We consider in dimension four weakly convergent sequences of approximate biharmonic maps into sphere with bi-tension fields bounded in L for some p > 1. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on R.

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Connecting Singularities with Controlled Length . . . . . . . . . . . . . . . . . . . . . ....

Recently, Sandeep Bhatt et.al [12] proved common fixed theorem for four self maps satisfying some contraction principles on a complex valued metric spaces. In this manuscript we obtain a common fixed point theorem for six maps in complex valued metric spaces having commuting and weakly compatible. Our theorem generalizes and extends the result of S. Bhatt et.al[12]. Mathematics Subject Classifi...

— For the real quadratic map Pa(x) = x2 + a and a given > 0 a point x has good expansion properties if any interval containing x also contains a neighborhood J of x with Pn a |J univalent, with bounded distortion and B(0, ) ⊆ Pn a (J) for some n ∈ N. The -weakly expanding set is the set of points which do not have good expansion properties. Let α denote the negative fixed point and M the first ...

Improved points (each point contributes 1~3pt improvement) Fully Convolutional Net Guided back propagation [2] Use the derivatives of multiple intermediate layers Aggregate multi-scale class saliency maps (3 scales) Assumption Raw saliency maps are affected by both class-specific saliency and generic object-ness The degree of class saliency factors should be larger than the generic object-ness ...