In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression. In the latter case, the variables appearing in the coefficients are called parameters, must be distinguished from the other variables. For example, in 7 x 2 − 3 x y + 1.5 + y, the first two terms have the coefficients 7 and −3. The third term 1.5 is a constant coefficient. The final term does not have any explicitly written coefficient factor that would not change the term. Coefficients are numbers as in this example, although they could be parameters of the problem or any expression in these parameters. In such a case one must distinguish between symbols representing variables and symbols representing parameters. Following René Descartes, the variables are denoted by x, y... and the parameters by a, b, c... but it is not always the case. For example, if y is considered as a parameter in the above expression, the coefficient of x is −3y, the constant coefficient is 1.5 + y. When one writes a x 2 + b x + c, it is supposed that x is the only variable and that a, b and c are parameters.
Any polynomial in one variable x can be written as a k x k + ⋯ + a 1 x 1 + a 0 for some positive integer k, where a k, …, a 1, a 0 are coefficients. For the largest i with a i ≠ 0, a i is called the leading coefficient of the polynomial. So for example the leading coefficient of the polynomial 4 x 5 + x 3 + 2 x 2 is 4; some specific coefficients that occur in mathematics have received a name. For example, the binomial coefficients occur in the expanded form of n, are tabulated in Pascal's triangle. In linear algebra, a system of linear equations is associated with a coefficient matrix, used in Cramer's rule to find a solution to the system; the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given M =; the leading coefficient of the first row is 1. Though coefficients are viewed as constants in elementary algebra, they can be variables more generally. For example, the coordinates of a vector v in a vector space with basis, are the coefficients of the basis vectors in the expression v = x 1 e 1 + x 2 e 2 + ⋯ + x n e n.
Degree of a polynomial Monic polynomial Sabah Al-hadad and C. H. Scott College Algebra with Applications, page 42, Winthrop Publishers, Cambridge Massachusetts ISBN 0-87626-140-3. Gordon Fuller, Walter L Wilson, Henry C Miller, College Algebra, 5th edition, page 24, Brooks/Cole Publishing, Monterey California ISBN 0-534-01138-1. Steven Schwartzman The Words of Mathematics: an etymological dictionary of mathematical terms used in English, page 48, Mathematics Association of America, ISBN 0-88385-511-9
Caroline von Wolzogen, born Caroline von Lengefeld, was a German writer in the Weimar Classicism circle. Her best-known works are a novel, Agnes von Lilien, a biography of Friedrich Schiller, her brother-in-law. Caroline von Lengefeld was the oldest child of an aristocratic family in Rudolstadt. Though her family belonged to the lower nobility, after her father died the financial situation was somewhat troubled. At 16, Caroline became engaged to Friedrich Wilhelm Ludwig von Beulwitz, a prominent local courtier, through the arrangement of both families. Much of her long engagement was spent with her family in Switzerland, a trip paid for by von Beulwitz. Lacking shared interests, the marriage was unhappy from the start. Caroline's closest confidante in the early years of her marriage was her cousin Wilhelm von Wolzogen, who, in 1785, introduced her and her sister to his friend Schiller a young and rather poor Weimar poet. In 1788, Schiller moved to a nearby town to be closer to the Lengefelds, both Caroline and her sister became closer to him.
Caroline felt a strong attraction toward him, though how far she considered taking it has been disputed by scholars. Schiller became engaged to Charlotte in August, 1789, credited Caroline for bringing them together. In the early 1790s, inspired by her friendship with Schiller and other literary figures in Weimar, Caroline began writing herself. Caroline von Beulwitz began writing her first novel, Agnes von Lilien, in 1793; the novel describes a young woman raised by a stepfather and growing up in isolation in the countryside, poor but educated in both classical and modern learning. A meeting with a much older and wealthier man, with whom she falls in love, begins a process of discovery of the world at large, including the politics and scandals of court life. Agnes discovers that her own background unknown to her, ties her to that world, which she embraces; as one critic has said, despite its interest in female subjectivity, "Agnes von Lilien is less about the establishment of a new society than it is about the restoration of the old to new legitimacy."In 1795, Schiller began a new periodical called Die Horen, which would contain articles on philosophy and history as well as fiction, organized around the central tenets of Weimar classicism.
