Background and composition.

In the book "Chicken Soup for the Soul: The Story Behind the Song", Aguilera revealed the occasion, theme and meaning of "Fighter". She talked about her "very chaotic and abusive" home, where she did not feel "safe". In school, Aguilera was picked on and alienated because of her musical passion. However, it made her become "smarter and stronger". To release herself, Aguilera started to write songs at the age of 15, both music and lyrics; and it was the way how she found her voice. The writing process of "Fighter" began during her promotion for her debut album in 1999, when she was "a part of the big craze pop phenomenon". According to Aguilera, her debut album helped her a lot to develop the process. She wanted to make an "emotionally rich and positive empowering" song, especially for women, in order for them to speak for themselves be strong. About the idea of the track, she revealed, "I was coming up with titles and ideas and deciding what I wanted to write about. I had to sit down and make sense of my feelings and experiences. I learned a lot from the first record that helped me to develop. I took the good and the bad and considered some of the choices I made and became better because of it. Sal Cinquemani from Slant Magazine characterized "Fighter" as a hybrid of R&B and rock. Meanwhile, a reviewer of "Billboard" described the song as arena rock-influenced, and AOL Music's Nana-Adwoa Ofori noted the elements of rock and roll. However, Nick Levin from Digital Spy detailed "Fighter" as an arena rock piece. The song was inspired by band Guns N' Roses' song "November Rain" (1992). Written in the key of E minor, "Fighter" has a moderate tempo of 96 beats per minute. Brian Hiatt from "Entertainment Weekly" and Chuck Taylor for "Billboard" likened the track's musical style to that of Janet Jackson's "Black Cat". Aguilera's vocals on the track span from the low-note of G to the high-note of G; Taylor labelled Aguilera's vocals "tornado of a vocal."  At the beginning of "Fighter", the guitar sound was arranged in the chord progression of Em – G/D – D – C – Em/B – B – Am – C/G – G – B. Aguilera speaks the lyrics, "After all you put me through, you'd think I'd despise you / But in the end, I wanna thank you, 'cause you made me that much stronger" on the guitar theme by Dave Navarro. Lyrically, Aguilera wants to thank the man who did her wrong rather than insult him, because he helped make her stronger and work harder, thus making her a fighter. At the chorus, she sings, "'Cause it makes me that much stronger/ Makes me work a little bit harder/ Makes me that much wiser/ So thanks for making me a fighter". The chords in the guitar part are E – F – G – A – B − C – B – A – G – F – E. She continues, "Made me learn a little bit faster/ Made my skin a little bit thicker/ Makes me that much smarter/ So thanks for making me a fighter". The lyrics of "Fighter" have been recognized as "empowering".  On the first episode of "RuPaul's Drag Race Untucked" season 10, Aguilera said the song was about someone she loved but "deserved it".

Reception.

Critical reception.

"Fighter" received mostly positive reviews from music critics. David Brownie from "Entertainment Weekly" called it "spunkier than one would expect from a dance-floor strumpet who loves to flaunt her lung power." Chuck Taylor writing for "Billboard" complimented "Fighter" for demonstrating that Aguilera "[has] got the goods to rise above what so many lesser acts depend on for celebrity." On behalf of the same publication, Andrew Unterberger wrote that "Fighter" and "Can't Hold Us Down" are two tracks that helped "expand audience expectations of her image and sound." Digital Spy's Nick Levine named it a "strutting arena rock" song, while Nick Butler from Sputnikmusic simply called it "great." "The New York Times" editor Kelefa Sanneh positively viewed the track's theme as "fearless" and "full of mildly rebellious rhetoric." On a less positive side, BBC Music's Jacqueline Hodges called the song "hilarious", while Jancee Dunn from "Rolling Stone" wrote that the song "is a sterile foray into rock."

Chart performance.

In the United States, "Fighter" debuted at number 61 on the "Billboard" Hot 100 chart on April 12, 2003, becoming the week's best-debuting single. In the following week, it jumped to number 56. On the issue dated April 26, 2003, the single charted at number 46. In its fourth week charting, "Fighter" raised to number 38. The single grew ten positions, charting at number 28 on May 10. On May 17, 2003, it charted at number 22. "Fighter" finally peaked at number 20 in its seventh week charting, becoming Aguilera's ninth top-twenty hit on the chart. On the Pop Songs chart, it peaked at number five. The single also peaked at number 28 on the Adult Pop Songs. On November 1, 2003, "Fighter" was certified gold by the Recording Industry Association of America (RIAA) for shipping more than 500,000 copies in the country. As of August 2014, the single has sold 1,184,000 million digital units in the United States. On the Canadian Singles Chart, it peaked at number three.  Throughout Europe, "Fighter" also attained moderate success on charts, peaking within the top 15 in most of the countries where it charted. It reached number 11 in Belgium (Flanders) and Switzerland, number 12 in Norway and Sweden, number 13 in Germany, and number 15 in Denmark, Italy and Spain. In Hungary, it peaked at number 8 on the Mega Top 100 Singles. The single also reached the top five in the Netherlands. On the UK Singles Chart, "Fighter" was a commercial success, peaking at number three and remained there for 13 weeks, becoming the longest-running single from "Stripped" on the chart. As of February 2013, "Fighter" has sold 159,000 copies in the United Kingdom. The single also garnered success in Australia and New Zealand, peaking at number five and 14 respectively in the two regions. Due to its chart success in Australia, the Australian Recording Industry Association (ARIA) certified "Fighter" gold for its shipments of 35,000 copies there.

Music video.

The music video for "Fighter" was directed by Floria Sigismondi, who revealed that it would display Aguilera "like I don't think she's been portrayed before". On March 10, 2003 and March 12, 2003 the video was filmed in Los Angeles, California and was inspired by the director's signature dark theatrics and the life circle of moths. Sigismondi explained the theme and plot of the clip to MTV News: "The song is sort of about transformation, so I took that in a nature kind of way, the way nature deals with transformation. It's basically about coming from a very poisoned place to an empowerment, a place of strength. I've always had this fear of moths, and I subconsciously wrote this thing with these moths in it, so I guess I have to deal with it. They're furry and they carry dust. I found out in old mythology they are supposed to represent the soul. I think that's very appropriate".  The video begins with Aguilera wearing a black velvet kimono, with a pale complexion and long black hair, refers to a larva. Initially, she is trapped in a glass box, and her kimono is billowing like a balloon. Three Gothic ballerinas eat fruit and then collapse. Aguilera then breaks free from the box by pounding on it until it shatters. She furiously removes three moth pins from her back, and then tosses aside her kimono. A tattered, white, moth-covered dress is revealed, symbolizing her metaphoric evolution from the larva to a pupa. In addition, her hair becomes white, and moths fly around her. Intercut scenes of moths and Aguilera's blue eyes are then shown. Near the end, Aguilera wears an Elvira-type spider dress, again proclaiming that she is a "fighter" before kicking at the camera.  The music video for "Fighter" garnered numerous awards. At the 2003 Belgian TMF Awards, the clip won Best Video International. It garnered Aguilera and Sigismondi a Juno Award for Video of the Year at the 2004 ceremony, which was held at Rexall Place in Edmonton, Alberta, Canada. It also earned four MVPA Awards for Best Pop Video, Best Cinematography, Best Make-Up and Best Styling in a Video in 2004, held at Orpheum Theater in Los Angeles, California.

Live performances.

Aguilera performed "Fighter" on a number of shows. The singer performed the song for the first time on "Saturday Night Live" on March 15, 2003. Aguilera also performed "Fighter" at the 2003 MTV Video Music Awards, held at Radio City Music Hall in New York City on August 28, 2003, in a medley with "Dirrty".<ref name="mtvvma"

"Fighter" is a song recorded by American singer Christina Aguilera for her fourth studio album, "Stripped" (2002). The song was written by Aguilera and Scott Storch, and produced by the latter. It was released by RCA Records as the third single from "Stripped" on March 13, 2003. Inspired by Guns N' Roses' song "November Rain", "Fighter" was characterized as a hybrid of rock and R&B that incorporates elements of arena rock and rock and roll. The track sees Aguilera thanking a man who had done wrong to her for making her a "fighter."


History.

The town is capital of the Luhya kingdom of Wanga. King Nabongo Mumia, who came to power in 1880, was the last sovereign king of Wanga. He was succeeded by his son Shitawa who ruled after his death in 1949 till the late seventies. He then was succeeded by Mumia II who is currently in power. His role remains largely non executive, but the royal family draws taxes from the trade that goes on in the county council of Mumias, which is to date still regarded as the seat of power. This includes taxes from the Mumias Sugar Company. The family still owns the land in the county although bits and pieces have been sold off to private developers. The entire Royal Family is still very closely linked to the choices of political leaders in the region as well as to their royal ties of the Abashitsetse clan. Each family has its own meetings (families keep the family tree with major families arising from the last sovereign Wanga government, with the brothers of King Mumia forming the Patriarchal Heads of the family). One other very noticeable family is the Kadima family. Mumias has a noticeable Muslim community, unique in western Kenya. It derives from trade links between Wanga state and coastal Kenya.  The town was known as "Lureko" until it was renamed Mumias.  The Nabongo Cultural Centre in Matungu showcasing the Wanga Kingdom was opened in the outskirts of Mumias in 2008, near the traditional homestead of Wanga kings (Nabongos).

Mosque.

The area of Lukoye has a mosque called "Sheikh Khalifa Mosque", which was built in 1991 with Kuwaiti assistance.

Mumias is a town in Kakamega County of Kenya. The town has an urban population of 116,358 (2009 census). Mumias was the center of the Mumias District. The town is linked by road to Kakamega (in east), Busia (west), Bungoma (north), Butere (south). The village of Buchinga is located between Mumias and Kakamega.


Early life.

Born in Prince Edward Island, Canada, Simpson moved with his family to Oneida County, New York when he was six. Although he did poorly in school, he was very intelligent and a voracious reader. During the Civil War, he served in the Illinois Volunteer Infantry, but was discharged for medical reasons.  After the war, Simpson moved to Indiana, where he signed on as a deckhand on a steamship that traversed the Great Lakes. By the time he had risen to the position of captain, he had married and started a family. Deciding to live a more stationary life, he moved to Jackson County, Kansas and bought himself a farm.

