The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Neurolinguistic analysis: aspects of language and speech deviations in Palestinian Arabic aphasics

The characteristics of aphasics’ speech in various languages have been the core of numerous studies, but Arabic in general, and Palestinian Arabic in particular, is still a virgin field in this respect. However, it is of vital importance to have a clear picture of the specific aspects of Palestinian Arabic that might be affected in the speech of aphasics in order to establish screening, diagnosis and therapy programs based on a clinical linguistic database. Hence the central questions of this study are what are the main neurolinguistic features of the Palestinian aphasics’ speech at the phonetic-acoustic level and to what extent are the results similar or not to those obtained from other languages. In general, this study is a survey of the most prominent features of Palestinian Broca’s aphasics’ speech. The main acoustic parameters of vowels and consonants are analysed such as vowel duration, formant frequency, Voice Onset Time (VOT), intensity and frication duration. The deviant patterns among the Broca’s aphasics are displayed and compared with those of normal speakers. The nature of deficit, whether phonetic or phonological, is also discussed. Moreover, the coarticulatory characteristics and some prosodic patterns of Broca’s aphasics are addressed. Samples were collected from six Broca’s aphasics from the same local region. The acoustic analysis conducted on a range of consonant and vowel parameters displayed differences between the speech patterns of Broca’s aphasics and normal speakers. For example, impairments in voicing contrast between the voiced and voiceless stops were found in Broca’s aphasics. This feature does not exist for the fricatives produced by the Palestinian Broca’s aphasics and hence deviates from data obtained for aphasics’ speech from other languages. The Palestinian Broca’s aphasics displayed particular problems with the emphatic sounds. They exhibited deviant coarticulation patterns, another feature that is inconsistent with data obtained from studies from other languages. However, several other findings are in accordance with those reported from various other languages such as impairments in the VOT. The results are in accordance with the suggestions that speech production deficits in Broca’s aphasics are not related to phoneme selection but rather to articulatory implementation and some speech output impairments are related to timing and planning deficits.