Permanent

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both permanent and determinant are special cases of a more general function of a matrix called the immanant.

Definition

The permanent of an n-by-n matrix A = (a_i,j) is defined as

The sum here extends over all elements σ of the symmetric group S_n; i.e. over all permutations of the numbers 1, 2, ..., n.

For example,

and

The definition of the permanent of A differs from that of the determinant of A in that the signatures of the permutations are not taken into account.

The permanent of a matrix A is denoted per A, perm A, or Per A, sometimes with parentheses around the argument. In his monograph, Minc (1984) uses Per(A) for the permanent of rectangular matrices, and uses per(A) when A is a square matrix. Muir (1882) uses the notation .

The word, permanent, originated with Cauchy in 1812 as “fonctions symétriques permanentes” for a related type of function, and was used by Muir (1882) in the modern, more specific, sense.

Randonneuring

Randonneuring (also known as Audax in the UK, Australia and Brazil) is a long-distance cycling sport with its origins in audax cycling. In randonneuring, riders attempt courses of 200 km or more, passing through predetermined "controls" (checkpoints) every few tens of kilometers. Riders aim to complete the course within specified time limits, and receive equal recognition regardless of their finishing order. Riders may travel in groups or alone as they wish, and are expected to be self-sufficient between controls. A randonneuring event is called a randonnée or brevet, and a rider who has completed a 200 km event is called a randonneur. The international governing body for randonneuring is Audax Club Parisien (ACP), which works with other randonneuring organisations worldwide through Les Randonneurs Mondiaux (RM). Randonneuring is popular in France, and has a following in the Netherlands, Belgium, United Kingdom, Australia, USA, Canada, Brazil and India.

History

Karlgeorg Hoefer

Karlgeorg Hoefer (February 6, 1914 – October 8, 2000) was a German calligrapher and typographer.

Hoefer was born in Schlesisch-Drehnow (now Drzonów) in Silesia. He taught typography at the Hochschule für Gestaltung Offenbach (until 1970 "Werkkunstschule Offenbach"). He held several calligraphy workshops for calligraphic societies in Los Angeles, San Francisco, Portland, Boston, Minneapolis-St. Paul, Portland and Washington. In 1987 he founded the Schreibwerkstatt-Klingspor Offenbach and supported the Klingspor Museum in Offenbach am Main.

He designed fonts for Linotype, Klingspor, and Ludwig & Mayer.

Today his most commonly seen font is the FE-Schrift, the standard font for German number plates.

He died in Offenbach in 2000.

External links

Julie (mango)

The 'Julie' mango is a named mango cultivar that was made popular in the Caribbean.

History

The origin of the 'Julie' mango is not known for sure but recent genetic studies show that it was possibly descended from cultivars introduced to the Caribbean through Jamaica from Réunion.; its monoembryonic trait suggests it is descended from the Indian line of mangoes.

'Julie' was recognized for its outstanding flavor and its dwarf growth habit. It was introduced to the United States via south Florida by Lawrence Zill, a nurseryman and horticulturalist known for producing new mango varieties. Several Florida varieties are descended directly or indirectly from 'Julie', including 'Sophie Fry', 'Gary' and 'Carrie'. 'Julie' is also the parent of 'Graham', a variety from Trinidad.

'Julie' proved to be difficult to adapt to the humid climate of Florida, however, and was very susceptible to fungus, making it unsuitable for commercial growing. Nevertheless, the variety was sold as nursery stock for home growing and continues to be done so on a limited scale. It remains a popular variety in the West Indies, where it is often referred to as 'Saint Julian' mango.

Julie Berthelsen

Julie Ivalo Broberg Berthelsen also known by her mononym Julie (born June 7, 1979) is a Danish-born Greenlandic pop singer and songwriter. She is known largely for her success on the TV series Popstars. Although she finished in second place, she has become more popular and successful than the first place winner. She grew up in Nuuk, the capital of Greenland.

Julie has given a variety of performances, the most noteworthy of which was at Christiansborg Palace, in front of the Danish Royal family for the wedding of Crown Prince Frederik and Crown Princess Mary in May 2004. Another performance worthy of note was her rendition of the Beatles song "Ob-La-Di, Ob-La-Da" on 22 November 2008 at The White Concert, held in Horsens, Denmark on the 40th anniversary of the release of "The Beatles" (aka "The White Album").

Discography

Albums

Singles

Julie (2004 film)

Julie is a Hindi film produced by N.R.Pachisia and directed by Deepak Shivdasani. The film stars Neha Dhupia, Priyanshu Chatterjee, Yash Tonk, Sanjay Kapoor and Achint Kaur.

Its sequel Julie 2 starring Raai Laxmi ,which is also directed by Deepak Shivdasani is scheduled for a worldwide release on 12 August 2016.

Plot

When Julie (Neha Dhupia), a girl next door from Goa, gets dumped by her boyfriend, Neil (Yash Tonk), she moves to Mumbai. There, she is physically abused by her boss, Rohan (Sanjay Kapoor). Heartbroken and emotionless, she loses faith in love and decides to become a call girl. A chance meeting with Mihir Shandilya (Priyanshu Chatterjee), a multi-millionaire and one of the most eligible bachelors in town, leads to their instant liking for each other. Mihir is completely besotted by her beauty and, being a family-oriented man, proposes marriage to her. All is well except that Mihir and his family are unaware of the fact that Julie is a high-profile prostitute. During a TV interview, Mihir surprises everyone by mentioning Julie is the 'someone special' in his life. Julie is now in a dilemma. How she tells her future husband about her socially unacceptable profession and if Mihir accepts her forms the rest of the story.