At present, most commercial computer-aided manufacturing （CAM） systems are deficient in efficiency and performances on generating tool path during machining impellers. To solve the problem, this article develops a s...At present, most commercial computer-aided manufacturing （CAM） systems are deficient in efficiency and performances on generating tool path during machining impellers. To solve the problem, this article develops a special software to plan cutting path for ruled surface impellers. An approximation algorithm to generate cutting path for machining integral ruled surface impellers is proposed. By fitting sampling data points of an impeller blade into a curve, a model of ruled surface blade of an impeller is built up. Furthermore, by calculating the points where the cutter axis vector intersects the free-form hub surface of an impeller, problems about, for instance, the ambiguity in calculation and machining the wide blade surface with a short flute cutter are solved. Finally, an integral impeller cutting path is planned by way of an integrated cutter location control algorithm. Simulation and machining tests with an impeller are performed on a 5-axis computer numerically controlled （CNC） mill machine, which shows the feasibility of the proposed algorithm.展开更多
Predicting the cutting forces required for five-axis flank milling is a challenging task due to the difficulties involved in determining the Undeformed Chip Thickness(UCT) and CutterWorkpiece Engagement(CWE). To solve...Predicting the cutting forces required for five-axis flank milling is a challenging task due to the difficulties involved in determining the Undeformed Chip Thickness(UCT) and CutterWorkpiece Engagement(CWE). To solve these problems, this paper presents a new mechanistic cutting force model based on the geometrical analysis of a flank milling process. In the model,the part feature and corresponding cutting location data are taken as input information. The UCT considering cutter runout is calculated according to the instantaneous feed rate of the element cutting edges. A solid-discrete-based method is used to precisely and efficiently identify the CWE between the end mill and the surface being machined. Then, after calibrating the specific force coef-ficients, the mechanistic milling force can be obtained. During the validation process, two practical operations, three-axis flank milling of a vertical surface and five-axis flank milling of a nondevelopable ruled surface, are conducted. Comparisons between predicted and measured cutting forces demonstrate the reliability of the proposed cutting force model.展开更多
Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical on...Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical one that can be used to express the closeness between the tool surface and the surface to be machined. A novel tool path planning method is proposed for flank or plunge milling ruled surfaces based on the minimization of the one-sided Hausdorff distance （HD） from the mapping curve to the surface to be machined. It is a nonlinear optimization problem in best uniform approximation （BUA） or Chebyshev sense. A mathematical programming model for computing the minimum one-sided HD is proposed. The linearization method of the programming model is provided and the final optimal solutions are obtained by simplex method. The effectiveness of the proposed BUA method is verified by two numerical examples and compared with the least squares （LS） and double point offset （DPO） methods. The variation in tool orientation induced by the optimization of the tool positions is also evaluated.展开更多
Ruled surfaces found in engineering parts are often blended with a constraint surface,like the blade surface and hub surface of a centrifugal impeller.It is significant to accurately machine these ruled surfaces in fl...Ruled surfaces found in engineering parts are often blended with a constraint surface,like the blade surface and hub surface of a centrifugal impeller.It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path,while current models in fulfilling these goals are complex and rare.In this paper,a tool path planning method with optimal cutter locations(CLs)is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints.To be specific,a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter.Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm.Fairing angular curves are derived from candidates in this pool,and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness.On this basis,an adaptive interval determination model is developed for deviation control of interpolated cutter locations.This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique.Finally,tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time,and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.展开更多
Izumiya and Takeuchi （2003） obtained some characterizations for Ruled surfaces. Turgut and Haclsalihoglu （1998） defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi ...Izumiya and Takeuchi （2003） obtained some characterizations for Ruled surfaces. Turgut and Haclsalihoglu （1998） defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi （1995） and Jung and Pak （1996） studied Ruled surfaces. This study uses the method in （lzumiya and Takeuchi, 2003） to investigate cylindrical helices and Bertrand curves as curves on timelike Ruled surfaces in Minkowski 3-space R1^3. We have studied singularities of the rectifying developable （surface） of a timelike curve. We observed that the rectifying developable along a timelike curve a is non-singular if and only if a is a cylindrical helice. In this case the rectifying developable is a cylindrical surface.展开更多
In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directr...In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.展开更多
On the tasis of study in the mathematical model of 3-dimensional ruled surface (RS),this paper introduces a new concept of distance paramcter (DP) and also puts forward that themethod of modeling a RS depends on not o...On the tasis of study in the mathematical model of 3-dimensional ruled surface (RS),this paper introduces a new concept of distance paramcter (DP) and also puts forward that themethod of modeling a RS depends on not only two boundary curves but also DP. According toabove theory, the formulas to calculate corresponding point coordinates to any kind of top and bot-tom profile of a workpiece and formulas to calcuate the maximum inclination angle of ruling linehave been obtained. Then a different top and bottom RS mathining method including profile withline-are combination as well as parametric curves has been achieved by 4-axes simultancous con-trol programming proposed.展开更多
A new concept of design and manufacturing of ruled surface based on line geometry is proposed. Some practical algorithm for CAD system is derived. Some problems in design and manufacturing of ruled surface can be solv...A new concept of design and manufacturing of ruled surface based on line geometry is proposed. Some practical algorithm for CAD system is derived. Some problems in design and manufacturing of ruled surface can be solved by using the algorithm.展开更多
In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the ...In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.展开更多
This paper studies representation of rigid combination of a directed line and a reference point on it （here referred to as a ＂point-line＂） using dual quatemions. The geometric problem of rational ruled surface des...This paper studies representation of rigid combination of a directed line and a reference point on it （here referred to as a ＂point-line＂） using dual quatemions. The geometric problem of rational ruled surface design is viewed as the kinematic prob- lem of rational point-line motion design. By using the screw theory in kinematics, mappings from the spaces of lines and point-lines in Euclidean three-dimensional space into the hyperplanes in dual quaternion space are constructed, respectively. The problem of rational point-line motion design is then converted to that of projective Bezier or B-spline image curve design in hyperplane of dual quatemions. This kinematic method can unify the geometric design of ruled surfaces and tool path generation for five-axis numerical control （NC） machining.展开更多
This paper presents symbolic algorithms to determine whether a given surface(implicitly or parametrically defined)is a rational ruled surface and find a proper parametrization of the ruled surface.However,in practical...This paper presents symbolic algorithms to determine whether a given surface(implicitly or parametrically defined)is a rational ruled surface and find a proper parametrization of the ruled surface.However,in practical applications,one has to deal with numerical objects that are given approximately,probably because they proceed from an exact data that has been perturbed under some previous measuring process or manipulation.For these numerical objects,the authors adapt the symbolic algorithms presented by means of the use of numerical techniques.The authors develop numeric algorithms that allow to determine ruled surfaces"close"to an input(not necessarily ruled)surface,and the distance between the input and the output surface is computed.展开更多
Severe ground-level ozone(O_(3))pollution over major Chinese cities has become one of the most challenging problems,which have deleterious effects on human health and the sustainability of society.This study explored ...Severe ground-level ozone(O_(3))pollution over major Chinese cities has become one of the most challenging problems,which have deleterious effects on human health and the sustainability of society.This study explored the spatiotemporal distribution characteristics of ground-level O_(3) and its precursors based on conventional pollutant and meteorological monitoring data in Zhejiang Province from 2016 to 2021.Then,a high-performance convolutional neural network(CNN)model was established by expanding the moment and the concentration variations to general factors.Finally,the response mechanism of O_(3) to the variation with crucial influencing factors is explored by controlling variables and interpolating target variables.The results indicated that the annual average MDA8-90th concentrations in Zhejiang Province are higher in the northern and lower in the southern.When the wind direction(WD)ranges from east to southwest and the wind speed(WS)ranges between 2 and 3 m/sec,higher O_(3) concentration prone to occur.At different temperatures(T),the O_(3) concentration showed a trend of first increasing and subsequently decreasing with increasing NO_(2) concentration,peaks at the NO_(2) concentration around 0.02mg/m^(3).The sensitivity of NO_(2) to O_(3) formation is not easily affected by temperature,barometric pressure and dew point temperature.Additionally,there is a minimum IRNO_(2) at each temperature when the NO_(2) concentration is 0.03 mg/m^(3),and this minimum IRNO_(2) decreases with increasing temperature.The study explores the response mechanism of O_(3) with the change of driving variables,which can provide a scientific foundation and methodological support for the targeted management of O_(3) pollution.展开更多
