Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we characterized maps ϕ:B(H)→B(H), which are surjective up to compact preserving set left semi-Weyl in both directions. As application, proved that ϕ preserves essential approximate point spectrum if only ideal is invariant under induced map φ Calkin automor...

Abstract In this paper, we study the local behavior of nonnegative solutions fractional semi-linear equations ( − Δ ) σ u = p with an isolated singularity, where ∈ 0 , 1 and n 2 + . We first use blow up method a Liouville type theorem to derive upper bound. Then establish monotonicity formula sufficient condition for removable singularity give classification singularities. When result has been ...

These are lecture notes from a course given at the summer school on ‘Current topics in Mathematical Physics’, held at Luminy in September 2013. We discuss ground state solutions for semi-linear PDEs in R . In particular, we prove their existence, radial symmetry and uniqueness up to translations.

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound ...

In the predictability minimization approach, input patterns are fed into a system consisting of adaptive, initially unstructured feature detectors. There are also adaptive predictors constantly trying to predict current feature detector outputs from other feature detector outputs. Simultaneously, however, the feature detectors try to become as unpredictable as possible, resulting in a co-evolut...