title: Confocal microscopy

text: Microlens enhanced or dual spinning-disk confocal microscopes work under the same principles as spinning-disk confocal microscopes except a second spinning-disk containing micro-lenses is placed before the spinning-disk containing the pinholes. Every pinhole has an associated microlens. The micro-lenses act to capture a broad band of light and focus it into each pinhole significantly increasing the amount of light directed into each pinhole and reducing the amount of light blocked by the spinning-disk. Microlens enhanced confocal microscopes are therefore significantly more sensitive than standard spinning-disk systems. Yokogawa Electric invented this technology in 1992.


title: Confocal microscopy

text: Programmable array microscopes (PAM) use an electronically controlled spatial light modulator (SLM) that produces a set of moving pinholes. The SLM is a device containing an array of pixels with some property (opacity, reflectivity or optical rotation) of the individual pixels that can be adjusted electronically. The SLM contains microelectromechanical mirrors or liquid crystal components. The image is usually acquired by a charge coupled device (CCD) camera.


title: Confocal microscopy

text: Each of these classes of confocal microscope have particular advantages and disadvantages. Most systems are either optimized for recording speed (i.e. video capture) or high spatial resolution. Confocal laser scanning microscopes can have a programmable sampling density and very high resolutions while Nipkow and PAM use a fixed sampling density defined by the camera's resolution. Imaging frame rates are typically slower for single point laser scanning systems than spinning-disk or PAM systems. Commercial spinning-disk confocal microscopes achieve frame rates of over 50 per second – a desirable feature for dynamic observations such as live cell imaging.


title: Confocal microscopy

text: In practice, Nipkow and PAM allow multiple pinholes scanning the same area in parallel as long as the pinholes are sufficiently far apart.


title: Confocal microscopy

text: Cutting-edge development of confocal laser scanning microscopy now allows better than standard video rate (60 frames per second) imaging by using multiple microelectromechanical scanning mirrors.


title: Confocal microscopy

text: Confocal X-ray fluorescence imaging is a newer technique that allows control over depth, in addition to horizontal and vertical aiming, for example, when analyzing buried layers in a painting.


title: Confocal microscopy

text: CLSM is a scanning imaging technique in which the resolution obtained is best explained by comparing it with another scanning technique like that of the scanning electron microscope (SEM). CLSM has the advantage of not requiring a probe to be suspended nanometers from the surface, as in an AFM or STM, for example, where the image is obtained by scanning with a fine tip over a surface. The distance from the objective lens to the surface (called the "working distance") is typically comparable to that of a conventional optical microscope. It varies with the system optical design, but working distances from hundreds of micrometres to several millimeters are typical.


title: Confocal microscopy

text: In CLSM a specimen is illuminated by a point laser source, and each volume element is associated with a discrete scattering or fluorescence intensity. Here, the size of the scanning volume is determined by the spot size (close to diffraction limit) of the optical system because the image of the scanning laser is not an infinitely small point but a three-dimensional diffraction pattern. The size of this diffraction pattern and the focal volume it defines is controlled by the numerical aperture of the system's objective lens and the wavelength of the laser used. This can be seen as the classical resolution limit of conventional optical microscopes using wide-field illumination. However, with confocal microscopy it is even possible to improve on the resolution limit of wide-field illumination techniques because the confocal aperture can be closed down to eliminate higher orders of the diffraction pattern. For example, if the pinhole diameter is set to 1 Airy unit then only the first order of the diffraction pattern makes it through the aperture to the detector while the higher orders are blocked, thus improving resolution at the cost of a slight decrease in brightness. In fluorescence observations, the resolution limit of confocal microscopy is often limited by the signal-to-noise ratio caused by the small number of photons typically available in fluorescence microscopy. One can compensate for this effect by using more sensitive photodetectors or by increasing the intensity of the illuminating laser point source. Increasing the intensity of illumination laser risks excessive bleaching or other damage to the specimen of interest, especially for experiments in which comparison of fluorescence brightness is required. When imaging tissues that are differentially refractive, such as the spongy mesophyll of plant leaves or other air-space containing tissues, spherical aberrations that impair confocal image quality are often pronounced. Such aberrations however, can be significantly reduced by mounting samples in optically transparent, non-toxic perfluorocarbons such as perfluorodecalin, which readily infiltrates tissues and has a refractive index almost identical to that of water.


title: Confocal microscopy

text: CLSM is widely used in various biological science disciplines, from cell biology and genetics to microbiology and developmental biology. It is also used in quantum optics and nano-crystal imaging and spectroscopy.


