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

Professional Concerns

In the contribution which follows, Collett B. Dilworth, Jr., of the English Department at East Carolina University, gets to the very heart of why literature is taught in schools. He broaches the question of how literary study relates to the basic skills, and he ties his rationale in with questions of accountability and its handmaiden, competency testing. Probably the heart of Dilworth\u27s argument is in his statement, The student of literature is not primarily looking for information, s/he is looking for experience

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

Allelomimesis as universal clustering mechanism for complex adaptive systems

Animal and human clusters are complex adaptive systems and many are organized in cluster sizes $s$ that obey the frequency-distribution $D(s)\propto s^{-\tau}$. Exponent $\tau$ describes the relative abundance of the cluster sizes in a given system. Data analyses have revealed that real-world clusters exhibit a broad spectrum of $\tau$-values, $0.7\textrm{(tuna fish schools)}\leq\tau\leq 2.95\textrm{(galaxies)}$. We show that allelomimesis is a fundamental mechanism for adaptation that accurately explains why a broad spectrum of $\tau$-values is observed in animate, human and inanimate cluster systems. Previous mathematical models could not account for the phenomenon. They are hampered by details and apply only to specific systems such as cities, business firms or gene family sizes. Allelomimesis is the tendency of an individual to imitate the actions of its neighbors and two cluster systems yield different $\tau$ values if their component agents display different allelomimetic tendencies. We demonstrate that allelomimetic adaptation are of three general types: blind copying, information-use copying, and non-copying. Allelomimetic adaptation also points to the existence of a stable cluster size consisting of three interacting individuals.Comment: 8 pages, 5 figures, 2 table

Fmoc solid phase synthesis of polyamides containing pyrrole and imidazole amino acids

Polyamides containing N-methylimidazole (Im) and N-methylpyrrole (Py) amino acids are synthetic ligands that have an affinity and specificity for DNA comparable to those of many naturally occurring DNA binding proteins. A machine-assisted Fmoc solid phase synthesis of polyamides has been optimized to afford high stepwise coupling yields (>99%). Two monomer building blocks, Fmoc-Py acid and Fmoc-Im acid, were prepared in multigram scale. Cleavage by aminolysis followed by HPLC purification affords up to 200 mg quantities of polyamide with purities and yields greater than or equal to those reported using Boc chemistry. A broader set of reaction conditions will increase the number and complexity of minor groove binding polyamides which may be prepared and help ensure compatibility with many commercially available peptide synthesizers

A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas