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

Giving and receiving rewards

Awards in the form of orders, medals, decorations, prizes, and titles are ubiquitous in monarchies and republics, private organizations, and not-for-profit and profit-oriented firms. Nevertheless, this kind of nonmaterial extrinsic incentive has been given little attention in the social sciences, including psychology. The demand for awards relies on an individual's desire for distinction, and the supply of awards is governed by the desire to motivate. The technique of analytic narratives is used to show that a number of empirically testable propositions about awards are consistent with observable data