This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems...This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.展开更多
There is promising indication of helium-rich natural gas in Weihe Basin.However,the lack of a detailed investigation on the origin and the spatial distribution of helium source rocks(mainly Yanshanian granites)limits ...There is promising indication of helium-rich natural gas in Weihe Basin.However,the lack of a detailed investigation on the origin and the spatial distribution of helium source rocks(mainly Yanshanian granites)limits the helium potentiality evaluation in Weihe Basin(WB).We performed three-dimensional(3 D)inversions of magnetic data in Weihe Basin and its adjacent areas to figure out the crustal thermal structure and the temporal-spatial distribution of deep granite in the basin.Based on this,we have proposed a geological model of helium accumulation and predicted the potential area of helium distribution.The results of 3 D magnetic inversion indicate that the granites in the deep Weihe Basin are mostly located at the central and southern parts of the basin,which are connected spatially with the granites in the North Qinling Orogenic Belt.These granites were all derived from largescale intra-continental orogeny in the Qinling area during the mid-Mesozoic,providing a good material basis for crust-derived helium in the basin.The local uplift of the Curie surface makes the thermal fluid more actively,which contributes to helium accumulation.The faults developed in the WB are the migration pathway of crust-derived helium and the upward migration of the mantle-derived helium.The wells with high percentage helium are mostly located near the Weihe fault and the areas on the south of it.The Wugong-Xi’an-Lantian area in the central and the Lintong-Weinan-Tongguan area in the eastern Weihe Basin are the most promising helium distribution areas.Furthermore,the region from the north of Taibai Mountain to Baoji City in the western Weihe Basin may also be another potential area of Helium resource.展开更多
Annual accumulation records covering 1935 to 2004 were reconstructed using Geladaindong ice core in the source of Yangtze River. A significant positive correlation between annual accumulation and precipitation from ne...Annual accumulation records covering 1935 to 2004 were reconstructed using Geladaindong ice core in the source of Yangtze River. A significant positive correlation between annual accumulation and precipitation from nearby meteorological stations was found, suggesting ice core accumulation could be taken as a precipitation proxy in the region. In the past 70 years, precipitation in the Geladaindong region was low from 1930s to early 1960s, and the lowest value occurred in the later 1950s. Since 1960s, precipitation increased dramatically and reached the maximum around 1980s, then decreased slightly in 1990s. By using Mann-Kendall rank statistical test method, a change point for precipitation was de- termined in 1967. Analysis of the atmospheric circulation over the Tibetan Plateau suggested that, compared with the southwest wind during the low precipitation period (before 1967), it extended about 2 latitudes northward during high precipitation period (after 1967). Moreover, during the high precipita- tion, the trough over the Bal Karshi Lake was also enhanced, and both the meridional wind and vapor transporting displayed a remarkable aggrandizement.展开更多
Consider the following integro-differential operator arising from neutron transport in a finite closed convex medium V surrounded by vacuum: A·=-vΩ·grad_r·-v∑(r, v)·+∫_D∫_E k(r, v, Ω, v’, Ω...Consider the following integro-differential operator arising from neutron transport in a finite closed convex medium V surrounded by vacuum: A·=-vΩ·grad_r·-v∑(r, v)·+∫_D∫_E k(r, v, Ω, v’, Ω’)·dv’ dΩ’, D(A)={ψ∈L^P(G)|Aψ∈L^P(G); ψ(r, v, Ω)=0 for r∈V and Ω entering V}, where (r, v, Ω)∈ G=V×E×D, E=(0, v_M], 0【V_M【+∞, D is the surface of the unit sphere in R^3 and 1【p【+∞.展开更多
基金the National Natural Science Foundation of China (Nos.10431010,10501005)Science Foundation for Young Teachers of NENU (No.20070103)
文摘This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.
基金supported by the National Natural Science Foundation of China(No.41904115)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2018JQ4034)。
文摘There is promising indication of helium-rich natural gas in Weihe Basin.However,the lack of a detailed investigation on the origin and the spatial distribution of helium source rocks(mainly Yanshanian granites)limits the helium potentiality evaluation in Weihe Basin(WB).We performed three-dimensional(3 D)inversions of magnetic data in Weihe Basin and its adjacent areas to figure out the crustal thermal structure and the temporal-spatial distribution of deep granite in the basin.Based on this,we have proposed a geological model of helium accumulation and predicted the potential area of helium distribution.The results of 3 D magnetic inversion indicate that the granites in the deep Weihe Basin are mostly located at the central and southern parts of the basin,which are connected spatially with the granites in the North Qinling Orogenic Belt.These granites were all derived from largescale intra-continental orogeny in the Qinling area during the mid-Mesozoic,providing a good material basis for crust-derived helium in the basin.The local uplift of the Curie surface makes the thermal fluid more actively,which contributes to helium accumulation.The faults developed in the WB are the migration pathway of crust-derived helium and the upward migration of the mantle-derived helium.The wells with high percentage helium are mostly located near the Weihe fault and the areas on the south of it.The Wugong-Xi’an-Lantian area in the central and the Lintong-Weinan-Tongguan area in the eastern Weihe Basin are the most promising helium distribution areas.Furthermore,the region from the north of Taibai Mountain to Baoji City in the western Weihe Basin may also be another potential area of Helium resource.
基金Supported by the National Natural Science Foundation of China (Grant No. 40401054 and 40121101)the National Basic Research Program of China (Grant No. 2005CB422004)+1 种基金the "Talent Project" and Innovation Project of Chinese Academy of Sciences (Grant Nos. KZCX3-SW-339 and 334)Dean Foundation of CAS
文摘Annual accumulation records covering 1935 to 2004 were reconstructed using Geladaindong ice core in the source of Yangtze River. A significant positive correlation between annual accumulation and precipitation from nearby meteorological stations was found, suggesting ice core accumulation could be taken as a precipitation proxy in the region. In the past 70 years, precipitation in the Geladaindong region was low from 1930s to early 1960s, and the lowest value occurred in the later 1950s. Since 1960s, precipitation increased dramatically and reached the maximum around 1980s, then decreased slightly in 1990s. By using Mann-Kendall rank statistical test method, a change point for precipitation was de- termined in 1967. Analysis of the atmospheric circulation over the Tibetan Plateau suggested that, compared with the southwest wind during the low precipitation period (before 1967), it extended about 2 latitudes northward during high precipitation period (after 1967). Moreover, during the high precipita- tion, the trough over the Bal Karshi Lake was also enhanced, and both the meridional wind and vapor transporting displayed a remarkable aggrandizement.
基金Project supported by the Natural Science Foundation of Xi'an Jiaotong University.
文摘Consider the following integro-differential operator arising from neutron transport in a finite closed convex medium V surrounded by vacuum: A·=-vΩ·grad_r·-v∑(r, v)·+∫_D∫_E k(r, v, Ω, v’, Ω’)·dv’ dΩ’, D(A)={ψ∈L^P(G)|Aψ∈L^P(G); ψ(r, v, Ω)=0 for r∈V and Ω entering V}, where (r, v, Ω)∈ G=V×E×D, E=(0, v_M], 0【V_M【+∞, D is the surface of the unit sphere in R^3 and 1【p【+∞.
