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Dave Brubeck

David Warren Brubeck (December 6, 1920 – December 5, 2012) was an American jazz pianist and composer. Often regarded as a foremost exponent of cool jazz, Brubeck's work is characterized by unusual time signatures and superimposing contrasting rhythms, meters, tonalities, and combining different styles and genres, like classic, jazz, and blues.

Born in Concord, California, Brubeck was drafted into the US Army, but was spared from combat service when a Red Cross show he had played at became a hit. Within the US Army, Brubeck formed one of the first racially diverse bands. In 1951, Brubeck formed the Dave Brubeck Quartet, which kept its name despite shifting personnel. The most successful—and prolific—lineup of the quartet was the one between 1958 and 1968. This lineup, in addition to Brubeck, featured saxophonist Paul Desmond, bassist Eugene Wright and drummer Joe Morello. A U.S. Department of State-sponsored tour in 1958 featuring the band inspired several of Brubeck's subsequent albums, most notably the 1959 album Time Out. Despite its esoteric theme and contrarian time signatures, Time Out became Brubeck's highest-selling album, and the first jazz album to sell over one million copies. The lead single from the album, "Take Five", a tune written by Desmond in time, similarly became the highest-selling jazz single of all time. The quartet followed up Time Out with four other albums in non-standard time signatures, and some of the other songs from this series became hits as well, including "Blue Rondo à la Turk" (in ) and "Unsquare Dance" (in ). Brubeck continued releasing music until his death in 2012.

Brubeck's style ranged from refined to bombastic, reflecting both his mother's classical training and his own improvisational skills. He expressed elements of atonality and fugue. Brubeck, with Desmond, used elements of West Coast jazz near the height of its popularity, combining them with the unorthodox time signatures seen in Time Out. Like many of his contemporaries, Brubeck played into the style of the French composer Darius Milhaud, especially his earlier works, including "Serenade Suite" and "Playland-At-The-Beach". Brubeck's fusion of classical music and jazz would come to be known as "third stream", although Brubeck's use of third stream would predate the coining of the term. John Fordham of The Guardian commented: "Brubeck's real achievement was to blend European compositional ideas, very demanding rhythmic structures, jazz song-forms and improvisation in expressive and accessible ways."

Brubeck was the recipient of several music awards and honors throughout his lifetime. In 1996, Brubeck received a Grammy Lifetime Achievement Award. In 2008, Brubeck was inducted into the California Hall of Fame, and a year later, he was given an honorary Doctor of Music degree from Berklee College of Music. Brubeck's 1959 album Time Out was added to the Library of Congress' National Recording Registry in 2005. Noted as "one of Jazz's first pop stars" by the Los Angeles Times, Brubeck rejected his fame, and felt uncomfortable with Time magazine featuring him on the cover before Duke Ellington.

Ancestry and early life
Brubeck had Swiss ancestry (the family surname was originally Brodbeck), while his maternal grandparents were English and German. He was born on December 6, 1920, in Concord, California, and grew up in Ione, California. His father, Peter Howard "Pete" Brubeck, was a cattle rancher, while his mother, Elizabeth (née Ivey), who had studied piano in England under Myra Hess and intended to become a concert pianist, taught piano for extra money.

Brubeck did not intend to become a musician, although his two older brothers, Henry and Howard, were already on that track. Brubeck did, however, take lessons from his mother. He could not read music during these early lessons, attributing the difficulty to poor eyesight, but "faked" his way through well enough that his deficiency went mostly unnoticed. Planning to work with his father on their ranch, Brubeck entered the liberal arts college College of the Pacific in Stockton, California, in 1938 to study veterinary science. He switched his major to music at the urging of the head of zoology at the time, Dr. Arnold, who told him, "Brubeck, your mind's not here. It's across the lawn in the conservatory. Please go there. Stop wasting my time and yours." Later, Brubeck was nearly expelled when one of his professors discovered that he was unable to sight-read. Several others came forward to his defense, however, arguing that his ability to write counterpoint and harmony more than compensated, and demonstrated his skill with music notation. The college was still concerned, but agreed to allow Brubeck to graduate only after he promised never to teach piano.

Military service
After graduating in 1942, Brubeck was drafted into the United States Army, serving in Europe in the Third Army under George S. Patton. He volunteered to play piano at a Red Cross show; the show was a resounding success, and Brubeck was spared from combat service. He created one of the U.S. armed forces' first racially integrated bands, "The Wolfpack". It was in the military, in 1944, that Brubeck met Paul Desmond. After serving nearly four years in the army, he returned to California for graduate study at Mills College in Oakland. He was a student of Darius Milhaud, who encouraged him to study fugue and orchestration, but not classical piano. While on active duty, he received two lessons from Arnold Schoenberg at UCLA in an attempt to connect with high modernist theory and practice. However, the encounter did not end on good terms since Schoenberg believed that every note should be accounted for, an approach which Brubeck could not accept, although according to his son Chris Brubeck, there is a twelve-tone row in The Light in the Wilderness, Dave Brubeck's first oratorio. In it, Jesus's Twelve Disciples are introduced each singing their own individual notes; it is described as "quite dramatic, especially when Judas starts singing 'Repent' on a high and straining dissonant note".

