State-of-the-art first-order automated theorem proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably proving theorems that would be considered relatively simple by humans. For example, when reasoning about sets, relations, or functions, first-order systems still exhibit serious weaknesses. While it has...

This paper presents two views of stepwise enhancement, one a pragmatic syntax-based approach and the other a semantic approach based on higher-order functions and relating to shape and polytypism. The approaches are outlined, and the perhaps surprisingly close relationship between the two described. By combining the advantages of both approaches, it is shown how more code in both functional and...

In the exact propagator for finite temperature gluons the location of the transverse and longitudinal poles in the gluon propagator are unknown functions of wave vector: ωT (k) and ωL(k). The residues of the poles, also unknown, fix the normalization of the one gluon vector potential and thus of the field strength. The naive energy density ~ E · ~ D + ~ B · ~ H is not correct because of dispers...

Current research in therapies for restoring a functional form of sight to the blind includes interfacing electronic neurostimulators with some point of the visual pathway. This approach requires controlling a number of waveform parameters which might vary for every implanted patient and for every channel in an interface that may have hundred or thousands of electrodes. Therefore, the clinical, ...

The two mass model (2MM) as introduced by Ishizaka & Flanagan (1972) and simplified by Steinecke & Herzel (1995) describes many features of the vocal fold oscillation patterns [1,2]. Particularly, it was shown that a large variety of voice disorders may be explained by means of high-speed observations with subsequent interpretation by the 2MM. Laryngeal symmetry was identified as an important p...

By combining weighted distances and distances based on neighbourhood sequences, a new family of distance functions with potentially low rotational dependency is obtained. The basic theory for these distance functions, including functional form of the distance between two points, is presented for the face-centered cubic grid and the body-centered cubic grid. By minimizing an error function, the ...

Numerous studies have investigated economies of scale and scope in higher education as a means of providing public and private providers of college and university teaching and research and their stakeholders with knowledge of the cost structures that underpin provision in this economically and socially important sector. However, debate continues on the precise nature of these economies of scale...