Cut-elimination, introduced by Gentzen, plays an important role in automating the analysis of mathematical proofs. The removal of cuts corresponds to the elimination of intermediate statements (lemmas), resulting in an analytic proof. CERes is a method of cut-elimination by resolution that relies on global proof transformations, in contrast to reductive methods, which use local proof-rewriting ...

We have previously developed a mathematical treatment of a calculus for class transformations that preserve or extend a set of objects. Methods for automating the maintenance of structural and behavioral consistency in systems based on evolving class structures have been provided for the object-preserving and object-extending transformations. This work extends the calculus of class transformati...

Shepard's analysis of how shape, motion, and color are perceptually represented can be generalized. Apparent motion and shape may be associated with a group of spatial transformations, accounting for rigid and plastic motion, and perceived object color may be associated with a group of illuminant transformations, accounting for the discriminability of surface-reflectance changes and illuminant ...

An analysis of a discrete time-frequency distribution yields a new periodic wide band probing signal for use in unknown system identiication. The derivation is based on mathematical properties of the discrete Wigner distribution. Like the continuous distribution, the discrete version also sat-isses the covariance property, meaning transformations in the time-frequency plane are equivalent to tr...

We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In parti...

As part of the Petri Net Baukastenn Pad99b] the Expert View presents mathematical concepts and results of Petri net theory in a structured and application oriented way. Consistent formal Petri net techniques and transformations between these are main issues. We introduce the notions of formal Petri net techniques, abstract Petri net frames, instantiations, and transformations. These notions are...

The beam transfer matrix, often called the ABCD matrix, is one of the essential mathematical instruments in optics. It is a unimodular matrix whose determinant is 1. If all the elements are real with three independent parameters, this matrix is a 2 x 2 representation of the group Sp(2). It is shown that a real ABCD matrix can be generated by two shear transformations. It is then noted that, in ...

We show how to transform UML (Uniied Modeling Language) state diagrams into graphs by making explicit the intended semantics of the diagram. The process of state expansion in nested state diagrams is explained by graph transformations in three steps: (1) adding boundary nodes introducing a precise interface for the state to be expanded, (2) expanding the state, and (3) removing the boundary nod...

The navigational tasks of computing time-to-impact and controlling movements within specific range are addressed here. By using specially designed lenses various components of these procedures, consisting of mathematical transformations, can be provided at image acquisition time, and therefore, speed up execution time. This s t u 4 discusses the optical implementation of different correlators b...

Certain changes in pulse shape do not affect the resolution capability of a sonar system. These changes can be expressed as mathematical transformations that leave invariant important properties of the wide-band ambiguity function. Such transformations provide a large number of signal and filter functions, all of which satisfy a given range-Doppler resolution requirement. The sonar designer can...