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

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

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

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

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

Cryptic photosynthesis, Extrasolar planetary oxygen without a surface biological signature

On the Earth, photosynthetic organisms are responsible for the production of virtually all of the oxygen in the atmosphere. On the land, vegetation reflects in the visible, leading to a red edge that developed about 450 Myr ago and has been proposed as a biosignature for life on extrasolar planets. However, in many regions of the Earth, and particularly where surface conditions are extreme, for example in hot and cold deserts, photosynthetic organisms can be driven into and under substrates where light is still sufficient for photosynthesis. These communities exhibit no detectable surface spectral signature to indicate life. The same is true of the assemblages of photosynthetic organisms at more than a few metres depth in water bodies. These communities are widespread and dominate local photosynthetic productivity. We review known cryptic photosynthetic communities and their productivity. We link geomicrobiology with observational astronomy by calculating the disk-averaged spectra of cryptic habitats and identifying detectable features on an exoplanet dominated by such a biota. The hypothetical cryptic photosynthesis worlds discussed here are Earth-analogs that show detectable atmospheric biomarkers like our own planet, but do not exhibit a discernable biological surface feature in the disc-averaged spectrum.Comment: 23 pages, 2 figures, Astrobiology (TBP) - updated Table 1, typo in detectable O2 correcte

Restricted three body problems at the nanoscale

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C60 fullerenes at the nanoscale. We find that the maximum angular frequency of the two and three fullerenes systems reach the terahertz range and we determine the stationary points and the points which have maximum velocity for the carbon atom for the carbon atom and the two fullerenes system

Detection of Gravitational Redshift on the Solar Disk by Using Iodine-Cell Technique

With an aim to examine whether the predicted solar gravitational redshift can be observationally confirmed under the influence of the convective Doppler shift due to granular motions, we attempted measuring the absolute spectral line-shifts on a large number of points over the solar disk based on an extensive set of 5188-5212A region spectra taken through an iodine-cell with the Solar Domeless Telescope at Hida Observatory. The resulting heliocentric line shifts at the meridian line (where no rotational shift exists), which were derived by finding the best-fit parameterized model spectrum with the observed spectrum and corrected for the earth's motion, turned out to be weakly position-dependent as ~ +400 m/s near the disk center and increasing toward the limb up to ~ +600 m/s (both with a standard deviation of sigma ~ 100 m/s). Interestingly, this trend tends to disappear when the convectiveshift due to granular motions (~-300 m/s at the disk center and increasing toward the limb; simulated based on the two-component model along with the empirical center-to-limb variation) is subtracted, finally resulting in the averaged shift of 698 m/s (sigma = 113 m/s). Considering the ambiguities involved in the absolute wavelength calibration or in the correction due to convective Doppler shifts (at least several tens m/s, or more likely up to <~100 m/s), we may regard that this value is well consistent with the expected gravitational redshift of 633 m/s.Comment: 28 pages, 12 figures, electronic materials as ancillary data (table3, table 4, ReadMe); accepted for publication in Solar Physic