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Bartel Leendert van der Waerden

Bartel Leendert van der Waerden was a Dutch mathematician and historian of mathematics. Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926, he was much influenced by Emmy Noether at Germany. Amsterdam awarded him a Ph. D. for a thesis on algebraic geometry, supervised by Hendrick de Vries. Göttingen awarded him the habilitation in 1928. In that year, at the age of 25, he accepted a professorship at the University of Groningen. In his 27th year, van der Waerden published his Moderne Algebra, an influential two-volume treatise on abstract algebra, still cited, the first treatise to treat the subject as a comprehensive whole; this work systematized an ample body of research by Emmy Noether, David Hilbert, Richard Dedekind, Emil Artin. In the following year, 1931, he was appointed professor at the University of Leipzig. In July 1929 he married the sister of mathematician Franz Rellich, Camilla Juliana Anna and they had three children.

During the rise of the Third Reich and through World War II, van der Waerden remained at Leipzig, passed up opportunities to leave Nazi Germany for Princeton and Utrecht. However, he was critical of the Nazis and refused to give up his Dutch nationality, both of which led to difficulties for him. Following the war, van der Waerden was repatriated to the Netherlands rather than returning to Leipzig, but struggled to find a position in the Dutch academic system, in part because his time in Germany made his politics suspect and in part due to Brouwer's opposition to Hilbert's school of mathematics. After a year visiting Johns Hopkins University and two years as a part-time professor, in 1950 van der Waerden filled the chair in mathematics at the University of Amsterdam. In 1951, he moved to the University of Zurich, where he spent the rest of his career, supervising more than 40 Ph. D. students. Van der Waerden is remembered for his work on abstract algebra, he wrote on algebraic geometry, number theory, combinatorics, analysis and statistics, quantum mechanics.

In his years, he turned to the history of mathematics and science. His historical writings include Ontwakende wetenschap, translated into English as Science Awakening, Sources of Quantum Mechanics and Algebra in Ancient Civilizations, A History of Algebra. Van der Waerden has over 1000 academic descendants, most of them through three of his students, David van Dantzig, Herbert Seifert, Hans Richter. Alexander Soifer, The Mathematical Coloring Book, Springer-Verlag ISBN 978-0-387-74640-1. Soifer devotes four chapters and over 100 pages to biographical material about van der Waerden, some of which he had published earlier in the journal Geombinatorics. Alexander Soifer The Scholar and the State: In Search of Van der Waerden, Springer books ISBN 978-3-0348-0711-1 Schlote, K.-H. 2005, "Moderne Algebra" in Grattan-Guinness, I. ed. Landmark Writings in Western Mathematics. Elsevier: 901–16. O'Connor, John J.. Dold-Samplonius, Yvonne. "Interview with Bartel Leendert van Der Waerden". Notices of the American Mathematical Society.

44: 313–320. Freudenthal, H. 1962, "Review: B. L. van der Waerden, Science Awakening" in Bull. Amer. Math. Soc. 68:543–45. Bartel Leendert van der Waerden at the Mathematics Genealogy Project

West Midlands Chambers of Commerce

West Midlands Chambers of Commerce LLP is a collaborative partnership of the 6 Chambers of Commerce in the West Midlands region of the United Kingdom. It brings together the regions Chambers of Commerce, which between them have over 9,000 companies as registered members; the head office of the WMCC is located at the same address as the Birmingham chamber. It operates through delivery teams based at the offices of its member chambers, giving it a total of six offices; as well as Birmingham these are located in Worcester, Stoke-on-Trent, Walsall and Telford. The head of the WMCC is the chair Louise Bennett. In total there are 332 chamber employees, within the 6 regional Chambers including specialist advisers and project managers as well as administrative and support staff; the West Midlands Chambers of Commerce LLP has six member chambers, each of, an accredited member of the British Chambers of Commerce. The members are: Greater Birmingham Chambers of Commerce Group Black Country Chamber of Commerce Coventry and Warwickshire Chamber of Commerce Herefordshire and Worcestershire Chamber of Commerce Staffordshire Chambers of Commerce Shropshire Chamber of CommerceBetween them these chambers have a total membership of over 9,000 businesses.

The WMCC describes its core mission as "the delivery of specialist business services across the West Midlands". A priority is developing international investment in the West Midlands area; the WMCC acts as a single point of contact for government agencies or other private sector entities who wish to place contracts for the delivery of business support services across the West Midlands region: it can act as both contractor and contract manager. The WMCC is working with businesses, lobbying the government and local authorities, to increase the emphasis on exports for manufacturers based in the West Midlands. In May 2013 WMCC introduced a new service aimed at making it easier for businesses to export; this involves providing a simple way to generate all the documentation required to ship goods overseas, including letters of credit, by using a centralised management system. This allows a business to enter the information once rather than having to do it for each individual document. Online training courses are being developed to teach business owners the special requirements of international trade

Outlaw (railroading jargon)

The term outlaw, or outlawed refers to a crew which can no longer move because the crew has reached the maximum number of hours they are allowed to work, thereby outlawing their controlling the further movement of any train. All they may do is be relieved or deadhead to a "home terminal" or an "away from home terminal" to begin a period of rest. In the United States railroad employees who are involved in the movement of trains are governed by the Hours of Service Act; the legislation is related to similar regulations which apply to other modes of transportation, but with different specific limitations. The Act, administered by the Federal Railroad Administration, covers "train employees", "signal employees" and "dispatching service employees.", as defined by the statute. This act is in place and in effect to ensure said employees receive "sufficient periods of rest" to ensure that they can perform their jobs safely; the law specifies how many hours employees may work, both continuously and with a period of off time, differentiated as being too short to be considered a period of rest.

