Conchoidal transform of two plane curves

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in \PP^2 \times \PP^2. We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve $C$ we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.Comment: 18 pages Revised version: slight title change, improved exposition, fixed proof of Theorem 5.3 Accepted for publication in Appl. Algebra Eng., Commun. Comput

Ultramafic xenoliths from the Bearpaw Mountains, Montana, USA: evidence for multiple metasomatic events in the lithospheric mantle beneath the Wyoming craton

Ultramafic xenoliths in Eocene minettes of the Bearpaw Mountains volcanic field (Montana, USA), derived from the lower lithosphere of the Wyoming craton, can be divided based on textural criteria into tectonite and cumulate groups. The tectonites consist of strongly depleted spinel lherzolites, harzburgites and dunites. Although their mineralogical compositions are generally similar to those of spinel peridotites in off-craton settings, some contain pyroxenes and spinels that have unusually low Al2O3 contents more akin to those found in cratonic spinel peridotites. Furthermore, the tectonite peridotites have whole-rock major element compositions that tend to be significantly more depleted than non-cratonic mantle spinel peridotites (high MgO, low CaO, Al2O3 and TiO2) and resemble those of cratonic mantle. These compositions could have been generated by up to 30% partial melting of an undepleted mantle source. Petrographic evidence suggests that the mantle beneath the Wyoming craton was re-enriched in three ways: (1) by silicate melts that formed mica websterite and clinopyroxenite veins; (2) by growth of phlogopite from K-rich hydrous fluids; (3) by interaction with aqueous fluids to form orthopyroxene porphyroblasts and orthopyroxenite veins. In contrast to their depleted major element compositions, the tectonite peridotites are mostly light rare earth element (LREE)-enriched and show enrichment in fluid-mobile elements such as Cs, Rb, U and Pb on mantle-normalized diagrams. Lack of enrichment in high field strength elements (HFSE; e.g. Nb, Ta, Zr and Hf) suggests that the tectonite peridotites have been metasomatized by a subduction-related fluid. Clinopyroxenes from the tectonite peridotites have distinct U-shaped REE patterns with strong LREE enrichment. They have 143Nd/144Nd values that range from 0·5121 (close to the host minette values) to 0·5107, similar to those of xenoliths from the nearby Highwood Mountains. Foliated mica websterites also have low 143Nd/144Nd values (0·5113) and extremely high 87Sr/86Sr ratios in their constituent phlogopite, indicating an ancient (probably mid-Proterozoic) enrichment. This enriched mantle lithosphere later contributed to the formation of the high-K Eocene host magmas. The cumulate group ranges from clinopyroxene-rich mica peridotites (including abundant mica wehrlites) to mica clinopyroxenites. Most contain >30% phlogopite. Their mineral compositions are similar to those of phenocrysts in the host minettes. Their whole-rock compositions are generally poorer in MgO but richer in incompatible trace elements than those of the tectonite peridotites. Whole-rock trace element patterns are enriched in large ion lithophile elements (LILE; Rb, Cs, U and Pb) and depleted in HFSE (Nb, Ta Zr and Hf) as in the host minettes, and their Sr–Nd isotopic compositions are also identical to those of the minettes. Their clinopyroxenes are LREE-enriched and formed in equilibrium with a LREE-enriched melt closely resembling the minettes. The cumulates therefore represent a much younger magmatic event, related to crystallization at mantle depths of minette magmas in Eocene times, that caused further metasomatic enrichment of the lithosphere

Shaping a Corporate Identity From Below; the Role of the BAT Bulletin.

Existing studies that have explored the use of company journals as a mode of corporate communication during the early 20th century have invariably adopted an instrumentalist view of these publications. Company journals have been seen as a means of projecting to employees a top-down view of organisations. This article identifies a counter-example in which the origins of a company journal, the 'Bat Bulletin', are seen to arise as the result of an initiative stemming from the employees themselves. These antecedents gave the 'Bat Bulletin' a high degree of legitimacy amongst staff and provided the company with an important means of establishing a unified corporate culture across a disparate group international operating companies. Over time, however, the contents of the journal gradually became more conventional, and it was eventually closed down when the strategy of international integration ceased to be a desirable corporate objective during the 1930's