The rational ruled surface is a typical modeling surface in computer aided geometric design.A rational ruled surface may have different representations with respective advantages and disadvantages.In this paper,the au...The rational ruled surface is a typical modeling surface in computer aided geometric design.A rational ruled surface may have different representations with respective advantages and disadvantages.In this paper,the authors revisit the representations of ruled surfaces including the parametric form,algebraic form,homogenous form and Plucker form.Moreover,the transformations between these representations are proposed such as parametrization for an algebraic form,implicitization for a parametric form,proper reparametrization of an improper one and standardized reparametrization for a general parametrization.Based on these transformation algorithms,one can give a complete interchange graph for the different representations of a rational ruled surface.For rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces,the characterization methods are recalled to identify the ruled surfaces from them.展开更多
We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a speci...We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.展开更多
The ruled surfaces of normals and binormals of a space curve is locally classified under the left-right action according to the types of the curve. In order to do this some useful results are obtained on the relations...The ruled surfaces of normals and binormals of a space curve is locally classified under the left-right action according to the types of the curve. In order to do this some useful results are obtained on the relationship of the powers of terms in the Taylor series of an invertible function and its inverse.展开更多
The reduced density matrices （RDMs） of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper...The reduced density matrices （RDMs） of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical origins of these ruled surfaces for bosonic systems. The emergence of ruled surfaces was recently proposed as signatures of symmetry- breaking phase. We show that, apart from being signatures of symmetry-brealdng, ruled surfaces can also be the consequence of gapless quantum systems by demonstrating an explicit example in terms of a two-mode Ising model. Our analysis was largely simplified by the quantum de Finetti＇s theorem--in the limit of large system size, these RDMs are the convex set of all the symmetric separable states. To distinguish ruled surfaces originated from gapless systems from those caused by symmetry- breaking, we propose to use the finite size scaling method for the corresponding geometry. This method is then applied to the two-mode XY model, successfully identifying a ruled surface as the consequence of gapless systems.展开更多
Understanding the ecogeographic mechanisms driving morphological variation is pivotal in biogeographic studies. However, patterns and determinants of such variation remain contentious, particularly in amphibians. Alth...Understanding the ecogeographic mechanisms driving morphological variation is pivotal in biogeographic studies. However, patterns and determinants of such variation remain contentious, particularly in amphibians. Although several hypotheses have been formulated and investigated in amphibians, their validity remains disputed with mixed support. Using the Sichuan spiny frog(Nanorana sichuanensis) as an indicator, we investigated the morphological variations across geographic and environmental gradients to explore the underlying ecogeographic mechanisms. We found that both the body size and limb characteristics of N.sichuanensis were not significantly related to latitude or elevation, suggesting that it did not follow Bergmann's or Allen's rules. Eye diameter decreased linearly with increasing elevation and latitude, whereas snout length increased with increasing elevation and latitude. Heat balance, endurance, seasonality, water availability, and primary productivity collectively explain body size variation. Hierarchical partitioning identified primary productivity and thermal excursion as the most influential factors, explaining significant variability in body size and other morphological features. Specifically, primary productivity accounted for 52.40% of the variation in body size, whereas thermal excursion had the greatest impact on eye diameter(36.23%) and snout length(72.17%). Based on body size and dimensionally reduced morphological features, our results identified ecogeographic patterns, assessed the validity of different hypotheses, and examined how environmental factors influence these morphological variations. More generally, our study offers comprehensive insights into the ecogeographic variation observed in mountain amphibians,provides a critical evaluation of existing ecogeographic hypotheses, and infers possible morphological adaptations in response to environmental change.展开更多
The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vecto...The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface.展开更多
