Suppose that M is a complete Kähler manifold such its holomorphic sectional curvature bounded from below by constant and radial also below. N strongly pseudoconvex complex Finsler above negative constant. In this paper, we establish Schwarz lemma for mappings f into N. As applications, obtain Liouville type rigidity result N, as well theorem bimeromorphic compact manifold.

we obtain the expression of ricci tensor for a $gcr$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $gcr$-lightlike submanifold of anindefinite complex space form. moreover, we have proved that everyproper totally umbilical $gcr$-lightlike submanifold of anindefinite kaehler manifold is a totally geodesic $gcr$-lightlikesubmanifold.

This paper designs an Optimized Adaptive Combined Hierarchical Sliding Mode Controller (OACHSMC) for a time-varying crane model in presence of uncertainties. Uncertainties have always been one of the most important challenges in designing control systems, which include the unknown parameters or un-modeled dynamics in the systems. Sliding mode controller (SMC) is able to compensate the system in...

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

We propose an illumination strategy for interferometric imaging that allows for robust depth recovery from intensity-only measurements. For an array with colocated sources and receivers, we show that all the possible interferometric data for multiple sources, receivers and frequencies can be recovered from intensity-only measurements provided that we have sufficient source location and frequenc...