Tests of Gaussianity

We review two powerful methods to test the Gaussianity of the cosmic microwave background (CMB): one based on the distribution of spherical wavelet coefficients and the other on smooth tests of goodness-of-fit. The spherical wavelet families proposed to analyse the CMB are the Haar and the Mexican Hat ones. The latter is preferred for detecting non-Gaussian homogeneous and isotropic primordial models containing some amount of skewness or kurtosis. Smooth tests of goodness-of-fit have recently been introduced in the field showing some interesting properties. We will discuss the smooth tests of goodness-of-fit developed by Rayner and Best for the univariate as well as for the multivariate analysis.Comment: Proceedings of "The Cosmic Microwave Background and its Polarization", New Astronomy Reviews, (eds. S. Hanany and K.A. Olive), in pres

Searching for Radio Pulsars in 3EG Sources at Urumqi Observatory

Since mid-2005, a pulsar searching system has been operating at 18 cm on the 25-m radio telescope of Urumqi Observatory. Test observations on known pulsars show that the system can perform the intended task. The prospect of using this system to observe 3EG sources and other target searching tasks is discussed.Comment: a training project about MSc thesi

Goodness-of-fit tests of Gaussianity: constraints on the cumulants of the MAXIMA data

In this work, goodness-of-fit tests are adapted and applied to CMB maps to detect possible non-Gaussianity. We use Shapiro-Francia test and two Smooth goodness-of-fit tests: one developed by Rayner and Best and another one developed by Thomas and Pierce. The Smooth tests test small and smooth deviations of a prefixed probability function (in our case this is the univariate Gaussian). Also, the Rayner and Best test informs us of the kind of non-Gaussianity we have: excess of skewness, of kurtosis, and so on. These tests are optimal when the data are independent. We simulate and analyse non-Gaussian signals in order to study the power of these tests. These non-Gaussian simulations are constructed using the Edgeworth expansion, and assuming pixel-to-pixel independence. As an application, we test the Gaussianity of the MAXIMA data. Results indicate that the MAXIMA data are compatible with Gaussianity. Finally, the values of the skewness and kurtosis of MAXIMA data are constrained by |S| \le 0.035 and |K| \le 0.036 at the 99% confidence level.Comment: New Astronomy Reviews, in pres

Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

The influence of fibre length, diameter and concentration on the strength and strain to failure of glass fibre-reinforced polyamide 6,6

Results of an investigation of the mechanical performance of injection moulded long glass fibre-reinforced polyamide 6,6 composites are presented. The glass fibre content in these composites was varied over the range 10-50% by weight using fibres with average diameters of 10, 14, and 17 μm. Mechanical testing and analysis of the apparent interfacial shear strength was carried out at 23 and 150 °C on dry-as-moulded and boiling water conditioned samples. The results from these composites are compared with standard extrusion compounded short glass fibre materials. The influence of fibre diameter and concentration on the residual fibre length, fibre orientation distribution and composite strength and elongation to failure is presented and discussed in comparison to the predictions of some of the available micromechanical models

Plasma Turbulence in the Local Bubble

Turbulence in the Local Bubble could play an important role in the thermodynamics of the gas that is there. The best astronomical technique for measuring turbulence in astrophysical plasmas is radio scintillation. Measurements of the level of scattering to the nearby pulsar B0950+08 by Philips and Clegg in 1992 showed a markedly lower value for the line-of-sight averaged turbulent intensity parameter $$than is observed for other pulsars, consistent with radio wave propagation through a highly rarefied plasma. In this paper, we discuss the observational progress that has been made since that time. At present, there are four pulsars (B0950+08, B1133+16, J0437-4715, and B0809+74) whose lines of sight seem to lie mainly within the local bubble. The mean densities and line of sight components of the interstellar magnetic field along these lines of sight are smaller than nominal values for pulsars, but not by as much expected. Three of the four pulsars also have measurements of interstellar scintillation. The value of the parameter$$ is smaller than normal for two of them, but is completely nominal for the third. This inconclusive status of affairs could be improved by measurements and analysis of ``arcs'' in ``secondary spectra'' of pulsars.Comment: Submitted to Space Science Reviews as contribution to Proceedings of ISSI (International Space Science Institute) workshop "From the Heliosphere to the Local Bubble". Refereed version accepted for publicatio

Multibeam Maser Survey of methanol and excited OH in the Magellanic clouds: new detections and maser abundance estimates

‘The definitive version is available at www.blackwell-synergy.com.’ Copyright Blackwell Publishing DOI: 10.1111/j.1365-2966.2008.12888.xPeer reviewe