Quantized vortices are important topological excitations in Bose–Einstein condensates. The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in m...Quantized vortices are important topological excitations in Bose–Einstein condensates. The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in many numerical and analytical studies. We successfully derive the Padéapproximate solutions for quantized vortices with winding numbers ω = 1, 2, 3, 4, 5, 6 in the context of the Gross–Pitaevskii equation for a uniform condensate. Compared with the numerical solutions, we find that(1) they approximate the entire solutions quite well from the core to infinity;(2) higher-order Padé approximate solutions have higher accuracy;(3) Padé approximate solutions for larger winding numbers have lower accuracy. The healing lengths of the quantized vortices are calculated and found to increase almost linearly with the winding number. Based on experiments performed with 87Rb cold atoms, the healing lengths of quantized vortices and the number of particles within the healing lengths are calculated, and they may be checked by experiment. Our results show that the Gross–Pitaevskii equation is capable of describing the structure of quantized vortices and physics at length scales smaller than the healing length.展开更多
Artificial Intelligence has been playing a profound role in the global economy,social progress,and people’s daily life.With the increasing capabilities and accuracy of AI,the application of AI will have more impacts ...Artificial Intelligence has been playing a profound role in the global economy,social progress,and people’s daily life.With the increasing capabilities and accuracy of AI,the application of AI will have more impacts on manufacturing and service areas in the era of industry 4.0.This study conducts a systematic literature review to study the state-of-the-art on AI in industry 4.0.This paper describes the development of industries and the evolution of AI.This paper also identifies that the development and application of AI will bring not only opportunities but also challenges to industry 4.0.The findings provide a valuable reference for researchers and practitioners through a multi-angle systematic analysis of AI.In the era of industry 4.0,AI system will become an innovative and revolutionary assistance to the whole industry.展开更多
We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence.The motivation for introducing such a dependence notion is to conform with...We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence.The motivation for introducing such a dependence notion is to conform with the preferences of decision makers who are mostly risk averse but would be risk seeking at some wealth levels.We investigate some tractable equivalent properties for this new dependence notion,and explore its properties,including the invariance under increasing and concave transformations,and the invariance under convolution.We also extend our results to a combined fractional-degree expectation dependence notion includingε-almost firstdegree expectation dependence.Two applications on portfolio diversification problem and optimal investment in the presence of a background risk illustrate the usefulness of the approaches proposed in the present paper.展开更多
基金Undergraduate Innovation and Entrepreneurship Program Grant No.S201910579797National Natural Science Foundation of China with Grant No.12005088,11847001,11747017+1 种基金Guangdong Basic and Applied Basic Research Foundation with Grant No.2021A1515010246supported by the Lingnan Normal University Project with Grant No.YL20200203,ZL1930。
文摘Quantized vortices are important topological excitations in Bose–Einstein condensates. The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in many numerical and analytical studies. We successfully derive the Padéapproximate solutions for quantized vortices with winding numbers ω = 1, 2, 3, 4, 5, 6 in the context of the Gross–Pitaevskii equation for a uniform condensate. Compared with the numerical solutions, we find that(1) they approximate the entire solutions quite well from the core to infinity;(2) higher-order Padé approximate solutions have higher accuracy;(3) Padé approximate solutions for larger winding numbers have lower accuracy. The healing lengths of the quantized vortices are calculated and found to increase almost linearly with the winding number. Based on experiments performed with 87Rb cold atoms, the healing lengths of quantized vortices and the number of particles within the healing lengths are calculated, and they may be checked by experiment. Our results show that the Gross–Pitaevskii equation is capable of describing the structure of quantized vortices and physics at length scales smaller than the healing length.
文摘Artificial Intelligence has been playing a profound role in the global economy,social progress,and people’s daily life.With the increasing capabilities and accuracy of AI,the application of AI will have more impacts on manufacturing and service areas in the era of industry 4.0.This study conducts a systematic literature review to study the state-of-the-art on AI in industry 4.0.This paper describes the development of industries and the evolution of AI.This paper also identifies that the development and application of AI will bring not only opportunities but also challenges to industry 4.0.The findings provide a valuable reference for researchers and practitioners through a multi-angle systematic analysis of AI.In the era of industry 4.0,AI system will become an innovative and revolutionary assistance to the whole industry.
文摘We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence.The motivation for introducing such a dependence notion is to conform with the preferences of decision makers who are mostly risk averse but would be risk seeking at some wealth levels.We investigate some tractable equivalent properties for this new dependence notion,and explore its properties,including the invariance under increasing and concave transformations,and the invariance under convolution.We also extend our results to a combined fractional-degree expectation dependence notion includingε-almost firstdegree expectation dependence.Two applications on portfolio diversification problem and optimal investment in the presence of a background risk illustrate the usefulness of the approaches proposed in the present paper.
