Gradient Mappings

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

The Coarea Formula for Sobolev Mappings

We extend Federer’s coarea formula to mappings f belonging to the Sobolev class W (R;R), 1 ≤ m < n, p > m, and more generally, to mappings with gradient in the Lorentz space L(R). This is accomplished by showing that the graph of f in R is a Hausdorff n-rectifiable set.

Some Remarks about Metric Spaces, Spherical Mappings, Functions and Their Derivatives

If p ∈ Rn, then we have the radial projection map from Rn\{p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a funct...

Evolving efficient learning algorithms for binary mappings

Gradient descent training of sigmoidal feed-forward neural networks on binary mappings often gets stuck with some outputs totally wrong. This is because a sum-squared-error cost function leads to weight updates that depend on the derivative of the output sigmoid which goes to zero as the output approaches maximal error. Although it is easy to understand the cause, the best remedy is not so obvi...