On Axonometric Projection of the Contour of a Sphere

Ovaj se članak bavi pitanjem koje se javlja u nastavi nacrtne geometrije za studente preddiplomskog studija u području geodezije i kartografije: Ako se aksonometrijska slika konture kugle konstruira pomoću metode presjeka (L. Eckhart, 1937), tada parovi konturnih točaka, promatranih s obzirom na smjerove presjeka dviju nepridruženih pomoćnih projekcija, određuju općenito dva nekonjugirana promjera konturne elipse i njima konjugirane smjerove. Obratno, elipsa je općenito određena s dva zadana promjera i njima konjugiranim smjerovima. Promatra li se konstrukcija konturne elipse s ravninskog aspekta, iz ovog se načina konstrukcije može izvesti Pascalov teorem.The present article refers to a question that arose during the lecture of descriptive geometry for undergraduate students in the fields of geodesy and cartography: If the axonometric projection of the contour of a sphere is constructed with the help of the cutting method (L. Eckhart, 1937), the pairs of contour points with regard to the cutting directions of two non-associated auxiliary projections determine two in general non conjugate diameters and their conjugate directions of the ellipse of contour. Conversely an ellipse is in general overdetermined by two given diameters and their conjugate directions. The theorem of Pascal can be deduced from the figure of construction whereby the construction of the ellipse of contour is considered from a planar point of view

Zur Differentialgeometrie zweiparametriger Geradenmengen im KLEINschen Modell

In der vorliegenden Arbeit werden Geradenkongruenzen des projektiv abgeschlossenen dreidimensionalen euklidischen Raumes differentialgeometrisch untersucht. Nach J. PLÜCKER lassen sich Geraden in gleicher Weise als Grundelemente eines Geradenraumes auffassen wie die Punkte in einem Punktraum. Unter Beachtung dieser Überlegung scheint eine "natürliche" Behandlung der Geradenkongruenzen interessant und sinnvoll. Sie bildet den Gegenstand der vorliegenden Dissertation. Ein besonderes Augenmerk richtet sich dabei auf die Frage nach "kleinsten" Geradenkongruenzen ("Minimalkongruenzen") in der Geradenmenge des reellen projektiv abgeschlossenen dreidimensionalen euklidischen Raumes. Dahinter verbirgt sich eine gewisse Analogiebildung in der Liniengeometrie, die der klassischen Differentialgeometrie entstammt. Die Geradenkongruenzen bilden hierbei das liniengeometrische Analogon zu den Flächen des dreidimensionalen (Punkt-)Raumes. Das Wort "Kleinste" stellt im Geradenraum einen Bezug zu den Minimalflächen in der Differentialgeometrie her. Nun gestatten diese Fragestellungen in der Liniengeometrie eine anschauliche Interpretation, sobald man ein Punktmodell des Geradenraumes vorliegen hat. Einparametrige Geradenmannigfaltigkeiten (Regelflächen) lassen sich darin als Kurven und Geradenkongruenzen als zweidimensionale Flächen auffassen. Die vierparametrige Geradenmenge des reellen projektiven dreidimensionalen Raumes ist in diesem Modell eine Quadrik vom Index 2 in einem reellen projektiven fünfdimensionalen Raum, die so genannte KLEINsche Hyperquadrik. Der Modellwechsel wird durch die KLEINsche Abbildung vollzogen.In the available work line congruences of the projectively extended three-dimensional euclidean space will be analysed. Following to J. PLÜCKER lines can be seen as basic elements of an line space like in the same way points in a point-space. Taking this fact in consideration a "natural" handling with line congruences might be interesting and reasonable. A special detail in the thesis is the question to minimal congruences in the set of lines of the projectively extended euclidean three-space. It can also be seen as an analogous problem in the geometry of lines which can be find in the differential geometry of surfaces. In this case the line congruences are similar to the surfaces of the three-dimensional (point-)space. The phrase "minimal" means in the line space the connection to the minimal surfaces in the differential geometry. These questions offer in line geometry demonstrative interpretation possibilities if a point-model in the line space exists. One-parameter manifolds of lines (rule surfaces) can be seen in this ambiance as curves and line congruences as two dimensional surfaces. The four-parametric set of lines in the projectively extended three-dimensional euclidian space is in this model a quadric of the index 2 in a real projective five-dimensional space, the so called KLEIN-quadric. The changing of the model is managed by the KLEIN-mapping

