This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouvill...This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.展开更多
In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly va...In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.展开更多
Aiming at the problems of increasing uncertainty of low-carbon generation energy in active distribution network(ADN)and the difficulty of security assessment of distribution network,this paper proposes a two-phase sch...Aiming at the problems of increasing uncertainty of low-carbon generation energy in active distribution network(ADN)and the difficulty of security assessment of distribution network,this paper proposes a two-phase scheduling model for flexible resources in ADN based on probabilistic risk perception.First,a full-cycle probabilistic trend sequence is constructed based on the source-load historical data,and in the day-ahead scheduling phase,the response interval of the flexibility resources on the load and storage side is optimized based on the probabilistic trend,with the probability of the security boundary as the security constraint,and with the economy as the objective.Then in the intraday phase,the core security and economic operation boundary of theADNis screened in real time.Fromthere,it quantitatively senses the degree of threat to the core security and economic operation boundary under the current source-load prediction information,and identifies the strictly secure and low/high-risk time periods.Flexibility resources within the response interval are dynamically adjusted in real-time by focusing on high-risk periods to cope with future core risks of the distribution grid.Finally,the improved IEEE 33-node distribution system is simulated to obtain the flexibility resource scheduling scheme on the load and storage side.Thescheduling results are evaluated from the perspectives of risk probability and flexible resource utilization efficiency,and the analysis shows that the scheduling model in this paper can promote the consumption of low-carbon energy from wind and photovoltaic sourceswhile reducing the operational risk of the distribution network.展开更多
Electrolysis tanks are used to smeltmetals based on electrochemical principles,and the short-circuiting of the pole plates in the tanks in the production process will lead to high temperatures,thus affecting normal pr...Electrolysis tanks are used to smeltmetals based on electrochemical principles,and the short-circuiting of the pole plates in the tanks in the production process will lead to high temperatures,thus affecting normal production.Aiming at the problems of time-consuming and poor accuracy of existing infrared methods for high-temperature detection of dense pole plates in electrolysis tanks,an infrared dense pole plate anomalous target detection network YOLOv5-RMF based on You Only Look Once version 5(YOLOv5)is proposed.Firstly,we modified the Real-Time Enhanced Super-Resolution Generative Adversarial Network(Real-ESRGAN)by changing the U-shaped network(U-Net)to Attention U-Net,to preprocess the images;secondly,we propose a new Focus module that introduces the Marr operator,which can provide more boundary information for the network;again,because Complete Intersection over Union(CIOU)cannot accommodate target borders that are increasing and decreasing,replace CIOU with Extended Intersection over Union(EIOU),while the loss function is changed to Focal and Efficient IOU(Focal-EIOU)due to the different difficulty of sample detection.On the homemade dataset,the precision of our method is 94%,the recall is 70.8%,and the map@.5 is 83.6%,which is an improvement of 1.3%in precision,9.7%in recall,and 7%in map@.5 over the original network.The algorithm can meet the needs of electrolysis tank pole plate abnormal temperature detection,which can lay a technical foundation for improving production efficiency and reducing production waste.展开更多
Forman has developed a version of discrete Morse theory that can be understood in terms of arrow patterns on a(simplicial,polyhedral or cellular)complex without closed orbits,where each cell may either have no arrows,...Forman has developed a version of discrete Morse theory that can be understood in terms of arrow patterns on a(simplicial,polyhedral or cellular)complex without closed orbits,where each cell may either have no arrows,receive a single arrow from one of its facets,or conversely,send a single arrow into a cell of which it is a facet.By following arrows,one can then construct a natural Floer-type boundary operator.Here,we develop such a construction for arrow patterns where each cell may support several outgoing or incoming arrows(but not both),again in the absence of closed orbits.Our main technical achievement is the construction of a boundary operator that squares to 0 and therefore recovers the homology of the underlying complex.展开更多
We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained fo...We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained for fractional Sobolev spaces H^-1/2 （or H00^-l/2）. Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims,展开更多
An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG model...An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG modelis adopted at the median level. A BRep data structure capable of modelingnon-manifold is adopted. NURBS representation is used for all curved surfaces.Quadric surfaces have dual representations consisting of their geometric datasuch as radius, center point, and center tals. Boundary representation of freeform surfaces is easily built by sweeping and skinning method with NURBSgeometry Set operations on curved solids with boundary representation areperformed by an evaluation process consisting of four steps. A file exchangefacility is provided for the conversion between product data described by STEPand product information generated by GEMS4.0展开更多
基金partially supportedby Ministerio de Ciencia e Innovacion-SPAINFEDER,project MTM2010-15314supported by the Ministry of Science and Education of the Republic of Kazakhstan through the Project No.0713 GF
文摘This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.
