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Attractor

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close if disturbed. In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector; the attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities. If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions. An attractor can be a point, a finite set of points, a curve, a manifold, or a complicated set with a fractal structure known as a strange attractor. If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.

A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a repeller. A dynamical system is described by one or more differential or difference equations; the equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is necessary to integrate the equations, either through analytical means or through iteration with the aid of computers. Dynamical systems in the physical world tend to arise from dissipative systems: if it were not for some driving force, the motion would cease; the dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the phase space of the dynamical system corresponding to the typical behavior is the attractor known as the attracting section or attractee.

Invariant sets and limit sets are similar to the attractor concept. An invariant set is a set. Attractors may contain invariant sets. A limit set is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed off the limit set may get knocked off and never return to the vicinity of the limit set. For example, the damped pendulum has two invariant points: the point x0 of minimum height and the point x1 of maximum height; the point x0 is a limit set, as trajectories converge to it. Because of the dissipation due to air resistance, the point x0 is an attractor. If there was no dissipation, x0 would not be an attractor. Aristotle believed that objects moved only as long as they were pushed, an early formulation of a dissipative attractor. Exponential divergence of trajectories complicates detailed predictions, but the world is knowable due to the existence of robust attractors.

Let t represent time and let f be a function which specifies the dynamics of the system. That is, if a is a point in an n-dimensional phase space, representing the initial state of the system f = a and, for a positive value of t, f is the result of the evolution of this state after t units of time. For example, if the system describes the evolution of a free particle in one dimension the phase space is the plane R2 with coordinates, where x is the position of the particle, v is its velocity, a =, the evolution is given by f =. An attractor is a subset A of the phase space characterized by the following three conditions: A is forward invariant under f: if a is an element of A so is f, for all t > 0. There exists a neighborhood of A, called the basin of attraction for A and denoted B, which consists of all points b that "enter A in the limit t → ∞". More formally, B is the set of all points b in the phase space with the following property:For any open neighborhood N of A, there is a positive constant T such that f ∈ N for all real t > T.

There is no proper subset of A having the first two properties. Since the basin of attraction contains an open set containing A, every point, sufficiently close to A is attracted to A; the definition of an attractor uses a metric on the phase space, but the resulting notion depends only on the topology of the phase space. In the case of Rn, the Euclidean norm is used. Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive measure, others relax the requirement that B be a neighborhood. Attractors are subsets of the phase space of a dynamical system; until the 1960s, attractors were tho

Edward Enoch Jenkins

Sir Enoch Jenkins was a British lawyer and judge. He served as Attorney General of Fiji from 1938 to 1945, he subsequently served as Chief Justice of Nyasaland. Jenkins was born in Cardiff, Wales, on 8 February 1895 to Briar Dene, he was known by his middle name. Educated at Howard Gardens Municipal Secondary School in Cardiff, he studied at University College of South Wales and Monmouthshire in Cardiff. Jenkins served as a lieutenant with the Royal Field Artillery after the First World War, he was admitted to Cambridge University on 16 May 1919, taking up residence in Peterhouse on 8 October and beginning his matriculation on 21 October that year. He graduated with B. A. and LL. B degrees in 1922, he subsequently earned a postgraduate M. A. degree in 1928. Jenkins was called to the bar at Gray's Inn on 14 May 1924, he entered the colonial service in Nyasaland in 1925, before becoming Solicitor General of Northern Rhodesia in 1936. He served as Attorney General of Fiji from 1938 to 1945; as Chief Justice, he headed a commission of inquiry into a riot that had taken place at Zomba Prison in November 1949.

He was criticised by both Sir Geoffrey Colby, the Governor of Nyasaland, the Legislative Council, for paying undue attention to "matters of minor significance" and of ignoring what they believed was the fundamental cause of the problem: the breakdown of discipline in the prison over the previous two years. Sometime before September 1953, he was appointed a Justice of Appeal on the Kenya-based Court of Appeal for Eastern Africa, he sat as one of the judges on Jomo Kenyatta's unsuccessful appeal against his conviction for organizing the Mau Mau movement. He was still reported as serving on the Court of Appeal as of 24 December 1954

Patrick d'Arcy

Patrick d'Arcy was an Irish mathematician born in Kiltullagh, County Galway in the west of Ireland. His family, who were Catholics, suffered under the penal laws. In 1739 d'Arcy was sent abroad by his parents to an uncle in Paris, he was tutored in mathematics by Jean-Baptiste Clairaut, became a friend of Jean-Baptiste's son, Alexis-Claude Clairaut, a brilliant young mathematician. D'Arcy made original contributions to dynamics, he is best known for his part in the discovery of the principle of angular momentum, in a form, known as "the principle of areas," which he announced in 1746. See the article on areal velocity. D'Arcy had an illustrious military career in the French army, he obtained the title of "Count" in the French nobility. He was a generous patron of Irish refugees in France. In addition to his contributions to dynamics, he performed research on electricity. An experiment of his, reported in 1765, on visual perception is referred to: he built a machine in his garden to measure the duration of visual impressions.