title: Confocal microscopy

text: Clinically, CLSM is used in the evaluation of various eye diseases, and is particularly useful for imaging, qualitative analysis, and quantification of endothelial cells of the cornea. It is used for localizing and identifying the presence of filamentary fungal elements in the corneal stroma in cases of keratomycosis, enabling rapid diagnosis and thereby early institution of definitive therapy. Research into CLSM techniques for endoscopic procedures (endomicroscopy) is also showing promise. In the pharmaceutical industry, it was recommended to follow the manufacturing process of thin film pharmaceutical forms, to control the quality and uniformity of the drug distribution. Confocal microscopy is also used to study biofilms — complex porous structures that are the preferred habitat of microorganisms. Some of temporal and spatial function of biofilms can be understood only by studying their structure on micro- and meso-scales. The study of microscale is needed to detect the activity and organization of single microorganisms.


title: Confocal microscopy

text: CLSM is used as the data retrieval mechanism in some 3D optical data storage systems and has helped determine the age of the Magdalen papyrus.


title: Confocal microscopy

text: The IRENE system makes use of confocal microscopy for optical scanning and recovery of damaged historical audio.


title: Confocal microscopy

text: The point spread function of the pinhole is an ellipsoid, several times as long as it is wide. This limits the axial resolution of the microscope. One technique of overcoming this is 4Pi microscopy where incident and or emitted light are allowed to interfere from both above and below the sample to reduce the volume of the ellipsoid. An alternative technique is confocal theta microscopy. In this technique the cone of illuminating light and detected light are at an angle to each other (best results when they are perpendicular). The intersection of the two point spread functions gives a much smaller effective sample volume. From this evolved the single plane illumination microscope. Additionally deconvolution may be employed using an experimentally derived point spread function to remove the out of focus light, improving contrast in both the axial and lateral planes.


title: Confocal microscopy

text: There are confocal variants that achieve resolution below the diffraction limit such as stimulated emission depletion microscopy (STED). Besides this technique a broad variety of other (not confocal based) super-resolution techniques are available like PALM, (d)STORM, SIM, and so on. They all have their own advantages such as ease of use, resolution, and the need for special equipment, buffers, or fluorophores.


title: Confocal microscopy

text: To image samples at low temperatures, two main approaches have been used, both based on the laser scanning confocal microscopy architecture. One approach is to use a continuous flow cryostat: only the sample is at low temperature and it is optically addressed through a transparent window. Another possible approach is to have part of the optics (especially the microscope objective) in a cryogenic storage dewar. This second approach, although more cumbersome, guarantees better mechanical stability and avoids the losses due to the window.


title: Confocal microscopy

text: In 1940 Hans Goldmann, ophthalmologist in Bern, Switzerland, developed a slit lamp system to document eye examinations. This system is considered by some later authors as the first confocal optical system.


title: Confocal microscopy

text: In 1951 Hiroto Naora, a colleague of Koana, described a confocal microscope in the journal Science for spectrophotometry.


title: Confocal microscopy

text: The first confocal "scanning" microscope was built by Marvin Minsky in 1955 and a patent was filed in 1957. The scanning of the illumination point in the focal plane was achieved by moving the stage. No scientific publication was submitted and no images made with it were preserved.


title: Confocal microscopy

text: In the 1960s, the Czechoslovak Mojmír Petráň from the Medical Faculty of the Charles University in Plzeň developed the Tandem-Scanning-Microscope, the first commercialized confocal microscope. It was sold by a small company in Czechoslovakia and in the United States by Tracor-Northern (later Noran) and used a rotating Nipkow disk to generate multiple excitation and emission pinholes.


title: Confocal microscopy

text: The Czechoslovak patent was filed 1966 by Petráň and Milan Hadravský, a Czechoslovak coworker. A first scientific publication with data and images generated with this microscope was published in the journal Science in 1967, authored by M. David Egger from Yale University and Petráň. As a footnote to this paper it is mentioned that Petráň designed the microscope and supervised its construction and that he was, in part, a "research associate" at Yale. A second publication from 1968 described the theory and the technical details of the instrument and had Hadravský and Robert Galambos, the head of the group at Yale, as additional authors. In 1970 the US patent was granted. It was filed in 1967.


title: Confocal microscopy

text: In 1969 and 1971, M. David Egger and Paul Davidovits from Yale University, published two papers describing the first confocal "laser" scanning microscope. It was a point scanner, meaning just one illumination spot was generated. It used epi-Illumination-reflection microscopy for the observation of nerve tissue. A 5 mW Helium-Neon-Laser with 633 nm light was reflected by a semi-transparent mirror towards the objective. The objective was a simple lens with a focal length of 8.5 mm. As opposed to all earlier and most later systems, the sample was scanned by movement of this lens (objective scanning), leading to a movement of the focal point. Reflected light came back to the semitransparent mirror, the transmitted part was focused by another lens on the detection pinhole behind which a photomultiplier tube was placed. The signal was visualized by a CRT of an oscilloscope, the cathode ray was moved simultaneously with the objective. A special device allowed to make Polaroid photos, three of which were shown in the 1971 publication.