Knowing his sister-in-law was writing, Schiller asked for a submission, Agnes von Lilien was published anonymously in Die Horen in installments, from 1796 to 1797. This publication, its eventual publication as a two-volume novel in 1798, led to considerable attention for the novel, speculation as to its author's identity; some believed it was a work of Schiller's, others a work of Goethe's, though Friedrich Schlegel was quick to dismiss the latter claim. The fuss led to the revelation of its true author, treated to much celebration, albeit short-lived. After this brief burst of activity and fame, Caroline's literary output slowed, her other major works were written at a much date, toward the end of her life, she and the other women writers included in Die Horen demonstrated a new potential for both aesthetically and commercially successful writing by women, but the ultimate role of women in the Weimar circle, the intellectual legacy of works like Agnes von Lilien, has been debated. Critic Peter McIsaac has observed that, though they included women writers in Die Horen and Goethe wrote of expunging their "feminine" qualities, continued to regard works by women as "dilettantish" and belonging to a lower form than their own work.
The novel was republished in 1988, has gotten much more widespread and sympathetic treatment since. Between the writing and publication of Agnes von Lilien, Caroline's life had changed markedly. In 1794, after years of unhappiness, she left von Beulwitz and married Wilhelm von Wolzogen, the cousin who had introduced her to Schiller, her family, including Schiller, responded negatively to this decision, she and von Wolzogen spent the next two years removed from their relations in Stein am Rhein, Switzerland. The von Wolzogens returned to Weimar in 1796, where the success of Agnes von Lilien created new connections for Caroline in the literary world. In 1802 she was contacted by Anne Louise Germaine de Staël, who had read and admired the novel, which led to an extended visit and correspondence between de Staël and the Weimar circle. After Schiller's death in 1805 and the subsequent growth of his literary reputation, Caroline von Wolzogen began collecting correspondence and reminiscences of her and her sister's life with the poet.
These were published under the title Schillers Leben in 1830, the first biography of Schiller to be published. In the biography, Caroline depicted her subject as a man continually beset by illness and dying young, but whose determination to carry on with his literary efforts nonetheless is cast as heroic; as the first biography and the only one written by an intimate associate, it has remained the first source for most biographical work on Schiller since. In the final years of her life, decades after Agnes, Caroline von Wolzogen wrote her second and final novel, published in 1840. Set during the Wars of Liberation, the novel centers around a woman torn between an obscure soldier she loves and an aristocrat she is pressured to marry by her family; the novel celebrates the soldier's national devotion while Cordelia marries the aristocrat, albeit without consummating the marriage. Two
The Breeders' Cup Juvenile Turf is an American Thoroughbred horse race for two-year-old horses, run on a grass course at a distance of one mile. It is part of the Breeders' Cup World Championships, the de facto year-end championship for North American thoroughbred racing. All Breeders' Cups to date have been conducted in the United States, with the exception of the 1996 event in Canada; the race was run for the first time in 2007 during the first day of the expanded Breeders' Cup at host track, Monmouth Park Racetrack in Oceanport, New Jersey. The race received Grade II status in 2009; the American Graded Stakes Committee further upgraded the race to Grade I status for 2011. Beginning in 2007, the Breeders' Cup developed "The Breeders' Cup Challenge," a series of races in each division that allotted automatic qualifying bids to winners of defined races; each of the thirteen divisions has between two and twelve of these "Win and You're In" qualifying races. In the Breeders' Cup Juvenile Turf division, runners are limited to 14, with up to five automatic berths.
