Super edge-magic deficiency of join-product graphs

A graph $G$ is called \textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ such that $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \cup nK_1$ is super edge-magic or $+\infty$ if there exists no such integer. \emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph to each vertex of the second graph. In this paper, we study the super edge-magic deficiencies of a wheel minus an edge and join products of a path, a star, and a cycle, respectively, with isolated vertices.Comment: 11 page

Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory

The ubiquitous ADE classification has induced many proposals of often mysterious correspondences both in mathematics and physics. The mathematics side includes quiver theory and the McKay Correspondence which relates finite group representation theory to Lie algebras as well as crepant resolutions of Gorenstein singularities. On the physics side, we have the graph-theoretic classification of the modular invariants of WZW models, as well as the relation between the string theory nonlinear $\sigma$-models and Landau-Ginzburg orbifolds. We here propose a unification scheme which naturally incorporates all these correspondences of the ADE type in two complex dimensions. An intricate web of inter-relations is constructed, providing a possible guideline to establish new directions of research or alternate pathways to the standing problems in higher dimensions.Comment: 35 pages, 4 figures; minor corrections, comments on toric geometry and references adde

Reinventing grounded theory: some questions about theory, ground and discovery

Grounded theory’s popularity persists after three decades of broad-ranging critique. In this article three problematic notions are discussed—‘theory,’ ‘ground’ and ‘discovery’—which linger in the continuing use and development of grounded theory procedures. It is argued that far from providing the epistemic security promised by grounded theory, these notions—embodied in continuing reinventions of grounded theory—constrain and distort qualitative inquiry, and that what is contrived is not in fact theory in any meaningful sense, that ‘ground’ is a misnomer when talking about interpretation and that what ultimately materializes following grounded theory procedures is less like discovery and more akin to invention. The procedures admittedly provide signposts for qualitative inquirers, but educational researchers should be wary, for the significance of interpretation, narrative and reflection can be undermined in the procedures of grounded theory

Divisibility: A Problem Solving Approach Through Generalizing and Specializing

This paper describes a divisibility rule for any prime number as an engaging problem-solving activity for preservice secondary school mathematics teachers

Iron Rings, Doctor Honoris Causa Raoul Bott, Carl Herz, and a Hidden Hand

The degree of Doctor of Sciences, honoris causa, was conferred on Raoul Bott by McGill University in 1987. Much of the work to make this happen was done by Carl Herz. Some of the author's personal recollections of both professors are included, along with some context for the awarding of this degree and ample historical tangents. Some cultural aspects occurring in the addresses are elaborated on, primarily, the Canadian engineer's iron ring. This paper also reprints both the convocation address of Raoul Bott and the presentation of Carl Herz on that occasion.Comment: An edited and reformatted version of this paper, with an additional photo, will appear in a volume dedicated to Raoul Bott. The author hopes to expand on some aspects of this preprint in future version

The Death of Conrad Unger: Some Conjectures Regarding Parasitosis and Associated Suicide Behavior

The death by suicide of Gary J. Shipley’s close friend, Conrad Unger (writer, theorist and amateur entomologist), has prompted him to confront not only the cold machinery of self-erasure, but also its connections to the literary life and notions surrounding psychological bewitchment, to revaluate in both fictional and entomological terms just what it is that drives writers like Unger to take their own lives as a matter of course, as if that end had been there all along, knowing, waiting. Like Gérard de Nerval, David Foster Wallace, Ann Quin and Virginia Woolf before him, Unger was not merely a writer who chose to end his life, but a writer whose work appeared forged from the knowledge of that event’s temporary postponement. And while to the uninitiated these literary suicides would most likely appear completely unrelated to the suicide behaviors of insects parasitized by entomopathogenic fungi or nematomorpha, within the pages of this short study we are frequently presented with details that allow us to see the parallels between their terminal choreographies. He investigates what he believes are the essentially binary and contradictory motivations of his suicide case studies: where their self-dispatch becomes an instance of necro-autonomy (death as solution to an external thraldom, or the zombification of everyday life as something requiring the most extreme form of emancipation), while in addition being an instance of necro-equipoise (death as solution to an internal thraldom, or the anguish of no longer being able to slip back comfortably inside that very everydayness). The deadening claustrophobia of human life and achieving a stance outside of it: both barbs on the lines that can only ever detail the sickness, never cure it. Through extracts and synopses of Unger’s books, marginalia and underscorings selected from his extensive library, and a brief itinerary of his movements in that last month of exile, a picture of the writer’s suicidal obsession begins to form, and it forms at the expense of the man, the idea eating through his brain like a fungal parasite, disinterring the waking corpse to flesh its words