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Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero. Equivalently, the theorem states; the theorem is stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity n complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division. In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use some form of the analytic completeness of the real numbers, not an algebraic concept. Additionally, it is not fundamental for modern algebra. Peter Roth, in his book Arithmetica Philosophica, wrote that a polynomial equation of degree n may have n solutions. Albert Girard, in his book L'invention nouvelle en l'Algèbre, asserted that a polynomial equation of degree n has n solutions, but he did not state that they had to be real numbers.

Furthermore, he added that his assertion holds "unless the equation is incomplete", by which he meant that no coefficient is equal to 0. However, when he explains in detail what he means, it is clear that he believes that his assertion is always true; as will be mentioned again below, it follows from the fundamental theorem of algebra that every non-constant polynomial with real coefficients can be written as a product of polynomials with real coefficients whose degrees are either 1 or 2. However, in 1702 Leibniz erroneously said that no polynomial of the type x4 + a4 can be written in such a way. Nikolaus Bernoulli made the same assertion concerning the polynomial x4 − 4x3 + 2x2 + 4x + 4, but he got a letter from Euler in 1742 in which it was shown that this polynomial is equal to, with α = 4 + 2 7. Euler pointed out that x 4 + a 4 =. A first attempt at proving the theorem was made by d'Alembert in 1746. Among other problems, it assumed implicitly a theorem which would not be proved until more than a century and furthermore the proof assumed the fundamental theorem of algebra.

Other attempts were made by Euler, de Foncenex and Laplace. These last four attempts assumed implicitly Girard's assertion. In modern terms, Euler, de Foncenex and Laplace were assuming the existence of a splitting field of the polynomial p. At the end of the 18th century, two new proofs were published which did not assume the existence of roots, but neither of, complete. One of them, due to James Wood and algebraic, was published in 1798 and it was ignored. Wood's proof had an algebraic gap; the other one was published by Gauss in 1799 and it was geometric, but it had a topological gap, filled by Alexander Ostrowski in 1920, as discussed in Smale. A rigorous proof was first published by Argand in 1806. Gauss produced two other proofs in 1816 and another version of his original proof in 1849; the first textbook containing a proof of the theorem was Cauchy's Cours d'analyse de l'École Royale Polytechnique. It contained Argand's proof. None of the proofs mentioned so far is constructive, it was Weierstrass who raised for the first time, in the middle of the 19th century, the problem of finding a constructive proof o

Crossroads (mural)

Crossroads is a 2013 mural that consists of two paintings by artist Ismael Muhammud Nieves located within the Eskenazi Outpatient Care Center on the Sidney and Lois Eskenazi Hospital campus, near downtown Indianapolis, is part of the Eskenazi Health Art Collection. Crossroads is a 2013 mural that consists of two acrylic on canvas paintings by artist Ismael Muhammud Nieves; each framed work measures 158 x 49.5 inches. Inspired by sitting on a porch or gazing out a window, letting the mind wander across the landscape, Nieves created a bright composition of Indiana native flowers and plants by incorporating emblematic images from the Eskenazi Health art collection together with Native American and Indiana state symbols incorporated with graffiti shapes:“Indiana’s landscape is beautiful year-round; the landscape has been enjoyed through contemporary eyes as well as the Native Americans who call this land home. Throughout the mural are woodland scenes directly inspired from the Eskenazi Health Art Collection.

The animals and foliage in the murals are native to Indiana. Incorporating graffiti shapes and palette, in my opinion, creates a fun atmosphere for the waiting area. There are parts of my painting. I challenge the viewers to identify them.” -Ismael Muhammad Nieves Crossroads was commissioned by Eskenazi Health as part of a re-imagining of the organization's historical art collection and to support "the sense of optimism and energy" of its new campus in 2013. In response to its nationwide request for proposals, Eskenazi Health received more than 500 submissions from 39 states, which were narrowed to 54 finalists by an independent jury; each of the 54 proposals was assigned an area of the new hospital by Eskenazi Health's art committee and publicly displayed in the existing Wishard Hospital and online for public comment. Crossroads is credited as "Dedicated with gratitude, The Ruthelen and Andrew Burns Family." Crossroads is located in the Special Medicine and Infusion Center Waiting Room on the 4th level of the Eskenazi Outpatient Care Center on the Sidney & Lois Eskenazi Hospital campus.