Later life.

He married in 1870. In the late 1870s, a combination of hard times for farming in general and the death of his child in a sawmill accident drove Simpson to move south, to Barber County, Kansas, where he bought a ranch and a herd of cattle.  In late 1883 and early 1884, a long, hard winter killed his entire herd, and Simpson was reduced to working as the town marshal in Medicine Lodge, Kansas. It was during this time that Simpson, angry at his plight, first involved himself in politics, becoming an organizer for the Union Labor Party, a local offshoot of the defunct Greenback Party (of which he had been a member). He ran as their candidate for the state legislature in 1886 and 1888, but was defeated by the T. A. McNeal of the state's dominant Republican Party.  In 1889, the price of corn, the state's principal crop, dropped precipitously, and it was burned as fuel all across Kansas. Seizing the moment, remnants of the Farmers' Alliance organized into the People's Party, and Simpson joined on. At the convention of the Kansas People's Party, Simpson was easily nominated as the Party's candidate for Congress.  Simpson's Republican opponent was Colonel J. R. Hallowell, an attorney for a railroad who campaigned from the back of a private rail car. Simpson, campaigning on a populist platform of public ownership of railroads, a graduated income tax, the abolition of national banks, and universal suffrage, denounced Hallowell as a pampered scion of wealth whose feet were "encased in fine silk hosiery." Hallowell fired back that having silk socks was better than having none at all. With the help of populist campaigner Mary Elizabeth Lease, Simpson won a new nickname, "Sockless Jerry," and an 8,000-vote margin of victory in the race.  In Congress, Simpson was a forceful advocate for populist causes and became nationally known as the party's congressional leader. In 1892, he was re-elected by a slim 2,000-vote majority, running slightly behind James Weaver, the party's presidential nominee, who had also managed to seize the Democratic ballot line in Kansas. By 1894, however, the party's fortunes had already started to wane, and he was turned out of office in favor of Republican Chester I. Long in a close race.  Undaunted, Simpson returned in 1896, running hard against Long and upsetting him to win back his House seat. It didn't last, however, and Long defeated him once again in the election of 1898.  Deciding that he had lost his taste for farming, Simpson moved to New Mexico and took up real estate. A few years later, he suffered a debilitating brain aneurysm. Realizing that he probably didn't have much time left, he boarded a train back to Kansas. He died in a Wichita hospital on October 23, 1905. He is interred in Maple Grove Cemetery, Wichita.

Jeremiah Simpson (March 31, 1842 – October 23, 1905), nicknamed "Sockless Jerry" Simpson, was an American politician from the U.S. state of Kansas. An old-style populist, he was elected to the United States House of Representatives three times. He was a Georgist and former greenbacker.


Geography.

The municipality is divided into 5 popular councils (wards or quarters), named after the most important towns, which are: Melena del Sur, Mañalich, Guara, Lechuga and Monte-Zapote. Its population exceeds 20,000 inhabitants of whom about half live in the town.  In the beach area just live few permanent residents and then some fishermen, it is usually a recreation area. With the holiday season, during the months of July and August this move to a large number of people seeking the enjoyment of the water in the company of family and friends. The start of the holiday season is marked by activities organized by the inauguration of the Government in the locality.

History.

The foundation date is from the first years of the second part of the 18th century. In 1768 is the origin in terrain of the llanura of Güines, in the Corral «Melena del Sur» o «San Juan». The 14 of January 1878 is marked the "Ayuntamiento of Melena del Sur", and reorganized in the year 1899.  Foundation: There are several versions regarding the meaning of the name Melena, which is home to some Greek (Melaine: black) and was the predominant color of some of its most fertile land. Most likely due to the name of a place of early settlers who founded the San Juan de Melena corral, where he later built the first house, which led to the current town. Still debate about whether it was on its shores or in neighboring Batabanó where he first founded the city of Havana in 1515 before being transferred to the northern coast. As a result, the municipal coat of arms is the Latin phrase "HAVANA PRIMO HIC EST CONDIT", i.e.: Here was first founded Havana.  On the local People's Power Municipal is the direction of local government and is composed of several units which yield information on the progress of work as the economy, services, sports, culture, recreation, etc. Relations of solidarity with the City of La Oliva of Spain, who go to the island to support different tasks alongside people.  For Mañalich and Guara, crossing the railroad oldest Cuba and Latin America, which originally reported the cities of San Cristobal de Havana and St. Julian of the Güines, it now extends to the city of Cienfuegos, and is connected to the circuit northern railways.

Economy.

The municipality's economy is almost entirely composed of the Agricultural Crops Enterprise, followed by UBPC, CPA and CCS that comprise the Company and Agricultural Gregorio Arlee Mañalich emerged following the demise of its objects in such company as Agro-Industry (2006–2007) and his commitment to agricultural development just like the UBPC, CPA and CCS it. There are farms engaged in animal fattening and poultry are birds, pigs, turkeys, etc. and intensified breeding cattle by other institutions.

Education.

In order to Education, the municipality has an integrated system to ensure development of primary, secondary, middle and upper level, plus the emergence of the University of municipalization where three sites are responsible for the preparation of students in different degrees.  The Municipality has two polytechnic institutes where students are studying technical courses such as Accounting, Construction and other related specialties Agriculture among others. Among the pre-university is the Institute of Vocational Sciences Studienkolleg Félix Varela. In each classroom of the different centers are located enseñansa a television crew to be able to provide through this medium the teleclases a different student. In addition, each school has at least one computer lab to enhance the teaching of learners.

Health.

The development of Public Health is taking booming at the moment as part of the tasks undertaken by the Cuban Government to improve this system. With the existence of a home where the Mother is given to pregnant women who have problems during pregnancy, a physiotherapy room, a polyclinic with equipment to perform ultrasound, Rayos X, a clinical laboratory, a small recovery room for patients for their needs should be a short time lodging, plus an intensive care room equipped with modern technology for these purposes.  The Municipal Policlinico medical services on call 24 hours a day as well as laboratory services and Rays "X" and intensive care. The unification of the Central Municipal Ambulance Provincial with the Network helps ensure a better service in the care of emergencies.

Culture.

For the enjoyment and recreation of its inhabitants the Directorate of Culture has various libraries scattered localities in the municipality, as well as a House of Culture, the Melena del Sur Municipal Museum and an Art Gallery.

Melena del Sur is a town and a municipality located south of the Mayabeque Province, in Cuba. Bordered on the north and northwest by San José de las Lajas, on the east by the municipality of Güines, and west by Batabanó and by the south by the Gulf of Batabanó. In the south shore is located the only beach in the town, Mayabeque Beach. In this beach is the old outlet of the Mayabeque River (called Antiguo Mayabeque).


Life and career.

Ledgerwood was born in 1959 in the small farming community of Brazil, Indiana and identified as an artist from an early age. Her Midwest upbringing informed the sense of space and light in her early landscape-related work and her later use of craft and decorative forms relates to being from, in her words, a "family of quilters." Ledgerwood attended the Art Academy of Cincinnati (BFA, 1982), where she met her future husband, artist Tony Tasset. After graduating, she enrolled at the School of the Art Institute of Chicago (SAIC), attracted by that city's balance of affordability, available large studio spaces, and connection to the larger art world. At SAIC, she studied under artists Christina Ramberg and Phil Hanson, among others, earning an MFA in 1984.  Ledgerwood was part of a conceptually oriented group of Chicago artists that embraced theory and a global, rather than regional, view of the art world, distinguishing them from the earlier Chicago Imagists. She began exhibiting professionally in group shows at galleries such as Randolph Street and Feature in 1987–8; solo efforts at Scott Hanson Gallery (New York, 1989) and Robbin Lockett Gallery (Chicago, 1989–92) soon followed. In 1993, she began her teaching career at SAIC; she joined the Department of Art, Theory and Practice at Northwestern University in 1995, and was tenured in 2002. She has served as the department's Director of Graduate Studies and is the Alice Welsh Skilling Professor of Art. Ledgerwood has continued to exhibit widely, at galleries including Häusler Contemporary (Munich/Zurich, 2005–19), Tracy Williams Ltd. (New York, 2005–16), 1301PE (Los Angeles, 2002–19), Rhona Hoffman (Chicago, 2000–18), Feigen, Inc. (Chicago/New York, 1993–2000), and Barbara Davis (Houston, 2013–9).

Work and reception.

Ledgerwood emerged in the 1980s during a postmodern crisis of faith in painting's relevance, viability, patriarchal conceits, and commodification by the art market—issues her work addresses through a range of formal and feminist-critical strategies. Her early work investigated gender issues encoded in 19th-century landscape painting and mid-20th-century Abstract Expressionism through formal choices informed by being female. Her later work has shifted toward less referential, more direct abstraction focused on structure, light, color, decorative motifs, and physical presence and experience; it directly or indirectly references antecedents including Op Art, Matisse, Warhol, and the Pattern and Decoration movement. Critics identify as central to her work: transgressive use of color as a vehicle for content and critique; imposing scale; attention to spatial relationships between picture plane and edge and surrounding physical space; freely painted, shifting motifs of patterned basic shapes; an emphasis on performative and material aspects of painting; a phenomenological embrace of tenuousness and optical effects regarding the viewing experience.

Landscape-related abstraction (1988–1993).

Critic Kathryn Hixson described Ledgerwood's early paintings as cunningly painted "commodity object[s] of seemingly inspired, moody, atmospheric space" appropriated from the sublime traditions of Romanticism (Turner, Ryder) and color-field painting (Rothko, Newman), rather than inspired by nature. Largely monochromatic and monumental, they featured nearly uniform oil and encaustic surfaces that hovered between enveloping abstraction and irregular fields barely suggesting landscape (e.g., "Composition in Pink, Brown and Violet" or "Summer Fog", 1992), with occasional insertions of small, flat rectangles that blurred distinctions further. While traditional reviewers were sometimes less attuned to Ledgerwood's conceptual intent, others identified in her articulation of differences a subversion of conventional equations of sublime with masculine, and beauty with feminine. Maureen Sherlock suggested that Ledgerwood's canvasses restaged domestic, "demure and private gestures" in powerful, public form through their highly charged synthetic colors (pinks, roses, reds), which evoked female domains (cosmetics, the body, interior design), and intimate markmaking (dabs, finger-painting), which deflated the mythic power and profundity of Abstract-Expressionist gesture. David Pagel described the work as orchestrating a "double-sided viewing" that "surreptitiously traced the power of American abstraction back to nature" and played havoc with simplistic oppositions such as abstract/representational, pure paint/illusionism, culture/nature.