The affected employees include Dispatchers, Conductors and more. FRA Technical Bulletin G-00-02 - The Federal Hours Of Service Laws and Signal Service

Where We Come From

Where We Come From is the debut studio album by Jamaican dancehall artist Popcaan, released on 10 June 2014 by Mixpak Records. A prolific dancehall artist from Jamaica, Popcaan collaborated with several producers on the album: Dre Skull, Dubbel Dutch, Anju Blaxx, Jaime YVP and Adde Instrumentals. "Where We Come From" received critical acclaim upon release, placed on several year-end critics' lists for 2014. Upon release of the album, Popcaan was featured as the cover star on The Fader, garnered an 8.0 rating at Pitchfork, as well as positive reviews by NPR, The Guardian, The Washington Post, Dazed, Jamaican Observer, Complex, FACT, more. Where We Come From received acclaim from music critics. At Metacritic, which assigns a normalised rating out of 100 to reviews from mainstream critics, the album received an average score of 81, which indicates "universal acclaim", based on 5 reviews. Official website

Codariocalyx motorius

Codariocalyx motorius, known as the telegraph plant, dancing plant, or semaphore plant, is a tropical Asian shrub, one of a few plants capable of rapid movement. It is distributed throughout Bangladesh, Cambodia, India, Laos, Myanmar, Pakistan, Sri Lanka, Taiwan and Vietnam, it can be found on the Society Islands, a remote chain of islands in the South Pacific. It produces purple flowers; this plant has small, lateral leaflets which move at speeds rapid enough to be perceivable with the naked eye. This is a strategy to maximise light by tracking the sun; each leaf is equipped with a hinge that permits it to be moved to receive more sunlight, but the weight of these leaves means the plant must expend a lot of energy in moving it. To optimise its movement, each large leaf has two small leaflets at its base; these move along an elliptical path, sampling the intensity of sunlight, directing the large leaf to the area of most intensity. Another hypothesis has been offered that the rapid movements are intended to deter potential predators.

The common name is due to the rotation of the leaflets with a period of about three to five minutes. The plant is described in detail in Charles Darwin's 1880 The Power of Movement in Plants. Due to its special characteristic that it can "dance", the plant has been used as ornament in gardening, in which some are made as bonsais. Apart from ornamental value, the plant has medical value, due to its leaves and roots containing small amounts of tryptamine alkaloids DMT and 5-MeO-DMT. Trout’s Notes on the Genus Desmodium Chemistry, pharmacology and miscellany Keyes, WJ. "Dancing together. Social controls in parasitic plant development". Plant Physiol. 127: 1508–12. Doi:10.1104/pp.127.4.1508. PMC 1540184. PMID 11743095

Deterministic pushdown automaton

In automata theory, a deterministic pushdown automaton is a variation of the pushdown automaton. The class of deterministic pushdown automata accepts the deterministic context-free languages, a proper subset of context-free languages. Machine transitions are based on the current state and input symbol, the current topmost symbol of the stack. Symbols have no immediate effect. Machine actions include popping, or replacing the stack top. A deterministic pushdown automaton has at most one legal transition for the same combination of input symbol and top stack symbol; this is. A PDA M can be defined as a 7-tuple: M = where Q is a finite set of states Σ is a finite set of input symbols Γ is a finite set of stack symbols q 0 ∈ Q is the start state Z 0 ∈ Γ is the starting stack symbol A ⊆ Q, where A is the set of accepting states δ is a transition function, where δ: ⟶ P where ∗ is the Kleene star, meaning that Γ ∗ is "the set of all finite strings of elements of Γ ", ε denotes the empty string, P is the power set of a set X.

M is deterministic if it satisfies both the following conditions: For any q ∈ Q, a ∈ Σ ∪, x ∈ Γ, the set δ has at most one element. For any q ∈ Q, x ∈ Γ, if δ ≠ ∅ δ = ∅ for every a ∈ Σ. There are two possible acceptance criteria: acceptance by empty acceptance by final state; the two are not equivalent for the deterministic pushdown automaton. The languages accepted by empty stack are those languages that are accepted by final state and are prefix-free: no word in the language is the prefix of another word in the language; the usual acceptance criterion is final state, it is this acceptance criterion, used to define the deterministic context-free languages. If L is a language accepted by a PDA A, it can be accepted by a DPDA if and only if there is a single computation from the initial configuration until an accepting one for all strings belonging to L. If L can be accepted by a PDA it is a context free language and if it can be accepted by a DPDA it is a deterministic context-free language. Not all context-free languages are deterministic.

This makes the DPDA a weaker device than the PDA. For example, the language Lp of even-length palindromes on the alphabet of 0 and 1 has the context-free grammar S → 0S0 | 1S1 | ε. If a DPDA for this language exists, it sees a string 0n, it must use its stack to memoize the length n, in order to be able to distinguish its possible continuations 0n 11 0n ∈ Lp and 0n 11 0n+2 ∉ Lp. Hence, after reading 0n 11 0n, comparing the post-"11" length to the pre-"11" length will make the stack empty again. For this reason, the strings 0n 11 0n 0n 11 0n ∈ Lp and 0n 11 0n 0n+2 11 0n+2 ∉ Lp cannot be distinguished. Restricting the DPDA to a single state reduces the class of languages accepted to the LL languages, a proper subclass of the DCFL. In the case of a PDA, this restriction has no effect on the class of languages accepted. Closure properties of deterministic context-free languages are drastically different from the context-free languages; as an example they are (ef