金乡县是我国“蒜乡”,有2000多年的发展历史,年播种面积约70万亩,年总产80万吨,销往160多个国家。金乡大蒜种植面积大,产量高,质量好,出口量大,素有“世界大蒜看中国,中国大蒜看金乡”的美誉。本文通过面向对象分类提取,对金乡县小春...金乡县是我国“蒜乡”,有2000多年的发展历史,年播种面积约70万亩,年总产80万吨,销往160多个国家。金乡大蒜种植面积大,产量高,质量好,出口量大,素有“世界大蒜看中国,中国大蒜看金乡”的美誉。本文通过面向对象分类提取,对金乡县小春作物的种植面积和种植重心进行时空变化分析。得出以下结论:1) 在2016~2019年里,由于政策和市场、暴雪天气的原因,金乡县大蒜种植面积呈现先增加后减少的趋势,而小麦种植面积则是先减少后增加。2) 由于受土地总面积限制、自然条件变化等各方面因素的影响,大蒜的种植重心无明显偏移。由此也可以说明大蒜作为金乡县主要的种植农作物,其种植重心呈现稳定的状态,属平衡种植的发展类型。金乡县作为大蒜之乡,主要种植的农作物为大蒜,小麦种植作为辅助,受大蒜种植面积的影响,小麦重心偏移不规律且偏移距离相对较大。因此及时了解,准确掌握主要粮食作物大蒜、小麦种植面积、产量等信息对农业生产、农村政策、国家粮食市场的调节、进出口以及粮食政策的制定均有重要意义。Jinxiang County is China’s “garlic township”, has more than 2000 years of development history, the annual sowing area of about 700,000 mu, the annual total production of 800,000 tons, sold to more than 160 countries. Jinxiang garlic planting area is large, high output, good quality, export volume, known as “the world’s garlic to see China, China’s garlic to see Jinxiang” reputation. In this paper, the spatial and temporal changes of planting area and planting center of spring crops in Jinxiang County were analyzed by object-oriented classification. The following conclusions were drawn: 1) From 2016 to 2019, due to the policy, market and blizzard weather, the planting area of garlic in Jinxiang County showed a trend of increasing first and then decreasing, while the planting area of wheat decreased first and then increased. 2) Due to the restriction of total land area, changes in natural conditions and other factors, the planting center of gravity of garlic has not significantly shifted. It can also be shown that garlic as the main planting crop in Jinxiang County, its planting center of gravity presents a stable state, belongs to the development type of balanced planting. As the hometown of garlic, garlic is the main crop planted in Jinxiang County, with wheat planting as an auxiliary. Affected by the planting area of garlic, the wheat center of gravity shifts irregularly and the deviation distance is relatively large. Therefore, timely understanding and accurate grasp of the main food crops garlic, wheat planting area, yield and other information are of great significance to agricultural production, rural policies, national food market regulation, import and export and food policy formulation.展开更多
In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）dy ...In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）dy = g（u（x）,v（x））.To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.展开更多
In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2...In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.展开更多
文摘金乡县是我国“蒜乡”,有2000多年的发展历史,年播种面积约70万亩,年总产80万吨,销往160多个国家。金乡大蒜种植面积大,产量高,质量好,出口量大,素有“世界大蒜看中国,中国大蒜看金乡”的美誉。本文通过面向对象分类提取,对金乡县小春作物的种植面积和种植重心进行时空变化分析。得出以下结论:1) 在2016~2019年里,由于政策和市场、暴雪天气的原因,金乡县大蒜种植面积呈现先增加后减少的趋势,而小麦种植面积则是先减少后增加。2) 由于受土地总面积限制、自然条件变化等各方面因素的影响,大蒜的种植重心无明显偏移。由此也可以说明大蒜作为金乡县主要的种植农作物,其种植重心呈现稳定的状态,属平衡种植的发展类型。金乡县作为大蒜之乡,主要种植的农作物为大蒜,小麦种植作为辅助,受大蒜种植面积的影响,小麦重心偏移不规律且偏移距离相对较大。因此及时了解,准确掌握主要粮食作物大蒜、小麦种植面积、产量等信息对农业生产、农村政策、国家粮食市场的调节、进出口以及粮食政策的制定均有重要意义。Jinxiang County is China’s “garlic township”, has more than 2000 years of development history, the annual sowing area of about 700,000 mu, the annual total production of 800,000 tons, sold to more than 160 countries. Jinxiang garlic planting area is large, high output, good quality, export volume, known as “the world’s garlic to see China, China’s garlic to see Jinxiang” reputation. In this paper, the spatial and temporal changes of planting area and planting center of spring crops in Jinxiang County were analyzed by object-oriented classification. The following conclusions were drawn: 1) From 2016 to 2019, due to the policy, market and blizzard weather, the planting area of garlic in Jinxiang County showed a trend of increasing first and then decreasing, while the planting area of wheat decreased first and then increased. 2) Due to the restriction of total land area, changes in natural conditions and other factors, the planting center of gravity of garlic has not significantly shifted. It can also be shown that garlic as the main planting crop in Jinxiang County, its planting center of gravity presents a stable state, belongs to the development type of balanced planting. As the hometown of garlic, garlic is the main crop planted in Jinxiang County, with wheat planting as an auxiliary. Affected by the planting area of garlic, the wheat center of gravity shifts irregularly and the deviation distance is relatively large. Therefore, timely understanding and accurate grasp of the main food crops garlic, wheat planting area, yield and other information are of great significance to agricultural production, rural policies, national food market regulation, import and export and food policy formulation.
基金Supported by National Natural Science Foundation of China(11771354)
文摘In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）dy = g（u（x）,v（x））.To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.
文摘In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.
