Noose or Lifeline? The Role of Transport in Independent Namibia

INTRODUCTION As the struggle to end apartheid in South Africa intensifies, attention has increasingly been distracted fran the vexed issue of Namibian independence. All parties to the dispute have agreed for at least eight years on the desirability of independence for Africa's last colony, but attainment of that goal has been continually frustrated by South Africa; through the introduction of new obstacles. The current deadlock is over Pretoria's insistence that independence be linked to the withdrawal of Cuban troops from Angola. Meanwhile, yet another interim government has been appointed in Windhoek, onto which South Africa is making a sustained attempt to confer legitimacy as oppsition to SWAPO. (Continues..

Pulsar Braking Indices Revisited

Using the standard equation for the slowdown of a neutron star, we derive a formula for the braking index via integration rather than the conventional differentiation. The new formula negates the need to measure the second time derivative of the rotation frequency. We show that the method gives similar braking indices for PSR B1509-58 and the Crab pulsar to those already in the literature. We point out that our method is useful for obtaining the braking indices of moderate aged pulsars without the need for long, phase-connected timing solutions. We applied the method to 20 pulsars and discuss the implications of the results. We find that virtually all the derived braking indices are dominated by the effects of (unseen) glitches, the recovery from which corrupts the value of the frequency first derivative. However, any real, large, positive braking index has implications for magnetic field decay and offers support to recent models of pulsar evolution.Comment: 5 pages, 2 figures, 1 table, accepted by MNRA

Switch access to technology - A comprehensive Guide.

When most of us use a computer we use the standard interface of a keyboard and mouse. However, what do you do if you cannot use a keyboard or mouse? A number of alternative access systems exist, for example: alternative keyboards, tracker balls, touchscreens, head pointers etc. But for some people these devices are also an impossibility, and this is where switches 'kick in'. The main subject of this document is the switch user. For completeness we have include a brief mention of other input devices, which may be grouped together as 'alternative access systems'.We aim to: - Encourage developers to include switch access into their products - Standardise practice and terminology. This document explains some of the issues involved for people with severe physical difficulties who access computers and other electronic devices with switches. It details the ways in which switch users interact with computer programs and other technology designed to be directly accessible to them. The document includes some precise definitions of terms. It also attempts to survey the whole range of issues associated with switch use. As such it should be useful to professionals working or entering the field, those software developers considering switch users for the first time and also for those already developing in this area

Jost Functions and Jost Solutions for Jacobi Matrices, II. Decay and Analyticity

We present necessary and sufficient conditions on the Jost function for the corresponding Jacobi parameters $a_n -1$ and $b_n$ to have a given degree of exponential decay.Comment: 28 page

From Jack polynomials to minimal model spectra

In this note, a deep connection between free field realisations of conformal field theories and symmetric polynomials is presented. We give a brief introduction into the necessary prerequisites of both free field realisations and symmetric polynomials, in particular Jack symmetric polynomials. Then we combine these two fields to classify the irreducible representations of the minimal model vertex operator algebras as an illuminating example of the power of these methods. While these results on the representation theory of the minimal models are all known, this note exploits the full power of Jack polynomials to present significant simplifications of the original proofs in the literature.Comment: 14 pages, corrected typos and added comment on connections to the AGT conjecture in introduction, version to appear in J. Phys.

Lifting flat directions in lattice supersymmetry

We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the exact lattice supersymmetry. The basic idea is to modify the equations of motion of an auxiliary field, which determine the moduli space of the system. Applied to numerical calculations, the resulting improved lattice action leads to dramatically reduced violations of supersymmetric Ward identities and much more rapid approach to the continuum limit

Modular Transformations and Verlinde Formulae for Logarithmic (p+,p−)(p_+,p_-)-Models

The $(p_+,p_-)$ singlet algebra is a vertex operator algebra that is strongly generated by a Virasoro field of central charge $1-6(p_+-p_-)^2/p_+p_-$ and a single Virasoro primary field of conformal weight $(2p_+-1)(2p_--1)$. Here, the modular properties of the characters of the uncountably many simple modules of each singlet algebra are investigated and the results used as the input to a continuous analogue of the Verlinde formula to obtain the "fusion rules" of the singlet modules. The effect of the failure of fusion to be exact in general is studied at the level of Verlinde products and the rules derived are lifted to the $(p_+,p_-)$ triplet algebras by regarding these algebras as simple current extensions of their singlet cousins. The result is a relatively effortless derivation of the triplet "fusion rules" that agrees with those previously proposed in the literature.Comment: 22 pages, v2 minor changes; added ref

Stone-Type Dualities for Separation Logics

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar BI and Boolean BI (BBI), and extending to both classical and intuitionistic Separation Logic. We demonstrate the uniformity and modularity of this analysis by additionally capturing the bunched logics obtained by extending BI and BBI with modalities and multiplicative connectives corresponding to disjunction, negation and falsum. This includes the logic of separating modalities (LSM), De Morgan BI (DMBI), Classical BI (CBI), and the sub-classical family of logics extending Bi-intuitionistic (B)BI (Bi(B)BI). We additionally obtain as corollaries soundness and completeness theorems for the specific Kripke-style models of these logics as presented in the literature: for DMBI, the sub-classical logics extending BiBI and a new bunched logic, Concurrent Kleene BI (connecting our work to Concurrent Separation Logic), this is the first time soundness and completeness theorems have been proved. We thus obtain a comprehensive semantic account of the multiplicative variants of all standard propositional connectives in the bunched logic setting. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualizes the "resource semantics" interpretation underpinning Separation Logic amongst them