An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vert...An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.展开更多
The Songliao Basin in northeast China is one of the largest petroliferous basins worldwide,and features the T_(2)fault system,which consists of numerous minor extensional normal faults.This study combines high-resolut...The Songliao Basin in northeast China is one of the largest petroliferous basins worldwide,and features the T_(2)fault system,which consists of numerous minor extensional normal faults.This study combines high-resolution 3D seismic datasets to detail the characteristics of the T_(2)fault system,contributing two key findings:(1)The T_(2)faults are confirmed as polygonal fault systems,characterized by closely spaced,layer-bounded faults with small throws,high dip angles,and random orientations,forming intricate polygonal networks.(2)The study reveals the influence of tectonic stresses on the fault system,showing spatial variations across different tectonic units.In depressions,T_(2)faults exhibit short lengths,small throws,high density,and multiple directions.In contrast,in inverted anticline belts,they have longer lengths,bigger throws,higher density,and concordant orientations.These variations demonstrate the impact of tectonic inversion on the development of T_(2)faults.The significance of this research lies in presenting a typical polygonal fault system developed in a deep lake succession and was superposed the influence by regional tectonic stress coeval with its development.The new insights facilitate a reevaluation of the T_(2)fault system's role in hydrocarbon migration and accumulation within the Songliao Basin.展开更多
The electric vertical takeoff and landing(e VTOL)aircraft shows great potential for rapid military personnel deployment on the battlefield.However,its susceptibility to control loss,complex crashes,and extremely limit...The electric vertical takeoff and landing(e VTOL)aircraft shows great potential for rapid military personnel deployment on the battlefield.However,its susceptibility to control loss,complex crashes,and extremely limited bottom energy-absorbing space demands higher comprehensive crashworthiness of its subfloor thin-walled structures.This study investigated the energy absorption capacity of novel concave polygonal carbon fiber reinforced plastics(CFRP)tubes under multi-angle collisions.Quasistatic compression experiments and finite element simulations were conducted to assess the failure mode and energy absorption.The influences of cross-section shapes,loading conditions,and geometry parameters on crashworthiness metrics were further analyzed.The results revealed that,under the similar weight,concave polygonal tubes exhibited superior energy absorption under axial loads compared to regular polygonal and circular tubes,attributed to the increased number of axial splits.However,both regular and concave polygonal tubes,particularly the latter,demonstrated reduced oblique energy absorption compared to traditional square tubes with the increasing ratio of SEA value decreased from 20%-16%.Notably,this reduction in energy absorption can be compensated for by the implementation of inward and outward crusher plugs,and with them,the concave polygonal tubes demonstrated outstanding overall crashworthiness performance under multiple loading conditions.This concave cross-sectional design methods could serve as a guidance for the development of the eVTOL subfloor.展开更多
The phase volume fraction has an important role in the match of the strength and plasticity of dual phase steel.The different bainite contents(18–53 vol.%)in polygonal ferrite and bainite(PF+B)dual phase steel were o...The phase volume fraction has an important role in the match of the strength and plasticity of dual phase steel.The different bainite contents(18–53 vol.%)in polygonal ferrite and bainite(PF+B)dual phase steel were obtained by controlling the relaxation finish temperature during the rolling process.The effect of bainite volume fraction on the tensile deformability was systematically investigated via experiments and crystal plasticity finite element model(CPFEM)simulation.The experimental results showed that the steel showed optimal strain hardenability and strength–plasticity matching when the bainite reached 35%.The 3D-CPFEM models with the same grain size and texture characters were established to clarify the influence of stress/strain distribution on PF+B dual phase steel with different bainite contents.The simulation results indicated that an appropriate increase in the bainite content(18%–35%)did not affect the interphase strain difference,but increased the stress distribution in both phases,as a result of enhancing the coordinated deformability of two phases and improving the strength–plasticity matching.When the bainite content increased to 53%,the stress/strain difference between the two phases was greatly increased,and plastic damage between the two phases was caused by the reduction of the coordinated deformability.展开更多
Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take ...Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.展开更多
Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in ...Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.展开更多
Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological character...Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under perspective transformation. Then, the new concept of homograph is defined in terms of five topological characteristics and geometrical characteristics. Based on this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively and the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize the objects with different shapes but also distinguish between objects with same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.展开更多
Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are propose...Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.展开更多
Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the min...Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algo- rithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.展开更多
Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing pr...Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.展开更多
The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of...The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.展开更多
Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail med...Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail medium-or high-frequency frictional interactions are perceived as an essential reason of the high-order polygonal wear of railway wheels,which are potentially resulted by the flexible deformations of the train/track system or other external excitations.In this work,the effect of wheel/rail flexibility on polygonal wear evolution of heavy-haul locomotive wheels is explored with aid of the long-term wheel polygonal wear evolution simulations,in which different flexible modeling of the heavy-haul wheel/rail coupled system is implemented.Further,the mitigation measures for the polygonal wear of heavy-haul locomotive wheels are discussed.The results point out that the evolution of polygonal wear of heavy-haul locomotive wheels can be veritably simulated with consideration of the flexible effect of both wheelset and rails.Execution of mixed-line operation of heavy-haul trains and application of multicut wheel re-profiling can effectively reduce the development of wheel polygonal wear.This research can provide a deep-going understanding of polygonal wear evolution mechanism of heavy-haul locomotive wheels and its mitigation measures.展开更多
The task of identifying the quintic PH curve G^(0)“closest”to a given planar Bézier curve with or without prescribed arc length is discussed here using Gauss-Legendre polygon and Gauss-Lobatto polygon respectiv...The task of identifying the quintic PH curve G^(0)“closest”to a given planar Bézier curve with or without prescribed arc length is discussed here using Gauss-Legendre polygon and Gauss-Lobatto polygon respectively.By expressing the sum of squared differences between the vertices of Gauss-Legendre or Gauss-Lobatto polygon of a given Bézier and those of a PH curve,it is shown that this problem can be formulated as a constrained polynomial optimization problem in certain real variables,subject to two or three quadratic constraints,which can be efficiently solved by Lagrange multiplier method and Newton-Raphson iteration.Several computed examples are used to illustrate implementations of the optimization methodology.The results demonstrate that compared with Bézier control polygon,the method with Gauss-Legendre and Gauss-Lobatto polygon can produce the G^(0)PH curve closer to the given Bézier curve with close arc length.Moreover,good approximations with prescribed arc length can also be achieved.展开更多
The study on the entanglement polygon inequality of multipartite systems has attracted much attention.However,most of the results are on pure states.Here we consider the property for a class of mixed states,which are ...The study on the entanglement polygon inequality of multipartite systems has attracted much attention.However,most of the results are on pure states.Here we consider the property for a class of mixed states,which are the reduced density matrices of generalizedW-class states in multipartite higher dimensional systems.First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement,then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement.At last,we get an inequality for the mixed states,which can be regarded as a relation for bipartite entanglement.展开更多
The dynamic load distribution within in-service axlebox bearings of high-speed trains is crucial for the fatigue reliability assessment and forward design of axlebox bearings. This paper presents an in situ measuremen...The dynamic load distribution within in-service axlebox bearings of high-speed trains is crucial for the fatigue reliability assessment and forward design of axlebox bearings. This paper presents an in situ measurement of the dynamic load distribution in the four rows of two axlebox bearings on a bogie wheelset of a high-speed train under polygonal wheel–rail excitation. The measurement employed an improved strain-based method to measure the dynamic radial load distribution of roller bearings. The four rows of two axlebox bearings on a wheelset exhibited different ranges of loaded zones and different means of distributed loads. Besides, the mean value and standard deviation of measured roller–raceway contact loads showed non-monotonic variations with the frequency of wheel–rail excitation. The fatigue life of the four bearing rows under polygonal wheel–rail excitation was quantitatively predicted by compiling the measured roller–raceway contact load spectra of the most loaded position and considering the load spectra as input.展开更多
An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible numbe...An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.展开更多
