Study of radar pulse compression for high resolution satellite altimetry

Pulse compression techniques are studied which are applicable to a satellite altimeter having a topographic resolution of + 10 cm. A systematic design procedure is used to determine the system parameters. The performance of an optimum, maximum likelihood processor is analysed, which provides the basis for modifying the standard split-gate tracker to achieve improved performance. Bandwidth considerations lead to the recommendation of a full deramp STRETCH pulse compression technique followed by an analog filter bank to separate range returns. The implementation of the recommended technique is examined

Thermal testing by internal IR heating of the FEP module

A spacecraft module, to be integrated with the FLTSATCOM spacecraft, was tested in a simulated orbit environment separate from the host spacecraft. Thermal vacuum testing of the module was accomplished using internal IR heating rather than conventional external heat sources. For this configuration, the technique produced boundary conditions expected for flight to enable verification of system performance and thermal design details

Powers of sets in free groups

We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best possible for each n>0.Comment: 3 page

An evaluation of guided reading in three primary schools in the Western Cape

CITATION: Kruizinga, A. & Nathanson, R. R. 2010. An evaluation of guided reading in three primary schools in the Western Cape. Per Linguam : a Journal of Language Learning, 26(2): 67-76, doi: http://dx.doi.org/10.5785/26-2-22.The original publication is available at http://perlinguam.journals.ac.zaGiven that the South African government intends to improve its literacy rates by implementing Guided Reading in the primary schools, teachers are challenged to give good quality Guided Reading instruction. The study which this article draws on evaluates how teachers understand and implement Guided Reading in Grade 1 and 2 at three public schools in the Western Cape. Data were drawn from observations of teachers using Fountas & Pinnell’s Guided Reading instruction and a Guided Reading Self-Assessment Inventory. Analyses of the above-mentioned quantitative and qualitative research data indicate that South African teachers have a superficial understanding of Guided Reading. The study suggests that South African teachers struggle to implement Guided Reading in the classroom, because they do not create Guided Reading groups based on ongoing assessment and the teachers do not have access to levelled Guided Reading books. Furthermore, the new policy requirements for Guided Reading appear to fail to offer teachers a sufficient explanation of Guided Reading. I argue that, without addressing these basic requirements, it is unlikely that Guided Reading will be implemented with any success in the South African classrooms.http://perlinguam.journals.ac.za/pub/article/view/22Publisher's versio

Performance prediction and analysis of the lunar heat flow probes

This report describes the mathematical modeling of the thermal behavior of the heat flow probes and surrounding medium. The computer models developed simulate the thermal performance of the conductivity experiments and will aid in the interpretation of lunar data.Under Subcontract No. 8 of Prime Contract No. NAS 9-6037 with Columbia Universityby D. Nathanson and R. Merriam.Introduction -- Brief review of Heat Flow Experiment -- Description of thermal models -- Evaluation of computer mathematical models -- Predicted performance in the lunar environment -- Conclusions and recommendations -- Appendice

Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

SIC-POVMs and the Extended Clifford Group

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the generalized Pauli group). We then investigate the action of the extended Clifford group operators on symmetric informationally complete POVMs (or SIC-POVMs) covariant relative to the action of the generalized Pauli group. We show that each of the fiducial vectors which has been constructed so far (including all the vectors constructed numerically by Renes et al) is an eigenvector of one of a special class of order 3 Clifford unitaries. This suggests a strengthening of a conjuecture of Zauner's. We give a complete characterization of the orbits and stability groups in dimensions 2-7. Finally, we show that the problem of constructing fiducial vectors may be expected to simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We illustrate this point by constructing exact expressions for fiducial vectors in dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's original conjecture, and an alternative, possibly stronger version of the conjecture in version 1 of this paper; also a few other minor improvement

Sums of products of Ramanujan sums

The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1,..., g_r$ are polynomials with integer coefficients. A modified orthogonality relation of the Ramanujan sums is also derived.Comment: 13 pages, revise

Number theoretic example of scale-free topology inducing self-organized criticality

In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres