This paper studies the statistical query (SQ) complexity of estimating $d$-dimensional submanifolds in $\mathbb{R}^n$. We propose a purely geometric algorithm called Manifold Propagation, that reduces problem to three natural routines: projection, tangent space estimation, and point detection. then provide constructions these routines SQ framework. Given an adversarial $\mathrm{STAT}(\tau)$ ora...

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

in this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced. some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions occur to the geometric manifold but make the 1-chaotic manifold invariant. the existed retractions are discussed through new proved theorems. also we construct diffe...

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...