The“notice-necessary measures”rule began with the“notice-and-takedown”rule,which originated from the United States safe harbors rule,established to limit the liability of Internet Service Providers(ISPs)for helpin...The“notice-necessary measures”rule began with the“notice-and-takedown”rule,which originated from the United States safe harbors rule,established to limit the liability of Internet Service Providers(ISPs)for helping infringement in network infringement.China’s Tort Liability Law and Civil Code amended the“notice-and-takedown”rule so that when the right holder sends an effective notice of infringement to the ISP,the ISP shall take necessary measures more than removal to be exempted from liability.This article will discuss the transformation of the rule and types of necessary measures,and reconstruct the relationship between effectiveness of notice and types of necessary measures.展开更多
Currently,generative AI technologies and services worldwide are experiencing explosive growth.While driving technological innovation and productivity advancement in the social economy,they also precipitate multiple le...Currently,generative AI technologies and services worldwide are experiencing explosive growth.While driving technological innovation and productivity advancement in the social economy,they also precipitate multiple le-gal risks,ethical breaches in technology,and social governance challenges.Distinct regulatory pathways have emerged internationally:the EU promotes a rigid governance system through a unified regulatory framework and centralized oversight mechanisms,though concurrently exhibiting a trend of deferred legal application;the United States adopts an advocacy-based regulatory strategy combining principled guidance with corporate self-compliance;the United King-dom implements a non-mandatory principled framework establishing a compromise-based governance model.Grounded in China's strategic imperative to engage in global AI competition and informed by international experi-ences,the legal governance framework for generative AI must incorporate practical legislative imperatives,anchored in the dynamic adaptation between technological iteration and legal regulation,alongside the recalibration of developmen-tal efficacy against security risks.This necessitates establishing tiered safety thresholds and controllability require-ments within the governance architecture.Accordingly,there is an urgent need to enhance institutional provision and policy coordination,construct a multi-stakeholder long-term mechanism integrating administrative supervision,indus-try self-regulation,and technical governance,and formulate scenario-specific liability rules covering the entire life cycle from R&D to deployment-thereby avoiding arbitrary legislative uniformity.The ultimate objective is to forge a comprehensive governance ecosystem characterized by trustworthiness and security as its foundation,and prudence,in-clusiveness,and dynamic adaptability as its defining features.展开更多
基金Key Development Program of Science and Technology of Heilongjiang Province, China (GB05A501)
文摘At present, most commercial computer-aided manufacturing （CAM） systems are deficient in efficiency and performances on generating tool path during machining impellers. To solve the problem, this article develops a special software to plan cutting path for ruled surface impellers. An approximation algorithm to generate cutting path for machining integral ruled surface impellers is proposed. By fitting sampling data points of an impeller blade into a curve, a model of ruled surface blade of an impeller is built up. Furthermore, by calculating the points where the cutter axis vector intersects the free-form hub surface of an impeller, problems about, for instance, the ambiguity in calculation and machining the wide blade surface with a short flute cutter are solved. Finally, an integral impeller cutting path is planned by way of an integrated cutter location control algorithm. Simulation and machining tests with an impeller are performed on a 5-axis computer numerically controlled （CNC） mill machine, which shows the feasibility of the proposed algorithm.
基金co-supported by the Major National S&T Program(No.2014ZX04014-031)the National Natural Science Foundation of China(No.51225503)
文摘Predicting the cutting forces required for five-axis flank milling is a challenging task due to the difficulties involved in determining the Undeformed Chip Thickness(UCT) and CutterWorkpiece Engagement(CWE). To solve these problems, this paper presents a new mechanistic cutting force model based on the geometrical analysis of a flank milling process. In the model,the part feature and corresponding cutting location data are taken as input information. The UCT considering cutter runout is calculated according to the instantaneous feed rate of the element cutting edges. A solid-discrete-based method is used to precisely and efficiently identify the CWE between the end mill and the surface being machined. Then, after calibrating the specific force coef-ficients, the mechanistic milling force can be obtained. During the validation process, two practical operations, three-axis flank milling of a vertical surface and five-axis flank milling of a nondevelopable ruled surface, are conducted. Comparisons between predicted and measured cutting forces demonstrate the reliability of the proposed cutting force model.