Ismeal Muhammud Nieves spent his early years in New York City before moving to Indiana as a teen. After serving in the U. S. military, he attended Purdue University, where received his B. S. in electrical engineering. A self-taught artist, Nieves’s work has been exhibited at South Shore Arts, the Indianapolis Museum of Contemporary Art, the Indiana University Northwest Gallery for Contemporary Art, Sheldon Swope Art Museum in Terre Haute, 2612 Space and Supreme Gallery in Chicago, Crewest Gallery in Los Angeles, among others. Nieves has completed several public mural commissions and has been involved with Subsurface, a graffiti event in Indianapolis, he is based in Indiana. Eskenazi Health Art Collection Sidney & Lois Eskenazi Hospital Ismeal Muhammud, Artist's Website Eskenazi Health Art Installations

Ken Orr

Kenneth T. Orr was an American software engineer and consultant, known for his contributions in the field of software engineering to structured analysis and with the Warnier/Orr diagram. Orr received his BA in Mathematics and Physics in 1960 from Wichita State University, his MA in Philosophy in 1963 from the University of Chicago. Orr started his career as Director of Information Systems at the State of Kansas in 1970. In 1973 he founded his own firm Ken Orr & Associates, which he directed until 1985, he was Professor at the School of Technology and Information Management of the Washington University in St. Louis, where he directed its Center for the Innovative Application of Technology. From 1988 until his death he was President of the Ken Orr Institute. Beginning in 2000, Ken served as Senior Consultant. Ken Orr died on June 14, 2016. Books Orr, Ken. Structured systems development. New York: Yourdon Press. ISBN 9780917072062. Orr, Ken. Structured requirements definition. Topeka, Kansas: Ken Orr and Associates, Inc.

ISBN 9780960588404. Articles, a selection Orr, Ken. "Methodology: the experts speak". Byte. 14: 221–233. ISBN 9781447134312. Orr, Ken. "Data quality and systems theory". Communications of the ACM. Association for Computing Machinery. 41: 66–71. Doi:10.1145/269012.269023. Orr, Ken. "CMM versus agile development: Religious Wars and Software Development". Business Agility & Software Engineering. Cutter Consortium. 3. Word document version. Orr, Ken. "Agile requirements: opportunity or oxymoron?". IEEE Software. IEEE Computer Society. 21: 71–73. Doi:10.1109/MS.2004.1293075. The Ken Orr Institute

Lady Anne Berry

Lady Anne Sophia Berry was an English-New Zealand horticulturist who founded Rosemoor Garden. She offered the garden to the Royal Horticultural Society in 1988. In 1990 she married Bob Berry and went to live on his farm at Tiniroto, New Zealand, she created the Homestead Garden of Hackfalls Arboretum. Berry was born in 1919 to the Walpole family in England, her father was the fifth and last Earl of Orford. He married twice, his second marriage was on 15 September 1917 to Emily Gladys Oakes, daughter of Rev. Thomas Henry Royal Oakes, the mother of Anne. One of the Walpole family members had been recorded at the siege of Acre in 1191. Generations remained an established part of the British political and literary world; some famous ancestors were: Sir Robert Walpole, the first Earl of Orford, who became Britain's first prime minister in 1721. He made significant plantings at Houghton Hall, England. Horace Walpole, the youngest son of Sir Robert, who became the fourth and last Earl of Orford of the first creation in 1791.

He was a knowledgeable plantsman. Recreated for a cousin in 1806, the title passed through the generations, Berry's father becoming the last Earl in 1894, he was aged 67. He had no son, decided to make over the family estate of Wolterton Hall of 4,000 acres to a distant male cousin in 1928, he emigrated to Manurewa, New Zealand, in 1928, died in 1931. In 1923 he had bought a 40-acre property called Rosemoor in North Devon as a fishing lodge. Berry and her mother lived there after 1928, thus Berry spent part of her youth in New Zealand. The free life in New Zealand suited her. Berry didn't go to school and had a governess. Back in England as a debutante proved to be a restricting time with all the social niceties including being present at Court, her mother created some of the earliest garden features at Rosemoor, such as the Stone Garden, which still lies at the heart of Berry's garden. On 25 November 1939, Berry married Colonel Eric Palmer, her early married life was spent "camp following" the regiment, including two and a half years in Northern Ireland.