A burning coal, attached to an arm of a cross rotated by the machine, would be made to spin just fast enough to give the impression of a full fiery circle. With the collaboration of a dedicated observer with better eyesight than D'Arcy, he measured a 0,13 second duration for the visual sensation of the rotating burning coal, as seen in the dark from a circa 50 meter distance, he planned further experiments to measure the suspected differences between individuals, viewing distances and light intensity of objects. The experiment is mentioned by film scholars in the context of persistence of vision. D'Arcy was elected to the Academie Royale des Sciences in 1749, he died from cholera in Paris in October 1779. There is a copy of a portrait of d'Arcy in Wade, found in Charbonnier. C. S. Gillmor, "D'Arcy, Patrick," Dictionary of Scientific Biography, Vol. III, pp. 561–2, Scribner's, New York. Http://www.iol.ie/~mfinn/kiltullaghho.html M. le Chevalier D'Arcy, "Principe Géneral de Dynamique,"Mémoires de l'Académie des Sciences de Paris, 1747, pp. 348–356.

J. Casey, "Areal Velocity and Angular Momentum for Non-Planar Problems in Particle Mechanics," American Journal of Physics, Vol. 75, pp. 677–685, 2007. M. le Chevalier D'Arcy, "Sur la Durée de la Sensation de La vue," Mémoires de l'Académie des Sciences de Paris, pp. 439–451, 1765. N. J. Wade, Guest Editorial, Vol. 26, 1997. P. J. Charbonnier, Essais sur l'Histoire de la Balistique, Société d'Éditions Géographiques, Paris

Niederried bei Interlaken

Niederried bei Interlaken is a municipality in the Interlaken-Oberhasli administrative district in the canton of Bern in Switzerland. Niederried bei Interlaken is first mentioned in 1291 as Riede; the oldest trace of a settlement in the area is a neolithic grave in Ursisbalm and a La Tène grave at Städeli. The village only appeared in historical records after its founding. Between 1411 and 1439 the Herrschaft of Ringgenberg, which included Niederried, was given to Interlaken Abbey. In 1528, the city of Bern adopted the new faith of the Protestant Reformation and began imposing it on the Bernese Oberland; the Abbey unsuccessfully rebelled against the new faith. After Bern imposed its will on the Oberland, they secularized the Abbey and annexed all the Abbey lands. Niederried became a part of the Bernese bailiwick of Interlaken; the village occupies a narrow strip of land between the lake and the mountains so there was little land for farming. During the 19th century some tourists visited the village and in 1877 a pier was built for the tourist steam ships.

In 1916 the last leg of the Brünig railway line was completed, which passed through the narrow village. The name means "lower Ried near Interlaken." There are two explanations for the origin of the name Ried: from the Old High German riod, reoth or the Swiss German Ried. Niederried bei Interlaken has an area of 4.28 km2. Of this area, 0.92 km2 or 21.4% is used for agricultural purposes, while 2.36 km2 or 55.0% is forested. Of the rest of the land, 0.31 km2 or 7.2% is settled, 0.02 km2 or 0.5% is either rivers or lakes and 0.68 km2 or 15.9% is unproductive land. Of the built up area and buildings made up 4.9% and transportation infrastructure made up 2.3%. Out of the forested land, 50.6% of the total land area is forested and 3.7% is covered with orchards or small clusters of trees. Of the agricultural land, 8.2% is pastures and 13.3% is used for alpine pastures. All the water in the municipality is flowing water. Of the unproductive areas, 11.4 % is unproductive 4.4 % is too rocky for vegetation.

It lies in the Bernese Oberland on the north shore of Lake Brienz. The highest point is the Suggiture at the northern edge of the municipality. On 31 December 2009 the municipality's former district, was dissolved. On the following day, 1 January 2010, it joined the newly created Verwaltungskreis Interlaken-Oberhasli; the blazon of the municipal coat of arms is Argent a Semi Ibex rampant Sable langued Gules and a Base Vert. The green field appears on the coats of arms of both Oberried, it symbolizes the marsh from. On the coat of arms of Niederried the green field appears below the ibex, while on Oberried it is above; this makes the coat of arms an example of canting arms. Niederried bei Interlaken has a population of 357; as of 2010, 12.7% of the population are resident foreign nationals. Over the last 10 years the population has changed at a rate of -4.9%. Migration accounted for -8%, while births and deaths accounted for -0.3%. Most of the population speaks German as their first language, Italian is the second most common and Albanian is the third.