On Axonometric Projection of the Contour of a Sphere

Ovaj se članak bavi pitanjem koje se javlja u nastavi nacrtne geometrije za studente preddiplomskog studija u području geodezije i kartografije: Ako se aksonometrijska slika konture kugle konstruira pomoću metode presjeka (L. Eckhart, 1937), tada parovi konturnih točaka, promatranih s obzirom na smjerove presjeka dviju nepridruženih pomoćnih projekcija, određuju općenito dva nekonjugirana promjera konturne elipse i njima konjugirane smjerove. Obratno, elipsa je općenito određena s dva zadana promjera i njima konjugiranim smjerovima. Promatra li se konstrukcija konturne elipse s ravninskog aspekta, iz ovog se načina konstrukcije može izvesti Pascalov teorem.The present article refers to a question that arose during the lecture of descriptive geometry for undergraduate students in the fields of geodesy and cartography: If the axonometric projection of the contour of a sphere is constructed with the help of the cutting method (L. Eckhart, 1937), the pairs of contour points with regard to the cutting directions of two non-associated auxiliary projections determine two in general non conjugate diameters and their conjugate directions of the ellipse of contour. Conversely an ellipse is in general overdetermined by two given diameters and their conjugate directions. The theorem of Pascal can be deduced from the figure of construction whereby the construction of the ellipse of contour is considered from a planar point of view

On Axonometric Projection of the Contour of a Sphere

Ovaj se članak bavi pitanjem koje se javlja u nastavi nacrtne geometrije za studente preddiplomskog studija u području geodezije i kartografije: Ako se aksonometrijska slika konture kugle konstruira pomoću metode presjeka (L. Eckhart, 1937), tada parovi konturnih točaka, promatranih s obzirom na smjerove presjeka dviju nepridruženih pomoćnih projekcija, određuju općenito dva nekonjugirana promjera konturne elipse i njima konjugirane smjerove. Obratno, elipsa je općenito određena s dva zadana promjera i njima konjugiranim smjerovima. Promatra li se konstrukcija konturne elipse s ravninskog aspekta, iz ovog se načina konstrukcije može izvesti Pascalov teorem.The present article refers to a question that arose during the lecture of descriptive geometry for undergraduate students in the fields of geodesy and cartography: If the axonometric projection of the contour of a sphere is constructed with the help of the cutting method (L. Eckhart, 1937), the pairs of contour points with regard to the cutting directions of two non-associated auxiliary projections determine two in general non conjugate diameters and their conjugate directions of the ellipse of contour. Conversely an ellipse is in general overdetermined by two given diameters and their conjugate directions. The theorem of Pascal can be deduced from the figure of construction whereby the construction of the ellipse of contour is considered from a planar point of view

Are planetary nebulae derived from multiple evolutionary scenarios?

Our understanding of planetary nebulae has been significantly enhanced as a result of several recent large surveys (Parker et al., these proceedings). These new discoveries suggest that the `PN phenomenon' is in fact more heterogeneous than previously envisaged. Even after the careful elimination of mimics from Galactic PN catalogues, there remains a surprising diversity in the population of PNe and especially their central stars. Indeed, several evolutionary scenarios are implicated in the formation of objects presently catalogued as PNe. We provide a summary of these evolutionary pathways and give examples of each. Eventually, a full census of local PNe can be used to confront both stellar evolution theory and population synthesis models.Comment: 4 pages, 1 figure. To be published in Planetary Nebulae: an Eye to the Future, Proceedings of IAU Symposium 283, held in Puerto de la Cruz, Tenerife, Spain, July 25-29 201

Expression of the Inhibitory CD200 Receptor Is Associated with Alternative Macrophage Activation

Classical macrophage activation is inhibited by the CD200 receptor (CD200R). Here, we show that CD200R expression was specifically induced on human in vitro polarized macrophages of the alternatively activated M2a subtype, generated by incubation with IL-4 or IL-13. In mice, peritoneal M2 macrophages, elicited during infection with the parasites Taenia crassiceps or Tryponosoma brucei brucei, expressed increased CD200R levels compared to those derived from uninfected mice. However, in vitro stimulation of mouse peritoneal macrophages and T crassiceps infection in IL-4-/- and IL-4R-/- mice showed that, in contrast to humans, induction of CD200R in mice was not IL-4 or IL-13 dependent. Our data identify CD200R as a suitable marker for alternatively activated macrophages in humans and corroborate observations of distinct species- and/or site-specific mechanisms regulating macrophage polarization in mouse and man. Copyright (C) 2009 S. Karger AG, Base

Higgs-Dilaton cosmology: Are there extra relativistic species?