Rosemoor was loaned to the Red Cross as a rest home for Londoners from the East End suffering the effects of the Blitz. Her first son John Robert was born on 6 March 1943. Anthony Eric Fletcher was born 4 November 1945. After the war her husband established a dairy farm. Berry's passion was horses in those days. "Lady Anne's initiation into gardening was somewhat akin to the conversion of St. Paul." In 1959 Berry stayed in Algeciras, for two weeks to recuperate from measles. There she met Collingwood Ingram, a well-known English plantsman, who opened her eyes to the world of plants. Collingwood Ingram sent loads of plants to Rosemoor from his own garden in Kent; this was the start of a marvellous collection. In 1960 serious development of the garden started. Soon there were other mentors such as Lionel Fortescue, the Heathcoat-Amory family of Knightshayes Court and others. Berry grew a knowledge on conditions that plants needed. Travels to New Zealand and Australia, Papua New Guinea, North America and temperate South America allowed her to see plants and plant combinations growing in their natural habitats, gave her opportunities to collect material.

In the late 1960s she joined the Royal Horticultural Society. Robin Herbert, who became a president of RHS invited her to join Floral Committee'B' which judged woody plants and new introductions, she was a founder member of the National Council for the Preservation of Plants and Gardens. In 1965 Berry joined the International Dendrology Society. In the 1970s she chaired the tours committee for nine years until about 1983, she became chairperson of the society for nearly five years. In 1970 she visited New Zealand and went to see Eastwoodhill Arboretum, Gisborne, its founder, William Douglas Cook had died a few years before. "Despite its run-down condition it was to me a impressive collection, at that time managed single-handedly by Bill Crooks", she remembered. In 1977 a group of members of the IDS visited New Zealand again, she nominated Eastwoodhill for the first brass plaque presented by the IDS for tree collections of outstanding merit. She visited Abbotsford Arboretum, the creation of Bob Berry for the first time.

In 1979 Berry started a small nursery at Rosemoor. By 1987 the catalogue had expanded to over 1000 items, she developed a collection of less common trees, of Hollies and Dogwood resulting in Rosemoor holding part of the UK NCCPG National Collection for these plants. In 1980 her husband died. In 1988 she offered Rosemoor to the Royal Horticultural Society: the house and the garden, the remaining 32 acres of the estate, farmland. By 1990 Rosemoor was opened as a "garden for all seasons". In 1990 Berry led a group of IDS members to Hackfalls Arboretum for the second time, she married Bob Berry that same year. "The story of Bob and Anne Berry of Hackfalls is a classic one in terms of the bonds created by dendrology". The marriage took place in England. In July 2006 Bob and Anne Berry left Hackfalls Station to live in Gisborne. Bob Berry died in 2018 aged 102.

Lorna G. Schofield

Lorna Gail Tiangco Schofield is a United States District Judge of the United States District Court for the Southern District of New York. Schofield was born January 22, 1956, grew up in New Haven and graduated from New Haven Senior High School in 1974, she was elected as Governor of Hoosier Girls State, a program of the American Legion Auxiliary, in 1973. Schofield received her Bachelor of Arts degree from Indiana University in 1977, she received her Juris Doctor from the New York University School of Law in 1981. From 1981 to 1984, she was an associate at the law firm of Cleary, Steen & Hamilton. From 1984 to 1988, she served as an Assistant United States Attorney for the Southern District of New York, prosecuting domestic terrorism and tax fraud, she became an associate at the law firm of Debevoise & Plimpton LLP in New York City in 1988 and was promoted to partner in 1991. She specialized in white collar criminal defense. In addition, she has been involved with the American Bar Association, holding a number of leadership positions, including Chair of the Section on Litigation.