Jack Sheedy owned San Francisco-based Coronet Records, which had previously recorded area Dixieland bands. (This Coronet Records is distinct from the late 1950s New York-based budget label, and also from Australia-based Coronet Records.) In 1949, Sheedy was convinced to make the first recording of Brubeck's octet and later his trio. But Sheedy was unable to pay his bills and in 1949 gave up his masters to his record stamping company, the Circle Record Company, owned by Max and Sol Weiss. The Weiss brothers soon changed the name of their business to Fantasy Records.

The first Brubeck records sold well, and he made new records for Fantasy. Soon the company was shipping 40,000 to 50,000 copies of Brubeck records each quarter, making a good profit.

Dave Brubeck Quartet
In 1951, Brubeck organized the Dave Brubeck Quartet, with Paul Desmond on alto saxophone. The two took up residency at San Francisco's Black Hawk nightclub and had success touring college campuses, recording a series of live albums.

The first of these live albums, Jazz at Oberlin, was recorded in March 1953 in the Finney Chapel at Oberlin College. Brubeck's live performance was credited with legitimizing the field of jazz music at Oberlin, and the album is one of the earliest examples of cool jazz. Brubeck returned to College of the Pacific to record Jazz at the College of the Pacific in December of that year.

Following the release of Jazz at the College of the Pacific, Brubeck signed with Fantasy Records, believing that he had a stake in the company and worked as an artists and repertoire promoter for the label, encouraging the Weiss brothers to sign other contemporary jazz performers, including Gerry Mulligan, Chet Baker and Red Norvo. Upon discovering that the deal was for a half interest in his own recordings, Brubeck quit to sign with another label, Columbia Records.

College success
In June 1954, Brubeck released Jazz Goes to College, with double bassist Bob Bates and drummer Joe Dodge. The album is a compilation of the quartet's visits to three colleges: Oberlin College, University of Michigan, and University of Cincinnati, and features seven songs, two of which were written by Brubeck and Desmond. "Balcony Rock", the opening song on the album, was noted for its timing and uneven tonalities, themes that would be explored by Brubeck later.

Brubeck was featured on the cover of Time in November 1954, the second jazz musician to be featured, following Louis Armstrong in February 1949. Brubeck personally found this acclaim embarrassing, since he considered Duke Ellington more deserving and was convinced that he had been favored as a Caucasian. In one encounter with Ellington, he knocked on the door of Brubeck's hotel room to show him the cover; Brubeck's response was, "It should have been you."

Early bassists for the group included Ron Crotty, Bates, and Bates' brother Norman; Lloyd Davis and Dodge held the drum chair. In 1956, Brubeck hired drummer Joe Morello, who had been working with Marian McPartland; Morello's presence made possible the rhythmic experiments that were to come. In 1958, African-American bassist Eugene Wright joined for the group's Department of State tour of Europe and Asia. The group visited Poland, Turkey, India, Ceylon, Pakistan, Iran and Iraq on behalf of the Department of State. They spent two weeks in Poland, giving thirteen concerts and visiting with Polish musicians and citizens as part of the People-to-People program. Wright became a permanent member in 1959, finishing the "classic era" of the quartet's personnel. During this time, Brubeck was strongly supportive of Wright's inclusion in the band, and reportedly canceled several concerts when the club owners or hall managers objected to presenting an integrated band. He also canceled a television appearance when he found out that the producers intended to keep Wright off-camera.

Time Out
In 1959, the Dave Brubeck Quartet recorded Time Out. The album, which featured pieces entirely written by members of the quartet, notably uses unusual time signatures in the field of music—and especially jazz—a crux which Columbia Records was enthusiastic about, but which they were nonetheless hesitant to release.

The release of Time Out required the cooperation of Columbia Records president Goddard Lieberson, who underwrote and released Time Out, on the condition that the quartet record a conventional album of the American South, Gone with the Wind, to cover the risk of Time Out becoming a commercial failure.

Featuring the cover art of S. Neil Fujita, Time Out was released in December 1959, to negative critical reception. Nonetheless, on the strength of these unusual time signatures, the album quickly went Gold (and was eventually certified Double Platinum), and peaked at number two on the Billboard 200. It was the first jazz album to sell more than a million copies. The single "Take Five" off the album quickly became a jazz standard, despite its unusual composition and its time signature: time.

Time Out was followed by several albums with a similar approach, including Time Further Out: Miro Reflections (1961), using more, , and , plus the first attempt at ; Countdown—Time in Outer Space (dedicated to John Glenn, 1962), featuring and more ; Time Changes (1963), with much ,  and ; and Time In (1966). These albums (except Time In) were also known for using contemporary paintings as cover art, featuring the work of Joan Miró on Time Further Out, Franz Kline on Time in Outer Space, and Sam Francis on Time Changes.

