Introduction (to Dossier on Walter Benjamin and Education)

Although it is well known that Walter Benjamin played a leading role in the antebellum German Youth Movement, withdrawing from the presidency of the Berlin Independent Students Association and from other reformist activities only with the onset of World War I, scholars often do not ask whether this multifaceted student activism had any effect on his later thought and writing. This dossier proposes to investigate the early writings on youth and educational reform and their discernible afterlife in the better known historical-materialist phase of Benjamin’s career, including his writings on radio, film, children’s literature, and children’s theater, as well as his studies of Franz Kafka and Bertolt Brecht. The introduction provides brief summaries of the ten articles comprising the dossier and their relation to one another, and it addresses the question of the relevance of Benjamin’s ideas on education to contemporary debates concerning pedagogy

The real effects of reserve requirements : [Version February 1998]

We review arguments for and against reserve requirements and conclude that the main question is whether a distinction between money creation and intermediation can be made. We argue that such a distinction can be made in a money-in-advance economy and show that if the money-in-advance constraint is universally binding then reserve requirements on checkable accounts have no effect on intermediation. We then proceed to show that in a model in which trade is uncertain and sequential, a fractional reserve banking system gives rise to endogenous monetary shocks. These endogenous monetary shocks lead to fluctuations in capacity utilisation and waste. When the moneyin-advance constraint is universally binding, a 100% reserve requirement on checkable accounts can eliminate this waste

The Blaschke conjecture and great circle fibrations of spheres

We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.Comment: 61 pages, 8 figures, corrected errors in the published versio

Quantum Computing with Globally Controlled Exchange-type Interactions

If the interaction between qubits in a quantum computer has a non-diagonal form (e.g. the Heisenberg interaction), then one must be able to "switch it off" in order to prevent uncontrolled propagation of states. Therefore, such QC schemes typically demand local control of the interaction strength between each pair of neighboring qubits. Here we demonstrate that this degree of control is not necessary: it suffices to switch the interaction collectively - something that can in principle be achieved by global fields rather than with local manipulations. This observation may offer a significant simplification for various solid state, optical lattice and NMR implementations.Comment: 3 pages inc. 3 figure

Pre-images of quadratic dynamical systems

For a quadratic endomorphism of the affine line defined over the rationals we consider the problem of bounding the number of rational points that eventually land at a given constant after iteration, called pre-images of the constant. In the article "Uniform Bounds on Pre-Images Under Quadratic Dynamical Systems," it was shown that the number of rational pre-images is bounded as one varies the morphism in a certain one-dimensional family. Explicit values of the constant for pre-images of zero and -1 defined over the rational numbers were addressed in subsequent articles. This article addresses an explicit bound for any algebraic image constant and provides insight into the geometry of the "pre-image surfaces."Comment: to appear in Involve; 16page

Microwave detection of buried mines using non-contact, synthetic near-field focusing

Existing ground penetrating radars (GPR) are limited in their 3-D resolution. For the detection of buried land-mines, their performance is also seriously restricted by `clutter'. Previous work by the authors has concentrated on removing these limitations by employing multi-static synthetic focusing from a 2-D real aperture. This contribution presents this novel concept, describes the proposed implementation, examines the influence of clutter and of various ground features on the system's performance, and discusses such practicalities as digitisation and time-sharing of a single transmitter and receiver. Experimental results from a variety of scenarios are presented

Quantum Computing in Arrays Coupled by 'Always On' Interactions

It has recently been shown that one can perform quantum computation in a Heisenberg chain in which the interactions are 'always on', provided that one can abruptly tune the Zeeman energies of the individual (pseudo-)spins. Here we provide a more complete analysis of this scheme, including several generalizations. We generalize the interaction to an anisotropic form (incorporating the XY, or Forster, interaction as a limit), providing a proof that a chain coupled in this fashion tends to an effective Ising chain in the limit of far off-resonant spins. We derive the primitive two-qubit gate that results from exploiting abrupt Zeeman tuning with such an interaction. We also demonstrate, via numerical simulation, that the same basic scheme functions in the case of smoothly shifted Zeeman energies. We conclude with some remarks regarding generalisations to two- and three-dimensional arrays.Comment: 16 pages (preprint format) inc. 3 figure