Abd al-Rahman al-Sufi

'Abd al-Rahman al-Sufi (Persian: عبدالرحمن صوفی‎ was a Persian astronomer known as'Abd ar-Rahman as-Sufi,'Abd al-Rahman Abu al-Husayn,'Abdul Rahman Sufi, or'Abdurrahman Sufi and in the West as Azophi and Azophi Arabus. The lunar crater Azophi and the minor planet 12621 Alsufi are named after him. Al-Sufi published his famous Book of Fixed Stars in 964, describing much of his work, both in textual descriptions and pictures. Al-Biruni reports, he lived at the Buyid court in Isfahan.'Abd al-Rahman al-Sufi was one of the nine famous Muslim astronomers. His name implies, he lived at the court of Emir Adud ad-Daula in Isfahan and worked on translating and expanding Greek astronomical works the Almagest of Ptolemy. He contributed several corrections to Ptolemy's star list and did his own brightness and magnitude estimates which deviated from those in Ptolemy's work, with only 55% of Al-Sufi's magnitudes being identical to Ptolemy's, he was a major contributor of translation into Arabic of the Hellenistic astronomy, centered in Alexandria, the first to attempt to relate the Greek with the traditional Arabic star names and constellations, which were unrelated and overlapped in complicated ways.

Al-Sufi made his astronomical observations at a latitude of 32.7° in Isfahan. He identified the Large Magellanic Cloud, visible from Yemen, though not from Isfahan, he made the earliest recorded observation of the Andromeda Galaxy in 964 AD. These were the first galaxies other than the Milky Way to be observed from Earth. Al-Sufi published Kitab al-Kawatib al-Thabit al-Musawwar in AD 964 and dedicated it to Adud al-Dawla, the current ruler of Buwayhid at the time; this book describes the stars that they are composed of. Within the Book of Fixed Stars, Al-Sufi compared Greek and Arabic constellations and stars to equate the same ones to each other, he included two illustrations of each constellation, one showing the orientation of the stars from the perspective of outside the celestial globe and the other from the perspective of looking at the sky while standing on the earth. He separated the constellations into three groups: twenty-one northern constellations, twelve zodiac constellations, fifteen southern constellations.

For each of these forty-eight constellations, Al-Sufi provided a star chart that contains all of the stars that form the constellation. Each star chart names and numbers the individual stars in the constellation, provides their longitudinal and latitudinal coordinates, the magnitude or brightness of each star, its location north or south of the ecliptic. Although the magnitude was given for each star, of the 35 remaining copies of the Book of Fixed Stars the star magnitudes are not the same number for each star due to scribal error. Al-Sufi organized the stars in each of his drawings into two groups: the stars that form the image that the constellation is meant to depict, the stars that are in close proximity to the constellation but do not contribute to the overall image, he identified and described stars that Ptolemy did not, but he did not include them in his star charts. Al-Sufi states at the beginning of the Book of Fixed Stars that his charts are modeled after those that were produced by Ptolemy, so Al-Sufi left them out of his charts as well.

Eight hundred thirty-nine years had passed since Ptolemy had published the Almagest, so the longitudinal placement of the stars within constellations had changed. To account for the procession of the stars, Al-Sufi added 12° 42' to the longitudes Ptolemy had suggested for the placement of the stars. Al-Sufi differed in Ptolemy by having a three leveled scale to measure the magnitude of stars instead of a two leveled scale; this extra level increased the accuracy of his measurements. His methods of determining these magnitude measurements cannot be found in any remaining texts. Despite the importance of the Book of Fixed Stars in the history of astronomy, there is no English translation of the work. Al-Sufi observed that the ecliptic plane is inclined with respect to the celestial equator and more calculated the length of the tropical year. Al-Sufi wrote about the astrolabe, finding numerous additional uses for it: he described over 1000 different uses, in areas as diverse as astronomy, horoscopes, surveying, Qibla, Salat prayer, etc.

Al-Sufi's astronomical work was used by many other astronomers that came soon after him, including Ulugh Beg, both a prince and astronomer. Since 2006, Astronomy Society of Iran – Amateur Committee hold an international Sufi Observing Competition in the memory of Al-Sufi; the first competition was held in 2006 in the north of Semnan Province and the second was held in the summer of 2008 in Ladiz near the Zahedan. More than 100 attendees from Iran and Iraq participated in the event. On 7 December 2016, Google Doodle commemorated his 1113th birthday. List of Iranian scientists List of Muslim scientists Astronomy in Islam "Abd al-Rahman Al-Sufi's 1113th Birthday". 7 December 2016. Al-Qifti. Ikhbar al-'ulama' bi-akhbar al-hukama. In: Άbdul-Ramān al-Şūfī and his Book of the Fixed Stars: A Journey of Re-discovery by Ihsan Hafez, Richard F. Stephenson, Wayne Orchiston. In: Orchiston, Highlighting the history of astronomy in the Asia-Pacific region: proceedings of the ICOA-6 conference. Astrophysics and Space Science Procee