基金supported by the National Natural Science Foundation of China (51175065)
文摘Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical one that can be used to express the closeness between the tool surface and the surface to be machined. A novel tool path planning method is proposed for flank or plunge milling ruled surfaces based on the minimization of the one-sided Hausdorff distance （HD） from the mapping curve to the surface to be machined. It is a nonlinear optimization problem in best uniform approximation （BUA） or Chebyshev sense. A mathematical programming model for computing the minimum one-sided HD is proposed. The linearization method of the programming model is provided and the final optimal solutions are obtained by simplex method. The effectiveness of the proposed BUA method is verified by two numerical examples and compared with the least squares （LS） and double point offset （DPO） methods. The variation in tool orientation induced by the optimization of the tool positions is also evaluated.
基金supported by the National Natural Science Foundation of China(Nos.U22A20202 and 52205516)the China Postdoctoral Science Foundation(No.2022 M720641)。
文摘Ruled surfaces found in engineering parts are often blended with a constraint surface,like the blade surface and hub surface of a centrifugal impeller.It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path,while current models in fulfilling these goals are complex and rare.In this paper,a tool path planning method with optimal cutter locations(CLs)is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints.To be specific,a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter.Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm.Fairing angular curves are derived from candidates in this pool,and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness.On this basis,an adaptive interval determination model is developed for deviation control of interpolated cutter locations.This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique.Finally,tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time,and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.
文摘Izumiya and Takeuchi （2003） obtained some characterizations for Ruled surfaces. Turgut and Haclsalihoglu （1998） defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi （1995） and Jung and Pak （1996） studied Ruled surfaces. This study uses the method in （lzumiya and Takeuchi, 2003） to investigate cylindrical helices and Bertrand curves as curves on timelike Ruled surfaces in Minkowski 3-space R1^3. We have studied singularities of the rectifying developable （surface） of a timelike curve. We observed that the rectifying developable along a timelike curve a is non-singular if and only if a is a cylindrical helice. In this case the rectifying developable is a cylindrical surface.
文摘In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.
文摘On the tasis of study in the mathematical model of 3-dimensional ruled surface (RS),this paper introduces a new concept of distance paramcter (DP) and also puts forward that themethod of modeling a RS depends on not only two boundary curves but also DP. According toabove theory, the formulas to calculate corresponding point coordinates to any kind of top and bot-tom profile of a workpiece and formulas to calcuate the maximum inclination angle of ruling linehave been obtained. Then a different top and bottom RS mathining method including profile withline-are combination as well as parametric curves has been achieved by 4-axes simultancous con-trol programming proposed.
文摘A new concept of design and manufacturing of ruled surface based on line geometry is proposed. Some practical algorithm for CAD system is derived. Some problems in design and manufacturing of ruled surface can be solved by using the algorithm.
基金This paper is partially supported by the National Fundamental Research 973 Program of China under Grant No.2004CB318000.
文摘In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.
基金supported by the National Natural Science Foundation of China(Grant Nos.50835004 and 51005087)the National Basic Research Program of China(Grant No.2011CB706804)
文摘This paper studies representation of rigid combination of a directed line and a reference point on it （here referred to as a ＂point-line＂） using dual quatemions. The geometric problem of rational ruled surface design is viewed as the kinematic prob- lem of rational point-line motion design. By using the screw theory in kinematics, mappings from the spaces of lines and point-lines in Euclidean three-dimensional space into the hyperplanes in dual quaternion space are constructed, respectively. The problem of rational point-line motion design is then converted to that of projective Bezier or B-spline image curve design in hyperplane of dual quatemions. This kinematic method can unify the geometric design of ruled surfaces and tool path generation for five-axis numerical control （NC） machining.
基金partially supported by FEDER/Ministerio de Ciencia,Innovación y Universidades-Agencia Estatal de Investigacin/MTM2017-88796-P(Symbolic Computation New challenges in Algebra and Geometry together with its applications)the National Natural Science Foundation of China under Grant No.61872332the University of Chinese Academy of Sciences the Research Group ASYNACS(Ref.CCEE2011/R34)。
文摘This paper presents symbolic algorithms to determine whether a given surface(implicitly or parametrically defined)is a rational ruled surface and find a proper parametrization of the ruled surface.However,in practical applications,one has to deal with numerical objects that are given approximately,probably because they proceed from an exact data that has been perturbed under some previous measuring process or manipulation.For these numerical objects,the authors adapt the symbolic algorithms presented by means of the use of numerical techniques.The authors develop numeric algorithms that allow to determine ruled surfaces"close"to an input(not necessarily ruled)surface,and the distance between the input and the output surface is computed.