Note though that one horse may win multiple challenge races, while other challenge winners will not be entered in the Breeders' Cup for a variety of reasons such as injury or travel considerations. The 2019 "Win and You're In" races are: the Juvenile Stakes, a Group 3 race run in September at Leopardstown Racecourse in Dublin, Ireland the Summer Stakes, a Grade 3 race run in September at Woodbine Racetrack in Toronto, Canada the Royal Lodge Stakes, a Group 2 race run in Septem1ber at Rowley Mile in Newmarket, England the Bourbon Stakes, a Grade 3 race run in October at Keeneland Race Course in Lexington, Kentucky the Prix Jean-Luc Lagardere, a Group 1 race at Longchamp Racecourse in Paris, France Most wins by a jockey: 4 - Ryan Moore Most wins by a trainer: 4 - Aidan O'Brien Most wins by an owner: 4 - John Magnier / Michael Tabor / Derrick Smith Breeders' Cup Juvenile Turf "top three finishers" and starters Breeders' Cup World Thoroughbred Championships American Thoroughbred Racing top Attended Events Racing Post: 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 2018
Glass-to-metal seals are a important element of the construction of vacuum tubes, electric discharge tubes, incandescent light bulbs, glass encapsulated semiconductor diodes, reed switches, pressure tight glass windows in metal cases, metal or ceramic packages of electronic components. Properly done, such a seal is hermetic. To achieve such a seal, two properties must hold: The molten glass must be capable of wetting the metal, in order to form a tight bond, The thermal expansion of the glass and metal must be matched so that the seal remains solid as the assembly cools. Thinking for example about a metal wire in a glass bulb sealing, the metal glass contact can break if the CTEs are not well aligned. For the case that the CTE of the metal is larger than the CTE of the glass, the sealing shows a high probability to break upon cooling. By lowering the temperature, the metal wire shrinks more than the glass does, leading to a strong tensile force on the glass, which lead to breakage. On the other hand, if the CTE of the glass is larger than the CTE of the metal wire, the seal will tighten upon cooling since compression force is applied on the glass.
According to all requirements that need to be fulfilled and the strong necessity to align the CTE of both materials, there only a few companies offering specialty glass for glass-metal sealing. Such as SCHOTT AG and Morgan Advanced Materials. Glass and metal can bond together by purely mechanical means, which gives weaker joints, or by chemical interaction, where the oxide layer on the metal surface forms a strong bond with the glass; the acid-base reactions are main causes of interaction between glass-metal in the presence of metal oxides on the surface of metal. After complete dissolution of the surface oxides into the glass, further progress of interaction depends on the oxygen activity at the interface; the oxygen activity can be increased by diffusion of molecular oxygen through some defects like cracks. Reduction of the thermodynamically less stable components in the glass can increase the oxygen activity at the interface. In other words, the redox reactions are main causes of interaction between glass-metal in the absence of metal oxides on the surface of metal.
For achieving a vacuum-tight seal, the seal must not contain bubbles. The bubbles are most created by gases escaping the metal at high temperature; this is achieved by heating the metal in vacuum or sometimes in hydrogen atmosphere or in some cases in air at temperatures above those used during the sealing process. Oxidizing of the metal surface reduces gas evolution. Most of the evolved gas is produced due to the presence of carbon impurities in the metals; the glass-oxide bond is stronger than glass-metal. The oxide forms a layer on the metal surface, with the proportion of oxygen changing from zero in the metal to the stoichiometry of the oxide and the glass itself. A too-thick oxide layer tends to be porous on the surface and mechanically weak, compromising the bond strength and creating possible leakage paths along the metal-oxide interface. Proper thickness of the oxide layer is therefore critical. Metallic copper does not bond well to glass. Copper oxide, however, is wetted by molten glass and dissolves in it, forming a strong bond.
The oxide bonds well to the underlying metal. But copper oxide causes weak joints that may leak and its formation must be prevented. For bonding copper to glass, the surface needs to be properly oxidized; the oxide layer is to have the right thickness. To improve the bonding to glass, the oxide layer should be borated; this treatment stabilizes the oxide layer by forming a thin protective layer of sodium borate on its surface, so the oxide does not grow too thick during subsequent handling and joining. The layer should have uniform deep red to purple sheen; the boron oxide from the borated layer lowers its melting point. The oxidation occurs by oxygen diffusing through the molten borate layer and forming copper oxide, while formation of copper oxide is inhibited; the copper-to-glass seal should look brilliant red scarlet. Too thin an oxide layer appears light, up to the color of metallic copper, while too thick oxide looks too dark. Oxygen-free copper has to be used. Copper contains small inclusions of copper oxide.