Purpose–This study aims to investigate the cause of high-order wheel polygonization in a plateau high-speed electric multiple unit(EMU)train.Design/methodology/approach–A series of field tests were conducted to meas...Purpose–This study aims to investigate the cause of high-order wheel polygonization in a plateau high-speed electric multiple unit(EMU)train.Design/methodology/approach–A series of field tests were conducted to measure the vibration accelerations of the axle box and bogie when the wheels of the EMU train passed through tracks with normal rail roughness after re-profiling.Additionally,the dynamic characteristics of the track,wheelset and bogie were also measured.These measurements provided insights into the mechanisms that lead to wheel polygonization.Findings–The results of the field tests indicate that wheel polygonal wear in theEMUtrain primarily exhibits 14–16 and 25–27 harmonic orders.The passing frequencies of wheel polygonization were approximately 283–323 Hz and 505–545 Hz,which closely match the dominated frequencies of axle box and bogie vibrations.These findings suggest that the fixed-frequency vibrations originate from the natural modes of the wheelset and bogie,which can be excited by wheel/rail irregularities.Originality/value–The study provides novel insights into the mechanisms of high-order wheel polygonization in plateau high-speed EMU trains.Futher,the results indicate that operating the EMU train on mixed lines at variable speeds could potentially mitigate high-order polygonal wear,providing practical value for improving the safety,performance and maintenance efficiency of high-speed EMU trains.展开更多
This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas o...This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to 1/2.The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints.A new method is presented to verify the upper and lower bounds for the optimization problem.The upper bound is obtained by the affine regular decagon.Then Bilinear Matrix Inequalities(BMI)theory and the branch-and-bound technique are used to verify the lower bound of the problem.The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548.The relative error compared to the global optimum is 0.104%.展开更多
文摘An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.
基金supported by the Open Funds for Hubei Key Laboratory of Marine Geological Resources,China University of Geosciences(No.MGR202303)the National Natural Science Foundation of China(No.41672110)。
文摘The Songliao Basin in northeast China is one of the largest petroliferous basins worldwide,and features the T_(2)fault system,which consists of numerous minor extensional normal faults.This study combines high-resolution 3D seismic datasets to detail the characteristics of the T_(2)fault system,contributing two key findings:(1)The T_(2)faults are confirmed as polygonal fault systems,characterized by closely spaced,layer-bounded faults with small throws,high dip angles,and random orientations,forming intricate polygonal networks.(2)The study reveals the influence of tectonic stresses on the fault system,showing spatial variations across different tectonic units.In depressions,T_(2)faults exhibit short lengths,small throws,high density,and multiple directions.In contrast,in inverted anticline belts,they have longer lengths,bigger throws,higher density,and concordant orientations.These variations demonstrate the impact of tectonic inversion on the development of T_(2)faults.The significance of this research lies in presenting a typical polygonal fault system developed in a deep lake succession and was superposed the influence by regional tectonic stress coeval with its development.The new insights facilitate a reevaluation of the T_(2)fault system's role in hydrocarbon migration and accumulation within the Songliao Basin.
基金financially supported by the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(Grant No.24qnpy041)the Science and Technology Innovation Key R&D Program of Chongqing(Grant No.CSTB2023TIAD-STX0030)。
文摘The electric vertical takeoff and landing(e VTOL)aircraft shows great potential for rapid military personnel deployment on the battlefield.However,its susceptibility to control loss,complex crashes,and extremely limited bottom energy-absorbing space demands higher comprehensive crashworthiness of its subfloor thin-walled structures.This study investigated the energy absorption capacity of novel concave polygonal carbon fiber reinforced plastics(CFRP)tubes under multi-angle collisions.Quasistatic compression experiments and finite element simulations were conducted to assess the failure mode and energy absorption.The influences of cross-section shapes,loading conditions,and geometry parameters on crashworthiness metrics were further analyzed.The results revealed that,under the similar weight,concave polygonal tubes exhibited superior energy absorption under axial loads compared to regular polygonal and circular tubes,attributed to the increased number of axial splits.However,both regular and concave polygonal tubes,particularly the latter,demonstrated reduced oblique energy absorption compared to traditional square tubes with the increasing ratio of SEA value decreased from 20%-16%.Notably,this reduction in energy absorption can be compensated for by the implementation of inward and outward crusher plugs,and with them,the concave polygonal tubes demonstrated outstanding overall crashworthiness performance under multiple loading conditions.This concave cross-sectional design methods could serve as a guidance for the development of the eVTOL subfloor.