Circular-motif abstraction (1993–2002).

In the early 1990s, Ledgerwood transitioned toward patterned abstraction with directly drawn, sharper-edged circular forms that suggested shimmering light (e.g., "Blackness Light", 1992; "Rainlight", 1993) and increasingly delved into the experience of perception. This work employed monochromatic or limited palettes and dissolving grid arrangements of dots, circles or loops, creating complex, flat plays of oscillating color, tone, surface finish and figure-ground based on light conditions, viewer position and retinal effects; critics suggest that this indeterminacy introduces elements of extended time, discovery, and "unknowability" into the viewing experience. Ledgerwood explored this motif in various color palettes, combining blacks with pinks, purples, magentas and ultramarine (e.g., "Tranquilizer", 1997; "Basement Love", 1999) in a series exploring sexuality, and yellows on silver and white in another, Op-Art-like series. One of the latter works (the 17' x 35' "Groovin' on Lemon", 1995) comprised half of a temporary, site-specific installation commissioned for the new MCA Chicago building, which Ledgerwood described as "a meditation on light and rhythm." The adjacent, same-sized companion, "Groovin' on Violet", fully emerged only after a viewer's eyes adjusted, replicating the afterimage formed from viewing the other work.  In 1999, Ledgerwood presented "Cold Days", a body of work specifically created to interact with the changing winter light that would flood its January exhibition at Chicago's Renaissance Society. The show's centerpiece was a wall of five, 8' x 9' works painted in subtly modulating lilacs, pastel blues, greens, browns and metallic silvers that functioned as an environment. Bearing titles drawn from Miles Davis's "Kind of Blue" album, the paintings opened to a wide range of allusions, from pop culture, fashion and design to the glamour and effervescence of champagne bubbles to climate (brittle temperatures, the sheen of ice, winter light, whiteouts) and states of contemplation. Critics compared the work's myriad shifts between obscurity and clarity to those of the Rothko Chapel and Light and Space installations of Robert Irwin. Craig Adcock wrote that the paintings resided "between being and nonbeing, just between the abyss inside and the boundless horizon outside. The operative category is the sublime, shorn of its macho, Kantian implications." In 2002, Ledgerwood created a comparable body of work for exhibition in Los Angeles, titled "Sunny Days" (1301PE, 2002).

Patterned abstraction and wall paintings (2002– ).

Ledgerwood's later work shifted toward repeated vernacular motifs (chevron and diamond, quatrefoil, and floral patterns) and a more confrontational approach embracing discordant color, an integration of painting and drawing, and greater co-optation of architectural space, including that between painting and viewer. Michelle Grabner suggested this new work laid "bare Ledgerwood's distrust of elegance and finesse" with its contemporary, doodle-like drawing, loose Pop and quilt-like patterns, Matissean flatness, and funky interior-design palettes. "New York Times" critic Ken Johnson described later works in this vein as "paradoxical fusions of actuality and virtuality" painted with "the carefree abandon of an improvising jazz musician." He and others noted Ledgerwood's use of irregular white-bordered edges suggesting drooping, bowed tapestries or quilts pinned to walls (e.g., "Grandma's Flower Garden", 2006, above)—a reference to traditionally feminine arts—which combined with her overt decorative forms and de-stabilized grids to upend high-modernist conceits of seriousness.  Other critics, such as John Yau and Roberta Smith, have focused on an anarchic element in the work, which foregrounds imperfection and irregularity, process and messiness, humor and female sexuality, and challenges notions of the sublime and beautiful. Ledgerwood has written that a 2003 health scare prompted a reconsideration and shift in direction in her work, initially signaled—in title and form—in her show, "Ugly Beauty" (2004). Writers suggest that show's off-kilter diamond-patterned grids, unbalanced color interactions, and perspectival shifts posited a modernism reoriented toward fragility and an ungainly, lifelike mortality. Ledgerwood has frequently extended this work into architectural space, as she did in the public commission "Jour et Nuite" (Paris Metro RATP Station, 2007) and two solo shows—"Hard Jam" (Tracy Williams Ltd., New York, 2007) and "Chromatic Patterns" (Hausler Contemporary, Zürich, 2008)—that featured monumental paintings and site-specific wall painting installations. In the exhibitions, she created progressions of accumulating motifs and bands of color, with single works building to painted environments that assimilated interior architectural elements and replicated being inside a painting. Ledgerwood created variations on "Chromatic Patterns" in immense, site-specific installations at the Smart Museum of Art (2013–5), Graham Foundation for Advanced Studies in the Fine Arts (2014) and Art Institute of Chicago (2018).  In 2010s, Ledgerwood has also increasingly introduced three-dimensional elements into her practice. These include a body of smaller, simplified paintings featuring more thickly painted, iconic cruciform arrangements of circles and schematized floral shapes (e.g., "Post Punk Female Abstraction", 2010), passages of thick, viscous paint squeezed straight out of the tube, relief-like polyurethane "blob paintings," and large, painted ceramic vases.

Collections and recognition.

Ledgerwood's work belongs to the public art collections of the Metropolitan Museum of Art, Museum of Contemporary Art, Los Angeles, Art Institute of Chicago, Museum of Contemporary Art Chicago, Kunstmuseum St. Gallen (Switzerland), Hammer Museum, Chicago Public Library, Mary and Leigh Block Museum of Art, Milwaukee Art Museum, and Smart Museum of Art, among others. Ledgerwood is a recipient of awards from the Richard H. Driehaus Foundation, Artadia, and Louis Comfort Tiffany foundations, the National Endowment for the Arts, and the Illinois Arts Council.

Judy Ledgerwood (born 1959) is an American abstract painter and educator, who has been based in Chicago. Her work confronts fundamental, historical and contemporary issues in abstract painting within a largely high-modernist vocabulary that she often complicates and subverts. Ledgerwood stages traditionally feminine-coded elements—cosmetic and décor-related colors, references to ornamental and craft traditions—on a scale associated with so-called "heroic" abstraction; critics suggest her work enacts an upending or "domestication" of modernist male authority that opens the tradition to allusions to female sexuality, design, glamour and pop culture. Critic John Yau writes, "In Ledgerwood’s paintings the viewer encounters elements of humor, instances of surprise, celebrations of female sexuality, forms of vulgar tactility, and intense and unpredictable combinations of color. There is nothing formulaic about her approach." Ledgerwood has exhibited widely at galleries throughout the United States and in Europe and at institutions including the Art Institute of Chicago, Museum of Contemporary Art Chicago, Smart Museum of Art, and Renaissance Society. Her work belongs to the public art collections of the Metropolitan Museum of Art, Museum of Contemporary Art, Los Angeles, Art Institute of Chicago, and Museum of Contemporary Art Chicago, among others; a monograph, "Judy Ledgerwood", was published in 2009 by Hatje Cantz. Ledgerwood lives and works in the Chicago area with her husband, artist Tony Tasset, and teaches at Northwestern University.


Early years.

A native of Tallahassee, Florida, Sims attended North Florida Christian High School, where he began his high school football career by earning a varsity letter while only in the eighth grade, a feat not often heard of. A two-way player at running back and linebacker, Sims earned a total of five varsity letters. Playing in Class A, Florida's smallest classification, Sims led the Eagles to four state championships from 1998 to 2001. In his senior year, however, North Florida was eliminated in the region semifinals of the Class A playoffs, losing to Jay 19–14. As a junior, totaled 180 tackles, 41 tackles for loss, 12 sacks and forced seven fumbles on defense and rushed for over 600 yards and 17 touchdowns as a tailback. During his senior year, Sims registered 133 tackles (73 solo stops), 15 tackles for lost yardage, six forced fumbles, seven fumble recoveries and one blocked field goal attempt from his linebacker position and ran for 1,081 yards on 115 carries for 23 touchdowns as a running back.  Sims earned All-American honors by "Parade" and "USA Today". Regarded as a five-star recruit by "Rivals.com", Sims was ranked as the No. 1 inside linebacker in his class. In fact, he was also listed as the No. 1 prospect overall, ahead of Reggie Bush and Whitney Lewis., Sims remains the only linebacker ranked atop of the "Rivals" annual rankings. Recruited by virtually every school in the nation, Sims took official visits to Georgia, Florida, Auburn, Miami (FL), and Florida State. On National Signing Day, Sims chose the Seminoles over the Gators.

College career.

At Florida State, Sims wore #34, a number that was retired in honor of former Seminole football player, Ron Sellers. Sellers gave Sims and the university permission for Sims to wear the jersey number.  In 2003, as a true freshman at Florida State, Sims played in all 13 games of the season, including the Orange Bowl against Miami (FL), as a back-up outside linebacker. He finished ninth on the team with 42 tackles, and added two tackles for lost yardage, two pass break-ups, three quarterback hurries and a forced fumble. Sims was also one of the Seminoles' top special teams performers. He earned ACC Rookie of the Week for his efforts against Wake Forest, which included a season-high 10 tackles.  As a sophomore, Sims played in all 12 games, and made the starting lineup by the second week. For his exceptional play on the field in 2004, Sims was named to the second All-ACC team and ESPN named Sims to their first team All-American team. He finished second on the team with a single-season career-high 86 tackles, behind only A. J. Nicholson (88). Sims also recorded a single-season career-high nine tackles for lost yardage, 4.5 quarterback sacks, nine quarterback hurries, five pass break-ups, two forced fumbles and a blocked kick. In three games (North Carolina, Duke, and Florida), Sims recorded double-digit tackles, including a career-high 12 tackles against the Gators. In the Seminoles' 36–3 victory over Virginia, he had nine tackles, a career-high two sacks and a blocked punt. Sims followed that performance with eight tackles, one tackle for lost yardage, a sack and a pass break-up against Wake Forest. Each of those weeks, Sims earned ACC Defensive Back of the Week, as the only player in the ACC to earn the ACC Defensive Back of the Week honors multiple times during the season.  In July 2005, Sims was arrested on charges of battery and resisting an officer, allegedly shoving his then-girlfriend “repeatedly to the ground” during an argument in the parking lot of a FSU residence hall. Expectations for his junior year were high, as "The Sporting News" and other publications named him to their pre-season All-American teams. Sims had a productive, but not spectacular junior season, starting all 13 games, including the Orange Bowl.  Sims majored in Environmental Studies at Florida State. In January 2006, Sims announced that he would forgo his senior season to focus on a career in the NFL.

