Subdifferential set of an operator

Maximality of the sum of the subdifferential operator and a maximally monotone operator

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds, which is called the “sum problem”. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that domA ∩ int domB 6= ∅,...

Schrr Odinger Operator in an Overfull Set

When a wave function is represented as a linear combination over an overfull set of elementary states, an ambiguity arises since such a representation is not unique. We introduce a variational principle which eliminates this ambiguity, and results in an expansion which provides the best" representation to a given Schrr odinger operator. Operational simplicity of an expansion of a wave function ...

POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

An Operator Extension of Bohr's inequality

An upper estimate for the Clarke subdifferential of an infimal value function proved via the Mordukhovich subdifferential

The aim of this note is to give an alternative proof for a recent result due to Dorsch, Jongen and Shikhman, which provides an upper estimate for the Clarke subdifferential of an infimal value function. We show the validity of this result under a weaker condition than the one assumed in the mentioned paper, while the use of the Mordukhovich subdifferential, as an intermediate step, will conside...