On Affine Hypersurfaces with Parallel Cubic Form Relative to Affineα-connection

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.

Hybrid robust fault detection and isolation of satellite reaction wheel actuators

In this paper,a combined robust fault detection and isolation scheme is studied for satellite system subject to actuator faults,external disturbances,and parametric uncertainties.The proposed methodology incorporates a residual generation module,including a bank of filters,into an intelligent residual evaluation module.First,residual filters are designed based on an improved nonlinear differential algebraic approach so that they are not affected by external disturbances.The residual evaluation module is developed based on the suggested series and parallel forms.Further,a new ensemble classification scheme defined as blended learning integrates heterogeneous classifiers to enhance the performance.A wide range of simulations is carried out in a high-fidelity satellite simulator subject to the constant and time-varying actuator faults in the presence of disturbances,manoeuvres,uncertainties,and noises.The obtained results demonstrate the effectiveness of the proposed robust fault detection and isolation method compared to the traditional nonlinear differential algebraic approach.

On Laguerre Form and Laguerre Isoparametric Hypersurfaces

Let x ： M^n-1→ R^nbe an umbilical free hypersurface with non-zero principal curvatures.M is called Laguerre isoparametric if it satisfies two conditions, namely, it has vanishing Laguerre form and has constant Lauerre principal curvatures. In this paper, under the condition of having constant Laguerre principal curvatures, we show that the hypersurface is of vanishing Laguerre form if and only if its Laguerre form is parallel with respect to the Levi-Civita connection of its Laguerre metric.

Complete Hypersurfaces with Constant Laguerre Scalar Curvature in R^n

Let x ： M^n-1→ R^n be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of M under the Laguerre transformation group of Rn are Laguerre form C and Laguerre tensor L. In this paper, we prove the following theorem： Let M be an （n-1）-dimensional （n 〉 3） complete hypersurface with vanishing Laguerre form and with constant Laguerre scalar curvature R in R^n, denote the trace-free Laguerre tensor by L = L -1/n-1tr（L）· Id. If supM ｜｜L｜｜=0,then M is Laguerre equivalent to a Laguerre isotropic hypersurface; and if supM ｜｜L^-｜｜≡√（n-1）（n-2）R/ （n-1）（n-2）（n-3） , M isLaguerre equivalent to the hypersurface x^- ： H^1× S^n-2 → R^n.