title: Confocal microscopy

text: The authors speculate about fluorescent dyes for "in vivo" investigations. They cite Minsky's patent, thank Steve Baer, at the time a doctoral student at the Albert Einstein School of Medicine in New York City where he developed a confocal line scanning microscope, for suggesting to use a laser with 'Minsky's microscope' and thank Galambos, Hadravsky and Petráň for discussions leading to the development of their microscope. The motivation for their development was that in the Tandem-Scanning-Microscope only a fraction of 10 of the illumination light participates in generating the image in the eye piece. Thus, image quality was not sufficient for most biological investigations.


title: Confocal microscopy

text: In 1977 Colin J. R. Sheppard and Amarjyoti Choudhury, Oxford, UK, published a theoretical analysis of confocal and laser-scanning microscopes.<ref name="DOI10.1080/713819421"></ref> It is probably the first publication using the term "confocal microscope".


title: Confocal microscopy

text: In 1978, the brothers Christoph Cremer and Thomas Cremer published a design for a confocal laser-scanning-microscope using fluorescent excitation with electronic autofocus. They also suggested a laser point illumination by using a "4π-point-hologramme". This CLSM design combined the laser scanning method with the 3D detection of biological objects labeled with fluorescent markers for the first time.


title: Confocal microscopy

text: In 1978 and 1980, the Oxford-group around Colin Sheppard and Tony Wilson described a confocal microscope with epi-laser-illumination, stage scanning and photomultiplier tubes as detectors. The stage could move along the optical axis (z-axis), allowing optical serial sections.


title: Confocal microscopy

text: In 1979 Fred Brakenhoff and coworkers demonstrated that the theoretical advantages of optical sectioning and resolution improvement are indeed achievable in practice. In 1985 this group became the first to publish convincing images taken on a confocal microscope that were able to answer biological questions. Shortly after many more groups started using confocal microscopy to answer scientific questions that until then had remained a mystery due to technological limitations.


title: Confocal microscopy

text: In 1983 I. J. Cox and C. Sheppard from Oxford published the first work whereby a confocal microscope was controlled by a computer. The first commercial laser scanning microscope, the stage-scanner SOM-25 was offered by Oxford Optoelectronics (after several take-overs acquired by BioRad) starting in 1982. It was based on the design of the Oxford group.


title: Confocal microscopy

text: In the mid-1980s, William Bradshaw Amos and John Graham White and colleagues working at the Laboratory of Molecular Biology in Cambridge built the first confocal beam scanning microscope. The stage with the sample was not moving, instead the illumination spot was, allowing faster image acquisition: four images per second with 512 lines each. Hugely magnified intermediate images, due to a 1-2 meter long beam path, allowed the use of a conventional iris diaphragm as a ‘pinhole’, with diameters ~1 mm. First micrographs were taken with long-term exposure on film before a digital camera was added. A further improvement allowed zooming into the preparation for the first time. Zeiss, Leitz and Cambridge Instruments had no interest in a commercial production. The Medical Research Council (MRC) finally sponsored development of a prototype. The design was acquired by Bio-Rad, amended with computer control and commercialized as 'MRC 500'. The successor MRC 600 was later the basis for the development of the first two-photon-fluorescent microscope developed 1990 at Cornell University.


title: Confocal microscopy

text: Developments at the KTH Royal Institute of Technology in Stockholm around the same time led to a commercial CLSM distributed by the Swedish company Sarastro. The venture was acquired in 1990 by Molecular Dynamics, but the CLSM was eventually discontinued. In Germany, Heidelberg Instruments, founded in 1984, developed a CLSM, which was initially meant for industrial applications rather than biology. This instrument was taken over in 1990 by Leica Lasertechnik. Zeiss already had a non-confocal flying-spot laser scanning microscope on the market which was upgraded to a confocal. A report from 1990, mentioned some manufacturers of confocals: Sarastro, Technical Instrument, Meridian Instruments, Bio-Rad, Leica, Tracor-Northern and Zeiss.


title: Confocal microscopy

text: In 1989, Fritz Karl Preikschat, with his son Ekhard Preikschat, invented the scanning laser diode microscope for particle-size analysis. and co-founded Lasentec to commercialize it. In 2001, Lasentec was acquired by Mettler Toledo. They are used mostly in the pharmaceutical industry to provide in-situ control of the crystallization process in large purification systems.


title: Lederhosen

text: Lederhosen (; , ; singular in German usage: "Lederhose") are short or knee-length leather breeches that are worn as traditional garments in some regions of German-speaking countries. The longer ones are generally called "Bundhosen" or "Kniebundhosen". Once common workwear across Central Europe, these clothes—or Tracht—are particularly associated with Bavaria and the Tyrol region.


title: Lederhosen

text: Formerly, lederhosen were worn for hard physical work; they were more durable than a fabric garment. Today, they are mostly worn as leisurewear. Lederhosen and dirndl attire is also common at Oktoberfest events around the world.


title: Lederhosen

text: Lederhosen were widespread among men of the Alpine and surrounding regions, including Bavaria, Austria, the Allgäu, Switzerland, the autonomous Italian region of Trentino-Alto Adige/Südtirol (formerly part of Austria-Hungary) and the Alpine area of today's Slovenia.