As of 2008, the population was 50.6 % female. The population was made up of 23 non-Swiss men. There were 19 non-Swiss women. Of the population in the municipality, 106 or about 31.0% were born in Niederried bei Interlaken and lived there in 2000. There were 138 or 40.4% who were born in the same canton, while 41 or 12.0% were born somewhere else in Switzerland, 46 or 13.5% were born outside of Switzerland. As of 2010, children and teenagers make up 17.8% of the population, while adults make up 60.2% and seniors make up 22%. As of 2000, there were 130 people who never married in the municipality. There were 16 individuals who are divorced; as of 2000, there were 50 households that consist of only one person and 13 households with five or more people. In 2000, a total of 140 apartments were permanently occupied, while 123 apartments were seasonally occupied and 21 apartments were empty; as of 2010, the construction rate of new housing units was 3 new units per 1000 residents. The vacancy rate for the municipality, in 2011, was 0.9%.

The historical population is given in the following chart: In the 2011 federal election the most popular party was the Swiss People's Party which received 40.9% of the vote. The next three most popular parties were the Conservative Democratic Party, the Social Democratic Party and the Green Party. In the federal election, a total of 119 votes were cast, the voter turnout was 47.2%. As of 2011, Niederried bei Interlaken had an unemployment rate of 1.25%. As of 2008, there were a total of 44 people employed in the municipality. Of these, there were 10 people employed in the primary economic sector and about 4 businesses involved in this sector. 12 people were employed in the secondary sector and there were 3 businesses in this sector. 22 people were employed with 10 businesses in this sector. There were 167 residents of the municipality who were employed in some capacity, of which females made up 38.3% of the workforce. In 2008 there were a total of 35 full-time equivalent jobs; the number of jobs in th

Mutant Message

Mutant Message is an album by the Canadian indie rock band By Divine Right, released on December 8, 2009, on Hand Drawn Dracula. It was the band's first album since Sweet Confusion in 2004; the album was produced by José Miguel Contreras. The band's line up on the album consists of Contreras, Stew Heyduk and Darcy Rego, with guest vocals from Jason Nunes and Lily Frost; the album was a longlisted nominee for the 2010 Polaris Music Prize. "I Love a Girl" "Que Paso" "Wings too Big" "Cupid in Oilskins" "Figure Me Out" "Kiss My Chakras" "Pisco Sour" "2002-2003" "Help Me Find a Place to Land" "I Will Hook You Up"

Bose (surname)

Bose or Basu or Boshu is a surname found amongst Bengali Hindus. It stems from Sanskrit वासु vāsu. Boses belong to Kayastha caste in Bengal; the Bengali Kayasthas evolved between the 5th/6th century AD and 11th/12th century AD, its component elements being putative Kshatriyas and Brahmin. Boses are considered as Kulin Kayasthas of Gautam gotra, along with Ghoshes and Guhas; as of 2014, 56.4% of all known bearers of the surname Bose were residents of India and 20.1% were residents of Bangladesh. In India, the frequency of the surname was higher than national average in the following states and union territories: 1. West Bengal 2. Andaman and Nicobar Islands 3. Delhi Amar Bose, MIT professor and chairman of the Bose Corporation Ankiti Bose, Indian entrepreneur who works on the digitisation of the textile and apparel industry Ashish Bose, Demographer who coined BIMARU Benoy Basu, Indian revolutionary Buddhadeb Bosu, Bengali writer Girish Chandra Bose, Indian educator and botanist Jyoti Basu, Indian politician of the Communist Party, 6th chief minister of West Bengal Jagadish Chandra Bose, Bengali physicist, science fiction writer, student of radio science Kamal Bose, Indian cinematographer, winner of five Filmfare Awards Khudiram Bose, Indian freedom fighter Mankumari Basu, Bengali poet Mihir Bose, Indian-born British journalist, former BBC's sports editor N. S. Chandra Bose, medical doctor and politician Nandalal Bose, Indian painter Rahul Bose, Indian actor Rajsekhar Bose, Bengali writer and lexicographer Raj Chandra Bose, Indian mathematician and statistician Rash Behari Bose, Indian freedom fighter Sarat Chandra Bose, Indian lawyer and freedom fighter Soumya Sankar Bose, Indian Artist and Photographer Sarmila Bose, Indian journalist and researcher Satyendra Nath Bose, Indian physicist, best known for the Bose–Einstein statistics Sachindra Prasad Bose, designer of the Calcutta Flag Shree Bose, American scientist, winner of the inaugural Google Science Fair Sudhindra Bose, pioneer in teaching Asian politics and civilization in the United States Swadesh Bose, Bangladeshi economist Sugata Bose, Harvard professor, Member of Parliament and grandnephew of Netaji Subhas Chandra Bose Subhas Chandra Bose, fighter of the Indian independence movement and eminent personality of the Indian National Army Uma Bose,'The Nightingale of Bengal', musical prodigy Vivian Bose, judge of the Supreme Court of India and one of the founders of scouting in India Sterling Bose, American jazz trumpeter and cornetistvon Bose is an unrelated German surname Julius von Bose, Prussian Army general Countess Louise von Bose, German philanthropist Herbert von Bose, German civil servant Jobst-Hilmar von Bose, German soldier Hans-Jürgen von Bose, German composerBosé is an unrelated European surname Lucia Bosè or Lucía Bosé, Italian actress Miguel Bosé, Spanish singer and son of Lucia Bosè