笔者在教学之余发现了椭圆的一个十分优美的性质:定理:如图,设 P 为椭圆 (x^2)/(a^2)+(y^2)/(b^2)=1(a>b>0)上一点,AB、CD 分别为长、短轴,∠APB=α,∠CPD=β,∠CAD=γ,则 cot^2α+cot^2β=cot^2γ.证明:(1)若 P 与 A 或 B 重合。
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
Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are op...Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three "volume-point" heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on "volume-point" heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.展开更多
Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocr...Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocrystals are dispersed in a uniform microemulsion environment as ＂seeds＂ for further re-growth through a secondary solvothermal process. The growth of anisotropic morphologies has been explained by the presence and orientation of twin planes in the face-centered cubic Fe3O4 which direct the shape of the growing particles. In particular, reentrant grooves resulting from twin planes are favorable sites for the addition of adatoms, leading to anisotropic growth. Triangular nanosheets are believed to contain one twin face which directs the growth of the primary particles in two dimensions. Hexagonal nanosheets are believed to contain two parallel planes that allow the growth edges to regenerate one another. The growth mechanism is evidenced by the analysis of high-resolution transmission electron microscopy （HRTEM） results and the as-prepared Fe3O4 nanoparticles have been shown to be an effective catalyst in the synthesis of quinoxaline.展开更多
文摘笔者在教学之余发现了椭圆的一个十分优美的性质:定理:如图,设 P 为椭圆 (x^2)/(a^2)+(y^2)/(b^2)=1(a>b>0)上一点,AB、CD 分别为长、短轴,∠APB=α,∠CPD=β,∠CAD=γ,则 cot^2α+cot^2β=cot^2γ.证明:(1)若 P 与 A 或 B 重合。
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.
基金supported by the National Natural Science Foundation of China (Grant No. 51176203)the Natural Science Foundation of Naval University of Engineering (Grant No. HGDYDJJ10011)the Natural Science Foundation for Youngsters of Naval University of Engineering (Grant No. HGDQNJJ10017)
文摘Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three "volume-point" heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on "volume-point" heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.
基金This work was supported by the National Natural Science Foundation ol： China （Nos. 20901069, 50873093, and 21271156） and the Henan Province Scientific and Technological Research Program （No. 092102210054）.
文摘Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocrystals are dispersed in a uniform microemulsion environment as ＂seeds＂ for further re-growth through a secondary solvothermal process. The growth of anisotropic morphologies has been explained by the presence and orientation of twin planes in the face-centered cubic Fe3O4 which direct the shape of the growing particles. In particular, reentrant grooves resulting from twin planes are favorable sites for the addition of adatoms, leading to anisotropic growth. Triangular nanosheets are believed to contain one twin face which directs the growth of the primary particles in two dimensions. Hexagonal nanosheets are believed to contain two parallel planes that allow the growth edges to regenerate one another. The growth mechanism is evidenced by the analysis of high-resolution transmission electron microscopy （HRTEM） results and the as-prepared Fe3O4 nanoparticles have been shown to be an effective catalyst in the synthesis of quinoxaline.