Recent analyses of cosmological data suggest the presence of an extra relativistic component beyond the Standard Model content. The Higgs-Dilaton cosmological model predicts the existence of a massless particle -the dilaton- associated with the spontaneous symmetry breaking of scale invariance and undetectable by any accelerator experiment. Its ultrarelativistic character makes it a suitable candidate for contributing to the effective number of light degrees of freedom in the Universe. In this Letter we analyze the dilaton production at the (p)reheating stage right after inflation and conclude that no extra relativistic degrees of freedom beyond those already present in the Standard Model are expected within the simplest Higgs-Dilaton scenario. The elusive dilaton remains thus essentially undetectable by any particle physics experiment or cosmological observation.Comment: 7 pages, 1 figure, corrected typos; added reference

Comprehensive modelling of the planetary nebula LMC-SMP 61 and its [WC]-type central star

We present a comprehensive study of the Magellanic Cloud planetary nebula SMP 61 and of its nucleus, a Wolf-Rayet type star classified [WC 5-6]. We have performed a detailed spectral analysis of the central star, using the Potsdam code for expanding atmospheres in non-LTE. The fluxes from the model stellar atmosphere were used to compute photoionization models of the nebula. All the available observations, within their error bars, were used to constrain these models. We find that the ionizing fluxes predicted by the stellar model are basically consistent with the fluxes needed by the photoionization model to reproduce the nebular emission, within the error margins. However, there are indications that the stellar model overestimates the number and hardness of Lyman continuum photons. The photoionization models imply a clumped density structure of the nebular material. The observed CIII] 1909/CII 4267 line ratio implies the existence of carbon-rich clumps in the nebula. Such clumps are likely produced by stellar wind ejecta, possibly mixed with the nebular material. We discuss our results with regard to the stellar and nebular post-AGB evolution.Comment: 16 pages, 10 figures, Astronomy and Astrophysics in pres

Wind clumping and the wind-wind collision zone in the Wolf-Rayet binary gamma Velorum

We present XMM-Newton observations of gamma^2 Velorum (WR 11, WC8+O7.5III, P = 78.53 d), a nearby Wolf-Ray binary system, at its X-ray high and low states. At high state, emission from a hot collisional plasma dominates from about 1 to 8 keV. At low state, photons between 1 and 4 keV are absorbed. The hot plasma is identified with the shock zone between the winds of the primary Wolf-Rayet star and the secondary O giant. The absorption at low state is interpreted as photoelectric absorption in the Wolf-Rayet wind. This absorption allows us to measure the absorbing column density and to derive a mass loss rate 8x10^{-6} M_sun/yr for the WC8 star. This mass loss rate, in conjunction with a previous Wolf-Rayet wind model, provides evidence for a clumped WR wind. A clumping factor of 16 is required. The X-ray spectra below 1 keV (12 Ang) show no absorption and are essentially similar in both states. There is a rather clear separation in that emission from a plasma hotter than 5 MK is heavily absorbed in low state while the cooler plasma is not. This cool plasma must come from a much more extended region than the hot material. The Neon abundance in the X-ray emitting material is 2.5 times the solar value. The unexpected detection of CV (25.3 Ang) and CVI (31.6 Ang) radiative recombination continua at both phases indicates the presence of a cool (~40,000 K) recombination region located far out in the binary system.Comment: 16 page

AI-based detection of contrast-enhancing MRI lesions in patients with multiple sclerosis.

BACKGROUND Contrast-enhancing (CE) lesions are an important finding on brain magnetic resonance imaging (MRI) in patients with multiple sclerosis (MS) but can be missed easily. Automated solutions for reliable CE lesion detection are emerging; however, independent validation of artificial intelligence (AI) tools in the clinical routine is still rare. METHODS A three-dimensional convolutional neural network for CE lesion segmentation was trained externally on 1488 datasets of 934 MS patients from 81 scanners using concatenated information from FLAIR and T1-weighted post-contrast imaging. This externally trained model was tested on an independent dataset comprising 504 T1-weighted post-contrast and FLAIR image datasets of MS patients from clinical routine. Two neuroradiologists (R1, R2) labeled CE lesions for gold standard definition in the clinical test dataset. The algorithmic output was evaluated on both patient- and lesion-level. RESULTS On a patient-level, recall, specificity, precision, and accuracy of the AI tool to predict patients with CE lesions were 0.75, 0.99, 0.91, and 0.96. The agreement between the AI tool and both readers was within the range of inter-rater agreement (Cohen's kappa; AI vs. R1: 0.69; AI vs. R2: 0.76; R1 vs. R2: 0.76). On a lesion-level, false negative lesions were predominately found in infratentorial location, significantly smaller, and at lower contrast than true positive lesions (p < 0.05). CONCLUSIONS AI-based identification of CE lesions on brain MRI is feasible, approaching human reader performance in independent clinical data and might be of help as a second reader in the neuroradiological assessment of active inflammation in MS patients. CRITICAL RELEVANCE STATEMENT Al-based detection of contrast-enhancing multiple sclerosis lesions approaches human reader performance, but careful visual inspection is still needed, especially for infratentorial, small and low-contrast lesions