Hydrogen diffuses through the metal and reacts with the oxide, reducing it to copper and yielding water. The water molecules however can not diffuse through the metal, are trapped in the location of the inclusion, cause embrittlement; as copper oxide bonds well to the glass, it is used for combined glass-metal devices. The ductility of copper can be used for compensation of the thermal expansion mismatch in e.g. the knife-edge seals. For wire feed throughs, dumet wire – nickel-iron alloy plated with copper – is used, its maximum diameter is however limited to about 0.5 mm due to its thermal expansion. Copper can be sealed to glass without the oxide layer, but the resulting joint is less
Tina Mba is a Nigerian actress, nominated for Africa Movie Academy Award for Best Actress in a Supporting Role in the 7th Africa Movie Academy Awards. In 2017, she starred in Isoken, Bariga Suger, Okafor's Law amongst other films, was described as "actress of the year" by Pulse. At the 2017 Africa Magic Viewers Choice Awards, she was nominated for category, best actress in a comedy. In an interview with The Punch, she disclosed that the secret to her stellar interpretation of roles was from living the character and imagining herself in it, she stated that she would have preferred theatre to feature films, if she was paid for both. In 2016, she acted in a romantic drama, directed by Ikechukwu Onyeka. In October 2017, she starred in Omoye, an advocacy film against sexual violence. In 2017, she acted in Isoken alongside, Funke Akindele and Dakore Akande, she plays a mother, putting pressure on her daughter to get married and not be focused on her career. In the same year, YNaija recounts her previous roles in Tango with Me, Okafor's Law, etc. while stating that her stellar performances are not appreciated enough in the industry.
It opined that the "Naija" body language she brings to her character gives more realistic expression to her roles. Isoken Okafor's Law Make a Move Married but Living Single Heroes and Zeroes Tango with Me The Tenant Banana Island Ghost Three Wise Men Beneath Her Veil She is a native of Enugu State. Mba has two children. Tina Mba on IMDb
The 1973 Atlanta Braves season was the eighth season in Atlanta along with the 103rd season as a franchise overall. The highlight of the season was Hank Aaron finishing the season just one home run short of Babe Ruth as baseball's all-time home run king; the 1973 Atlanta Braves were the first team to boast three 40 home run hitters. They were Aaron, Darrell Evans, Davey Johnson. October 27, 1972: Rico Carty was traded by the Braves to the Texas Rangers for Jim Panther. January 10, 1973: Brian Asselstine was drafted by the Braves in the 1st round of the 1973 Major League Baseball Draft. January 21, 1973: Curt Blefary was signed as a free agent by the Braves. February 28, 1973: Pat Jarvis was traded by the Braves to the Montreal Expos for Carl Morton. March 26, 1973: Denny McLain was released by the Braves. Hank Aaron Dusty Baker Darrell Evans Ralph Garr Gary Gentry Rod Gilbreath Davey Johnson Johnny Oates Marty Perez May 19, 1973: Andre Thornton was traded by the Braves to the Chicago Cubs for Joe Pepitone.
June 7, 1973: Pat Dobson was traded by the Braves to the New York Yankees for Frank Tepedino, Wayne Nordhagen, players to be named later. The Yankees completed the deal by sending Dave Cheadle to the Braves on August 15 and Al Closter to the Braves on September 5. June 19, 1973: Joe Pepitone was released by the Braves. At the age of 39, Aaron managed to slug 40 home runs in 392 at bats, ending the season with 713, which at that time one home run short of the record, he hit home run number 713 on September 29, 1973, with one day remaining in the season, many expected him to tie the record. But in his final game that year, playing against the Houston Astros, he was unable to hit one out of the park. After the game, Aaron stated; that statement was not just about the death threats: one year earlier, September 30, 1972, was the last day that the legendary Roberto Clemente played, as he perished in the offseason. Note: Pos = Position. = Batting average. = Batting average. The Encyclopedia of Minor League Baseball.