On April 25, 2012, President Obama nominated Schofield to serve as a United States District Judge for the United States District Court for the Southern District of New York, to the seat vacated by Judge Shira A. Scheindlin. Schofield is the first Filipino American in the history of the United States to serve as an Article III federal judge. Schofield testified before the United States Senate Judiciary Committee on June 6, 2012; the committee reported Schofield's nomination to the full Senate on July 12, 2012. The Senate confirmed Schofield on December 2012 in a 91 -- 0 vote, she received her commission on December 13, 2012. Lorna G. Schofield at the Biographical Directory of Federal Judges, a public domain publication of the Federal Judicial Center. Lorna Schofield at Ballotpedia

Marine current power

Marine currents can carry large amounts of energy driven by the tides, which are a consequence of the gravitational effects of the planetary motion of the Earth, the Moon and the Sun. Augmented flow velocities can be found where the underwater topography in straits between islands and the mainland or in shallows around headlands plays a major role in enhancing the flow velocities, resulting in appreciable kinetic energy; the sun acts as the primary driving force, causing winds and temperature differences. Because there are only small fluctuations in current speed and stream location with minimal changes in direction, ocean currents may be suitable locations for deploying energy extraction devices such as turbines. Other effects such as regional differences in temperature and salinity and the Coriolis effect due to the rotation of the earth are major influences; the kinetic energy of marine currents can be converted in much the same way that a wind turbine extracts energy from the wind, using various types of open-flow rotors.

The total worldwide power in ocean currents has been estimated to be about 5,000 GW, with power densities of up to 15 kW/m2. The constant extractable energy density near the surface of the Florida Straits Current is about 1 kW/m2 of flow area, it has been estimated that capturing just 1/1,000th of the available energy from the Gulf Stream, which has 21,000 times more energy than Niagara Falls in a flow of water, 50 times the total flow of all the world’s freshwater rivers, would supply Florida with 35% of its electrical needs. The image to the right illustrates the high density of flow along the coast, note the high velocity white northward flow, perfect for extraction of ocean current energy. Countries that are interested in and pursuing the application of ocean current energy technologies include the European Union and China; the potential of electric power generation from marine tidal currents is enormous. There are several factors that make electricity generation from marine currents appealing when compared to other renewables: The high load factors resulting from the fluid properties.

The predictability of the resource, so that, unlike most of other renewables, the future availability of energy can be known and planned for. The large resource that can be exploited with little environmental impact, thereby offering one of the least damaging methods for large-scale electricity generation; the feasibility of marine-current power installations to provide base grid power if two or more separate arrays with offset peak-flow periods are interconnected. There are several types of open-flow devices. However, the more technically sophisticated designs, derived from wind-power rotors, are the most to achieve enough cost-effectiveness and reliability to be practical in a massive marine-current-power future scenario. Though there is no accepted term for these open-flow hydro-turbines, some sources refer to them as water-current turbines. There are two main types of water current turbines that might be considered: axial-flow horizontal-axis propellers, cross-flow Darrieus rotors. Both rotor types may be combined with any of the three main methods for supporting water-current turbines: floating moored systems, sea-bed mounted systems, intermediate systems.

Sea-bed-mounted monopile structures constitute the first-generation marine current power systems. They have the advantage of using existing engineering know-how, but they are limited to shallow waters; the possible use of marine currents as an energy resource began to draw attention in the mid-1970s after the first oil crisis. In 1974 several conceptual designs were presented at the MacArthur Workshop on Energy, in 1976 the British General Electric Co. undertook a government-funded study which concluded that marine current power deserved more detailed research. Soon after, the ITD-Group in UK implemented a research program involving a year performance testing of a 3-m hydroDarrieus rotor deployed at Juba on the White Nile; the 1980s saw a number of small research projects to evaluate marine current power systems. The main countries where studies were carried out were the UK, Japan. In 1992–1993 the Tidal Stream Energy Review identified specific sites in UK waters with suitable current speed to generate up to 58 TWh/year.

It confirmed a total marine current power resource capable theoretically of meeting some 19% of the UK electricity demand. In 1994–1995 the EU-JOULE CENEX project identified over 100 European sites ranging from 2 to 200 km2of sea-bed area, many with power densities above 10 MW/km2. Both the UK Government and the EU have committed themselves to internationally negotiated agreements designed to combat global warming. In order to comply with such agreements, an increase in large-scale electricity generation from renewable resources will be required. Marine currents have the potential to supply a substantial share of future EU electricity needs; the study of 106 possible sites for tidal turbines in the EU showed a total potential for power generation of about 50 TWh/year. If this resource is to be utilized, the technology required could form the basis of a major new industry to produce clean power for the 21st century. Contemporary applications of these technologies can be found here: List of tidal power stations.

Since the effects of tides on ocean currents are so large, their flow patterns are quite reliable, many ocean current energy extraction plants are placed in areas of high tidal flow ratesResearch on marine current power is conducted at