基金supported by the National Key Research and Development Program of China (Nos.2022YFC3702000 and 2022YFC3703500)the Key R&D Project of Zhejiang Province (No.2022C03146).
文摘Severe ground-level ozone(O_(3))pollution over major Chinese cities has become one of the most challenging problems,which have deleterious effects on human health and the sustainability of society.This study explored the spatiotemporal distribution characteristics of ground-level O_(3) and its precursors based on conventional pollutant and meteorological monitoring data in Zhejiang Province from 2016 to 2021.Then,a high-performance convolutional neural network(CNN)model was established by expanding the moment and the concentration variations to general factors.Finally,the response mechanism of O_(3) to the variation with crucial influencing factors is explored by controlling variables and interpolating target variables.The results indicated that the annual average MDA8-90th concentrations in Zhejiang Province are higher in the northern and lower in the southern.When the wind direction(WD)ranges from east to southwest and the wind speed(WS)ranges between 2 and 3 m/sec,higher O_(3) concentration prone to occur.At different temperatures(T),the O_(3) concentration showed a trend of first increasing and subsequently decreasing with increasing NO_(2) concentration,peaks at the NO_(2) concentration around 0.02mg/m^(3).The sensitivity of NO_(2) to O_(3) formation is not easily affected by temperature,barometric pressure and dew point temperature.Additionally,there is a minimum IRNO_(2) at each temperature when the NO_(2) concentration is 0.03 mg/m^(3),and this minimum IRNO_(2) decreases with increasing temperature.The study explores the response mechanism of O_(3) with the change of driving variables,which can provide a scientific foundation and methodological support for the targeted management of O_(3) pollution.
基金supported by Beijing Natural Science Foundation under Grant No.Z190004the National Natural Science Foundation of China under Grant No.61872332+2 种基金the University of Chinese Academy of Sciences and by FEDER/Ministerio de CienciaInnovación y Universidades Agencia Estatal de Investigación/MTM2017-88796-P(Symbolic Computation:New challenges in Algebra and Geometry together with its applications)the Research Group ASYNACS(Ref.CCEE2011/R34)。
文摘The rational ruled surface is a typical modeling surface in computer aided geometric design.A rational ruled surface may have different representations with respective advantages and disadvantages.In this paper,the authors revisit the representations of ruled surfaces including the parametric form,algebraic form,homogenous form and Plucker form.Moreover,the transformations between these representations are proposed such as parametrization for an algebraic form,implicitization for a parametric form,proper reparametrization of an improper one and standardized reparametrization for a general parametrization.Based on these transformation algorithms,one can give a complete interchange graph for the different representations of a rational ruled surface.For rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces,the characterization methods are recalled to identify the ruled surfaces from them.
文摘We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10261002 and 10671009)
文摘The ruled surfaces of normals and binormals of a space curve is locally classified under the left-right action according to the types of the curve. In order to do this some useful results are obtained on the relationship of the powers of terms in the Taylor series of an invertible function and its inverse.
基金supported by the Natural Sciences and Engineering Research Council of Canada, Canadian Institute for Advanced Research, the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, and the Perimeter Institute for Theoretical PhysicsResearch at Perimeter Institute was supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation+1 种基金Zheng-Xin Liu was supported by the Research Funds of Remin University of China (Grant No. 15XNFL19)the National Natural Science Foundation of China (Grant No. 11574392)
文摘The reduced density matrices （RDMs） of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical origins of these ruled surfaces for bosonic systems. The emergence of ruled surfaces was recently proposed as signatures of symmetry- breaking phase. We show that, apart from being signatures of symmetry-brealdng, ruled surfaces can also be the consequence of gapless quantum systems by demonstrating an explicit example in terms of a two-mode Ising model. Our analysis was largely simplified by the quantum de Finetti＇s theorem--in the limit of large system size, these RDMs are the convex set of all the symmetric separable states. To distinguish ruled surfaces originated from gapless systems from those caused by symmetry- breaking, we propose to use the finite size scaling method for the corresponding geometry. This method is then applied to the two-mode XY model, successfully identifying a ruled surface as the consequence of gapless systems.
