluation process showed that grip tightness and ball impact location are important factors that affect postimpact racket and arm kinematics. Associated with these factors, the model can be used for a better understanding of the eccentric contraction of the wrist extensors during one-handed backhand ground strokes, a hypothesized mechanism of tennis elbow