Later work
On a handful of albums in the early 1960s, clarinetist Bill Smith replaced Desmond. These albums were devoted to Smith's compositions and thus had a somewhat different aesthetic than other Brubeck Quartet albums. Nonetheless, according to critic Ken Dryden, "[Smith] proves himself very much in Desmond's league with his witty solos". Smith was an old friend of Brubeck's; they would record together, intermittently, from the 1940s until the final years of Brubeck's career.

In 1961, Brubeck and his wife, Iola, developed a jazz musical, The Real Ambassadors, based in part on experiences they and their colleagues had during foreign tours on behalf of the Department of State. The soundtrack album, which featured Louis Armstrong, Lambert, Hendricks & Ross, and Carmen McRae was recorded in 1961; the musical was performed at the 1962 Monterey Jazz Festival.

At its peak in the early 1960s, the Brubeck Quartet was releasing as many as four albums a year. Apart from the "College" and the "Time" series, Brubeck recorded four LP records featuring his compositions based on the group's travels, and the local music they encountered. Jazz Impressions of the U.S.A. (1956, Morello's debut with the group), Jazz Impressions of Eurasia (1958), Jazz Impressions of Japan (1964), and Jazz Impressions of New York (1964) are less well-known albums and they produced Brubeck standards such as "Summer Song", "Brandenburg Gate", "Koto Song", and "Theme from Mr. Broadway". (Brubeck wrote, and the Quartet performed, the theme song for this Craig Stevens CBS drama series; the music from the series became material for the New York album.) In 1961, Brubeck appeared in a few scenes of the British jazz/beat film All Night Long, which starred Patrick McGoohan and Richard Attenborough. Brubeck plays himself, with the film featuring close-ups of his piano fingerings. Brubeck performs "It's a Raggy Waltz" from the Time Further Out album and duets briefly with bassist Charles Mingus in "Non-Sectarian Blues".

Brubeck also served as the program director of WJZZ-FM (now WEZN-FM) while recording for the quartet. He achieved his vision of an all-jazz format radio station along with his friend and neighbor John E. Metts, one of the first African Americans in senior radio management.

The final studio album for Columbia by the Desmond/Wright/Morello quartet was Anything Goes (1966), featuring the songs of Cole Porter. A few concert recordings followed, and The Last Time We Saw Paris (1967) was the "Classic" quartet's swan-song.

Later career
Brubeck produced The Gates of Justice in 1968, a cantata mixing Biblical scripture with the words of Martin Luther King Jr.

In 1971, the new senior management at Columbia Records decided not to renew Brubeck's contract, as they wished to focus on rock music. He moved to Atlantic Records.

Brubeck's music was used in the 1985 film Ordeal by Innocence. He also composed for—and performed with his ensemble on—"The NASA Space Station", a 1988 episode of the CBS TV series This Is America, Charlie Brown.

Personal life
Brubeck founded the Brubeck Institute with his wife, Iola, at their alma mater, the University of the Pacific in 2000. What began as a special archive, consisting of the personal document collection of the Brubecks, has since expanded to provide fellowships and educational opportunities in jazz for students, also leading to having one of the main streets on which the school resides named in his honor, Dave Brubeck Way.

In 2008, Brubeck became a supporter of the Jazz Foundation of America in its mission to save the homes and the lives of elderly jazz and blues musicians, including those who had survived Hurricane Katrina. Brubeck supported the Jazz Foundation by performing in its annual benefit concert "A Great Night in Harlem".

Family
Dave Brubeck married jazz lyricist Iola Whitlock in September 1942; the couple were married for 70 years, until his death in 2012. Iola died at age 90 on March 12, 2014, from cancer in Wilton, Connecticut.

Brubeck had six children with Iola. Four of his children have been professional musicians. Darius, named after Brubeck's mentor Darius Milhaud and the eldest, is a pianist, producer, educator and performer. Dan is a percussionist, Chris is a multi-instrumentalist and composer, and Matthew, the youngest, is a cellist with an extensive list of composing and performance credits. Another son, Michael, died in 2009. Brubeck's children often joined him in concerts and in the recording studio.

Religion
Brubeck became a Catholic in 1980, shortly after completing the Mass To Hope which had been commissioned by Ed Murray, editor of the national Catholic weekly Our Sunday Visitor. Although he had spiritual interests before that time, he said, "I didn't convert to Catholicism, because I wasn't anything to convert from. I just joined the Catholic Church." In 1996, he received the Grammy Lifetime Achievement Award. In 2006, Brubeck was awarded the University of Notre Dame's Laetare Medal, the oldest and most prestigious honor given to American Catholics, during the university's commencement. He performed "Travellin' Blues" for the graduating class of 2006.

Death
Brubeck died of heart failure on December 5, 2012, in Norwalk, Connecticut, one day before his 92nd birthday. He was on his way to a cardiology appointment, accompanied by his son Darius. A birthday party concert had been planned for him with family and famous guests. A memorial tribute was held in May 2013.