Professional career.

2006 NFL Draft.

Described as a “three-down linebacker who plays bigger than his listed size,” Sims was selected as ninth overall in the first round of the 2006 NFL Draft by the Detroit Lions. He was the highest selected Seminoles defender since Corey Simon in 2000.

Detroit Lions.

Sims was targeted by Lions general manager Matt Millen to bolster the Lions' defense at weakside linebacker. On July 30, 2006, he signed a 5-year, $15.735 million contract with $12.1 million guaranteed. Sims started all 16 games his rookie season at outside linebacker, collecting 124 tackles (81 solo tackles) and was credited with a half sack and one pass deflection. On December 3, against the New England Patriots, Sims had a career-high 13 total tackles. On December 31, Sims made a key tackle on fourth down to give the Lions a big win against the Dallas Cowboys. On September 3, 2007, Sims was named one of five captains for the 2007 Detroit Lions. The Lions former head coach, Rod Marinelli, said that Sims' resembled that of Tampa Bay Buccaneers linebacker Derrick Brooks in his early years, being described as a fast, punishing, sure-tackler.

Philadelphia Eagles.

Sims was traded to the Philadelphia Eagles on April 19, 2010 in a three-team trade. The Denver Broncos sent tight end Tony Scheffler and a seventh-round draft pick in 2010 to the Detroit Lions, the Lions sent Sims to the Eagles, and the Eagles sent a fifth-round draft pick in 2010 to the Broncos.

Indianapolis Colts.

On August 2, 2011, Sims signed with the Indianapolis Colts as an unrestricted free agent. He wasn't re-signed at the end of the year.

Dallas Cowboys.

After the loss of Sean Lee to injury, on October 24, 2012, the Dallas Cowboys signed him as an unrestricted free agent to provide depth at linebacker. Sims quickly became a starter by his second game (against the Atlanta Falcons) and eventually the unit's defensive play caller, after injuries decimated the position further. He finished the season with 42 tackles, one sack, 2 quarterback pressures and 3 passes defensed. He also recorded 10 tackles in the Cowboys’ emotional week 14 win against the Cincinnati Bengals, a day after the team received news of the death of Jerry Brown and the arrest of Josh Brent.  On March 18, 2013, Sims was signed to a one-year contract at the league minimum salary. He registered 42 tackles, a forced fumble and started 6 games while replacing Bruce Carter, Justin Durant and Sean Lee at different times. He wasn't re-signed at the end of the season.

Arizona Cardinals.

On June 3, 2014, Sims signed 1-year deal to replace the suspended Daryl Washington. He was later released on August 7.

NFL statistics.

Key

Personal life.

On May 29, 2009, Sims married Brooke McGriff, who is pursuing a degree in Education at Tallahassee Community College.  Sims' mother, Alice Sims, formerly Alice Bennett, was an All-American sprinter on the Florida State track and field team from 1980 through 1983. His younger brother, Marcus Sims, a highly regarded high school running back, announced in February 2006 that he will also play his college football at Florida State before transferring to the University of North Alabama. His father Ernie, Sr. was also a running back at Florida State.  Sims owns a small collection of animals: 5 dogs and 1 type of reptile. Fox produced a segment for the Lions' game against the Minnesota Vikings in Detroit in 2007 which showcased his pets.  Sims currently resides in his home town of Tallahassee, FL, where he owns his own athletic training facility, called Ernie Sims' Big Hits Performance. He also has his own local sports talk radio show.

Ernie Sims III (born December 23, 1984) is a former American football linebacker. He played college football at Florida State and was drafted by the Detroit Lions in the first round of the 2006 NFL Draft. He also played for the Philadelphia Eagles, Indianapolis Colts and Dallas Cowboys.


Laplace operators in differential geometry

Connection Laplacian.

The connection Laplacian, also known as the rough Laplacian, is a differential operator acting on the various tensor bundles of a manifold, defined in terms of a Riemannian- or pseudo-Riemannian metric. When applied to functions (i.e. tensors of rank 0), the connection Laplacian is often called the Laplace–Beltrami operator. It is defined as the trace of the second covariant derivative:  where "T" is any tensor, formula_2 is the Levi-Civita connection associated to the metric, and the trace is taken with respect to the metric. Recall that the second covariant derivative of "T" is defined as  Note that with this definition, the connection Laplacian has negative spectrum. On functions, it agrees with the operator given as the divergence of the gradient.  If the connection of interest is the Levi-Civita connection one can find a convenient formula for the Laplacian of a scalar function in terms of partial derivatives with respect to a coordinate system:  where formula_5 is a scalar function, formula_6 is absolute value of the determinant of the metric (absolute value is necessary in the pseudo-Riemannian case, e.g. in General Relativity) and formula_7 denotes the inverse of the metric tensor.

Hodge Laplacian.

The Hodge Laplacian, also known as the Laplace–de Rham operator, is a differential operator acting on differential forms. (Abstractly, it is a second order operator on each exterior power of the cotangent bundle.) This operator is defined on any manifold equipped with a Riemannian- or pseudo-Riemannian metric.  where d is the exterior derivative or differential and "δ" is the codifferential. The Hodge Laplacian on a compact manifold has nonnegative spectrum.  The connection Laplacian may also be taken to act on differential forms by restricting it to act on skew-symmetric tensors. The connection Laplacian differs from the Hodge Laplacian by means of a Weitzenböck identity.

Bochner Laplacian.

The Bochner Laplacian is defined differently from the connection Laplacian, but the two will turn out to differ only by a sign, whenever the former is defined. Let "M" be a compact, oriented manifold equipped with a metric. Let "E" be a vector bundle over "M" equipped with a fiber metric and a compatible connection, formula_2. This connection gives rise to a differential operator where formula_11 denotes smooth sections of "E", and "T"M is the cotangent bundle of "M". It is possible to take the formula_12-adjoint of formula_2, giving a differential operator The Bochner Laplacian is given by which is a second order operator acting on sections of the vector bundle "E". Note that the connection Laplacian and Bochner Laplacian differ only by a sign:

Lichnerowicz Laplacian.

The Lichnerowicz Laplacian is defined on symmetric tensors by taking formula_17 to be the symmetrized covariant derivative. The Lichnerowicz Laplacian is then defined by formula_18, where formula_19 is the formal adjoint. The Lichnerowicz Laplacian differs from the usual tensor Laplacian by a Weitzenbock formula involving the Riemann curvature tensor, and has natural applications in the study of Ricci flow and the prescribed Ricci curvature problem.

Conformal Laplacian.

On a Riemannian manifold, one can define the conformal Laplacian as an operator on smooth functions; it differs from the Laplace–Beltrami operator by a term involving the scalar curvature of the underlying metric. In dimension "n" ≥ 3, the conformal Laplacian, denoted "L", acts on a smooth function "u" by  where Δ is the Laplace-Beltrami operator (of negative spectrum), and "R" is the scalar curvature. This operator often makes an appearance when studying how the scalar curvature behaves under a conformal change of a Riemannian metric. If "n" ≥ 3 and "g" is a metric and "u" is a smooth, positive function, then the conformal metric  has scalar curvature given by

In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides an overview of some of them.


Early life.

Felix Davidovich Krivin was born June 11, 1928 in a Jewish family in Mariupol. His family moved to Odessa in 1933. In 1945, after evacuation, Krivin moved to Izmail, where he finished evening school. He graduated from the Kiev State Pedagogical Institute in 1951.

Career.

Krivin worked as a mechanic apprentice before becoming a mechanic on the "Edelweiss" barge of Danube Shipping Company. He later became a night shift proofreader in "Pridunayskaya Pravda" ("Danubian Truth") where his first poems were published, and a radiojournalist at the Izmail regional Radio Committee.  Krivin worked as a teacher in Mariupol from 1951 to 1954. After living in Kiev in 1954-1955, he moved to Uzhhgorod, where he worked as a contributing editor at Zakarpattia Oblast publishing house. In 1962, he was accepted to the Writers' Union of Ukraine. In 1990, Krivin was a laureate of the Korolenko republican award.  Krivin was the author of more than 25 books which were published starting from the 1960s by various Soviet publishing houses. He collaborated with comedian Arkady Raikin, for whom he wrote interludes. In 2006, he became a laureate of the Subcarpathian Rus independent literature "Russian award".  One of his most famous creations are the "half-legends"; in 2018, a few of the stories were the first of his work to be published in English in the online edition of the World Literature Today journal, translated from Russian by Anna Burneika.

Personal life and death.

Krivin moved to Israel, where he settled with his wife in Beersheba in 1998. He died on December 24, 2016 at the age of 88.

Felix Davidovich Krivin (Ukrainian: Фе́лікс Дави́дович Кри́він, tr. "Félix Davídovich Krívin"; June 11, 1928 – December 24, 2016) was a Soviet, Ukrainian and Israeli writer and poet, author of intellectual humoristic prose, screenwriter.


Early life.

Radcliffe was born in Staten Island, New York in 1960. He grew up with his two parents, and two siblings, a sister and a younger brother. Radcliffe attended school in Staten Island until leaving to attend college at Buffalo State University in Buffalo, New York, earning two Bachelor's degrees in mathematics and physics. He came out in 1983 and later moved to Denver, Colorado that summer.

Career.