文摘In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.
基金supported by Key Technology Research and Application of Online Control Simulation and Intelligent Decision Making for Active Distribution Network(5108-202218280A-2-377-XG).
文摘Aiming at the problems of increasing uncertainty of low-carbon generation energy in active distribution network(ADN)and the difficulty of security assessment of distribution network,this paper proposes a two-phase scheduling model for flexible resources in ADN based on probabilistic risk perception.First,a full-cycle probabilistic trend sequence is constructed based on the source-load historical data,and in the day-ahead scheduling phase,the response interval of the flexibility resources on the load and storage side is optimized based on the probabilistic trend,with the probability of the security boundary as the security constraint,and with the economy as the objective.Then in the intraday phase,the core security and economic operation boundary of theADNis screened in real time.Fromthere,it quantitatively senses the degree of threat to the core security and economic operation boundary under the current source-load prediction information,and identifies the strictly secure and low/high-risk time periods.Flexibility resources within the response interval are dynamically adjusted in real-time by focusing on high-risk periods to cope with future core risks of the distribution grid.Finally,the improved IEEE 33-node distribution system is simulated to obtain the flexibility resource scheduling scheme on the load and storage side.Thescheduling results are evaluated from the perspectives of risk probability and flexible resource utilization efficiency,and the analysis shows that the scheduling model in this paper can promote the consumption of low-carbon energy from wind and photovoltaic sourceswhile reducing the operational risk of the distribution network.
文摘Electrolysis tanks are used to smeltmetals based on electrochemical principles,and the short-circuiting of the pole plates in the tanks in the production process will lead to high temperatures,thus affecting normal production.Aiming at the problems of time-consuming and poor accuracy of existing infrared methods for high-temperature detection of dense pole plates in electrolysis tanks,an infrared dense pole plate anomalous target detection network YOLOv5-RMF based on You Only Look Once version 5(YOLOv5)is proposed.Firstly,we modified the Real-Time Enhanced Super-Resolution Generative Adversarial Network(Real-ESRGAN)by changing the U-shaped network(U-Net)to Attention U-Net,to preprocess the images;secondly,we propose a new Focus module that introduces the Marr operator,which can provide more boundary information for the network;again,because Complete Intersection over Union(CIOU)cannot accommodate target borders that are increasing and decreasing,replace CIOU with Extended Intersection over Union(EIOU),while the loss function is changed to Focal and Efficient IOU(Focal-EIOU)due to the different difficulty of sample detection.On the homemade dataset,the precision of our method is 94%,the recall is 70.8%,and the map@.5 is 83.6%,which is an improvement of 1.3%in precision,9.7%in recall,and 7%in map@.5 over the original network.The algorithm can meet the needs of electrolysis tank pole plate abnormal temperature detection,which can lay a technical foundation for improving production efficiency and reducing production waste.
基金funding provided by Max Planck Societysupported by a stipend from the InternationalMax Planck Research School(IMPRS)“Mathematics in the Sciences.”。
文摘Forman has developed a version of discrete Morse theory that can be understood in terms of arrow patterns on a(simplicial,polyhedral or cellular)complex without closed orbits,where each cell may either have no arrows,receive a single arrow from one of its facets,or conversely,send a single arrow into a cell of which it is a facet.By following arrows,one can then construct a natural Floer-type boundary operator.Here,we develop such a construction for arrow patterns where each cell may support several outgoing or incoming arrows(but not both),again in the absence of closed orbits.Our main technical achievement is the construction of a boundary operator that squares to 0 and therefore recovers the homology of the underlying complex.
文摘We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained for fractional Sobolev spaces H^-1/2 （or H00^-l/2）. Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims,
文摘An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG modelis adopted at the median level. A BRep data structure capable of modelingnon-manifold is adopted. NURBS representation is used for all curved surfaces.Quadric surfaces have dual representations consisting of their geometric datasuch as radius, center point, and center tals. Boundary representation of freeform surfaces is easily built by sweeping and skinning method with NURBSgeometry Set operations on curved solids with boundary representation areperformed by an evaluation process consisting of four steps. A file exchangefacility is provided for the conversion between product data described by STEPand product information generated by GEMS4.0