基金supported by the Project of Liaoning Marine Economic Development(Development of high strength pipeline steel for submarine oil and gas transmission)State Key Laboratory of Metal Material for Marine Equipment and Application Funding(No.SKLMEA-K202205).
文摘The phase volume fraction has an important role in the match of the strength and plasticity of dual phase steel.The different bainite contents(18–53 vol.%)in polygonal ferrite and bainite(PF+B)dual phase steel were obtained by controlling the relaxation finish temperature during the rolling process.The effect of bainite volume fraction on the tensile deformability was systematically investigated via experiments and crystal plasticity finite element model(CPFEM)simulation.The experimental results showed that the steel showed optimal strain hardenability and strength–plasticity matching when the bainite reached 35%.The 3D-CPFEM models with the same grain size and texture characters were established to clarify the influence of stress/strain distribution on PF+B dual phase steel with different bainite contents.The simulation results indicated that an appropriate increase in the bainite content(18%–35%)did not affect the interphase strain difference,but increased the stress distribution in both phases,as a result of enhancing the coordinated deformability of two phases and improving the strength–plasticity matching.When the bainite content increased to 53%,the stress/strain difference between the two phases was greatly increased,and plastic damage between the two phases was caused by the reduction of the coordinated deformability.
基金supported by the National Natural Science Foundation of China (41431177 and 41422109)the Innovation Project of State Key Laboratory of Resources and Environmental Information System of China (O88RA20CYA)the Outstanding Innovation Team in Colleges and Universities in Jiangsu Province, China
文摘Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.
基金Foundation item： Supported by Natural Science Foundation of China（60675022）
文摘Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.
基金Supported by National Science Foundation(60675022)Key Laboratory of Nondestructive Test, Nanchang Institute of Aeronautical Technoloyg(ZD200629007)
文摘Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under perspective transformation. Then, the new concept of homograph is defined in terms of five topological characteristics and geometrical characteristics. Based on this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively and the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize the objects with different shapes but also distinguish between objects with same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.
文摘Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.
基金Project supported by the National Nature Science Foundation of China (Nos. 60473103 and 60473127) and the Natural Science Foundation of Shandong Province (No. Y2005G03), China
文摘Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algo- rithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.
文摘Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.
文摘The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.
基金Supported by National Natural Science Foundation of China(Grant Nos.U2268210,52302474,52072249).
文摘Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail medium-or high-frequency frictional interactions are perceived as an essential reason of the high-order polygonal wear of railway wheels,which are potentially resulted by the flexible deformations of the train/track system or other external excitations.In this work,the effect of wheel/rail flexibility on polygonal wear evolution of heavy-haul locomotive wheels is explored with aid of the long-term wheel polygonal wear evolution simulations,in which different flexible modeling of the heavy-haul wheel/rail coupled system is implemented.Further,the mitigation measures for the polygonal wear of heavy-haul locomotive wheels are discussed.The results point out that the evolution of polygonal wear of heavy-haul locomotive wheels can be veritably simulated with consideration of the flexible effect of both wheelset and rails.Execution of mixed-line operation of heavy-haul trains and application of multicut wheel re-profiling can effectively reduce the development of wheel polygonal wear.This research can provide a deep-going understanding of polygonal wear evolution mechanism of heavy-haul locomotive wheels and its mitigation measures.