title: Lederhosen

text: "La Couturière Parisienne", however, says that lederhosen were originally not exclusively a Bavarian garment but were worn all over Europe, especially by riders, hunters, and other people involved in outdoor activities. The flap ("drop front") may have been a unique Bavarian invention. The drop-front style became so popular in the 18th century that it was known in France as "à la bavaroise," "in the Bavarian style."


title: Lederhosen

text: The popularity of lederhosen in Bavaria dropped sharply in the 19th century. They began to be considered as uncultured peasants' clothing that was not fitting for modern city-dwellers. However, in the 1880s a resurgence set in, and several clubs were founded in Munich and other large cities devoted to preserving traditional rural clothing styles. The conception of lederhosen as a quintessentially Bavarian garment that is worn at festive occasions rather than at work dates largely from this time.


title: Lederhosen

text: Lederhosen have remained regionally popular and are popularly associated with virility and brawn. Some men wear them when gardening, hiking, working outdoors, or attending folk festivals or beer gardens. They are a symbol of regional pride in Bavaria and the other areas where they are worn, but are rarely seen elsewhere.


title: Lederhosen

text: Traditional lederhosen are hand made of tanned deer leather which makes the pants soft and light but very tearproof. As those leather pants are very valuable and can last a lifetime, some Bavarians even bequeath their lederhosen to the next generation. Some variations of modern lederhosen are made of heavier, lower quality leather, or imitations like velour leather which make them much cheaper but less durable. All variations are usually equipped with two side pockets, one hip pocket, one knife pocket, and a codpiece (drop front). For an Oktoberfest costume, people combine lederhosen with Haverlschuhe, stockings and a classic white or checked shirt.


title: Lederhosen

text: Lederhosen are also part of the traditional costume of Swabia and its former portion of the Black Forest in present-day Baden-Württemberg. However, the lederhosen in these areas were always worn below the knee and never in the short style which is common in Bavaria. These knee-length bundhosen are cuffed at the bottom, also unlike their Bavarian counterparts. While plaid shirts were worn with Swabian lederhosen at times, they are historically more commonly worn with a white linen shirt and colorful vest, most commonly red. Also unique to the region is the color of the lederhosen. In contrast to brown, most Swabians, including farmers, would wear black, while the region's winemakers wore yellow. These lederhosen also have a decorative motif that is unique to the region. Today, lederhosen and so-called traditional costumes are worn mainly for local festivals and partially designed according to modern fashion trends.


title: Lederhosen

text: German boys used to wear lederhosen up to the age of about sixteen years. These lederhosen were not decorated with embroidery, and had the typical suspenders/braces and drop-front flap. Even today, some German and French Scouts wear various forms of lederhosen, although in most cases they are not part of their official uniform.


title: Lederhosen

text: Lederhosen were also worn by Austrian boys from the 1930s to the 1970s. Today they are worn on special occasions, such as a Biergarten or Zeltfest. Girls wear the Dirndl, which is part of Southern German and Austrian Tracht.


title: Rob Brown (actor)

text: Robert Brown (born March 11, 1984) is an American actor. He is known for his roles in the films "Finding Forrester" (2000), "Coach Carter" (2005), "Take the Lead" (2006), and "" (2008), and for starring in the HBO series "Treme" (2010–13).


title: Rob Brown (actor)

text: Brown was born in Harlem, New York on March 11, 1984, the middle of three children. Brown's mother works as a substance abuse counselor. He was raised in Brooklyn. Brown attended Poly Prep Country Day School, where he played on the school's football team as a wide receiver. He graduated from Amherst College, where he balanced his education and acting career. Prior to being cast in "Finding Forrester", Brown's only acting experience was a school play during childhood.


title: Rob Brown (actor)

text: When he turned 16, Brown auditioned for "Finding Forrester", expecting to be cast as an extra. However, the film's director Gus Van Sant claimed Brown was the actor he was seeking to portray high school basketball player Jamal Wallace, and cast him in the role. Brown made his acting debut in the 2000 film, opposite Sean Connery. Brown received positive reviews in his first acting role. One critic believed Brown shined more than his veteran co-star. A film reviewer stated Brown held his own "remarkably well" alongside Connery, with a third opining the two actors had an "appealing chemistry."


title: Rob Brown (actor)

text: In 2005, he played the role of basketball player Kenyon Stone in the drama film "Coach Carter", starring Samuel L. Jackson. Reviewer A. O. Scott opined Brown had a "strong" showing in the movie. The following year, he appeared as a high school student Jason "Rock" Rockwell in the dance film "Take the Lead", starring Antonio Banderas and Alfre Woodard. Brown portrayed football player Ernie Davis in "" (2008).


