The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly ani...The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility （NLC）, that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features （i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them） and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.展开更多
This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles)...This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles) on a triangular mesh consisting of congruent isosceles triangles. As an example, we perform global analysis of an Escher-style trick art, i.e., a simpler version of “Ascending and Descending”. After defining the local structure on the trick art, we analyze its global structure and attribute its paradox to a singular point (i.e., a singular triangle) at the center. Then, the endless “Penrose stairs” is described as a closed trajectory around the isolated singular point. The approach fits well with graphical projection and gives a simple and intuitive example of the interaction between global and local structures. We could deal with higher dimensional objects as well by considering n-simplices (n > 2) instead of triangles.展开更多
目的构建基于Triangle模型的下肢静脉溃疡(venous leg ulcer,VLU)患者分层分级管理方案并评价其应用效果。方法于2024年1—4月采用文献回顾、小组讨论、专家会议方法构建包含低、中、高危分层标准及各级管理措施的方案,并选取于2024年5...目的构建基于Triangle模型的下肢静脉溃疡(venous leg ulcer,VLU)患者分层分级管理方案并评价其应用效果。方法于2024年1—4月采用文献回顾、小组讨论、专家会议方法构建包含低、中、高危分层标准及各级管理措施的方案,并选取于2024年5—6月入院的36例患者为对照组,2024年7—8月入院的36例VLU患者为观察组,对照组给予患者常规治疗及护理管理措施,并为患者实施常规健康教育;观察组在对照组的基础上,实施基于Triangle模型的VLU患者分层分级管理。比较2组患者干预前、干预后溃疡面积、溃疡愈合效果、溃疡愈合总有效率、治疗依从性和自我管理能力。结果干预后,观察组的溃疡面积显著小于对照组(P<0.05)、溃疡愈合效果显著优于对照组(P<0.05);观察组的溃疡愈合总有效率为86.11%,高于对照组的63.89%,2组比较差异有统计学意义(P<0.05);观察组的治疗依从性和自我管理能力显著优于对照组(P<0.05)。结论本研究构建的基于Triangle模型的VLU患者分层分级管理方案能够为患者提供科学有效的管理,促进患者溃疡愈合,提高患者的治疗依从性和自我管理能力。展开更多
In this paper, we present a robust subneighborhoods selection technique for feature detection on point clouds scattered over a piecewise smooth surface. The proposed method first identifies all potential features usin...In this paper, we present a robust subneighborhoods selection technique for feature detection on point clouds scattered over a piecewise smooth surface. The proposed method first identifies all potential features using covariance analysis of the local- neighborhoods. To further extract the accurate features from potential features, Gabriel triangles are created in local neighborhoods of each potential feature vertex. These triangles tightly attach to underlying surface and effectively reflect the local geometry struc- ture. Applying a shared nearest neighbor clustering algorithm on ~ 1 reconstructed normals of created triangle set, we classify the lo- cal neighborhoods of the potential feature vertex into multiple subneighborhoods. Each subneighborhood indicates a piecewise smooth surface. The final feature vertex is identified by checking whether it is locating on the intersection of the multiple surfaces. An advantage of this framework is that it is not only robust to noise, but also insensitive to the size of selected neighborhoods. Ex- perimental results on a variety of models are used to illustrate the effectiveness and robustness of our method.展开更多
Fractals play an important role in mathematics, aesthetic, science, and engineering. The representative Sierpinski-triangle fractals have been successfully constructed by V-shape molecules in experiments. The molecula...Fractals play an important role in mathematics, aesthetic, science, and engineering. The representative Sierpinski-triangle fractals have been successfully constructed by V-shape molecules in experiments. The molecular Sierpinski triangles formed by molecules with linear backbones have been theoretically predicted but not experimentally discovered. To achieve this goal in the experiment, we used[1,1’;4’,1’’;4’’,1’’’]-quaterphenyl-3,40 0-dicarbonitrile molecules as building blocks and employed cobalt atoms as cements, then successfully obtained metal-organic Sierpinski triangles with an order up to 2 on the Au（111） surface. There are twenty-four types of three-fold coordination nodes formed between the metal atom and organic ligands via coordinate interactions. The coexistence of various nodes is responsible for that the highest order of Sierpinski triangles is limited to 2.展开更多
Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposi...Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.展开更多
This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem （BVP） of the antiplane elasticity or the Laplace equation. The Schwar...This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem （BVP） of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition （or w ---- 0） along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the partic- ular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.展开更多
Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing sequence{an}.And each an in the sequence corresponds to finitely many ...Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing sequence{an}.And each an in the sequence corresponds to finitely many affine equivalent classes of Veech surfaces with area 1.In this article,we give an algorithm for calculating the area of the minimal triangles in a Veech surface and prove that the first element of{an}which corresponds to non arithmetic Veech surfaces is(5-√5)/20,which is uniquely realized by the area of the minimal triangles of the normalized golden L-shaped translation surface up to affine equivalence.展开更多
Quasiconformal mappings between hyperbolic triangles are considered.We give an explicit estimate of the dilation of the quasiconformal mappings,which generalizes Bishop's results.