Radcliffe was "discovered" in 1989 by photographer Chris Nelson. Nelson featured Radcliffe (as "Jack Radcliff") in his coffee table book "The Bear Cult", which helped establish the iconic imagery associated with the nascent gay "bear" subculture. He debuted in issue #9 of Nelson and Nelson's partner Richard Bulger's foundational publication "Bear Magazine" and continued to appear in the publication as a model for the magazine's company, Brush Creek Media, after moving to San Francisco in 1989. Nelson worked as the magazine's photographer, while Bulger served as the magazine's publisher.  During the same photoshoot, Radcliffe also shot his first solo pornographic video. Continuing to work as a regular model for Brush Creek Media, Radcliffe quickly became popular in the bear community. Several years later, Nelson and Bulger contacted Radcliffe concerning interest in shooting non-solo films for Brush Creek Media. Radcliffe appeared in seven adult films with Brush Creek Media and later appeared in additional films with Butch Bear and Massive Studio. He retired from adult acting after performing in "Massive Muscle Bears" with Massive Studio.

Other ventures.

Radcliffe worked as the chief financial officer of a software consulting company during the late 1990s and early 2000s. He currently works as a realtor.

Legacy and cultural impact.

Radcliffe is often cited as an enduring iconic representation (if not the most iconic representative) of the bear aesthetic in pornography, gay culture, and at large. He has been described as "the Marilyn Monroe of bear culture," a "poster boy of bear culture," and a "reigning bear icon." In a 2009 list of bear icons, LGBT pop culture website Queerty stated, "In the bear porn industry, Radcliffe is God. It’s easy to see why– if Plato were a bear, this would be his ideal."  Despite this, Radcliffe has downplayed his iconography within bear culture.  Radcliffe was the most featured cover model in the history of "Bear Magazine". In his 2001 forward for author and academic scholar Les K. Wright's "The Bear Book II: Further Readings in the History and Evolution of a Gay Male Subculture", former editor-in-chief of "Drummer" Jack Fritscher noted that Radcliffe remained Brush Creek Media's top box office earner and described him as an icon for the company. Wright also described Radcliffe as the first to embody the "bear beauty" aesthetic with his specifically marketed films. Conversely, Radcliffe has also been specifically identified as an example of the "muscle-bear" body type that later emerged in bear culture, contributing to a more muscular standard of beauty, seemingly in conflict with the "normal," "average," or fat ("chub") aesthetic origins of the bear community.

Jack Radcliffe (born Frank Martini; July 5, 1960) is an American pornographic film actor. Radcliffe is considered a pornographic icon, and in particular, an icon of gay bear subculture and its physical aesthetics.


Early life.

Brown was the only child born to lawyer and former Congressman William G. Brown Sr., and his second wife, Margaret Gay Brown (d. 1913), who survived her husband by nearly two decades and was close to her son. This father was a leading Unionist during the American Civil War, sometimes called the "Father of West Virginia", and would be the first Congressman elected to West Virginia's 2nd Congressional district when the state was formed.

Career.

William Jr. graduated from West Virginia University at Morgantown in 1877, where he was a member of Phi Sigma Kappa fraternity. The same year, he was admitted to the bar and opened his law practice in Preston County. Like his father, he also worked in banking. His father died in 1884, leaving a substantial estate. In 1896, young Brown lost his first bid to become a congressman. In 1910, voters elected Brown as a Democrat to the Sixty-second Congress. He was re-elected to the Sixty-third and Sixty-fourth Congresses. He served from March 4, 1911, until his death in Washington, D.C. on March 9, 1916. Congressman Brown was buried in the family plot at Kingwood Cemetery in Kingwood, West Virginia.

Personal life.

Brown married three times. His first marriage was in 1883 to Jessie Thomas, of Tyrone, Pennsylvania, who died three years later near the birth of their daughter Jessie. His second wife, Flora B. Martin, a West Virginia native, fell victim to pneumonia in 1912 afters about ten years of marriage. His third wife, actress and women's rights activist Izetta Jewel Kenney, whom he married in December 1914, gave birth to their daughter Izetta Jewel Gay Brown just a few weeks before Brown died in office in March, 1916.

William Gay Brown Jr. (April 7, 1856 – March 9, 1916) was a lawyer, and Democratic politician from West Virginia who served as a United States Representative. Congressman Brown was born in Kingwood, West Virginia in Preston County (then in Virginia) on April 7, 1856. He served as a member of the 62nd, 63rd, and 64th United States Congresses. He died in office on March 9, 1916.


Biography.

Known as J. Cheever Cowdin, he was born in New York City on March 17, 1889 to John Elliott Cowdin and Gertrude Cheever.  In 1936, Cowdin's Standard Capital was part of the lending group who had to exercise their rights to the shares held as loan collateral of the financially strapped Universal Pictures Corp. from Carl Laemmle. Cowdin would serve as Universal's President and Chairman of its Board of Directors until 1946. Comedian Groucho Marx played a lawyer based on Cowdin in the 1939 film ‘At the Circus’. The character was named “J. Cheever Loophole”. A director of Curtiss-Wright, Cowdin was considered a leader in aviation financing, notably associated with fellow financier George Newell Armsby in the investment house of Blair & Co., which merged with BancAmerica to form Bancamerica-Blair in 1931. Through Armsby, Cowdin was associated with aviation pioneer (and friend of Amelia Earhart) Floyd Odlum.  Cowdin served as chairman of the Committee on Government Finance of the National Association of Manufacturers.  Cowdin was married three times in the course of his life. He married his first wife, Florence Hopkins, in 1912; they divorced in 1926. Their union produced a son, John Cheever Cowdin, Jr. who in 1946 committed suicide at age 33 while in Nassau, Bahamas. According to the New York Times, Cowdin later married Katherine Andrea Parker Berens on December 30, 1941, in Yuma, Arizona. As a prominent American, the "TIME" magazine reported Cowdin's 1929 marriage to Manhattan socialite divorcee, Mrs. Katherine McCutcheon Abbott, in Bristol, Maine during a cruise on his yacht, "Surf".  He died on September 16, 1960.

Equine sportsman.

J. Cheever Cowdin served as president of Aqueduct Racetrack in Queens, New York. In 1941, the track renamed its Junior Champion Stakes Thoroughbred horse race to the Cowdin Stakes in his honor.  He was termed by Esquire Magazine not only one of the best-dressed men of his era, but "one of the Big Four of polo from the time of the great Tommy Hitchcock." The International Polo Club Palm Beach lists him on a 1927 team with W. Averell Harriman and Tommy Hitchcock. He also played in 1925

John Cheever Cowdin (March 17, 1889 – September 16, 1960) was an American financier and polo champion who was a head of Universal Pictures, Standard Capital Corporation of New York City, and was chairman of Ideal Chemicals.


Biography.

Early life.

Bowman was born in Masontown, Pennsylvania on January 21, 1879. He attended the public schools, and then moved with his parents to Morgantown, West Virginia. He graduated from the West Virginia University in 1902, where he was known to have been a brilliant student, winning the Inter-Society Oration and Debate prize, and where he had been a member of Phi Sigma Kappa fraternity.

Professional Years.

After graduation, he worked as a teller in a bank at Morgantown from 1902 until 1904, when he resigned to take up the study of law, again at West Virginia University. In 1904 he became a member of the then-professional law fraternity, Delta Chi. He was admitted to the bar in 1905 and commenced practice in Morgantown, West Virginia. In addition, he pursued an interest in coal mining, both as a shareholder and board member.  Bowman was appointed postmaster of Morgantown, West Virginia May 25, 1911, and served until April 14, 1915, when a successor was appointed. He was the city mayor in 1916 and 1917 but declined renomination for mayor. Bowman was elected as a Republican to the Sixty-ninth and to the three succeeding Congresses (March 4, 1925 – March 3, 1933) but was an unsuccessful candidate for reelection in 1932 to the Seventy-third Congress.  After leaving Congress, Bowman organized the Tropf coal company in Washington, D.C., and served as president until appointed a member of the Board of Veterans Appeals of the Veterans’ Administration in 1935. He also served several other coal companies in the role of corporate attorney.

Personal life.

In addition to his fraternal memberships during college, Bowman was a Freemason, with involvement in both the Rotary Club, and also holds membership in the Knights Templar, belonging to Morgantown Commandery No. 18, Knights Templar, and Osiris Temple of the Mystic Shrine at Wheeling. He also belongs to the Knights of Pythias, in all of which he was remembered by his biographers as "very popular." His religious faith is that of the Presbyterian Church. He married Miss Pearl Silveus of Pittsburgh, Pennsylvania on 3 June 1904, with whom he had two children.  He served in his role on VA Board until his death in Washington, D.C., on September 15, 1936. He was buried in East Oak Grove Cemetery, Morgantown, West Virginia where his wife and parents were later also buried.

Frank Llewellyn Bowman (January 21, 1879 – September 15, 1936) was an American politician who represented West Virginia in the United States House of Representatives from 1925 to 1933.


Uses.

People use net for many different occupations. Netting is one of the key components to fishing in mass quantities. This textile is used because of its sturdy yet flexible origin, which can carry weight yet, still be lightweight and compactable. Fisherman use netting when trawling, because it is sturdy enough to carry large amounts of weight as fish are trapped, pulled, then lifted out of water. Oftentimes, the filaments that make up the yarn are coated with wax or plastic. This coating adds a waterproof component to the textile that provides even more reliability.  Net is also used in medical practices to provide fabric insulation and wrapping under an industry standard sling. In the medical practice, netting provides cushion and protection, when used in layers, but still allows the skin to breathe under the fabric. Depending on what the netting is being used for, a different wax or plastic coating can be applied in order to cover the filaments that use up the yarn. Filaments can be made from synthetic or natural fibres, but that is all up to the manufacturer when deciphering what the textiles future entails. When netting is going to be exposed to water or heat often, manufacturers consider that and apply what best fits that textile.  Net is commonly used in camping tents. Air can easily pass through the holes, which allows breathability that doesn’t trap bacteria, and remain impermeable to pests and insects. Netting is often used for luggage bags to create transparent, breathable compartments that allow people to store items. Netting has many similar components to mesh, as they both allow air to pass through easily, and share a lot of the same uses. Bigger woven knits have varying different uses, and smaller, tighter woven knits are varied as well.