基金Supported by the National Natural Science Foundation of China(Grant No.11801225)。
文摘The task of identifying the quintic PH curve G^(0)“closest”to a given planar Bézier curve with or without prescribed arc length is discussed here using Gauss-Legendre polygon and Gauss-Lobatto polygon respectively.By expressing the sum of squared differences between the vertices of Gauss-Legendre or Gauss-Lobatto polygon of a given Bézier and those of a PH curve,it is shown that this problem can be formulated as a constrained polynomial optimization problem in certain real variables,subject to two or three quadratic constraints,which can be efficiently solved by Lagrange multiplier method and Newton-Raphson iteration.Several computed examples are used to illustrate implementations of the optimization methodology.The results demonstrate that compared with Bézier control polygon,the method with Gauss-Legendre and Gauss-Lobatto polygon can produce the G^(0)PH curve closer to the given Bézier curve with close arc length.Moreover,good approximations with prescribed arc length can also be achieved.
基金Project supported by the National Natural Science Foundation of China(Grant No.12301580).
文摘The study on the entanglement polygon inequality of multipartite systems has attracted much attention.However,most of the results are on pure states.Here we consider the property for a class of mixed states,which are the reduced density matrices of generalizedW-class states in multipartite higher dimensional systems.First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement,then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement.At last,we get an inequality for the mixed states,which can be regarded as a relation for bipartite entanglement.
基金supported by the National Natural Science Foundation of China (Grant No. 12302238)the National Key Research and Development Program of China (Grant Nos. 2021YFB3400701, 2022YFB3402904)。
文摘The dynamic load distribution within in-service axlebox bearings of high-speed trains is crucial for the fatigue reliability assessment and forward design of axlebox bearings. This paper presents an in situ measurement of the dynamic load distribution in the four rows of two axlebox bearings on a bogie wheelset of a high-speed train under polygonal wheel–rail excitation. The measurement employed an improved strain-based method to measure the dynamic radial load distribution of roller bearings. The four rows of two axlebox bearings on a wheelset exhibited different ranges of loaded zones and different means of distributed loads. Besides, the mean value and standard deviation of measured roller–raceway contact loads showed non-monotonic variations with the frequency of wheel–rail excitation. The fatigue life of the four bearing rows under polygonal wheel–rail excitation was quantitatively predicted by compiling the measured roller–raceway contact load spectra of the most loaded position and considering the load spectra as input.
基金Supported by National Natural Science Foundation of China(Grant No.12271139)。
文摘An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.
基金the Sichuan Science and Technology Program of China(No.2024NSFSC0160).
文摘Purpose–This study aims to investigate the cause of high-order wheel polygonization in a plateau high-speed electric multiple unit(EMU)train.Design/methodology/approach–A series of field tests were conducted to measure the vibration accelerations of the axle box and bogie when the wheels of the EMU train passed through tracks with normal rail roughness after re-profiling.Additionally,the dynamic characteristics of the track,wheelset and bogie were also measured.These measurements provided insights into the mechanisms that lead to wheel polygonization.Findings–The results of the field tests indicate that wheel polygonal wear in theEMUtrain primarily exhibits 14–16 and 25–27 harmonic orders.The passing frequencies of wheel polygonization were approximately 283–323 Hz and 505–545 Hz,which closely match the dominated frequencies of axle box and bogie vibrations.These findings suggest that the fixed-frequency vibrations originate from the natural modes of the wheelset and bogie,which can be excited by wheel/rail irregularities.Originality/value–The study provides novel insights into the mechanisms of high-order wheel polygonization in plateau high-speed EMU trains.Futher,the results indicate that operating the EMU train on mixed lines at variable speeds could potentially mitigate high-order polygonal wear,providing practical value for improving the safety,performance and maintenance efficiency of high-speed EMU trains.
基金supported by the National Natural Science Foundation of China under Grant No.12171159the National Natural Science Fund of China Research Fund for International Scientists under Grant No.12350410363。
文摘This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to 1/2.The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints.A new method is presented to verify the upper and lower bounds for the optimization problem.The upper bound is obtained by the affine regular decagon.Then Bilinear Matrix Inequalities(BMI)theory and the branch-and-bound technique are used to verify the lower bound of the problem.The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548.The relative error compared to the global optimum is 0.104%.