For two triangles to be congruent,SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle.If the congruent a...For two triangles to be congruent,SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle.If the congruent angles are not between the corresponding congruent sides,then such triangles could be different.It turns out that it is possible to describe four cases in which triangles are congruent even though congruent angles.For two triangles to be congruent,SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle.If the congruent angles are not between the corresponding congruent sides,then such triangles could be different.It turns out that it is possible to describe four cases in which triangles are congruent even though congruent angles are not between the corresponding congruent sides.Such a theorem could be named,for example,SSA theorem.Many texts state that two triangles cannot be shown to be congruent if the condition of SSA exists.However,the author describes cases in which such triangles could be proven congruent with the SSA theorem.An immediate consequence of this new understanding is the necessity of revising many problems and answers in high school and college-level texts related to congruent triangles.are not between the corresponding congruent sides.Such a theorem could be named,for example,SSA theorem.An immediate consequence of this new understanding is the necessity of revising many problems and answers in high school and college-level texts related to congruent triangles.展开更多
Il existe des régions qui ont une forme triangulaire dans la région du cou.Ces triangles sont formés par des vaisseaux,des muscles ou des os.Ils sont importants en anatomie topographique et sont des par...Il existe des régions qui ont une forme triangulaire dans la région du cou.Ces triangles sont formés par des vaisseaux,des muscles ou des os.Ils sont importants en anatomie topographique et sont des parties essentielles dans le corps humain.Donc il est necessaire de bien apprendre les compositions de ces triangles et ses significations cliniques.En principe,les triangles du cou sont faits de 2 régions(divisés par le muscle sterno-cléido-mastodien).Tous ces triangles du cou sont très utiles en clinique.Quelques-uns sont les signes pour trouver les vaisseaux ou les nerfs en opération,soit sont les positions de paracentèse,soit sont pour observer l'évolution de maladie.Si on les matrise bien,on peut diminuer l'hémorragie en opration et découvrir des cancers ou maladies le plus tt possible ce qui est très important pour traitement.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.51475208)
文摘The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility （NLC）, that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features （i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them） and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.
文摘This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles) on a triangular mesh consisting of congruent isosceles triangles. As an example, we perform global analysis of an Escher-style trick art, i.e., a simpler version of “Ascending and Descending”. After defining the local structure on the trick art, we analyze its global structure and attribute its paradox to a singular point (i.e., a singular triangle) at the center. Then, the endless “Penrose stairs” is described as a closed trajectory around the isolated singular point. The approach fits well with graphical projection and gives a simple and intuitive example of the interaction between global and local structures. We could deal with higher dimensional objects as well by considering n-simplices (n > 2) instead of triangles.
文摘目的构建基于Triangle模型的下肢静脉溃疡(venous leg ulcer,VLU)患者分层分级管理方案并评价其应用效果。方法于2024年1—4月采用文献回顾、小组讨论、专家会议方法构建包含低、中、高危分层标准及各级管理措施的方案,并选取于2024年5—6月入院的36例患者为对照组,2024年7—8月入院的36例VLU患者为观察组,对照组给予患者常规治疗及护理管理措施,并为患者实施常规健康教育;观察组在对照组的基础上,实施基于Triangle模型的VLU患者分层分级管理。比较2组患者干预前、干预后溃疡面积、溃疡愈合效果、溃疡愈合总有效率、治疗依从性和自我管理能力。结果干预后,观察组的溃疡面积显著小于对照组(P<0.05)、溃疡愈合效果显著优于对照组(P<0.05);观察组的溃疡愈合总有效率为86.11%,高于对照组的63.89%,2组比较差异有统计学意义(P<0.05);观察组的治疗依从性和自我管理能力显著优于对照组(P<0.05)。结论本研究构建的基于Triangle模型的VLU患者分层分级管理方案能够为患者提供科学有效的管理,促进患者溃疡愈合,提高患者的治疗依从性和自我管理能力。
基金Supported by National Natural Science Foundation of China(No.u0935004,61173102)the Fundamental Research Funds for the Central Unibersities(DUT11SX08)
文摘In this paper, we present a robust subneighborhoods selection technique for feature detection on point clouds scattered over a piecewise smooth surface. The proposed method first identifies all potential features using covariance analysis of the local- neighborhoods. To further extract the accurate features from potential features, Gabriel triangles are created in local neighborhoods of each potential feature vertex. These triangles tightly attach to underlying surface and effectively reflect the local geometry struc- ture. Applying a shared nearest neighbor clustering algorithm on ~ 1 reconstructed normals of created triangle set, we classify the lo- cal neighborhoods of the potential feature vertex into multiple subneighborhoods. Each subneighborhood indicates a piecewise smooth surface. The final feature vertex is identified by checking whether it is locating on the intersection of the multiple surfaces. An advantage of this framework is that it is not only robust to noise, but also insensitive to the size of selected neighborhoods. Ex- perimental results on a variety of models are used to illustrate the effectiveness and robustness of our method.
