China has made remarkable gains in industrialization and development. In the last years, in order to ensure the sustainability of its economic and social development, China gave more importance to the innovativeness o...China has made remarkable gains in industrialization and development. In the last years, in order to ensure the sustainability of its economic and social development, China gave more importance to the innovativeness of business enterprises. In the domestic arena, the sustainability of the growth model that China has followed over the past decades has been criticized because of its excessive reliance on capital and resources as opposed to knowledge and innovation. In 2006, that transformation has been at the centre of the government＇s ＂scientific development strategy＂. Today, in fact, innovation and promotion of entrepreneurship are essential conditions for competitiveness of firms and nations, for the long-term growth and, therefore, for the economy as a whole. This paper investigates the level of potential innovation reached in China in 2008 through a disaggregated analysis, evaluating the production capacity of the Chinese provinces. ＂Innovation＂ has been widely studied by economic literature, specially with reference to the output. In this paper, we will refer to the European Innovation Scoreboard （EIS） index, to measure the progress of innovation, which represents the skill to innovate of a territory, but not the achieved innovation. First, we will propose some methodological changes of this method, that allows to obtained a ranking, in order to better understand the results reached by the Chinese provinces; Then we will test a different methodology in order to measure the level of potential innovation overcoming the limits of current practice--from a composite index obtained through a mean of disaggregated indices to multivariate analysis.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
LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that ...LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).展开更多
文摘China has made remarkable gains in industrialization and development. In the last years, in order to ensure the sustainability of its economic and social development, China gave more importance to the innovativeness of business enterprises. In the domestic arena, the sustainability of the growth model that China has followed over the past decades has been criticized because of its excessive reliance on capital and resources as opposed to knowledge and innovation. In 2006, that transformation has been at the centre of the government＇s ＂scientific development strategy＂. Today, in fact, innovation and promotion of entrepreneurship are essential conditions for competitiveness of firms and nations, for the long-term growth and, therefore, for the economy as a whole. This paper investigates the level of potential innovation reached in China in 2008 through a disaggregated analysis, evaluating the production capacity of the Chinese provinces. ＂Innovation＂ has been widely studied by economic literature, specially with reference to the output. In this paper, we will refer to the European Innovation Scoreboard （EIS） index, to measure the progress of innovation, which represents the skill to innovate of a territory, but not the achieved innovation. First, we will propose some methodological changes of this method, that allows to obtained a ranking, in order to better understand the results reached by the Chinese provinces; Then we will test a different methodology in order to measure the level of potential innovation overcoming the limits of current practice--from a composite index obtained through a mean of disaggregated indices to multivariate analysis.
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.
基金supported by the Natural Science Foundation of USA (Grant No. DMS 0701578)supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Gttingen
文摘LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).