title: Rob Brown (actor)

text: Brown landed his first television role as jazz musician Delmond Lambreaux on drama series "Treme" in 2010. He continued portraying the character until the show ended in 2013. Brown was cast in the NBC drama "Blindspot" (2015−20) as FBI Special Agent Edgar Reade. He appeared as Bobby in "Don Jon" (2013) and played the role of Bryce in "Criminal Activities" (2015). In 2022, Brown recurred as Maurice Ward in miniseries "We Own This City".


title: Rob Brown (actor)

text: In 2013, Brown was arrested for allegedly purchasing a watch for his mother with a "fake" credit card at Macy's in New York City. He was later released with no charges against him, due to the fact that the (Amercian Express) credit card was actually his. Evidently, Macy's staff had become suspicious (possibly due to the cost of the watch, his age and/or his ethnicity) but had not taken basic steps to check the validity of the credit card with American Express or cross-check against his driving licence. Subsequently, CNN reported that the actor had "reached a “settlement in principle” in his racial profiling lawsuits against Macy’s and New York, according to court documents and a statement from the retailer."


title: Tony Hillerman

text: Anthony Grove Hillerman (May 27, 1925 – October 26, 2008) was an American author of detective novels and nonfiction works, best known for his mystery novels featuring Navajo Nation Police officers Joe Leaphorn and Jim Chee. Several of his works have been adapted as theatrical and television movies.


title: Tony Hillerman

text: Tony Hillerman was born in Sacred Heart, Oklahoma, to August Alfred Hillerman, a farmer and shopkeeper, and his wife, Lucy Grove. He was the youngest of their three children, and the second son. His paternal grandparents were born in Germany, and his maternal grandparents were born in England. He grew up in Pottawatomie County, Oklahoma, attending elementary and high school with Potawatomi children.


title: Tony Hillerman

text: Jeffrey Herlihy argues that this background made possible "a significantly different portrayal of Native Americans in his writing", in comparison to other authors of his time. "Growing up Indian," Hillerman said of his childhood, "you did not have an 'us and them.'"


title: Tony Hillerman

text: He was a decorated combat veteran of World War II, serving from August 1943 to October 1945 as a mortarman in the 103rd Infantry Division in the European theatre. He earned the Silver Star, the Bronze Star, and a Purple Heart. Hillerman attended the University of Oklahoma after the war, meeting Marie Unzner, a student in microbiology. The couple wed and had one biological child and five adopted children.


title: Tony Hillerman

text: From 1948 to 1962, he worked as a journalist, moving to Santa Fe, New Mexico, in 1952. In 1966, he moved his family to Albuquerque, where he earned a master's degree from the University of New Mexico. During his time as a writer for the "Borger News-Herald" in Borger, Texas, he became acquainted with the sheriff of Hutchinson County, the man upon whom he would pattern the main character in his Joe Leaphorn novels. He taught journalism from 1966 to 1987 at the University of New Mexico in Albuquerque, and also began writing novels. He lived there with his wife Marie until his death in 2008. At the time of his death, they had been married 60 years and had 10 grandchildren.


title: Tony Hillerman

text: A consistently bestselling author, he was ranked as New Mexico's 22nd-wealthiest man in 1996. He wrote 18 books in his Navajo series. He wrote more than 30 books total, among them a memoir and books about the Southwest, its beauty, and its history. His literary honors were awarded for his Navajo books. Hillerman's books have been translated into eight languages, among them Danish and Japanese.


title: Tony Hillerman

text: Hillerman's writing is noted for the cultural details he provides about his subjects: Hopi, Zuni, European settlers, federal agents, and especially the Navajo Nation Police. His works in nonfiction and in fiction reflect his appreciation of the natural wonders of the American Southwest and his appreciation of its indigenous people, particularly the Navajo. His mystery novels are set in the Four Corners area of New Mexico and Arizona, sometimes reaching into Colorado and Utah, with occasional forays to the big cities of Washington, DC, Los Angeles, and New York City. The protagonists are Joe Leaphorn and Jim Chee of the Navajo Nation Police. Lt. Leaphorn was introduced in Hillerman's first novel, "The Blessing Way" (1970). Sgt. Jim Chee was introduced in the fourth novel, "People of Darkness". The two first work together in the seventh novel, "Skinwalkers", considered his breakout novel, with a distinct increase in sales with the two police officers working together.


title: Tony Hillerman

text: Hillerman repeatedly acknowledged his debt to an earlier series of mystery novels written by British-born Australian author Arthur W. Upfield and set among Australian Aborigines in remote desert regions of tropical and subtropical Australia. The Upfield novels were first published in 1928 and featured a half-European, half-aboriginal Australian hero, Detective-Inspector Napoleon (Bony) Bonaparte. Bony worked with deep understanding of Aboriginal traditions. The character was based on the achievements of an Aboriginal person known as Tracker Leon, whom Upfield had met during his years in the Australian bush.


