Bootstrapping Analysis, Inferential Statistics and EXCEL

Performing a parametric statistical analysis requires the justification of a number of necessary assumptions. If assumptions are not justified research findings are inaccurate and in question. What happens when assumptions are not or cannot be addressed? When a certain statistic has no known sampling distribution what can a researcher do for statistical inference? Options are available for answering these questions and conducting valid research. This paper provides various numerical approximation techniques that can be used to analyze data and make inferences about populations from samples. The application of confidence intervals to inferential statistics is addressed. The analysis of data that is parametric as well as nonparametric is discussed. Bootstrapping analysis for inferential statistics is shown with the application of the Index Function and the use of macros and the Data Analysis Toolpak on the EXCEL spreadsheet. A variety of interesting observations are described

Parametric Statistics and the General Linear Model

Too many students acquire statistical knowledge and techniques independent of each other. The purpose of this paper is to illustrate the many connections mathematically between parametric statistics and the General Linear Model. With these various connections students will see that parametric statistical analyses are essentially one technique the General Linear Model. Parametric inferential statistics include t-tests of hypothesis, Analysis of Variance (ANOVA), correlation and regression. The ability of analyzing data in a variety of ways and using the General Liner Model (GLM) as a mathematical tool that can be applied for making these inferences are described. This paper shows connections between t-tests, ANOVA’s, correlations, and regression. The capabilities of EXCEL to do mathematics, apply the Data Analysis Toolpak, find p-values for these tests and perform matrix algebra operations are demonstrated. Numerous ways of achieving the same results are displayed

Jak zainteresować uczniów astronomią w szkole podstawowej, gimnazjum i szkole ponadgimnazjalnej?

Publikacja powstała w ramach projektu "Opracowanie i wdrożenie kompleksowego systemu pracy z uczniem zdolnym"Publikacja współfinansowana przez Unię Europejską w ramach Europejskiego Funduszu Społeczneg

The radio and IR counterparts of the ring nebula around HD211564

We report the detection of the radio and infrared counterparts of the ring nebula around the WN3(h) star HD211564 (WR152), located to the southwest of the HII region Sh2132. Using radio continuum data from the Canadian Galactic Plane Survey, we identified the radio counterparts of the two concentric rings, of about 9' and 16' in radius, related to the star. After applying a filling factor f = 0.05-0.12, electron densities and ionized masses are in the range 10-16 cm^-3 and 450-700 Mo, respectively. The analysis of the HI gas emission distribution allowed the identification of 5900 Mo of neutral atomic gas with velocities between -52 and -43 km/s probably linked to the nebula. The region of the nebula is almost free of molecular gas. Only four small clumps were detected, with a total molecular mass of 790 Mo. About 310 Mo are related to a small infrared shell-like source linked to the inner ring, which is also detected in the MSX band A. An IRAS YSO candidate is detected in coincidence with the shell-like IR source. We suggest that the optical nebula and its neutral counterparts originated from the stellar winds from the WR star and its massive progenitor, and are evolving in the envelope of a slowly expanding shell centered at (l,b) = (102 30, -0 50), of about 31 pc in radius. The bubble's energy conversion efficiency is in agreement with recent numerical analysis and with observational results.Comment: 11 pages, 7 figures, accepted in MNRA

A dusty pinwheel nebula around the massive star WR 104

Wolf-Rayet (WR) stars are luminous massive blue stars thought to be immediate precursors to the supernova terminating their brief lives. The existence of dust shells around such stars has been enigmatic since their discovery some 30 years ago; the intense radiation field from the star should be inimical to dust survival. Although dust-creation models, including those involving interacting stellar winds from a companion star, have been put forward, high-resolution observations are required to understand this phenomena. Here we present resolved images of the dust outflow around Wolf-Rayet WR 104, obtained with novel imaging techniques, revealing detail on scales corresponding to about 40 AU at the star. Our maps show that the dust forms a spatially confined stream following precisely a linear (or Archimedian) spiral trajectory. Images taken at two separate epochs show a clear rotation with a period of 220 +/- 30 days. Taken together, these findings prove that a binary star is responsible for the creation of the circumstellar dust, while the spiral plume makes WR 104 the prototype of a new class of circumstellar nebulae unique to interacting wind systems.Comment: 7 pages, 2 figures, Appearing in Nature (1999 April 08

Deposition of chromium nitride coatings from vacuum arc plasma in increased nitrogen pressure

The application of protective coatings on metal materials is the effective way to improve their durability. Chromium nitride coatings are applied mainly on tools due to good resistivity to oxidation compared to other metal nitride coatings and good wear resistance. Some characteristics of the coatings deposited in fixed position in regard of chromium cathode on the samples parallel directed to it and the other arranged opposite in the nitrogen pressure ranged from 0.5 to 3.0 Pa are investigated.Применение защитных покрытий на металлических материалах является эффективным способом улучшения их прочности. Покрытия из нитрида хрома применяются в основном на инструменте благодаря хорошему сопротивлению окислению, по сравнению с другими нитридными покрытиями, и хорошей износостойкости. Были исследованы некоторые характеристики покрытий, осажденных в фиксированном положении на лицевую и обратную стороны образцов, установленных в плоскости, параллельной по отношению к хромовому катоду, в диапазоне давлений азота от 0,5 до 3,0 Па.Застосування захисних покриттів на металевих матеріалах є ефективним способом поліпшення їх міцності. Покриття з нітриду хрому застосовуються в основному на інструменті завдяки гарному опору окисленню, в порівнянні з іншими нітридними покриттями та добрій зносостійкості. Були досліджені деякі характеристики покриттів, осаджених у фіксованому положенні на лицьову і зворотну сторони зразків, встановлених в площині, паралельній по відношенню до хромового катода, в діапазоні тисків азоту від 0,5 до 3,0 Па

