We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logari...We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.展开更多
Resources and environment carrying capacity is central to not only regional sustainable development but also major function-oriented zoning. This paper presents an evaluation index system for resources and environment...Resources and environment carrying capacity is central to not only regional sustainable development but also major function-oriented zoning. This paper presents an evaluation index system for resources and environment carrying capacity based on four aspects of carrying capacity(i.e., water resources, land resources, the environment, and ecosystems) by using a square deviation decision-making method, and on the basis of above effort evaluates the resources and environment carrying capacity across 31 provincial regions in China(not including Hong Kong, Macao and Taiwan regions of China). In addition, this paper evaluates the current state of socio-economic development, and analyzes the spatial distribution of resources and environment pressure. The results showed that distinct spatial differences in resources and environment carrying capacity and pressure across provincial regions. Resources and environment pressure is affected by both comprehensive resources and environment carrying capacity and socio-economic development. Regions subjected to lower degrees of resources and environment pressure will be restricted by resources and environmental problems through future courses of development owing to excessively low carrying capacities. By contrast, regions with higher comprehensive resources and environment carrying capacity will be subjected to excessively high levels of resources and environment pressure because of rapid socio-economic development. Both of resources and environment carrying capacity and pressure must therefore be considered in the allocation of country-binding targets to provincial regions.展开更多
The empirical models of sulfide capacity calculated by traditional optical basicity do not consider the charge compensation of alkaline metal ions to AP＋ in the molten slags, so that the deviations between the calcul...The empirical models of sulfide capacity calculated by traditional optical basicity do not consider the charge compensation of alkaline metal ions to AP＋ in the molten slags, so that the deviations between the calculated values and measured ones of sulfide capacity are inevitable. The relation between sulfide capacity and the corrected optical basicity put forward by Mills considering the charge compensation was investigated. Combined with the relation be- tween sulfide capacity and temperatures, a novel and accurate calculation model of sulfide capacity was proposed, which was applied to calculate the sulfide capacities of CaO-Al2 O3-SiO2-MgO and CaO-Al2 03-SiO2-MgO-TiO2 sys-tems, where the sum of the CaO and MgO concentrations in the slags must be not lower than the Al2O3 concentra tion. It was also found that the calculated values were in a good agreement with the measured values, and the mean deviations were 2.57% and 2.65%, respectively.展开更多
The sub-linear expectation or called G-expectation is a non-linear expectation having advantage of modeling non-additive probability problems and the volatilityuncertainty in finance.Let{Xn;n≥1}be a sequence of indep...The sub-linear expectation or called G-expectation is a non-linear expectation having advantage of modeling non-additive probability problems and the volatilityuncertainty in finance.Let{Xn;n≥1}be a sequence of independent random vari-ables in a sub-linear expectation space(Ω,H,E^(^)).Denote S_(n)=∑_(k=1)^(n)Xk and=V_(n)^(2)=∑_(k=1)^(n)X_(k)^(2).In this paper,a moderate deviation for self-normalized sums,thatis,the asymptotic capacity of the event{Sn/Vn≥x_(n)}for x_(n)=o(√n),is found both for identically distributed random variables and independent but not necessarilyidentically distributed random variables.As an application,the self-normalized lawsof the iterated logarithm are obtained.A Bernstein's type inequality is also establishedfor proving the law of the iterated logarithm.展开更多
Closing a single nozzle or multiple nozzles for a temporary casting operation(fewer strands casting)was common in a tundish due to insufficient molten steel or equipment failure.However,nozzle clogging usually happens...Closing a single nozzle or multiple nozzles for a temporary casting operation(fewer strands casting)was common in a tundish due to insufficient molten steel or equipment failure.However,nozzle clogging usually happens under the situation of fewer strands casting.Hence,a temperature deviation index was introduced to characterize the temperature stratification of molten steel for a large capacity tundish,and a new calculation method of residence time curve was used to describe the different flow types of molten steel at each outlet.Based on hydraulics experiment and numerical simulation,important parameters of present case and modified case were compared.Under the situation of fewer strands casting,the proportion of internal-recycle flow after modification decreased from 30.68%to 24.55%;the standard deviation of the response time reduced from 27.59 to 13.16,and the interquartile range of temperature deviation index changed from 0.89 to 0.27.展开更多
基金This research supported by Grants from the National Natural Science Foundation of China(No.11225104)and the Fundamental Research Funds for the Central Universities.