Brubeck is interred at Umpawaug Cemetery in Redding, Connecticut.

Legacy
The Los Angeles Times noted that he "was one of Jazz's first pop stars", even though he was not always happy with his fame. He felt uncomfortable, for example, that Time magazine had featured him on the cover before it did so for Duke Ellington, saying, "It just bothered me." The New York Times noted he had continued to play well into his old age, performing in 2011 and in 2010 only a month after getting a pacemaker, with Times music writer Nate Chinen commenting that Brubeck had replaced "the old hammer-and-anvil attack with something almost airy" and that his playing at the Blue Note Jazz Club in New York City was "the picture of judicious clarity".

In The Daily Telegraph, music journalist Ivan Hewett wrote: "Brubeck didn't have the réclame of some jazz musicians who lead tragic lives. He didn't do drugs or drink. What he had was endless curiosity combined with stubbornness", adding: "His work list is astonishing, including oratorios, musicals and concertos, as well as hundreds of jazz compositions. This quiet man of jazz was truly a marvel."

In The Guardian, John Fordham said "Brubeck's real achievement was to blend European compositional ideas, very demanding rhythmic structures, jazz song-forms and improvisation in expressive and accessible ways. His son Chris told The Guardian "when I hear Chorale, it reminds me of the very best Aaron Copland, something like Appalachian Spring. There's a sort of American honesty to it." Robert Christgau dubbed Brubeck the "jazz hero of the rock and roll generation".

The Economist wrote: "Above all they found it hard to believe that the most successful jazz in America was being played by a family man, a laid-back Californian, modest, gentle and open, who would happily have been a rancher all his days—except that he couldn't live without performing, because the rhythm of jazz, under all his extrapolation and exploration, was, he had discovered, the rhythm of his heart."

While on tour performing "Hot House" in Toronto, Chick Corea and Gary Burton completed a tribute to Brubeck on the day of his death. Corea played "Strange Meadow Lark", from Brubeck's album Time Out.

In the United States, May 4 is informally observed as "Dave Brubeck Day". In the format most commonly used in the U.S., May 4 is written "5/4", recalling the time signature of "Take Five", Brubeck's best-known recording. In September 2019, musicologist Stephen A. Crist's book, Dave Brubeck's Time Out, provided the first scholarly book length analysis of the seminal album. In addition to his musical analyses of each of the album's original compositions, Crist provides insight into Brubeck's career during a time he was rising to the top of the jazz charts.

Recognition
In 1975, the main-belt asteroid 5079 Brubeck was named after Brubeck.

Brubeck recorded five of the seven tracks of his album Jazz Goes to College in Ann Arbor, Michigan. He returned to Michigan many times, including a performance at Hill Auditorium where he received a Distinguished Artist Award from the University of Michigan's Musical Society in 2006. Brubeck was presented with a "Benjamin Franklin Award for Public Diplomacy" by United States Secretary of State Condoleezza Rice in 2008 for offering an American "vision of hope, opportunity and freedom" through his music. "As a little girl I grew up on the sounds of Dave Brubeck because my dad was your biggest fan", said Rice. The State Department said in a statement that "as a pianist, composer, cultural emissary and educator, Dave Brubeck's life's work exemplifies the best of America's cultural diplomacy". At the ceremony, Brubeck played a brief recital for the audience at the State Department. "I want to thank all of you because this honor is something that I never expected. Now I am going to play a cold piano with cold hands", Brubeck stated.

California Governor Arnold Schwarzenegger and First Lady Maria Shriver announced on May 28, 2008, that Brubeck would be inducted into the California Hall of Fame, located at The California Museum for History, Women and the Arts. The induction ceremony occurred December 10, and he was inducted alongside eleven other famous Californians.

On October 18, 2008, Brubeck received an honorary Doctor of Music degree from the prestigious Eastman School of Music in Rochester, New York. Similarly, at the Monterey Jazz Festival in September 2009, Brubeck was awarded an honorary Doctor of Music degree (D.Mus. honoris causa) from Berklee College of Music. On May 16, 2010, Brubeck was awarded an honorary Doctor of Music degree (honoris causa) from the George Washington University in Washington, D.C. The ceremony took place on the National Mall.

In September 2009, the Kennedy Center for the Performing Arts announced Brubeck as a Kennedy Center Honoree for exhibiting excellence in performance arts. The Kennedy Center Honors Gala took place on Sunday, December 6 (Brubeck's 89th birthday), and was broadcast nationwide on CBS on December 29 at 9:00 pm EST. When the award was made, President Barack Obama recalled a 1971 concert Brubeck had given in Honolulu and said, "You can't understand America without understanding jazz, and you can't understand jazz without understanding Dave Brubeck."

On July 5, 2010, Brubeck was awarded the Miles Davis Award at the Montreal International Jazz Festival. In 2010, Bruce Ricker and Clint Eastwood produced Dave Brubeck: In His Own Sweet Way, a documentary about Brubeck for Turner Classic Movies (TCM) to commemorate his 90th birthday in December 2010.