Types.

Hand-made netting.

Hand-made or machine-made net is used as the foundation fabric for many kinds of needlework, including Filet lace and tambour lace. Netting can be used for many things. This includes adding fullness to a dress. Most commonly wedding and prom dresses. It is also used for many costumes, including fairy outfits. Netting can also be used to make tutus for dancing costumes. Netting can also be referred to when considering the handmade craft. Using either the Lace-maker or the Net-maker method to tie the netting knot, you can create several types of netting. Diamond mesh netting goes back and forth, in rows. This technique is used for bags, hammocks, headbands and scarves. Another type is square mesh netting which also goes back and forth in rows but is worked in the diagonal. This type of net is used for trawling. The first row starts at one corner and the last row finishes the corner diagonal to the first corner. This is often used as a foundation for lacis or net embroidery. Spiral netting is a type of netting that goes around and around in a similar manner to knitting or crochet. There’s no beginning or ending to specific rounds since the pattern is continuous and just keeps going.

Knotless netting.

Different weaving patterns can be used for different kinds of netting. Depending on the use of the textile, size of the holes in the net will vary. Weaving patterns, opposed to knitting patterns, are more often used for knotless netting. Jason Mills states that, as there are no knots used to produce this kind of netting, it is usually less sturdy and movable. Each strand, when used for a knotless netting weave, can sometimes be coated before being woven to ensure more durability. If a weave is coated after being woven it can show to be more durable when exposed to heat or pressure- depending on the type of coat

Net or netting is any textile in which the yarns are fused, looped or knotted at their intersections, resulting in a fabric with open spaces between the yarns. Net has many uses, and comes in different varieties. Depending on the type of yarn or filament that is used to make up the textile, its characteristics can vary from durable to not durable.


Social activist.

He is the current chairperson of the Human Rights Commission of Pakistan, and the Dean of School of Media and Communication at Beaconhouse National University, Lahore. He is one of Pakistan's more prominent communication experts, with a specialization in political analysis.  One of the few media historians of Pakistan, Mehdi Hasan is a regular commentator and panellist for TV news channels and radio stations where he brings his academic research into social context.  His book "The Political History of Pakistan" is a widely used source of reference by journalists and producers. His long-held personal view is that distortion of facts by news media is distorting our history.  A long-time human rights activist and member of the Human Rights Commission of Pakistan's Governing Council, Dr. Mehdi Hasan has written many papers, and participated in multiple seminars. In 2015, addressing a public event at University of Gujrat, Pakistan, Dr Mehdi Hasan emphasized the urgent need to promote honest and impartial reporting and said that bad journalism is distorting the history of Pakistan. He added that all citizens of Pakistan have equal rights under the law regardless of their religions.

Education.

He holds a Ph.D. degree in mass communication, from the Punjab University, "Role of Press in Formation in Public Opinion 1857-1947", an M.A. degree in journalism, Punjab University, and was a Fulbright Scholar (1990) at the University of Colorado at Boulder, where he conducted research on "Coverage of Third World Countries in the American Mass Media". He has published research papers in the United States and Pakistan.

Journalist and news media personality.

As a journalist, his activities include:

Mehdi Hasan (born 1937) is a Pakistani left-wing journalist, media historian, and professor of Journalism and Mass communication at the Beaconhouse National University.


Career.

He began his professional career in 2005 and he set a personal best time of 2:11:26 to finish third in the Dubai Marathon. He returned to the race the following year and came one place further to winning, although he would have won if Joseph Ngeny Kiprotich, initially brought in as a pacemaker, hadn't decided to continue and finish the race instead. He competed in Asia for a second time that year and took fifth place at the Nagano Marathon, although he was leading the race throughout right until the 30 km mark. He failed to make much progression in the 2007 and 2008; years which were highlighted by a 13th-place finish at the Amsterdam Marathon and a fourth place at the Nagano Marathon, respectively.  He took part in the Frankfurt Marathon for the first time in 2009 and although he finished in ninth position, he set a personal best of 2:10:41. Gena began to make his mark on the road running circuit in 2010 as he began the year with a second-place finish behind Denis Ndiso at the Mumbai Marathon (an IAAF Gold Label Road Race). His first ever marathon win soon followed: he ran his fastest ever time (2:08:39) to gain victory at the Rome City Marathon. The event was made more special by the fact that it was in honour of the 50th anniversary of Ethiopian Abebe Bikila's Olympic gold in the 1960 Rome Olympic marathon, in which he became the first black African to win an Olympic gold medal. Gena marked the occasion by removing his shoes to run barefoot for the last 300 metres, mirroring the shoe-less running style of Bikila and earning a 5000€ bonus in the process.  Gena won his second marathon of 2010 in October at the Beijing International Marathon. Cold, wet weather severely affected the race, leaving him shivering as he crossed the line in 2:15:45, but his coach (former runner Haji Adillo) said he thought Gena could run around the 2:06 mark in good conditions. He was one of the favourite for the 2011 Xiamen Marathon in January, but he finished in fifth place. He attempted to retain his title in Rome in March 2011 but had to settle for second place, thirty seconds adrift of winner Dickson Chumba. He ran a half marathon best of 1:02:36 hours at the Göteborgsvarvet, and the Frankfurt Marathon in October saw him improve his marathon best to 2:08:31 hours (finishing in eighth).  On November 17, 2013, Gena finished second at the Istanbul Marathon in a time of 2:13:19 hours behind French athlete Abraham Kiprotich. He was subsequently promoted to first place following Kiprotich's disqualification for a doping offence.

Siraj Amda Gena, also known as Giday Amha and Siraj Amda Bene, (born 12 November 1984) is an Ethiopian long distance runner who specialises in the marathon. He won his first race in 2010, beating all-comers at the Rome City Marathon to set a personal best of 2:08:39.


History.

The "Canadian Historical Review" was founded at the University of Toronto in 1920 as a continuation of a previous journal, the "Review of Historical Publications Relating to Canada", itself founded by George Wrong, in 1897. The initiative to digitize the "CHR"s holdings includes material from this previous journal, and papers from as early as 1897 are available to subscribers online as a result.  The "Canadian Historical Review"s entries have changed as history and historiography itself have progressed. Marlene Shore's "The Contested Past: Reading Canada's History – Selections from the Canadian Historical Review", tracks these changes, tracing major themes of the "CHR" chronologically: "Nation and Diversity, 1920-1939; War, Centralization; and Reaction, 1940-1965; The Renewal of Diversity, 1966 to present; and Reflections." "The Contested Past" also suggests that the key themes in Canadian history reflected by the "CHR" are "Native-European contact, society and war, the nature of Canadian and Quebec nationalism, class-consciousness, and gender politics."

Editors.

The "CHR"s editors are Matthew Hayday and Jeffrey McNairn. Hayday, a professor at the University of Guelph since 2007, focuses on Canadian political history, particularly issues related to language policy, education, social movements, nationalism and identity politics. McNairn teaches nineteenth-century Canadian history at Queen's University, with special interest in the history of print, liberalism, British imperialism and state-civil society relations.  The Editorial Board comprises Harold Bérubé from Université de Sherbrooke, Jarvis Brownlie from the University of Manitoba, Kevin Brushett from the Royal Military College of Canada, Jordan Stanger-Ross from the University of Victoria and Shirley Tillotson from Dalhousie University. The Book Review Editor is Donald Wright from the University of New Brunswick.

"Canadian Historical Review" Prize.

Each year "CHR" awards a prize for best article of the year, known as the "Canadian Historical Review Prize". The winner for 2017 was Jan Noel, who won for her article "A Man of Letters and Gender Troubles of 1837", which appeared in the September 2017 issue.

The Canadian Historical Review (CHR) is a scholarly journal in Canada, founded in 1920 and published by the University of Toronto Press. The "CHR" publishes articles about the ideas, people, and events important to Canadian history, as well as book reviews and detailed bibliographies of recent Canadian historical publications. The "CHR" covers all topics of Canadian history, ranging from Indigenous issues to liberalism to the First World War. The "CHR" has two major objectives: "to promote high standards of research and writing in Canada... and to foster the study of Canadian history."


Dead center.

A dead center (one that does not turn freely, i.e., "dead") may be used to support the workpiece at either the fixed or rotating end of the machine. When used in the fixed position, a dead center produces friction between the workpiece and center, due to the rotation of the workpiece. Lubrication is therefore required between the center and workpiece to prevent friction welding from occurring. Additionally the tip of the center may have an insert of cemented carbide which will reduce the friction slightly and allow for faster speeds. Dead centers are typically fully hardened to prevent damage to the important mating surfaces of the taper and to preserve the 60° angle of the nose. As tungsten carbide is much harder than steel, a carbide-tipped center has greater wear resistance than a steel center.

Soft center.

Soft centers are a special version of the dead center in which the nose is deliberately left soft (unhardened) so that it may be readily machined to the correct angle prior to usage. This operation is performed on the headstock center to ensure that the center's axis is aligned with the spindle's axis.

Live or revolving center.

A revolving center, also known as a live center in some countries, is constructed so that the 60° center runs in its own bearings and is used at the non-driven or tailstock end of a machine. It allows higher turning speeds without the need for separate lubrication, and also greater clamping pressures. CNC lathes use this type of center almost exclusively and they may be used for general machining operations as well. Spring-loaded centers are designed to compensate for center variations, without damage to the work piece or center tip. This assures the operator of uniform constant tension while machining. Some live centers also have interchangeable shafts. This is valuable when situations require a design other than a 60° male tip. A live center, which may be hard or soft, is a plain center placed in the revolving mandrel; it moves and is therefore live.

Pipe center.

A pipe center, also known as a bull nose center is a type of live center which has a large diameter conical nose rather than a sharp point. This allows the center to be used in the bore of a pipe or other workpiece with a large interior diameter. While a pipe center ensures the workpiece remains concentric, its main advantage is that it supports the workpiece securely, and can be used for parts whose larger inner diameter prevents the use of a normal pointed center. Thin-walled material such as pipes easily collapses if excessive force is used at the chuck end.

