Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the...Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].展开更多
The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant sol...The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ（dφ（grad（lnb）））＋n/2 grad｜dφ（grad（lnb））｜2=0 and f is a non-constant solution of -1/b2Jψ（dψ（grad（lnf）））＋m/2grad｜dψ（grad（lnf））｜2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps.展开更多
This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" ...This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" />or <img src="Edit_95636a59-7d5d-4b6c-8bd5-f699dd9208df.bmp" alt="" /> and the product system <img src="Edit_c714caaf-0ed9-46bc-b3e1-b0223474a8f5.bmp" alt="" /> in sensitivity, infinite sensitivity, <em>F</em>-sensitivity, (<em>F</em><sub>1</sub>, <em>F</em><sub>2</sub>)-sensitivity. Then, the relation between (<em>X</em>, <em>f</em><sub>1,∞</sub>) or (<em>Y</em>, <em>g</em><sub>1,∞</sub>) and <img src="Edit_55b4ce47-89f3-4476-a8a8-4d4db5a4e8eb.bmp" alt="" /> in ergodic sensitivity is obtained. Where <img src="Edit_a99604c4-2f72-4e75-a998-8057b8790e03.bmp" alt="" /> is the set-valued dynamical system induced by a non-autonomous discrete dynamical system (<em>X</em>, <em>f</em><sub>1,∞</sub>).展开更多
In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Ri...In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M ×（μ,λ） N can not be proper f-harmonic maps,we use projection maps and product maps to construct nontrivial f-harmonic maps.Thus we obtain some similar results given in [21],such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps.Furthermore,we investigate non-trivial f-harmonicity of the product of two harmonic maps.展开更多
Digital maps of soil properties are now widely available.End-users now can access several digital soil mapping(DSM)products of soil properties,produced using different models,calibration/training data,and covariates a...Digital maps of soil properties are now widely available.End-users now can access several digital soil mapping(DSM)products of soil properties,produced using different models,calibration/training data,and covariates at various spatial scales from global to local.Therefore,there is an urgent need to provide easy-to-understand tools to communicate map uncertainty and help end-users assess the reliability of DSM products for use at local scales.In this study,we used a large amount of hand-feel soil texture(HFST)data to assess the performance of various published DSM products on the prediction of soil particle size distribution in Central France.We tested four DSM products for soil texture prediction developed at various scales(global,continental,national,and regional)by comparing their predictions with approximately 3200 HFST observations realized on a 1:50000 soil survey conducted after release of these DSM products.We used both visual comparisons and quantitative indicators to match the DSM predictions and HFST observations.The comparison between the low-cost HFST observations and DSM predictions clearly showed the applicability of various DSM products,with the prediction accuracy increasing from global to regional predictions.This simple evaluation can determine which products can be used at the local scale and if more accurate DSM products are required.展开更多
基金Supported by the National Natural Science Foundation of China(11501404)Jiangsu Planned Talent Projects(2016-JY-078)+1 种基金Jiangsu Jiaogai Projects Fundations(2017JSJG490)Jiangsu Qing Lan Project(PY2016006)。
文摘Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].
基金The National Natural Science Foundation of China(No.10971029)
文摘The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ（dφ（grad（lnb）））＋n/2 grad｜dφ（grad（lnb））｜2=0 and f is a non-constant solution of -1/b2Jψ（dψ（grad（lnf）））＋m/2grad｜dψ（grad（lnf））｜2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps.
文摘This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" />or <img src="Edit_95636a59-7d5d-4b6c-8bd5-f699dd9208df.bmp" alt="" /> and the product system <img src="Edit_c714caaf-0ed9-46bc-b3e1-b0223474a8f5.bmp" alt="" /> in sensitivity, infinite sensitivity, <em>F</em>-sensitivity, (<em>F</em><sub>1</sub>, <em>F</em><sub>2</sub>)-sensitivity. Then, the relation between (<em>X</em>, <em>f</em><sub>1,∞</sub>) or (<em>Y</em>, <em>g</em><sub>1,∞</sub>) and <img src="Edit_55b4ce47-89f3-4476-a8a8-4d4db5a4e8eb.bmp" alt="" /> in ergodic sensitivity is obtained. Where <img src="Edit_a99604c4-2f72-4e75-a998-8057b8790e03.bmp" alt="" /> is the set-valued dynamical system induced by a non-autonomous discrete dynamical system (<em>X</em>, <em>f</em><sub>1,∞</sub>).
基金Partially supported by Guangxi Natural Science Foundation (2011GXNSFA018127)
文摘In this paper,we study f-harmonicity of some special maps from or into a doubly warped product manifold.First we recall some properties of doubly twisted product manifolds.After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M ×（μ,λ） N can not be proper f-harmonic maps,we use projection maps and product maps to construct nontrivial f-harmonic maps.Thus we obtain some similar results given in [21],such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps.Furthermore,we investigate non-trivial f-harmonicity of the product of two harmonic maps.
文摘Digital maps of soil properties are now widely available.End-users now can access several digital soil mapping(DSM)products of soil properties,produced using different models,calibration/training data,and covariates at various spatial scales from global to local.Therefore,there is an urgent need to provide easy-to-understand tools to communicate map uncertainty and help end-users assess the reliability of DSM products for use at local scales.In this study,we used a large amount of hand-feel soil texture(HFST)data to assess the performance of various published DSM products on the prediction of soil particle size distribution in Central France.We tested four DSM products for soil texture prediction developed at various scales(global,continental,national,and regional)by comparing their predictions with approximately 3200 HFST observations realized on a 1:50000 soil survey conducted after release of these DSM products.We used both visual comparisons and quantitative indicators to match the DSM predictions and HFST observations.The comparison between the low-cost HFST observations and DSM predictions clearly showed the applicability of various DSM products,with the prediction accuracy increasing from global to regional predictions.This simple evaluation can determine which products can be used at the local scale and if more accurate DSM products are required.