The Concord Boulevard Park in his hometown of Concord, California, was posthumously renamed to "Dave Brubeck Memorial Park" in his honor. Mayor Dan Helix favorably recalled one of his performances at the park, saying: "He will be with us forever because his music will never die."

Awards

 * Connecticut Arts Award (1987)
 * National Medal of Arts, National Endowment for the Arts (1994)
 * DownBeat Hall of Fame (1994)
 * Grammy Lifetime Achievement Award (1996)
 * Doctor of Sacred Theology, Doctorate honoris causa, University of Fribourg, Switzerland (2004)
 * Laetare Medal (University of Notre Dame) (2006)
 * BBC Jazz Lifetime Achievement Award (2007)
 * Benjamin Franklin Award for Public Diplomacy (2008)
 * Inducted into California Hall of Fame (2008)
 * Eastman School of Music Honorary Degree (2008)
 * Kennedy Center Honors (2009)
 * George Washington University Honorary Degree (2010)
 * Honorary Fellow of Westminster Choir College, Princeton, New Jersey (2011)

title: Dave Brubeck


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Dye

A dye is a colored substance that chemically bonds to the substrate to which it is being applied. This distinguishes dyes from pigments which do not chemically bind to the material they color. Dye is generally applied in an aqueous solution and may require a mordant to improve the fastness of the dye on the fiber.

The majority of natural dyes are derived from non-animal sources such as roots, berries, bark, leaves, wood, fungi and lichens. However, due to large-scale demand and technological improvements, most dyes used in the modern world are synthetically produced from substances such as petrochemicals. Some are extracted from insects and/or minerals.

Synthetic dyes are produced from various chemicals. The great majority of dyes are obtained in this way because of their superior cost, optical properties (color), and resilience (fastness, mordancy). Both dyes and pigments are colored, because they absorb only some wavelengths of visible light. Dyes are usually soluble in some solvent, whereas pigments are insoluble. Some dyes can be rendered insoluble with the addition of salt to produce a lake pigment.

History

Textile dyeing dates back to the Neolithic period. Throughout history, people have dyed their textiles using common, locally available materials. Scarce dyestuffs that produced brilliant and permanent colors such as the natural invertebrate dyes Tyrian purple and crimson kermes were highly prized luxury items in the ancient and medieval world. Plant-based dyes such as woad, indigo, saffron, and madder were important trade goods in the economies of Asia and Europe. Across Asia and Africa, patterned fabrics were produced using resist dyeing techniques to control the absorption of color in piece-dyed cloth. Dyes from the New World such as cochineal and logwood were brought to Europe by the Spanish treasure fleets, and the dyestuffs of Europe were carried by colonists to America.

Dyed flax fibers have been found in the Republic of Georgia in a prehistoric cave dated to 36,000 BP. Archaeological evidence shows that, particularly in India and Phoenicia, dyeing has been widely carried out for over 5,000 years. Early dyes were obtained from animal, vegetable or mineral sources, with no to very little processing. By far the greatest source of dyes has been from the plant kingdom, notably roots, berries, bark, leaves and wood, only few of which are used on a commercial scale.

Early industrialization was conducted by J. Pullar and Sons in Scotland. The first synthetic dye, mauve, was discovered serendipitously by William Henry Perkin in 1856. The discovery of mauveine started a surge in synthetic dyes and in organic chemistry in general. Other aniline dyes followed, such as fuchsine, safranine, and induline. Many thousands of synthetic dyes have since been prepared.

The discovery of mauve also led to developments within immunology and chemotherapy. In 1863 the forerunner to Bayer AG was formed in what became Wuppertal, Germany. In 1891, Paul Ehrlich discovered that certain cells or organisms took up certain dyes selectively. He then reasoned that a sufficiently large dose could be injected to kill pathogenic microorganisms, if the dye did not affect other cells. Ehrlich went on to use a compound to target syphilis, the first time a chemical was used in order to selectively kill bacteria in the body. He also used methylene blue to target the plasmodium responsible for malaria.

Chemistry
The color of a dye is dependent upon the ability of the substance to absorb light within the visible region of the electromagnetic spectrum (380-750 nm). An earlier theory known as Witt theory stated that a colored dye had two components, a chromophore which imparts color by absorbing light in the visible region (some examples are nitro, azo, quinoid groups) and an auxochrome which serves to deepen the color. This theory has been superseded by modern electronic structure theory which states that the color in dyes is due to excitation of valence π-electrons by visible light.

Types
Dyes are classified according to their solubility and chemical properties.

Acid dyes are water-soluble anionic dyes that are applied to fibers such as silk, wool, nylon and modified acrylic fibers using neutral to acid dye baths. Attachment to the fiber is attributed, at least partly, to salt formation between anionic groups in the dyes and cationic groups in the fiber. Acid dyes are not substantive to cellulosic fibers. Most synthetic food colors fall in this category. Examples of acid dye are Alizarine Pure Blue B, Acid red 88, etc.