Cup center.

There are two types of cup centers. The woodworking variety is a variation of the traditional live center. This type of cup center has a central point like a normal live center and also has a ring surrounding it. The ring supports the softer material around the center point and prevents the wood from splitting under pressure from the central point. A different variety of cup center is used for metalworking. The metalworking variety of cup center has a tapered hole rather than a conical point. It supports the part by making contact with the outside diameter of the end of the part, rather than using a center hole.

Drive center.

A drive center, also known as a grip center, is used in the driving end of a machine (headstock). It is often used in woodworking or where softer materials are machined.  It consists of a dead center surrounded by hardened teeth, which bite into a softer workpiece allowing the workpiece to be driven directly by the center. This allows the full diameter of the workpiece to be machined in a single operation, in contrast with the usual requirement where a carrier is attached to the workpiece at the driven end. The use of modified shell end mills in a drive center, instead of hardened pins, enables better gripping and prevents breakdown time due to pin stop.

Spring center.

A spring center is a metalworking lathe center for maintaining a cutting tool like a reamer or a tap, in axial alignment with a hole being worked on. It consists of a point backed by a spring to push the cutting tool into the workpiece.

A lathe center, often shortened to center, is a tool that has been ground to a point to accurately position a workpiece on an axis. They usually have an included angle of 60°, but in heavy machining situations an angle of 75° is used.


Life.

Charles Reade was born at Ipsden, Oxfordshire, to John Reade and Anne Marie Scott-Waring, and had at least four brothers. He studied at Magdalen College, Oxford, taking his B.A. in 1835, and became a fellow of his college. He was subsequently dean of arts and vice-president, taking his degree of D.C.L. in 1847. His name was entered at Lincoln's Inn in 1836; he was elected Vinerian Fellow in 1842, and was called to the bar in 1843. He kept his fellowship at Magdalen all his life but, after taking his degree, he spent most of his time in London. William Winwood Reade, the influential historian, was his nephew.

Writings.

Reade began his literary career as a dramatist, and he chose to have "dramatist" stand first in the list of his occupations on his tombstone. As an author, he always had an eye to stage effect in scene and situation as well as in dialogue. His first comedy, "The Ladies' Battle", appeared at the Olympic Theatre in May 1851. It was followed by "Angela" (1851), "A Village Tale" (1852), "The Lost Husband" (1852), and "Gold" (1853).  But Reade's reputation was made by the two-act comedy, "Masks and Faces", in which he collaborated with Tom Taylor. It was produced in November 1852, and later was expanded into three acts. By the advice of the actress, Laura Seymour, he turned the play into a prose story which appeared in 1853 as "Peg Woffington". The same year he wrote "Christie Johnstone", a close study of Scottish fisher folk. In 1854 he produced, in conjunction with Tom Taylor, "Two Loves and a Life", and "The King's Rival", and, unaided, "The Courier of Lyons" (well known under its later title, "The Lyons Mail") and his adaptation of Tobias Smollett's "Peregrine Pickle". In the next year appeared "Art" (1855), afterwards known as "Nance Oldfield". He made his name as a novelist in 1856, when he published "It Is Never Too Late to Mend", a novel written to reform abuses in prison discipline and the treatment of criminals. The truth of some details was challenged, and Reade defended himself vigorously. Five more novels followed in quick succession: "The Course of True Love Never Did Run Smooth" (1857), "White Lies" (1857), "Jack of all Trades" (1858), "The Autobiography of a Thief" (1858), and "Love Me Little, Love Me Long" (1859). "White Lies" started as a translation of Auguste Maquet's play "Le Château de Grantier." After managers declined the manuscript, Reade adapted the story, weaving it into a novel which was serialised in "The London Journal" and published in three volumes the same year. He produced an adaptation of this on stage as "The Double Marriage" in 1867.  In 1861 Reade published what would become his most famous work, based on a few lines by the medieval humanist Erasmus about the life of his parents. The novel began life as a serial in "Once a Week" in 1859 under the title "A Good Fight", but when Reade disagreed with the proprietors of the magazine over some of the contentious subject matter (principally the unmarried pregnancy of the heroine), he abruptly curtailed the serialisation with a false happy ending. Reade continued to work on the novel and published it in 1861, thoroughly revised and extended, as "The Cloister and the Hearth". It became recognised as one of the most successful historical novels. Returning from the 15th century to modern English life, he next produced "Hard Cash" (originally published as "Very Hard Cash")(1863), in which he highlighted the abuses of private lunatic asylums. Three more such novels followed: "Foul Play" (1869), in which he exposed the iniquities of ship-knackers, and paved the way for the labours of Samuel Plimsoll; "Put Yourself in His Place" (1870), in which he dealt with trade unions; and "A Woman-Hater" (1877), in which he continued his commentary on trade unions while also tackling the topic of women doctors. "The Wandering Heir" (1875), of which he also wrote a version for the stage, was suggested by the Tichborne Case.  Reade also published three elaborate studies of character: "Griffith Gaunt" (1866), "A Terrible Temptation" (1871), "A Simpleton" (1873). He rated the first of these as his best novel. At intervals throughout his literary career, he sought to gratify his dramatic ambition, hiring a theatre and engaging a company for the production of his plays. An example of his persistence was seen in the case of "Foul Play". He wrote this in 1869 in combination with Dion Boucicault with a view to stage adaptation. The play was more or less a failure; but he produced another version alone in 1877, under the title of "A Scuttled Ship", which was a notable failure. His greatest success as a dramatist attended his last attempt – "Drink" – an adaptation of Émile Zola's "L'Assommoir", produced in 1879.  In that year his friend Laura Seymour, who may have been his mistress and had kept house for him since 1854, died. Reade's health failed from that time. On his death, he left behind him a completed novel, "A Perilous Secret", which showed he was still skilled in the arts of weaving a complicated plot and devising thrilling situations. Reade was an amateur of the violin, and among his works is an essay on Cremona violins with the title, "A Lost Art Revived." Reade is buried alongside Laura Seymour, in the churchyard of St. Mary's Church, Willesden, in north-west London.  Reade sub-titled a number of his novels "A matter-of-fact romance;" this referred to his practice of basing his novels largely on newspaper cuttings, which he began collecting for this purpose in 1848. He also conducted his own research, observing prisons personally, for example, as well as borrowing at times heavily from other novelists' works.  Reade's novels were popular, and he was among England's highest-paid novelists. However, many libraries refused to carry his works on the grounds that they were indecent.

Reputation.

Reade fell out of fashion by the turn of the century—"it is unusual to meet anyone who has voluntarily read him," wrote George Orwell in an essay on Reade—but during the 19th century Reade was one of England's most popular novelists. He was not highly regarded by critics. The following assessment by Justin McCarthy, writing in 1872, is typical: A strong, healthy air of honest and high purpose breathes through nearly all the stories. An utter absence of cant, affectation, and sham distinguishes them. A surprising variety of descriptive power, at once bold, broad, and realistic is one of their great merits. Mr. Reade can describe a sea-fight, a storm, the forging of a horseshoe, the ravages of an inundation, the trimming of a lady's dress, the tuning of a piano, with equal accuracy and apparent zest.... Indeed, Mr. Reade wants no quality which is necessary to make a powerful story-teller, while he is distinguished from all mere story-tellers by the fact that he has some great social object to serve in nearly everything he undertakes to detail. More than this I do not believe he is, nor, despite the evidences of something yet higher which were given in 'Christie Johnstone' and 'The Cloister and the Hearth,' do I think he ever could have been. He is a magnificent specimen of the modern special correspondent, endowed with the additional and unique gift of a faculty for throwing his report into the form of a thrilling story. But it requires something more than this, something higher than this, to make a great novelist whom the world will always remember. Mr. Reade is unsurpassed in the second class of English novelists, but he does not belong to the front rank. His success has been great in its way, but it is for an age and not for time. The author George Orwell summed up Reade's attraction as "the same charm as one finds in R. Austin Freeman's detective stories or Lieutenant-Commander Gould's collections of curiosities—the charm of useless knowledge," going on to say that  Reade was a man of what one might call penny-encyclopaedic learning. He possessed vast stocks of disconnected information which a lively narrative gift allowed him to cram into books which would at any rate pass as novels. If you have the sort of mind that takes a pleasure in dates, lists, catalogues, concrete details, descriptions of processes, junk-shop windows and back numbers of the "Exchange and Mart," the sort of mind that likes knowing exactly how a medieval catapult worked or just what objects a prison cell of the eighteen-forties contained, then you can hardly help enjoying Reade. During his career, the prolific Reade was involved in several literary feuds involving accusations of plagiarism. He strongly defended himself, but invoked standards on literary borrowing that are looser than those of today. Reade is frequently discussed in studies of evolving attitudes toward plagiarism.  Reade is credited with the quote: "Sow a thought, and you reap an act; Sow an act, and you reap a habit; Sow a habit, and you reap a character; Sow a character, and you reap a destiny”. These days it is often adapted to: "Mind your thoughts for they become your words; mind your words for they become your actions; mind your actions for they become your habits; mind your habits for they become your character; mind your character for it becomes your destiny."(This was used in the film, "The Iron Lady" (2011), spoken by Meryl Streep playing Margaret Thatcher, the former Prime Minister.)

Marriage and family.

Reade and his late wife had an adopted daughter. He cut off relations with her after she eloped at age sixteen with an actor. After her husband abandoned her, she worked as an actress for a number of years. She performed 2000 times in a production of Reade's "It Is Never Too Late to Mend." She wound up destitute in a workhouse in Kent.

Allusions.

Ira Gershwin’s lyric “It’s never too late to Mendelssohn...”, which appears in both "Oh, Kay!" and "Lady In The Dark", is a play on the title of Reade's book.  John Betjeman's poem "In Willesden Churchyard" includes a reference to "Laura Seymour's grave-/ 'So long the loyal counsellor and friend'/Of that Charles Reade whose coffin lies with hers/Was she his mistress?" followed by a long imagined passage about their possible relationship.