Bomaderry, New South Wales

Bomaderry is a town in the Shoalhaven council district area of New South Wales, Australia. At the 2016 census, it had a population of 6,661 people, it is on the north shore of the Shoalhaven River, across the river from Nowra, the major town of the City of Shoalhaven, of which Bomaderry is locally regarded as being a suburb of the city. Bomaderry township was opened in 1892, it was part of the Shoalhaven Estate owned by David Berry whose brother Alexander Berry had built a road to the area in 1858. When David died in 1889 the estate was sold in portions; the subdivision plans. In 1893 the railway was extended to Bomaderry and the town began to grow from this time. One of the first houses in Bomaderry was Lynburn, it was built in 1895 by the architect Howard Joseland for Jane Morton, the widow of Henry Gordon Morton, the manager of the Shoalhaven Estate. A photo shortly after its construction is shown; the road over the bridge in the photo is now the Princes Highway. After the town opened in 1892 several factories moved into the area.

Messrs Denham Bros. built a bacon and ham factory in about 1900. A milk condensery opened in 1901, located near the railway station but moved to the bank of the Shoalhaven River close to Bolong Road. In 1912 the Nowra Co-op Dairy Company established a milk Depot at Bomaderry and this was a major boost to the local economy for many years. Bomaderry has a number of heritage-listed sites, including: 59 Beinda Street: Bomaderry Aboriginal Children's Home Illawarra railway: Bomaderry railway station Its railway station is the terminus of the South Coast railway line, part of the NSW TrainLink network. Bomaderry High School is one of the major high schools in the Shoalhaven. Nowra Anglican College is a K-12 school located in Bomaderry. Bomaderry Public School is the main primary school in the area with over 250 students. According to the 2016 census of Population, there were 6,661 people in Bomaderry. Aboriginal and Torres Strait Islander people made up 7.4% of the population. 79.7% of people were born in Australia.

The next most common country of birth was England at 4.1%. 88.5% of people spoke only English at home. The most common responses for religion were No Religion 28.4%, Anglican 24.4% and Catholic 18.7%. Bomaderry area attractions Bomaderry Soldiers Rest Home collection

Empirical process

In probability theory, an empirical process is a stochastic process that describes the proportion of objects in a system in a given state. For a process in a discrete state space a population continuous time Markov chain or Markov population model is a process which counts the number of objects in a given state. In mean field theory, limit theorems are considered and generalise the central limit theorem for empirical measures. Applications of the theory of empirical processes arise in non-parametric statistics. For X1, X2... Xn independent and identically-distributed random variables in R with common cumulative distribution function F, the empirical distribution function is defined by F n = 1 n ∑ i = 1 n I ( − ∞, x ], where IC is the indicator function of the set C. For every x, Fn is a sequence of random variables which converge to F surely by the strong law of large numbers; that is, Fn converges to F pointwise. Glivenko and Cantelli strengthened this result by proving uniform convergence of Fn to F by the Glivenko–Cantelli theorem.

A centered and scaled version of the empirical measure is the signed measure G n = n It induces a map on measurable functions f given by f ↦ G n f = n f = n By the central limit theorem, G n converges in distribution to a normal random variable N for fixed measurable set A. Similarly, for a fixed function f, G n f converges in distribution to a normal random variable N, provided that E f and E f 2 exist. Definition c ∈ C is called an empirical process indexed by C, a collection of measurable subsets of S. F ∈ F is called an empirical process indexed by F, a collection of measurable functions from S to R. A significant result in the area of empirical processes is Donsker's theorem, it has led to a study of Donsker classes: sets of functions with the useful property that empirical processes indexed by these classes converge weakly to a certain Gaussian process. While it can be shown that Donsker classes are Glivenko–Cantelli classes, the converse is not true in general; as an example, consider empirical distribution functions.

For real-valued iid random variables X1, X2... Xn they are given by F n = P n ( = P n I ( − ∞, x ]. In this case, empirical processes are indexed by a class C =, it has been shown that C is a Donsker class, in particular, n converges weakly in ℓ ∞ to a Brownian bridge B. Khmaladze transformation Weak convergence of measures Glivenko–Cantelli theorem Billingsley, P.. Probability and Measure. New York: John Wiley and Sons. ISBN 0471007102. Donsker, M. D.. "Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems". The Annals of Mathematical Statistics. 23: 277–281. Doi:10.1214/aoms/1177729445. Dudley, R. M