Basic dyes are water-soluble cationic dyes that are mainly applied to acrylic fibers, but find some use for wool and silk. Usually acetic acid is added to the dye bath to help the uptake of the dye onto the fiber. Basic dyes are also used in the coloration of paper.

Direct or substantive dyeing is normally carried out in a neutral or slightly alkaline dye bath, at or near boiling point, with the addition of either sodium chloride (NaCl) or sodium sulfate (Na2SO4) or sodium carbonate (Na2CO3). Direct dyes are used on cotton, paper, leather, wool, silk and nylon. They are also used as pH indicators and as biological stains.

Laser dyes are used in the production of some lasers, optical media (CD-R), and camera sensors (color filter array).

Mordant dyes require a mordant, which improves the fastness of the dye against water, light and perspiration. The choice of mordant is very important as different mordants can change the final color significantly. Most natural dyes are mordant dyes and there is therefore a large literature base describing dyeing techniques. The most important mordant dyes are the synthetic mordant dyes, or chrome dyes, used for wool; these comprise some 30% of dyes used for wool, and are especially useful for black and navy shades. The mordant potassium dichromate is applied as an after-treatment. It is important to note that many mordants, particularly those in the heavy metal category, can be hazardous to health and extreme care must be taken in using them.

Vat dyes are essentially insoluble in water and incapable of dyeing fibres directly. However, reduction in alkaline liquor produces the water-soluble alkali metal salt of the dye. This form is often colorless, in which case it is referred to as a Leuco dye, and has an affinity for the textile fibre. Subsequent oxidation reforms the original insoluble dye. The color of denim is due to indigo, the original vat dye.

Reactive dyes utilize a chromophore attached to a substituent that is capable of directly reacting with the fiber substrate. The covalent bonds that attach reactive dye to natural fibers make them among the most permanent of dyes. "Cold" reactive dyes, such as Procion MX, Cibacron F, and Drimarene K, are very easy to use because the dye can be applied at room temperature. Reactive dyes are by far the best choice for dyeing cotton and other cellulose fibers at home or in the art studio.

Disperse dyes were originally developed for the dyeing of cellulose acetate, and are water-insoluble. The dyes are finely ground in the presence of a dispersing agent and sold as a paste, or spray-dried and sold as a powder. Their main use is to dye polyester, but they can also be used to dye nylon, cellulose triacetate, and acrylic fibers. In some cases, a dyeing temperature of 130 C is required, and a pressurized dyebath is used. The very fine particle size gives a large surface area that aids dissolution to allow uptake by the fiber. The dyeing rate can be significantly influenced by the choice of dispersing agent used during the grinding.

Azoic dyeing is a technique in which an insoluble Azo dye is produced directly onto or within the fiber. This is achieved by treating a fiber with both diazoic and coupling components. With suitable adjustment of dyebath conditions the two components react to produce the required insoluble azo dye. This technique of dyeing is unique, in that the final color is controlled by the choice of the diazoic and coupling components. This method of dyeing cotton is declining in importance due to the toxic nature of the chemicals used.

Sulfur dyes are inexpensive dyes used to dye cotton with dark colors. Dyeing is effected by heating the fabric in a solution of an organic compound, typically a nitrophenol derivative, and sulfide or polysulfide. The organic compound reacts with the sulfide source to form dark colors that adhere to the fabric. Sulfur Black 1, the largest selling dye by volume, does not have a well defined chemical structure.

Some dyes commonly used in Staining:

Food dyes
One other class that describes the role of dyes, rather than their mode of use, is the food dye. Because food dyes are classed as food additives, they are manufactured to a higher standard than some industrial dyes. Food dyes can be direct, mordant and vat dyes, and their use is strictly controlled by legislation. Many are azo dyes, although anthraquinone and triphenylmethane compounds are used for colors such as green and blue. Some naturally occurring dyes are also used.

Other important dyes
A number of other classes have also been established, including:
 * Oxidation bases, for mainly hair and fur
 * Laser dyes: rhodamine 6G and coumarin dyes.
 * Leather dyes, for leather
 * Fluorescent brighteners, for textile fibres and paper
 * Solvent dyes, for wood staining and producing colored lacquers, solvent inks, coloring oils, waxes.
 * Contrast dyes, injected for magnetic resonance imaging, are essentially the same as clothing dye except they are coupled to an agent that has strong paramagnetic properties.
 * Mayhems dye, used in water cooling for looks, often rebranded RIT dye