title: Tony Hillerman

text: Hillerman discussed his debt to Upfield in many interviews and in his introduction to the posthumous 1984 reprint of Upfield's "A Royal Abduction." In the introduction, he described the appeal of the descriptions in Upfield's crime novels. It was descriptions both of the harsh Outback areas and of "the people who somehow survived upon them" that lured him. "When my own Jim Chee of the Navajo Tribal Police unravels a mystery because he understands the ways of his people, when he reads the signs in the sandy bottom of a reservation arroyo, he is walking in the tracks Bony made 50 years ago."


title: Tony Hillerman

text: He also mentioned Eric Ambler, Graham Greene, and Raymond Chandler as authors who influenced him as he wrote the Leaphorn and Chee novels.


title: Tony Hillerman

text: In an interview published in "Le Monde", Hillerman said his Navajo name means "He who is afraid of his horse".


title: Tony Hillerman

text: Tony Hillerman died on October 26, 2008, of pulmonary failure in Albuquerque at the age of 83, and was interred at Santa Fe National Cemetery.


title: Tony Hillerman

text: Hillerman's novels were popular in France. Hillerman credits that popularity both to French curiosity about other cultures and to his translator, Pierre Bondil.


title: Tony Hillerman

text: Hillerman is considered one of New Mexico's foremost novelists. The Tony Hillerman Library was dedicated in Albuquerque in 2008, and the Tony Hillerman Middle School (part of Volcano Vista High School) opened in 2009. "Dance Hall of the Dead", published in 1973, earned Hillerman the Grand Prix de Littérature Policière in 1987, a French international literary honor. Hillerman was awarded an Honorary Doctorate of Literature (Litt.D.) from the University of New Mexico in 1990. He was awarded the Owen Wister Award in 2008 for "Outstanding Contributions to the American West."


title: Tony Hillerman

text: Hillerman was a decorated combat veteran of World War II; he earned the Silver Star, the Bronze Star, and a Purple Heart as a mortarman in the 103rd Infantry Division.


title: Tony Hillerman

text: He won and was nominated for numerous awards for his writing and his work with other writers. His first nomination came in 1972, with his novel "The Fly on the Wall" being nominated for an Edgar Award in the "Best Mystery Novel" category. Two years later his novel "Dance Hall of the Dead", second book in the Leaphorn-Chee series, won the 1974 Edgar Award for Best Novel. He was again nominated for the "Best Mystery Novel" Edgar Award in 1979 for "Listening Woman" and lastly in 1989 for "A Thief of Time". Hillerman's non-fictional work "Talking Mysteries" was nominated in 1992 for the Edgar Award in the "Best Critical or Biographical" category.


title: Tony Hillerman

text: In 1987, Hillerman received the Grand Prix de Littérature Policière for "Dance Hall of the Dead". In 1991, Hillerman received the MWA's Grand Master Award. Hillerman received the Nero Award for "Coyote Waits" and the Navajo Tribe's Special Friends of the Dineh Award.


title: Tony Hillerman

text: Hillerman has also been successful at the annual Anthony Awards. His novel "Skinwalkers" won the 1988 Anthony Award for "Best Novel", and in the following year "A Thief of Time" was nominated for the 1989 Anthony Award in the same category. His next nomination was for his "Talking Mysteries" non-fictional work which was nominated at the 1992 Anthony Awards. His novel "Sacred Clowns" received a "Best Novel" nomination at the 1994 Anthony Awards, and the following year his short-story collection "The Mysterious West" won the 1995 Anthony Award in the "Best Anthology/Short Story Collection" category. His last win came at the 2002 Anthony Awards at which he won the "Best Non-fiction/Critical Work" award for his memoir "Seldom Disappointed".


title: Tony Hillerman

text: Two of the Navajo Police novels won The Spur award, given by the Western Writers of America annually. "Skinwalkers" won the award in 1987 for Western Novel, and "The Shape Shifter" won in 2007 for Best Western Short Novel.


title: Tony Hillerman

text: Hillerman's novels were recognized at the Macavity Awards. "A Thief of Time" won the "Best Novel" award in 1989, and "Talking Mysteries" won the "Best Critical/Biographical" award in 1992. "Seldom Disappointed" also received a nomination in the "Best Biographical/Critical Mystery Work" category in 2002.


title: Tony Hillerman

text: He received the Parris Award in 1995 by Southwest Writer's Workshop for his outstanding service to other writers. In 2002, Hillerman received the Agatha Malice Domestic Award for Lifetime Achievement, given by Malice Domestic for mystery novels in the spirit of Agatha Christie.


title: Tony Hillerman

text: The first three books feature Joe Leaphorn only (and only as a supporting secondary character in the first novel.) The next three books feature Jim Chee only. Leaphorn and Chee begin working together in the seventh novel, "Skinwalkers".