Mechanical and tribological characteristics of zirconium based ceramic coatings for micro-bearing application

The application of metal materials with ceramic coatings is the effective way of alternative bearing surfaces formation. The oxide ZrO₂, nitride ZrN and oxynitride ZrON coatings were deposited by magnetron sputtering method on stainless steel (AlSi 316) discs. The adhesion properties, hardness and elastic modulus were evaluated by standard methods. The surface parameters were observed by scanning electron microscopy (SEM). The chemical composition of the coatings was analyzed by energy dispersive X-ray (EDX) spectroscopy. Friction coefficients and wear resistance were measured in the tribological tests. Results show that the mechanical parameters increased in the case of oxynitride in comparison with oxide and nitride coatings.Использование металлических материалов с керамическими покрытиями является эффективным способом формирования альтернативных поверхностей скольжения. Покрытия оксидов ZrO₂, нитридов ZrN и оксинитридов ZrON были нанесены на стальные диски (AlSi 316) методом магнетронного напыления. Адгезия, твердость и упругие модули покрытий измерялись стандартными методами. Параметры поверхности оценивались методом сканирующей электронной микроскопии. Химический состав покрытий анализировался методом энергетически дисперсной спектроскопии. Коэффициент трения и износ оценивали в трибологических тестах. Результаты демонстрируют, что механические параметры возрастают в случае оксинитридных покрытий по сравнению с нитридами и оксидами.Використання металевих матеріалів із керамічними покриттями є ефективним засобом формування альтернативних поверхонь ковзання. Покриття оксидів ZrO₂, нітридів ZrN та оксинітридів ZrON були нанесені на сталеві диски (AlSi 316) методом магнетронного розпилювання. Адгезія, твердість та пружні модулі покриттів вимірювались стандартними методами. Параметри поверхні оцінювались методом скануючої електронної мікроскопії. Хімічний склад покриттів було проаналізовано методом енергетично дисперсної спектроскопії. Коефіцієнт тертя та знос оцінювали в трибологічних тестах. Результати продемонстрували, що механічні параметри зростають у випадку оксинітридних покриттів порівняно з нітридами та оксидами

Unveiling the molecular environment of the ring nebula RCW 78

We present a study of the ionized, neutral atomic, and molecular gas associated with the ring nebula RCW 78 around the WR star HD 117688 (= WR 55). We based our study on CO observations carried out with the SEST and NANTEN telescopes. We report the detection of molecular gas with velocities in the range -56 to -33 km/s. The CO emission is mainly connected to the western section, with a total molecular mass of 1.3 x 10^5 solar masses. The analysis of the HI gas distribution reveals the HI envelope of the molecular cloud, while the radio continuum emission shows a ring-like structure, which is the radio counterpart of the optical nebula. The gas distribution is compatible with the western section of RCW 78 having originated in the photodissociation and ionization of the molecular gas by HD 117688, and with the action of the stellar winds of the WR star. A number of infrared point sources classified as YSO candidates showed that stellar formation activity is present in the molecular gas linked to the nebula. The fact that the expansion of the bubble have triggered star formation in this region can not be discarded.Comment: 15 pages, 11 Postscript figures, to be published in A&

Massive Binary WR112 and Properties of Wolf-Rayet Dust

Some hot, massive, population-I Wolf-Rayet (WR) stars of the carbon subclass are known to be prolific dust-producers. How dust can form in such a hostile environment remains a mystery. Here we report the discovery of a relatively cool, extended, multi-arc dust envelope around the star WR112, most likely formed by wind-wind collision in a long-period binary system. We derive the binary orbital parameters, the dust temperature and the dust mass distributions in the envelope. We find that amorphous carbon is a main constituent of the dust, in agreement with earlier estimates and theoretical predictions. However, the characteristic size of the dust grains is estimated to be ~1 micron, significantly larger than theoretical limits. The dust production rate is 6.1*10^[-7] M_Sun / yr and the total detectable dust mass is found to be about 2.8*10^[-5] M_Sun (for d=4.15 kpc). We also show that, despite the hostile environment, at least ~20% of the initially-formed dust may reach the interstellar medium.Comment: 8pp, 3 figures (2 of them in colour). The Astrophysical Journal Letters (2002) in pres

A 2.3-Day Periodic Variability in the Apparently Single Wolf-Rayet Star WR 134: Collapsed Companion or Rotational Modulation?

We present the results of an intensive campaign of spectroscopic and photometric monitoring of the peculiar Wolf-Rayet star WR 134 from 1989 to 1997. This unprecedentedly large data set allows us to confirm unambiguously the existence of a coherent 2.25 +/- 0.05 day periodicity in the line-profile changes of He II 4686, although the global pattern of variability is different from one epoch to another. This period is only marginally detected in the photometric data set. Assuming the 2.25 day periodic variability to be induced by orbital motion of a collapsed companion, we develop a simple model aiming at investigating (i) the effect of this strongly ionizing, accreting companion on the Wolf-Rayet wind structure, and (ii) the expected emergent X-ray luminosity. We argue that the predicted and observed X-ray fluxes can only be matched if the accretion on the collapsed star is significantly inhibited. Additionally, we performed simulations of line-profile variations caused by the orbital revolution of a localized, strongly ionized wind cavity surrounding the X-ray source. A reasonable fit is achieved between the observed and modeled phase-dependent line profiles of He II 4686. However, the derived size of the photoionized zone substantially exceeds our expectations, given the observed low-level X-ray flux. Alternatively, we explore rotational modulation of a persistent, largely anisotropic outflow as the origin of the observed cyclical variability. Although qualitative, this hypothesis leads to greater consistency with the observations.Comment: 34 pages, 16 figures. Accepted by the Astrophysical Journa