Similar to Nomizu-Pinkall's geometric characterization of the Cayley surface and Hu-Li-Zhang's characterization of the Cayley hypersurface,how can one characterize the generalized Cayley hypersurfaces?In this ...Similar to Nomizu-Pinkall's geometric characterization of the Cayley surface and Hu-Li-Zhang's characterization of the Cayley hypersurface,how can one characterize the generalized Cayley hypersurfaces?In this paper,by the affineα-connection of statistical manifolds,we study affine hypersurfaces with parallel cubic form relative to the affineα-connection.As the main results,we complete the classification of such hypersurfaces if its affine metric is either definite,or Lorentzian withα≠-1.Moreover,we give a new characterization of the generalized Cayley hypersurfaces to answer the question.展开更多
In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we...In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.展开更多
A new coarse-to-fine strategy was proposed for nonrigid registration of computed tomography(CT) and magnetic resonance(MR) images of a liver.This hierarchical framework consisted of an affine transformation and a B-sp...A new coarse-to-fine strategy was proposed for nonrigid registration of computed tomography(CT) and magnetic resonance(MR) images of a liver.This hierarchical framework consisted of an affine transformation and a B-splines free-form deformation(FFD).The affine transformation performed a rough registration targeting the mismatch between the CT and MR images.The B-splines FFD transformation performed a finer registration by correcting local motion deformation.In the registration algorithm,the normalized mutual information(NMI) was used as similarity measure,and the limited memory Broyden-Fletcher- Goldfarb-Shannon(L-BFGS) optimization method was applied for optimization process.The algorithm was applied to the fully automated registration of liver CT and MR images in three subjects.The results demonstrate that the proposed method not only significantly improves the registration accuracy but also reduces the running time,which is effective and efficient for nonrigid registration.展开更多
In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of...In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.展开更多
For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of wh...For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)^(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.展开更多
基金supported by NNSF of China(Grant No.11401173)supported by NNSF of China(Grant No.12171437)supported by NNSF of China(Grant No.12101194)。
文摘Similar to Nomizu-Pinkall's geometric characterization of the Cayley surface and Hu-Li-Zhang's characterization of the Cayley hypersurface,how can one characterize the generalized Cayley hypersurfaces?In this paper,by the affineα-connection of statistical manifolds,we study affine hypersurfaces with parallel cubic form relative to the affineα-connection.As the main results,we complete the classification of such hypersurfaces if its affine metric is either definite,or Lorentzian withα≠-1.Moreover,we give a new characterization of the generalized Cayley hypersurfaces to answer the question.
基金supported by the NNSF of China (12101194,11401173).
文摘In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.
基金Project(61240010)supported by the National Natural Science Foundation of ChinaProject(20070007070)supported by Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘A new coarse-to-fine strategy was proposed for nonrigid registration of computed tomography(CT) and magnetic resonance(MR) images of a liver.This hierarchical framework consisted of an affine transformation and a B-splines free-form deformation(FFD).The affine transformation performed a rough registration targeting the mismatch between the CT and MR images.The B-splines FFD transformation performed a finer registration by correcting local motion deformation.In the registration algorithm,the normalized mutual information(NMI) was used as similarity measure,and the limited memory Broyden-Fletcher- Goldfarb-Shannon(L-BFGS) optimization method was applied for optimization process.The algorithm was applied to the fully automated registration of liver CT and MR images in three subjects.The results demonstrate that the proposed method not only significantly improves the registration accuracy but also reduces the running time,which is effective and efficient for nonrigid registration.
基金Supported by the National Natural Science Foundation of China (10671117)Academic Mainstay Foundation of Hubei Provincial De-partment of Education (D200729002)Science Foundation of China Three Gorges University
文摘In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.
基金Supported by the National Natural Science Foundation of China(11561020,11371224)Supported by the Science and Technology Plan of the Gansu Province(145RJZG227)
文摘For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)^(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.
