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Lemaître coordinates

Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius; the original Schwarzschild coordinate expression of the Schwarzschild metric, in natural units, is given as d s 2 = d t 2 − d r 2 1 − r s r − r 2, where d s 2 is the invariant interval. This metric has a coordinate singularity at the Schwarzschild radius r = r s. Georges Lemaître was the first to show that this is not a real physical singularity but a manifestation of the fact that the static Schwarzschild coordinates cannot be realized with material bodies inside the Schwarzschild radius. Indeed, inside the Schwarzschild radius everything falls towards the centre and it is impossible for a physical body to keep a constant radius. A transformation of the Schwarzschild coordinate system from to the new coordinates, d τ = d t + r s r − 1 d r d ρ = d t + r r s − 1 d r, leads to the Lemaître coordinate expression of the metric, d s 2 = d τ 2 − r s r d ρ 2 − r 2 where r = 2 / 3 r s 1 / 3.

The trajectories with ρ constant are timelike geodesics with τ the proper time along these geodesics. They represent the motion of falling particles which start out with zero velocity at infinity. At any point their speed is just equal to the escape velocity from that point. In Lemaître coordinates there is no singularity at the Schwarzschild radius, which instead corresponds to the point 3 2 = r s. However, there remains a genuine gravitational singularity at the center, where ρ − τ = 0, which cannot be removed by a coordinate change; the Lemaître coordinate system is synchronous, that is, the global time coordinate of the metric defines the proper time of co-moving observers. The radially falling bodies reach the centre within finite proper time. Along the trajectory of a radial light ray, d r = d τ, {\displaystyl

Saša Papac

Saša Papac is a Bosnian retired professional footballer. Before joining Rangers, Papac had played in both his native country of Bosnia and Herzegovina for Široki Brijeg and in Austria for Kärnten and Austria Vienna, he spent the early part of his career as a central defender but during his time at Rangers developed into a left back known for his high level of performance. Papac started his career with NK Široki Brijeg in the Premier League of Bosnia and Herzegovina in 2000, he made fourteen appearances. He moved to Austria with FC Kärnten a year later. Papac spent three years with Kärnten, making 100 scoring on three occasions; when Kärnten were relegated from the Austrian Bundesliga in 2004 he joined Austria Vienna. Whilst in Vienna he would make 76 appearances and win the league in 2006, he was part of the side which won successive Austrian Cups in 2005 and 2006. He signed for Rangers on 31 August 2006 for a fee of £450,000, he became Rangers' third signing from Austria Vienna in the 2006 summer transfer window, after Libor Sionko and Filip Šebo.

Papac made his debut for Rangers on 17 September 2006, coming on as a half time substitute for Steven Smith in a Scottish Premier League game against Hibernian. The side went on to lose the match 2–1. With the arrival of Walter Smith in January 2007, Papac lost his place in the first team, he struggled to get into the side, making only one appearance in over two months, but returned towards the end of the season on the left side of defence. He was linked with a move to Saint-Etienne in the summer but rejected it in order to claim a first-team spot. In the 2007–08 season Papac was a regular at left-back and played in the Scottish Cup, League Cup and UEFA Cup finals. Papac netted his first goal for Rangers on his 83rd appearance for the club, during a league match against Dundee United on 4 November 2008, he signed a two-year contract extension in November 2008 that would keep him at the club until the summer of 2011. In season 2008 -- 09, Papac won both the League and Scottish Cup. Papac made 46 appearances the following season and won the League for the second consecutive time along with the League Cup.

On 17 May 2011, Papac signed a new one-year contract extension with Rangers just two days after helping the club to a third consecutive championship. In August 2011, it was announced that Papac would miss about a month of the footballing season after suffering from a bout of pneumonia. On 4 May 2012, Papac announced that he would be leaving Rangers at the end of the current footballing season. On 28 August 2012, Papac announced his retirement from professional football for health reasons, after failing to recover properly from a groin injury. Papac made his debut on 7 September 2002, against Romania but quit in March 2007, citing problems with the staff at the Bosnian FA. In January 2008, he decided to return to the international set under new boss Meho Kodro. Shortly after Kodro's dismissal, he was called up by new coach Miroslav Blažević but refused to come and retired from international football claiming it was to give space to new young players. However, in 2010 it emerged. In June 2011, Glasgow newspaper The Herald reported.

