Retelling the Future: Don Juan Manuel's "Exenplo XI" and the Power of Fiction

In this paper I look at how “Exenplo XI” is both product and reflection of the various traditions and cultures of medieval Iberia and how Juan Manuel forges a new version of this story from these inherited traditions in order to showcase problems of concern to his fourteenth-century audience, namely, the tension between ecclesiastical and Andalusi systems of thought and their representatives and how the author’s manipulation of the frame and the power of fiction itself echoes Don Yllán’s manipulation of magic to test the dean’s mettle. Then I turn to the lessons of “Exenplo XI” regarding the transmission of knowledge and who controls it, as well as the function of speculative fiction and its ability to explore alternative realities and potential futures for both fictional audience (Conde Lucanor) and contemporary twenty-first-century readers

Monotone Volume Formulas for Geometric Flows

We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latter being non-decreasing along the flow. In the case where S=Ric is the Ricci curvature of M, the result corresponds to Perelman's well-known reduced volume monotonicity for the Ricci flow. Some other examples are given in the second section of this article, the main examples and motivation for this work being List's extended Ricci flow system, the Ricci flow coupled with harmonic map heat flow and the mean curvature flow in Lorentzian manifolds with nonnegative sectional curvatures. With our approach, we find new monotonicity formulas for these flows.Comment: v2: final version (as published

A discussion of higher order software concepts as they apply to functional requirements and specifications

The entry guidance software functional requirements (requirements design phase), its architectural requirements (specifications design phase), and the entry guidance software verified code are discussed. It was found that the proper integration of designs at both the requirements and specifications levels are of high priority consideration

Iterated fibre sums of algebraic Lefschetz fibrations

Let M denote the total space of a Lefschetz fibration, obtained by blowing up a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum M(n), generalizing the construction of the elliptic surfaces E(n). For a Lefschetz pencil on a simply-connected minimal surface of general type we partially calculate the Seiberg-Witten invariants of the fibre sum M(n) using a formula of Morgan-Szabo-Taubes. As an application we derive an obstruction for self-diffeomorphisms of the boundary of the tubular neighbourhood of a general fibre in M(n) to extend over the complement of the neighbourhood. Similar obstructions are known in the case of elliptic surfaces.Comment: 14 pages; to appear in Quart. J. Mat

Towards a better understanding of the low income consumer

Research on low-income or poorer consumers and the disadvantages that they encounter in the marketplace is the focus of this paper. A number of commonly held beliefs about low-income consumers need to be challenged but since these consumers are not high priority as target markets there is little investment in the market research that might go some way to dispel them. This paper aims to challenge some of these beliefs and to suggest how this research might be further developed by drawing together research and theories from a range of disciplines including consumer research, psychology and sociological constructs

Representing homology classes by symplectic surfaces

We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.Comment: 5 page

Cyclic group actions and embedded spheres in 4-manifolds

In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is given by one half of the Euler characteristic of the 4-manifold. The result also shows that in some cases the 4-manifold does not admit such actions of a certain order at all or that any such action has to be pseudofree.Comment: 13 pages; to appear in Proc. Amer. Math. So