As the Earth entering into the Anthropocene, global sustainable development requires ecological research to evolve into the large-scale, quantitative, and predictive era. It necessitates a revolution of ecological obs...As the Earth entering into the Anthropocene, global sustainable development requires ecological research to evolve into the large-scale, quantitative, and predictive era. It necessitates a revolution of ecological observation technology and a long-term accumulation of scientific data. The ecosystem flux tower observation technology is the right one to meet this requirement. However, the unique advantages and potential values of global-scale flux tower observation are still not fully appreciated. Reviewing the development history of global meteorological observation and its scientific contributions to the society, we can get an important enlightenment to re-cognize the scientific mission of flux observation.展开更多
For a conservation law with convex condition and initial data in L∞(R), it had been commonly believed that the number of discontinuity lines (or shock waves) of the solution is at most countable since Theorem 1 in Ol...For a conservation law with convex condition and initial data in L∞(R), it had been commonly believed that the number of discontinuity lines (or shock waves) of the solution is at most countable since Theorem 1 in Oleinik's seminal paper published in 1956 asserted this fact. In 1977, the author gave an example to show that there is an initial data in C∞(R) ∩ L∞(R) such that the number of shock waves is uncountable. And in 1980, he gave an example to show that there is an initial data in C(R)∩L∞(R) such that the measure of original points of shock waves on the real axis is positive. In this paper, he proves further that the set consisting of initial data in C(R) ∩ L∞(R) with the property: almost all points on the real axis are original points of shock waves, is dense in C(R) ∩ L∞(R). All these results show that Oleinik's assertion on the countability of discontinuity lines is wrong.展开更多
基金Science and Technology Service Network Initiative of the Chinese Academy of Sciences(KFJ-SW-STS-169)National Natural Science Foundation of China(41671045 and 31600347)
文摘As the Earth entering into the Anthropocene, global sustainable development requires ecological research to evolve into the large-scale, quantitative, and predictive era. It necessitates a revolution of ecological observation technology and a long-term accumulation of scientific data. The ecosystem flux tower observation technology is the right one to meet this requirement. However, the unique advantages and potential values of global-scale flux tower observation are still not fully appreciated. Reviewing the development history of global meteorological observation and its scientific contributions to the society, we can get an important enlightenment to re-cognize the scientific mission of flux observation.
基金supported by National Natural Science Foundation of China (Grant No.10771206)
文摘For a conservation law with convex condition and initial data in L∞(R), it had been commonly believed that the number of discontinuity lines (or shock waves) of the solution is at most countable since Theorem 1 in Oleinik's seminal paper published in 1956 asserted this fact. In 1977, the author gave an example to show that there is an initial data in C∞(R) ∩ L∞(R) such that the number of shock waves is uncountable. And in 1980, he gave an example to show that there is an initial data in C(R)∩L∞(R) such that the measure of original points of shock waves on the real axis is positive. In this paper, he proves further that the set consisting of initial data in C(R) ∩ L∞(R) with the property: almost all points on the real axis are original points of shock waves, is dense in C(R) ∩ L∞(R). All these results show that Oleinik's assertion on the countability of discontinuity lines is wrong.
