We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of strengthened CauchySchwarz inequalities is derived using these identities. Also, an analogous version of this result is given for strengthened Hölder inequalities.

We introduce a type and effect system, for an imperative object calculus, whichinfers sharing possibly introduced by the evaluation of an expression, repre-sented as an equivalence relation among its free variables. This direct represen-tation of sharing effects at the syntactic level allows us to express in a naturalway, and to generalize, widely-used notions in literature, not...

Qualitative spatial reasoning is important for many spatial in formation systems including GISs It is based on the manipulation of qual itative spatial relationships and is used to infer spatial relationships which are not stored explicitly in the Geographic DataBase GDB to answer spa tial queries given partial spatial knowledge and to maintain the consistency of the GDB This paper compares the...

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which generalizations Hilbert spaces. We demonstrate how these can be employed derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator complex space. Some our expand upon the existing literature on numerical with space operators, import...