title: Tony Hillerman

text: In 2013, Hillerman's daughter Anne Hillerman published "Spider Woman's Daughter" (), the first new novel since 2006 featuring Hillerman's Navajo Police characters; the novel's protagonist is Jim Chee's wife, Officer Bernadette Manuelito. Leaphorn's involvement is curtailed in the first chapter of the book. Leaphorn is the victim of an assassination attempt, spends half of the book in a coma, and later was severely limited in his ability to communicate. Chee and Bernadette Manuelito are the crime solvers from that book forward in the series, with Leaphorn never fully active in the investigations. There have been seven books in Anne Hillerman's continuation series so far:


title: Marianna Palka

text: Marianna Bronislawa Barbara Palka (born 7 September 1981) is a Scottish actress, producer, director, and writer. She is the writer, director and star of the film "Good Dick", which screened at the Sundance Film Festival.


title: Marianna Palka

text: Palka was born in Glasgow, Scotland. At the age of 17, Palka moved to New York City to study at the Atlantic Theater Company.


title: Marianna Palka

text: Palka wrote, directed and starred in "Good Dick", which competed in the Dramatic Competition at the 2008 Sundance Film Festival. The film also featured Jason Ritter, Martin Starr, Mark Webber, Charles Durning and Tom Arnold. "The New York Times" said the film "surmounts its indie-movie quirkiness with exceptional acting and a sincere belief in the salvation of its wounded characters.” Palka returned to 2010 Sundance Film Festival as a Juror with the Alfred P. Sloan Foundation.


title: Marianna Palka

text: Palka appeared in Peter Mullan’s "Neds", Jeremiah Jones’ "Restive", Bryce Dallas Howard’s "When You Find Me", Nathan Sutton's "Autumn Wanderer" and Sylvia Sether's "King of Norway." In 2014, Palka produced and was the subject of the HBO Lucy Walker documentary "The Lion's Mouth Opens", which follows the process of Palka discovering she has inherited the genetic mutation that causes Huntington’s disease, and which was nominated for an Emmy Award and shortlisted for an Academy Award nomination. Palka made a cameo in the HBO series "Girls" as Jessa's (Jemima Kirke) sister. As of 2017, Palka appears as Reggie 'Vicky the Viking' Walsh in the Netflix series "G.L.O.W" .


title: Marianna Palka

text: Palka wrote, directed and starred in "Bitch", based on a true story from Scottish doctor R.D. Laing of a mother acting like a dog after a psychotic break. The film made its round in film festivals around the world, after its world premiere at 2017 Sundance Film Festival. In 2017, Palka directed the feature film "EGG" starring Christina Hendricks, Alysia Reiner and Anna Camp and produced by Michele Ganeless.


title: Marianna Palka

text: In 2010, Palka performed in "Love, Loss, and What I Wore" at The Geffen Playhouse in Los Angeles. In 2012, she was in The Ensemble Theater in Santa Barbara, California, reading of "The Good Soldier". She appeared in Martin McDonagh's "The Lonesome West" at the Actor's Gang Theatre, Los Angeles, and in Conor McPherson's "Dublin Carol" at the Ensemble Theatre Company.


title: The Double (2013 film)

text: The Double is a 2013 British black comedy thriller film written and directed by Richard Ayoade and starring Jesse Eisenberg and Mia Wasikowska. It is based on the 1846 novella "The Double" by Fyodor Dostoyevsky, about a man driven to breakdown when he is usurped by a doppelgänger. It was produced by Alcove Entertainment, with Michael Caine, Graeme Cox (Attercop), Tessa Ross (Film4) and Nigel Williams as executive producers.


title: The Double (2013 film)

text: Downtrodden Simon James (Jesse Eisenberg) has worked at his office for seven years, but he is ignored by his boss, named The Colonel, and colleagues. From his apartment he spies on a beautiful co-worker he admires, Hannah (Mia Wasikowska), who lives in the apartment opposite him. He sees her throwing away art and secretly retrieves and admires it. One night, Simon sees a man jump to his death from the floor above Hannah's apartment. He talks to detectives, who explain that if the man had jumped a few feet to the right, he would have been badly hurt but would have survived.


title: The Double (2013 film)

text: Simon's boss (Wallace Shawn) announces the arrival of a new employee, James Simon (also played by Eisenberg), who looks identical to Simon, which causes Simon to faint upon first glance. Assertive and charming, James is Simon's polar opposite. Much to Simon's annoyance, James not only gets respect from their co-workers but no one seems to notice that they are identical in appearance. James, on the other hand, does notice this and sees Simon's pain. Out of pity, he decides to buddy-up with Simon and give him advice about how to seduce Hannah. Hannah then asks James on a date through Simon. On the date, Simon pretends to be James, with the real James giving him instructions via earpiece. When Simon becomes nervous, the two swap places and James kisses Hannah, angering Simon. James asks Simon to take an aptitude test in his place and seduces their boss's surly, rebellious daughter, Melanie (Yasmin Paige), whom Simon was instructed to tutor, something he is reluctant to do.


