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An analytical Pascal matrix transform is proposed for conversions of transfer functions between s- and z-domains. The transform is formulated uniformly for first-order a-to-z transforms, and its Pascal matrix is derived logically and analytically. The inverse transform is then formed in terms of its forward transform matrices without computing the matrix in verses. Computation examples show that the presented Pascal matrix transform works simply and efficiently. [ABSTRACT FROM AUTHOR]

The purpose of this correspondence is to present an approach for verifying that explicitly stated integrity constraints are not violated by certain transactions. We utilize a relational model wherein constraints are given in a language based on the first-order predicate calculus. Transactions are written in terms of a Pascal-like host language with embedded first-order predicate calculus capabilities allowing queries and updates. The technique for proving consistency of the transactions is based upon the Hoare axiomatic approach. We illustrate the method by means of an explicit example of a database updated by four types of transaction. A generalized transaction consistency verifier embodying this approach would considerably enhance transaction programming in a relational database management system. [ABSTRACT FROM AUTHOR]