文摘We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.
基金Under the auspices of Science and Technology Service Network Initiative of the Chinese Academy of Sciences(No.KEJ-EW-ZY-004)
文摘Resources and environment carrying capacity is central to not only regional sustainable development but also major function-oriented zoning. This paper presents an evaluation index system for resources and environment carrying capacity based on four aspects of carrying capacity(i.e., water resources, land resources, the environment, and ecosystems) by using a square deviation decision-making method, and on the basis of above effort evaluates the resources and environment carrying capacity across 31 provincial regions in China(not including Hong Kong, Macao and Taiwan regions of China). In addition, this paper evaluates the current state of socio-economic development, and analyzes the spatial distribution of resources and environment pressure. The results showed that distinct spatial differences in resources and environment carrying capacity and pressure across provincial regions. Resources and environment pressure is affected by both comprehensive resources and environment carrying capacity and socio-economic development. Regions subjected to lower degrees of resources and environment pressure will be restricted by resources and environmental problems through future courses of development owing to excessively low carrying capacities. By contrast, regions with higher comprehensive resources and environment carrying capacity will be subjected to excessively high levels of resources and environment pressure because of rapid socio-economic development. Both of resources and environment carrying capacity and pressure must therefore be considered in the allocation of country-binding targets to provincial regions.
基金Sponsored by National Natural Science Foundation of China(51090384)
文摘The empirical models of sulfide capacity calculated by traditional optical basicity do not consider the charge compensation of alkaline metal ions to AP＋ in the molten slags, so that the deviations between the calculated values and measured ones of sulfide capacity are inevitable. The relation between sulfide capacity and the corrected optical basicity put forward by Mills considering the charge compensation was investigated. Combined with the relation be- tween sulfide capacity and temperatures, a novel and accurate calculation model of sulfide capacity was proposed, which was applied to calculate the sulfide capacities of CaO-Al2 O3-SiO2-MgO and CaO-Al2 03-SiO2-MgO-TiO2 sys-tems, where the sum of the CaO and MgO concentrations in the slags must be not lower than the Al2O3 concentra tion. It was also found that the calculated values were in a good agreement with the measured values, and the mean deviations were 2.57% and 2.65%, respectively.
基金Grants from the National Natural Science Foundation of China(No.11225104)973 Program(No.2015CB352302)the Fundamental Research Funds for the CentralUniversities.
文摘The sub-linear expectation or called G-expectation is a non-linear expectation having advantage of modeling non-additive probability problems and the volatilityuncertainty in finance.Let{Xn;n≥1}be a sequence of independent random vari-ables in a sub-linear expectation space(Ω,H,E^(^)).Denote S_(n)=∑_(k=1)^(n)Xk and=V_(n)^(2)=∑_(k=1)^(n)X_(k)^(2).In this paper,a moderate deviation for self-normalized sums,thatis,the asymptotic capacity of the event{Sn/Vn≥x_(n)}for x_(n)=o(√n),is found both for identically distributed random variables and independent but not necessarilyidentically distributed random variables.As an application,the self-normalized lawsof the iterated logarithm are obtained.A Bernstein's type inequality is also establishedfor proving the law of the iterated logarithm.
基金the National Natural Science Foundation of China(Grant No.51774031).
文摘Closing a single nozzle or multiple nozzles for a temporary casting operation(fewer strands casting)was common in a tundish due to insufficient molten steel or equipment failure.However,nozzle clogging usually happens under the situation of fewer strands casting.Hence,a temperature deviation index was introduced to characterize the temperature stratification of molten steel for a large capacity tundish,and a new calculation method of residence time curve was used to describe the different flow types of molten steel at each outlet.Based on hydraulics experiment and numerical simulation,important parameters of present case and modified case were compared.Under the situation of fewer strands casting,the proportion of internal-recycle flow after modification decreased from 30.68%to 24.55%;the standard deviation of the response time reduced from 27.59 to 13.16,and the interquartile range of temperature deviation index changed from 0.89 to 0.27.
