Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of ...Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.展开更多
In this study, the kinetic energy formula of the projection curve under 1-parameter closed homothetic motion is expressed and as a result, theorem is given. Also some special cases are given related with that formula.
In this paper, we study the intersection multiplicity of algebraic curves at a point both in R^2 and in real projective plane P^2. We introduce the fold point of curves and provide conditions for the relations between...In this paper, we study the intersection multiplicity of algebraic curves at a point both in R^2 and in real projective plane P^2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.展开更多
Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper...Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.展开更多
In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of...In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.展开更多
in the design of civil and water conservancy projects, the identical slope suffice isfrequently used. Its mathematical model may be formulated as an envelope of a cone when itS vertexmoves along the cylindrical helix....in the design of civil and water conservancy projects, the identical slope suffice isfrequently used. Its mathematical model may be formulated as an envelope of a cone when itS vertexmoves along the cylindrical helix. According to the principle of conStrUcting the envelope curves of afamily of circles, the parametric equstion for the identical slope surface is established. The parametricform makes it most convenient to draw the contour lines and grade lines, and is well suited toproduce indexed projection of identical slope surface in civil and water conservancy projects.展开更多
This paper proposes the concept of projection curves based on the theory of CT image reconstruction to probe the internal structure of the working panel prior to formal mining of the working panel.As well as reducing ...This paper proposes the concept of projection curves based on the theory of CT image reconstruction to probe the internal structure of the working panel prior to formal mining of the working panel.As well as reducing costs,this method provides safe and efficient excavation of the working panel.According to the results of the numerical model and the actual working panel,the new method has been proven to be accurate in detecting the location of the fault that extends into the face.Concealed faults of the internal working panel,as well as the start and end points of the fault,can be detected by this method.Engineering practice has proven that the method is highly reliable,has a highly decisive impact on faults for coal mining,and can be used to guide the safe mining of the working panel.展开更多
Climate change is the most important factor to increase in short-duration high-intensity rainfall and consequent flooding.Intensity-Duration-Frequency(IDF)curves are commonly used tools in Stormwater design,so a metho...Climate change is the most important factor to increase in short-duration high-intensity rainfall and consequent flooding.Intensity-Duration-Frequency(IDF)curves are commonly used tools in Stormwater design,so a method to derive future IDF curves including climate change effect could be necessary for the mainstreaming climate change information into storm water planning.The objective of the present study is to define a mechanism to reflect the effect of climate change into the projected rainfall IDF relationships.For this,the continuously observed hourly rainfall data from 1969 to 2018 were divided into five subgroups.Then the IDF curve of each subgroup is defined.The rainfall intensity for the next 30 years was then estimated using a linear regression model.The obtained result indicates that for the same duration and for the same return period,the rainfall intensity is likely to increase over time:17%(2019-2028),25%(2029-2038)and 32%(2039-2048).However,the findings presented in this paper will be useful for local authorities and decision makers in terms of improving stormwater design and future flood damage will be avoided.展开更多
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10371098 and the Natural Science Foundation of Shaanxi Province of ChinaIt is my pleasure to thank Prof. Qu Chang-Zheng for his helpful discussion
文摘Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.
文摘In this study, the kinetic energy formula of the projection curve under 1-parameter closed homothetic motion is expressed and as a result, theorem is given. Also some special cases are given related with that formula.
基金Teaching reform research project of Shandong vocational education(2017228)
文摘In this paper, we study the intersection multiplicity of algebraic curves at a point both in R^2 and in real projective plane P^2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.
基金The NSF(11601209)of ChinaResearch Foundation(201601239)for Doctor of Liaoning Province+1 种基金Scientific Research Fund(L201683660)of Liaoning Provincial Education DepartmentYouth Foundation(LS2015L002)of Liaoning Normal University
文摘Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.
基金The second author was supported by the National Natural Science Foundation of China(11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)The third author was supported by the Foundation of Guangzhou Civil Aviation College(18X0428).
文摘In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.
文摘in the design of civil and water conservancy projects, the identical slope suffice isfrequently used. Its mathematical model may be formulated as an envelope of a cone when itS vertexmoves along the cylindrical helix. According to the principle of conStrUcting the envelope curves of afamily of circles, the parametric equstion for the identical slope surface is established. The parametricform makes it most convenient to draw the contour lines and grade lines, and is well suited toproduce indexed projection of identical slope surface in civil and water conservancy projects.
基金supported by the National Natural Science Foundation of China general Projects(No.51174193)the Youth Fund Project of the National Natural Science Foundation of China(No.51004102)the National High Technology Research and Development Program of China(No.2012AA062101)
文摘This paper proposes the concept of projection curves based on the theory of CT image reconstruction to probe the internal structure of the working panel prior to formal mining of the working panel.As well as reducing costs,this method provides safe and efficient excavation of the working panel.According to the results of the numerical model and the actual working panel,the new method has been proven to be accurate in detecting the location of the fault that extends into the face.Concealed faults of the internal working panel,as well as the start and end points of the fault,can be detected by this method.Engineering practice has proven that the method is highly reliable,has a highly decisive impact on faults for coal mining,and can be used to guide the safe mining of the working panel.
文摘Climate change is the most important factor to increase in short-duration high-intensity rainfall and consequent flooding.Intensity-Duration-Frequency(IDF)curves are commonly used tools in Stormwater design,so a method to derive future IDF curves including climate change effect could be necessary for the mainstreaming climate change information into storm water planning.The objective of the present study is to define a mechanism to reflect the effect of climate change into the projected rainfall IDF relationships.For this,the continuously observed hourly rainfall data from 1969 to 2018 were divided into five subgroups.Then the IDF curve of each subgroup is defined.The rainfall intensity for the next 30 years was then estimated using a linear regression model.The obtained result indicates that for the same duration and for the same return period,the rainfall intensity is likely to increase over time:17%(2019-2028),25%(2029-2038)and 32%(2039-2048).However,the findings presented in this paper will be useful for local authorities and decision makers in terms of improving stormwater design and future flood damage will be avoided.