On 1 July 2011, Papac confirmed. On 10 August 2011, Papac returned to play a friendly match versus Greece in Sarajevo, he played his last match versus Greece before quitting the national team in October 2006. In 2015, he was hired as a scout for the Bosnian-Herzegovinian national team. On 15 November 2017, Papac was announced as new director of football of Željezničar Sarajevo, he did not want to extend his contract and announced on 27 May 2018 that when his contract expires on 1 June 2018, he will leave the position which he did. He wished it good luck in its future; as of 7 April 2012. Austria ViennaAustrian Bundesliga: 2005-06 Austrian Cup: 2004-05, 2005-06RangersScottish Premier League: 2008–09, 2009–10, 2010–11 Scottish Cup: 2007-08, 2008-09 Scottish League Cup: 2007-08, 2009-10, 2010-11 Saša Papac at Soccerbase

Ehsan Alvanzadeh

Ehsan Alvanzadeh is an Iranian football forward who plays for Iranian football club Fajr Sepasi in the Azadegan League. Alvanzadeh was part of Esteghlal Khuzestan U21 during 2012–14, he was promoted to first team in Summer 2013 by Abdollah Veisi. He netted in his debut match against Rah Ahan as October 17, 2013; as Summer 2014 he joined Naft Masjed Soleyman with 2 years contract. As 7 June 2016 He Joined FC Persepolis With 3 Years Contract; as of 31 October 2014. PersepolisPersian Gulf Pro League: 2016–17, 2017–18 Iranian Super Cup: 2017, 2018 AFC Champions League runner-up: 2018 Ehsan Alvanzadeh at Ehsan Alvanzadeh at

Zubeida Agha

Zubeida Agha was among the first Pakistani Modern Artists. After the creation of Pakistan in 1947, she was the first artist to hold an exhibition of her paintings, she helped bring the modern idiom to Pakistan. Zubeida Agha was born in 1922 in Faislabad, Pakistan. After graduating from Kinnaird College for Women University, she worked with painter B. C. Sanyal from 1944 to 1946. At this time, she became well- acquainted with the works of Picasso, she was influenced by the works of Mario Perlingeri, an Italian prisoner of war in India at that time. The Society of Fine Arts awarded her first prize for modern painting in 1946, she joined Saint Martin's School of Art, London in 1950 moving on to Ecole des Beaux Arts, Paris in 1951. In 1961, she was appointed executive director of the Contemporary Art Gallery in Rawalpindi, receiving the President's Award for Pride of Performance in 1965. Zubeida Agha is considered as a premiere painter of Pakistan and a pioneer of modern art in the country. In the 1940s, she had the determination to launch a modern style of painting.

Her style of art first baffled and overwhelmed art critics and viewers. Colourist painting is characterized by the use of intense colour. Zubeida Agha was one of the great colourist painters in the history of Pakistani painting, she uses colour not only for itself, but to lend truthfulness and depth of meaning to her images, using her amazing imagination to provoke the viewer into thought. In November 2002, a large exhibit of Zubeida Agha paintings was held at Lahore. On 14 August 2006, Pakistan Post issued a Rs. 40 sheetlet of stamps to posthumously honour 10 Pakistani painters. Besides Zubeida Agha, the other nine painters were: Laila Shahzada, Askari Mian Irani, Ali Imam, Shakir Ali, Anna Molka Ahmed, Zahoor ul Akhlaq, Ahmed Pervez and Bashir Mirza. Zubeida Agha is called a torch-bearer of modern art in Pakistan. Other times she is named'The grande dame of Pakistani art', her work is on permanent display at the National Art Gallery of Pakistan National Council of the Arts in Islamabad, Pakistan.

National Art Gallery is displaying some works of Pakistani legends of visual art on permanent basis to serve as inspiration and to educate the coming generations. Ten Great Painters Stamps by Pakistan Post Posthumous tribute to Ten Great Painters by Pakistan Post

Brephulopsis cylindrica

Brephulopsis cylindrica is a species of air-breathing land snail, a terrestrial pulmonate gastropod mollusk in the family Enidae. The specific name cylindricus cannot be used for this species because Bulimus cylindricus Menke, 1828 is a junior homonym of Bulimus cylindricus Gray, 1825; the correct name is most Brephulopsis fusiformis. The distribution of this species includes: Belarus - since 2010 Ukraine The color of the shell is bluish white or white, sometimes with dark streaks and opaque; the shell has 9-12 not convex whorls. The aperture is inside yellow-brownish in color, with a weak white lip. Columella is thickened; the width of the shell is 7.5–9 mm. The height of the shell is 22–35 mm; this article incorporates public domain text from the reference