Spinor algebra and null solutions of the wave equation

In this paper we exploit the ideas and formalisms of twistor theory, to show how, on Minkowski space, given a null solution of the wave equation, there are precisely two null directions in $\ker df$, at least one of which is a shear-free ray congruence

Metaphysical conceits involving death in the writings of John Donne

Much has been written in the past fifty years about John Donne and his work. His troubled life and enigmatic writings have made him seem a kindred spirit to a confused age. To our day the dissonant, abrupt, and calculatedly reckless style and the concern with the harsh realities of love and death have relevance which heretofore had been misunderstood or ignored

Oculomotor Deficits in Diseases of the Basal Ganglia: Parkinson\u27s and Huntington\u27s Diseases

Oculomotor deficits are now recognized as being present in several neurological diseases of the basal ganglia. The present report will focus primarily on those observed in Huntington\u27s and Parkinson\u27s diseases. Neuronal cell loss in the pars compacta of the substantia nigra, degeneration of the nigrostriatal pathway, and consequent depletion of the neurotransmitter dopamine is the most obvious etiological abnormality in Parkinson\u27s disease. Huntington\u27s disease, on the other hand, involves the selective genetically-driven atrophy of the striatum (caudate and putamen). In order to attempt to understand oculomotor dysfunction, as a component of basal ganglia disease, it is necessary to first establish a definition of the basal ganglia, its relevant connections, and their associated neurotransmitters and functions

Biharmonic Riemannian submersions from 3-manifolds

An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic (i.e, minimal). In a later paper [CMO2], Cadeo-Monttaldo-Oniciuc shown that the theorem remains true if the target Euclidean space is replaced by a 3-dimensional hyperbolic space form. In this paper, we prove the dual results for Riemannian submersions, i.e., a Riemannian submersion from a 3-dimensional space form of non-positive curvature into a surface is biharmonic if and only if it is harmonic