Most non-trivial applications use some form of input/output (I/O), such as network communication. When model checking such an application, a simple state space exploration scheme is not applicable: Backtracking during the state space search causes states to be revisited, and I/O operations to be repeated. Because I/O operations are visible by the environment, software model checking needs to en...

let ? be an open connected subset of the complex plane c and let t be a bounded linear operator on a hilbert space h. for ? in ? let e the orthogonal projection onto the null-space of t-?i . we discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. a generalized gram- schmidt process is also given.

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...