Chromophoric dyes
By the nature of their chromophore, dyes are divided into:
 * Category:Acridine dyes, derivates of acridine
 * Category:Anthraquinone dyes, derivates of anthraquinone
 * Arylmethane dyes
 * Category:Diarylmethane dyes, based on diphenyl methane
 * Category:Triarylmethane dyes, derivates of triphenylmethane
 * Category:Azo dyes, based on -N=N- azo structure
 * Phthalocyanine dyes, derivatives of phthalocyanine
 * Quinone-imine dyes, derivatives of quinone
 * Category:Azin dyes
 * Category:Eurhodin dyes
 * Category:Safranih
 * dyes, derivates of safranin
 * Indamins
 * Category:Indophenol dyes, derivates of indophenol
 * Category:Oxazin dyes, derivates of oxazin
 * Oxazone dyes, derivates of oxazone
 * Category:Thiazine dyes
 * Category:Thiazole dyes
 * Category:Safranin dyes
 * Xanthene dyes
 * Fluorene dyes, derivatives of fluorene
 * Pyronin dyes
 * Category:Fluorone dyes, based on fluorone
 * Category:Rhodamine dyes, derivatives of rhodamine

Pollution
Dyes produced by the textile, printing and paper industries are a source of pollution of rivers and waterways. An estimated 700,000 tons of dyestuffs are produced annually (1990 data). The disposal of that material has received much attention, using chemical and biological means.

Vital dyes
A “vital dye” or stain is a dye capable of penetrating living cells or tissues without causing immediate visible degenerative changes. Such dyes are useful in medical and pathological fields in order to selectively color certain structures (such as cells) in order to distinguish them from surrounding tissue and thus make them more visible for study (for instance, under a microscope). As the visibility is meant to allow study of the cells or tissues, it is usually important that the dye not have other effects on the structure or function of the tissue that might impair objective observation.

A distinction is drawn between dyes that are meant to be used on cells that have been removed from the organism prior to study (supravital staining) and dyes that are used within a living body - administered by injection or other means (intravital staining) - as the latter is (for instance) subject to higher safety standards, and must typically be a chemical known to avoid causing adverse effects on any biochemistry (until cleared from the tissue), not just to the tissue being studied, or in the short term.

The term "vital stain" is occasionally used interchangeably with both intravital and supravital stains, the underlying concept in either case being that the cells examined are still alive. In a stricter sense, the term "vital staining" means the polar opposite of "supravital staining." If living cells absorb the stain during supravital staining, they exclude it during "vital staining"; for example, they color negatively while only dead cells color positively, and thus viability can be determined by counting the percentage of total cells that stain negatively. Because the dye determines whether the staining is supravital or intravital, a combination of supravital and vital dyes can be used to more accurately classify cells into various groups (e.g., viable, dead, dying).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Dye


text:
Talk:Ordinary differential equation

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This article was the subject of a Wiki Education Foundation-supported course assignment, between 28 August 2021 and 10 December 2021. Further details are available on the course page. Student editor(s): Madelynrahman.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 05:48, 17 January 2022 (UTC)

Removal of content
I deleted the section Linear equations rather than wasting time cleaning it up, since everything is covered in far more detial and in better presentation in the main article Linear differential equation.

Furthermore the subsections within that section: Fundamental systems for homogeneous equations with constant coefficients and General Case, had zero references and were not exactly easy for a reader to follow anyway... they are no more. F = q(E+v×B) ⇄ ∑ici 09:34, 31 May 2012 (UTC)

 * There was a link to the section Linear ordinary differential equations in the article Stiff equation. I just now updated the link to point to the section Reduction of order instead, as this section describes not only the reduction of order but also the vector representation of such a system.  Please consider leaving the existing section in place so that the vector representation will still be described in a convenient place.  If the vector representation is deleted, it should be moved somewhere and documented in the talk pages for its source and destination pages. — Anita5192 (talk) 17:48, 31 May 2012 (UTC)

 * Of course I'll leave that section alone - thats relavent! My only implications were that the theory of linear equations should be kept in the other article (which is also in bad shape in places.....), rather than repeating too much here. Thank you for feedback - appreciated. =) F = q(E+v×B) ⇄ ∑ici 23:27, 31 May 2012 (UTC)

Global uniqueness and maximum domain of solution
It would be nice to have a counter-example with domain ℝ\{x_0 + 1/y_0}, that satisfies the initial condition, but has a different definition on the other interval. Soulpa7ch (talk) 18:49, 17 September 2012 (UTC)

Error!
f(x, y) = y^2 is *not* Lipschitz continuous. Please rectify or make clear (that you mean "locally Lipschitz"). — Preceding unsigned comment added by 2607:4000:200:12:21A:92FF:FE83:373 (talk) 23:24, 21 January 2013 (UTC)

Argument of function belongs in numerator
In the Background section, I moved the argument of x(t) back into the numerator of the derivative because that is where it commonly is placed in textbooks. See, e.g., Simmons, George F. Differential Equations with Applications and Historical Notes. p.123. — Anita5192 (talk) 20:32, 6 November 2014 (UTC)

Proposed merge with Strang splitting
seems to be one of the possible solutions Shrikanthv (talk) 10:53, 3 December 2014 (UTC)
 * Operator splitting is used for dimensional splitting of Partial differential equations as well, which has (almost 😉) nothing to do with ODEs. Merging strang splitting here thus doesn't make sense. I'd support merging strang splitting into a general article on splitting methods though. -- Pberndt (talk) 08:54, 19 April 2016 (UTC)