基金supported by the National Natural Science Foundation of China (Nos. 21522301, 21373020, 21403008, 61621061, 21433011, 61271050)the Ministry of Science and Technology (Nos. 2014CB239302 and 2013CB933404)
文摘Fractals play an important role in mathematics, aesthetic, science, and engineering. The representative Sierpinski-triangle fractals have been successfully constructed by V-shape molecules in experiments. The molecular Sierpinski triangles formed by molecules with linear backbones have been theoretically predicted but not experimentally discovered. To achieve this goal in the experiment, we used[1,1’;4’,1’’;4’’,1’’’]-quaterphenyl-3,40 0-dicarbonitrile molecules as building blocks and employed cobalt atoms as cements, then successfully obtained metal-organic Sierpinski triangles with an order up to 2 on the Au（111） surface. There are twenty-four types of three-fold coordination nodes formed between the metal atom and organic ligands via coordinate interactions. The coexistence of various nodes is responsible for that the highest order of Sierpinski triangles is limited to 2.
文摘Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.
文摘This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem （BVP） of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition （or w ---- 0） along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the partic- ular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.
基金Supported by National Natural Science Foundation of China(11701039)Youth and Research and Innovation Program of BUPT(2017RC18)。
文摘Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing sequence{an}.And each an in the sequence corresponds to finitely many affine equivalent classes of Veech surfaces with area 1.In this article,we give an algorithm for calculating the area of the minimal triangles in a Veech surface and prove that the first element of{an}which corresponds to non arithmetic Veech surfaces is(5-√5)/20,which is uniquely realized by the area of the minimal triangles of the normalized golden L-shaped translation surface up to affine equivalence.
基金Partially Supported by NSFC(Grant No.12071047)Fundamental Research Funds for the Central Universities(Grant No.500421126).
文摘Quasiconformal mappings between hyperbolic triangles are considered.We give an explicit estimate of the dilation of the quasiconformal mappings,which generalizes Bishop's results.
文摘For two triangles to be congruent,SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle.If the congruent angles are not between the corresponding congruent sides,then such triangles could be different.It turns out that it is possible to describe four cases in which triangles are congruent even though congruent angles.For two triangles to be congruent,SAS theorem requires two sides and the included angle of the first triangle to be congruent to the corresponding two sides and included angle of the second triangle.If the congruent angles are not between the corresponding congruent sides,then such triangles could be different.It turns out that it is possible to describe four cases in which triangles are congruent even though congruent angles are not between the corresponding congruent sides.Such a theorem could be named,for example,SSA theorem.Many texts state that two triangles cannot be shown to be congruent if the condition of SSA exists.However,the author describes cases in which such triangles could be proven congruent with the SSA theorem.An immediate consequence of this new understanding is the necessity of revising many problems and answers in high school and college-level texts related to congruent triangles.are not between the corresponding congruent sides.Such a theorem could be named,for example,SSA theorem.An immediate consequence of this new understanding is the necessity of revising many problems and answers in high school and college-level texts related to congruent triangles.
文摘Il existe des régions qui ont une forme triangulaire dans la région du cou.Ces triangles sont formés par des vaisseaux,des muscles ou des os.Ils sont importants en anatomie topographique et sont des parties essentielles dans le corps humain.Donc il est necessaire de bien apprendre les compositions de ces triangles et ses significations cliniques.En principe,les triangles du cou sont faits de 2 régions(divisés par le muscle sterno-cléido-mastodien).Tous ces triangles du cou sont très utiles en clinique.Quelques-uns sont les signes pour trouver les vaisseaux ou les nerfs en opération,soit sont les positions de paracentèse,soit sont pour observer l'évolution de maladie.Si on les matrise bien,on peut diminuer l'hémorragie en opration et découvrir des cancers ou maladies le plus tt possible ce qui est très important pour traitement.