基金supported by the National Natural Science Foundation of China (32071544, 32271737)the Interdisciplinary Innovation Team of the Chinese Academy of Sciences (CAS) “Light of West China” Program (xbzg-zdsys-202207)。
文摘Understanding the ecogeographic mechanisms driving morphological variation is pivotal in biogeographic studies. However, patterns and determinants of such variation remain contentious, particularly in amphibians. Although several hypotheses have been formulated and investigated in amphibians, their validity remains disputed with mixed support. Using the Sichuan spiny frog(Nanorana sichuanensis) as an indicator, we investigated the morphological variations across geographic and environmental gradients to explore the underlying ecogeographic mechanisms. We found that both the body size and limb characteristics of N.sichuanensis were not significantly related to latitude or elevation, suggesting that it did not follow Bergmann's or Allen's rules. Eye diameter decreased linearly with increasing elevation and latitude, whereas snout length increased with increasing elevation and latitude. Heat balance, endurance, seasonality, water availability, and primary productivity collectively explain body size variation. Hierarchical partitioning identified primary productivity and thermal excursion as the most influential factors, explaining significant variability in body size and other morphological features. Specifically, primary productivity accounted for 52.40% of the variation in body size, whereas thermal excursion had the greatest impact on eye diameter(36.23%) and snout length(72.17%). Based on body size and dimensionally reduced morphological features, our results identified ecogeographic patterns, assessed the validity of different hypotheses, and examined how environmental factors influence these morphological variations. More generally, our study offers comprehensive insights into the ecogeographic variation observed in mountain amphibians,provides a critical evaluation of existing ecogeographic hypotheses, and infers possible morphological adaptations in response to environmental change.
基金Supported by Grant for the Institute of Mathematicsthe University of Tsukuba and TGRC-KOSEF(1993)
文摘The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface.
文摘The“notice-necessary measures”rule began with the“notice-and-takedown”rule,which originated from the United States safe harbors rule,established to limit the liability of Internet Service Providers(ISPs)for helping infringement in network infringement.China’s Tort Liability Law and Civil Code amended the“notice-and-takedown”rule so that when the right holder sends an effective notice of infringement to the ISP,the ISP shall take necessary measures more than removal to be exempted from liability.This article will discuss the transformation of the rule and types of necessary measures,and reconstruct the relationship between effectiveness of notice and types of necessary measures.
基金This Research Was Funded by the Key Project of Humanities and Social Science Study from the Ministry of Education"Research on the Consideration and Promotion of Human Rights Benchmarks in Global Data Competition"(19JJD820009)。
文摘Currently,generative AI technologies and services worldwide are experiencing explosive growth.While driving technological innovation and productivity advancement in the social economy,they also precipitate multiple le-gal risks,ethical breaches in technology,and social governance challenges.Distinct regulatory pathways have emerged internationally:the EU promotes a rigid governance system through a unified regulatory framework and centralized oversight mechanisms,though concurrently exhibiting a trend of deferred legal application;the United States adopts an advocacy-based regulatory strategy combining principled guidance with corporate self-compliance;the United King-dom implements a non-mandatory principled framework establishing a compromise-based governance model.Grounded in China's strategic imperative to engage in global AI competition and informed by international experi-ences,the legal governance framework for generative AI must incorporate practical legislative imperatives,anchored in the dynamic adaptation between technological iteration and legal regulation,alongside the recalibration of developmen-tal efficacy against security risks.This necessitates establishing tiered safety thresholds and controllability require-ments within the governance architecture.Accordingly,there is an urgent need to enhance institutional provision and policy coordination,construct a multi-stakeholder long-term mechanism integrating administrative supervision,indus-try self-regulation,and technical governance,and formulate scenario-specific liability rules covering the entire life cycle from R&D to deployment-thereby avoiding arbitrary legislative uniformity.The ultimate objective is to forge a comprehensive governance ecosystem characterized by trustworthiness and security as its foundation,and prudence,in-clusiveness,and dynamic adaptability as its defining features.
