Abstract In this paper we consider the lower order eigenvalues of biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a type of general inequalities for them. In particular, we study the lower order eigenvalues of biharmonic operator on compact submanifolds of Euclidean spaces, of spheres, and of projective spaces. We obtain some estimates for lower orde...

In this work we present two new algorithms for the detection of circles and ellipses which use the FHT algorithm as a basis: Fast Circle Hough Transform (FCHT) and Fast Ellipse Hough Transform (FEHT). The first stage of these two algorithms, devoted to obtaining the centers of the figures, is computationally the most costly. With the objective of improving the execution times of this stage it h...

State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothness parameters is necessary. As a special case, we show Nesterov’s accelerate...