Charles Reade (8 June 1814 – 11 April 1884) was an English novelist and dramatist, best known for "The Cloister and the Hearth".


Definition of the Weyl quantization of a general observable.

The following explains the Weyl transformation on the simplest, two-dimensional Euclidean phase space. Let the coordinates on phase space be, and let be a function defined everywhere on phase space. In what follows, we fix operators "P" and "Q" satisfying the canonical commutation relations, such as the usual position and momentum operators in the Schrödinger representation. We assume that the exponentiated operators formula_1 and formula_2 constitute an irreducible representation of the Weyl relations, so that the Stone–von Neumann theorem (guaranteeing uniqueness of the canonical commutation relations) holds.

The basic formula.

The Weyl transform (or Weyl quantization) of the function is given by the following operator in Hilbert space,  Throughout, formula_3 is the reduced Planck constant.  It is instructive to perform the "p" and "q" integrals in the above formula first, which has the effect of computing the ordinary Fourier transform formula_4 of the function formula_5, while leaving the operator formula_6. In that case, the Weyl transform can be written as  We may therefore think of the Weyl map as follows: We take the ordinary Fourier transform of the function formula_8, but then when applying the Fourier inversion formula, we substitute the quantum operators formula_9 and formula_10 for the original classical variables formula_11 and formula_12, thus obtaining a "quantum version of formula_5."  A less symmetric form, but handy for applications, is the following,

In the position representation.

The Weyl map may then also be expressed in terms of the integral kernel matrix elements of this operator,

The inverse map.

The inverse of the above Weyl map is the Wigner map, which takes the operator back to the original phase-space kernel function, If one replaces formula_16 in the above expression with an arbitrary operator, the resulting function may depend on Planck's constant, and may well describe quantum-mechanical processes, provided it is properly composed through the star product, below. In turn, the Weyl map of the Wigner map is summarized by "Groenewold's formula",

The Weyl quantization of polynomial observables.

While the above formulas give a nice understanding of the Weyl quantization of a very general observable on phase space, they are not very convenient for computing on simple observables, such as those that are polynomials in formula_12 and formula_11. In later sections, we will see that on such polynomials, the Weyl quantization represents the totally symmetric ordering of the noncommuting operators formula_10 and formula_9. For example, the Wigner map of the quantum angular-momentum-squared operator L is not just the classical angular momentum squared, but it further contains an offset term, which accounts for the nonvanishing angular momentum of the ground-state Bohr orbit.

Properties.

Weyl quantization of polynomials.

The action of the Weyl quantization on polynomial functions of formula_12 and formula_11 is completely determined by the following symmetric formula: for all real numbers formula_25 and formula_26. From this formula, it is not hard to show that the Weyl quantization on a function of the form formula_27 gives the average of all possible orderings of formula_28 factors of formula_10 and formula_30 factors of formula_9. For example, we have While this result is conceptually natural, it is not convenient for computations when formula_28 and formula_30 are large. In such cases, we can use instead McCoy's formula This expression gives an apparently different answer for the case of formula_36 from the totally symmetric expression above. There is no contradiction, however, since the canonical commutation relations allow for more than one expression for the same operator. (The reader may find it instructive to use the commutation relations to rewrite the totally symmetric formula for the case of formula_37 in terms of the operators formula_38, formula_39, and formula_40 and verify the first expression in McCoy's formula with formula_41.)  It is widely thought that the Weyl quantization, among all quantization schemes, comes as close as possible to mapping the Poisson bracket on the classical side to the commutator on the quantum side. (An exact correspondence is impossible, in light of Groenewold's theorem.) For example,

Deformation quantization.

Intuitively, a deformation of a mathematical object is a family of the same kind of objects that depend on some parameter(s). Here, it provides rules for how to deform the "classical" commutative algebra of observables to a quantum non-commutative algebra of observables.  The basic setup in deformation theory is to start with an algebraic structure (say a Lie algebra) and ask: Does there exist a one or more parameter(s) family of "similar" structures, such that for an initial value of the parameter(s) one has the same structure (Lie algebra) one started with? (The oldest illustration of this may be the realization of Eratosthenes in the ancient world that a flat earth was deformable to a spherical earth, with deformation parameter 1/"R".) E.g., one may define a noncommutative torus as a deformation quantization through a -product to implicitly address all convergence subtleties (usually not addressed in formal deformation quantization). Insofar as the algebra of functions on a space determines the geometry of that space, the study of the star product leads to the study of a non-commutative geometry deformation of that space.  In the context of the above flat phase-space example, the star product (Moyal product, actually introduced by Groenewold in 1946),, of a pair of functions in, is specified by  The star product is not commutative in general, but goes over to the ordinary commutative product of functions in the limit of. As such, it is said to define a deformation of the commutative algebra of.  For the Weyl-map example above, the -product may be written in terms of the Poisson bracket as  Here, Π is the Poisson bivector, an operator defined such that its powers are and where {"f", "f"} is the Poisson bracket. More generally, where formula_50 is the binomial coefficient.  Thus, e.g., Gaussians compose hyperbolically, or etc. These formulas are predicated on coordinates in which the Poisson bivector is constant (plain flat Poisson brackets). For the general formula on arbitrary Poisson manifolds, cf. the Kontsevich quantization formula.  Antisymmetrization of this -product yields the Moyal bracket, the proper quantum deformation of the Poisson bracket, and the phase-space isomorph (Wigner transform) of the quantum commutator in the more usual Hilbert-space formulation of quantum mechanics. As such, it provides the cornerstone of the dynamical equations of observables in this phase-space formulation.  There results a complete phase space formulation of quantum mechanics, completely equivalent to the Hilbert-space operator representation, with star-multiplications paralleling operator multiplications isomorphically.  Expectation values in phase-space quantization are obtained isomorphically to tracing operator observables with the density matrix in Hilbert space: they are obtained by phase-space integrals of observables such as the above with the Wigner quasi-probability distribution effectively serving as a measure.  Thus, by expressing quantum mechanics in phase space (the same ambit as for classical mechanics), the above Weyl map facilitates recognition of quantum mechanics as a deformation (generalization, cf. correspondence principle) of classical mechanics, with deformation parameter. (Other familiar deformations in physics involve the deformation of classical Newtonian into relativistic mechanics, with deformation parameter "v/c"; or the deformation of Newtonian gravity into General Relativity, with deformation parameter Schwarzschild-radius/characteristic-dimension. Conversely, group contraction leads to the vanishing-parameter undeformed theories—classical limits.)  Classical expressions, observables, and operations (such as Poisson brackets) are modified by -dependent quantum corrections, as the conventional commutative multiplication applying in classical mechanics is generalized to the "noncommutative star-multiplication" characterizing quantum mechanics and underlying its uncertainty principle.  Despite its name, Deformation Quantization does not constitute a successful quantization scheme, namely a method to produce a quantum theory out of a classical one. It amounts to a mere representation change from Hilbert space to phase space.

Generalizations.

In more generality, Weyl quantization is studied in cases where the phase space is a symplectic manifold, or possibly a Poisson manifold. Related structures include the Poisson–Lie groups and Kac–Moody algebras.

In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions in the quantum phase space formulation and Hilbert space operators in the Schrödinger picture.


Early life, education, and military service.

Born in St. Joseph, Missouri, he moved with his parents to Yuma County, Colorado in 1887. He settled in Denver in 1889, and attended the public schools and Sacred Heart College of Denver (now called Regis University). During the Spanish–American War, he commanded a company in the Philippine campaign of 1899, for which he was awarded the Distinguished Service Cross. Means "distinguished himself before the fall of Manila by swimming the Singalon river to reconnoiter the Spanish works", escaping capture when he was spotted. Returning from the war, he expressed a desire for the United States to permanently incorporate the Philippines, envisioning Manila surpassing Hong Kong as a trading center. In 1901, he graduated from the law department of the University of Michigan at Ann Arbor, and was admitted to the bar and commenced practice in Denver. From 1902 to 1904, he was county judge of Adams County, and in 1908 was an unsuccessful candidate for election to the Sixty-first United States Congress. Following this defeat, he was appointed deputy district attorney for Adams County, Colorado.  Means was elected commander-in-chief of the Army of the Philippines in 1913, and of the Veterans of Foreign Wars in 1914. He served during the First World War as a lieutenant colonel and commandant of the Fortieth Division School of Arms. He commanded the 4th Infantry in the Meuse–Argonne offensive. Means ran for a seat in the U.S. Senate in 1920, losing the Republican nomination to Samuel D. Nicholson, who would go on to win the seat. He was attorney for the City and County of Denver in 1923 and 1924.

Political career and later life.

Means was elected as a Republican to the United States Senate on November 4, 1924, in a special election to fill the vacancy caused by Nicholson's death. During the campaign, his Democratic opponent nicknamed him "Puffed Rice", but this did not hinder Means' election. Means was one of several candidates reported to have benefited from the support of the state's Ku Klux Klan organization. He served in the Senate from December 1, 1924, to March 3, 1927, chairing the Committee on Claims (Sixty-ninth Congress). During his tenure, he authored legislation deeming Armistice Day (later called Veterans Day) a national holiday in the United States. During this time, Means also became directing head of the Ku Klux Klan in Colorado. In 1926 he was an unsuccessful candidate for reelection, as he was again defeated in the Republican primary, this time by Charles W. Waterman, who "rode to victory on the wave of anti-klan sentiment".  In 1926 and 1927, Means was commander in chief of the United Spanish War Veterans, and in 1927 he became president of the National Tribune Corporation and publisher of the "National Tribune" and "Stars and Stripes" in Washington, D.C. In response to the enactment of the initial New Deal measures in 1933, Means fiercely criticized the FDR administration declaring it to have been "conceived by income-tax dodgers" and "born of ruthless, vicious propaganda", and calling it "a stain upon the honor of the United States". Means retired in 1937, and died in Denver on January 30, 1949, following a six-month bout with heart problems. He was interred in Denver's Fairmount Cemetery.

Rice William Means (November 16, 1877January 30, 1949) was an American war hero who became a Ku Klux Klan leader and a Republican United States Senator from Colorado.