More rigor in the definitions of $$n$$th order ODEs
In the definition of an $$n$$th order linear ODE $$\left( y^{(n)} = \sum_{i=0}^{n-1}a_i(x)y^{(i)} + r(x) \ \forall x \in I \right)$$, all the article says is that the $$a_i$$ and $$r$$ are continuous. It doesn't even say $$\forall x \in I$$ at the end of the equation. I think we should give the domains and codomains of all the functions in the equation, i.e. we should say that $$a_0, a_1, ..., a_{n-1}, r: I \to \mathbb{R}$$ are continuous and $$y: I \to \mathbb{R}$$ is $$n$$ times differentiable (from which it follows from the equation that $$y$$ is actually $$n$$ times continuously differentiable).

In the definition of a general $$n$$th order ODE (implicit form $$F(x, y, y', ..., y^{(n)}) = 0 \ \forall x \in I)$$ and explicit form $$y^{(n)} = F(x, y, y', ..., y^{(n-1)}) \ \forall x \in I)$$), the article says even less. Again there is no $$\forall x \in I$$, and it doesn't say that $$y: I \to \mathbb{R}$$ should be $$n$$ times differentiable. The most problematic part however is that nothing at all is said about $$F$$. In the implicit case, its domain and codomain are given by $$F: I \times U \to \mathbb{R}$$ where $$U \subseteq \mathbb{R}^{n+1}$$, and in the explicit case it is $$F: I \times U \to \mathbb{R}$$ where $$U \subseteq \mathbb{R}^n$$.

In the same way that we demand that $$a_0, a_1, ..., a_{n-1}, r: I \to \mathbb{R}$$ are continuous in the definition of a linear ODE, are there any agreed upon assumptions on $$F$$ in the definition of a general ODE? Later in the article in the 'Local existence and uniqueness theorem simplified' section, when talking about the first order system $$\vec{y}' = \vec{F}(x, \vec{y})$$ (where yet again all the terms are not fully explained, or even made clear that they are vector quantities), it says that we should have $$\vec{F}$$ and $$\frac{\partial \vec{F}}{\partial \vec{y}}$$ continuous in some vicinity of the initial condition in order to guarantee the existence and uniqueness of a solution. Is there a similar result which applies to the general $$n$$th order ODE $$F(x, y, y', ..., y^{(n)}) = 0 \ \forall x \in I$$ or $$y^{(n)} = F(x, y, y', ..., y^{(n-1)}) \ \forall x \in I$$? (I could probably figure it out by converting them into first order systems and reverse engineering, but I'll see what you guys say first).

So in summary, 1) do you guys think that we should modify the definitions of linear and general ODEs by explaining all the terms in the equations more fully, and 2) are there agreed upon assumptions on $$F$$ in the literature in the definition of a general (implicit and explicit) $$n$$th order ODE? At the moment, having $$F$$ being identically $$1$$ for an implicit $$n$$th order ODE satisfies the definition given in the article. — Preceding unsigned comment added by Joel Brennan (talk • contribs) 14:56, 21 April 2018 (UTC)

 * I agree with your first point, although for the sake of compactness I would include the assumptions valid for all the definitions in advance rather than in every definition. I'm sorry that I cannot answer to your second point. I also think that, after the general definition it would not be correct saying "There are further classifications". It could be said "general definitions for particular types of differential equations". However, i find it redundant and in some cases wrong what is presented. For instance, the type "homogeneous" refers only to linear equations so it is misleading this presentation. I would perhaps delete all this and just say that there are different particular types of equations, and provide the links to the correspondent articles, which I think are ok. What do you think? Conjugado (talk) 19:11, 2 January 2019 (UTC)

Software section
The software section doesn't actually include ODE solver software, but instead links to languages which have submodules that can solve ODEs. I tried to improve the software section by linking directly to one of the more popular submodules, DifferentialEquations.jl solvers, but MrOllie keeps deleting the reference. Should this section instead be renamed to "Languages with ODE Solver Software"? If that's the case, languages like Python, R, etc. should probably be removed, since their ODE solvers are wrappers for the C++ and Fortran implementations of methods like dopri5, dop853, and lsode. — Preceding unsigned comment added by 71.232.17.207 (talk) 12:26, 18 October 2019 (UTC)

 * The section should include only entries with some demonstrated notability in the form of a preexisting Wikipedia article. See WP:WTAF - MrOllie (talk) 12:28, 18 October 2019 (UTC)

 * So notability of an ODE solver is not defined in terms of users, Github metrics, citing articles, etc., but instead in terms of whether there's a preexisting Wikipedia article? It's fine if it's consistent, but that seems like an odd criteria. — Preceding unsigned comment added by 71.232.17.207 (talk) 13:08, 18 October 2019 (UTC)

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title: Talk:Ordinary differential equation