title: The Double (2013 film)

text: Simon gets his revenge on James by revealing to Hannah that James is cheating on her with Melanie. Furious, James blackmails Simon for his apartment keys using explicit photos he took of himself with Melanie, knowing their boss will believe it is Simon in the photos. At work, Simon accuses James of being an imposter and is fired after going on a maniacal tirade. As he is about to kill himself, he sees Hannah lying unconscious in her apartment. He calls an ambulance and accompanies her to the hospital, where it is revealed that she not only overdosed but also miscarried (she had become pregnant after a sexual encounter with James). Simon then takes Hannah back home, relieved that she has survived. Still upset, however, Hannah states that she wanted to die and she suggests that Simon kill himself. She goes through Simon's jacket pockets and discovers earrings he had bought for her and her salvaged art.


title: The Double (2013 film)

text: Simon learns his mother has died and finds James at her funeral. Simon punches him and discovers that they share injuries; as James's nose bleeds, so does Simon's. He finds Hannah and tells her he wants to be noticed. He goes to his apartment and handcuffs the sleeping James to his bed, then goes to the ledge above Hannah's apartment, steps to the right, and jumps. He is badly hurt. Hannah runs to him and an ambulance arrives. Lacking medical attention, the handcuffed James appears to be on the brink of death as he lies motionless on the apartment floor.


title: The Double (2013 film)

text: Inside the ambulance, The Colonel (James Fox) and Hannah watch over Simon. The Colonel tells Simon that he is "special", to which the latter responds with a half-smile, "I'd like to think I'm pretty unique".


title: The Double (2013 film)

text: In February 2012 it was reported that Richard Ayoade would direct "The Double", starring Jesse Eisenberg and Mia Wasikowska, in the United Kingdom. Principal photography began on 20 May 2012 in London.


title: The Double (2013 film)

text: The score by Andrew Hewitt features a recurring progression of heavy chords played by strings. The chord progression comes from the song "Der Doppelgänger" by Franz Schubert.


title: The Double (2013 film)

text: "The Double" premiered at the 2013 Toronto International Film Festival on 7 September 2013. On 15 October 2013 it was announced that Magnolia Pictures had acquired the US rights for a 2014 release.


title: The Double (2013 film)

text: The film opened in two cinemas in the United States and grossed $14,646. It ended up grossing $145,511 in North America and $1,306,588 internationally for a total of $1,452,099.


title: The Double (2013 film)

text: The film received positive reviews from critics and has a "Certified Fresh" rating of 83% on Rotten Tomatoes based on 131 reviews, with an average rating of 6.9/10. The consensus states "Hauntingly bleak and thrillingly ambitious, "The Double" offers Jesse Eisenberg a pair of compelling roles while reaffirming writer-director Richard Ayoade's remarkable talent." The film also has a score of 68 out of 100 on Metacritic based on 31 critics, indicating "Generally favorable reviews".


title: The Double (2013 film)

text: Writer/Director Richard Ayoade had really outdone himself. The way he re-imagined and modernized Fyodor Dostoevsky's novella "The Double", is a pure artistic vision. The dark tones are only enhanced by the light notes of humor throughout the film. Ayoade's avant garde, experimental style and minimalist set design sound like an odd couple, but they actually work great together.


title: The Double (2013 film)

text: In his best work since "The Social Network", Eisenberg portrays the polarized personalities of Simon and James with such ease. The story basically rests on his shoulders as we follow him on his descent into madness. In between the fast-paced dialogue and front-lit shots there is also a very complex story that leaves the ending open to interpretation.


title: Jheri curl

text: The Jheri curl (often spelled Jerry curl or Jeri Curl) is a permanent wave hairstyle that was popular among African Americans during the 1980s and early 1990s. Invented by the hairdresser Jheri Redding, the Jheri curl gives the wearer a glossy, loosely curled look. It was touted as a "wash and wear" style that was easier to care for than the other popular chemical treatment of the day, the relaxer.


title: Jheri curl

text: A Jheri curl requires a two-part application that consists of a softener (often called a "rearranging cream") to loosen the hair, and a solution to set the curls. The rearranging cream uses pungent chemicals, causing the naturally tight curls to loosen. The looser curls are then set and a chemical solution is then added to the hair to permanently curl it.


title: Jheri curl

text: "Perming" is time and labor-intensive, and expensive to maintain. The chemicals required for the process often cause the wearer's natural hair to become brittle and dry.


title: Jheri curl

text: To maintain the look of the Jheri curl, wearers are required to apply a curl activator spray and moisturizers daily, and sleep with a plastic cap over the hair to prevent it from drying out. These products are expensive; a typical bottle of activator was small, retailed from $3 to $6, and was quickly depleted. The activator in particular has the undesirable side effect of being very greasy, and often stains clothing and furniture.


title: Jheri curl

text: Washing the hair cleanses it of the styling products and also shows the damage done to the hair by the chemical process. As the hair grows out, the wearer is required to touch up the new hair growth, further adding to the overall expense.


title: Jheri curl

text: To resolve the problems associated with the cost of the look, Comer Cottrell invented a cheap kit (which he called the "Curly Kit") that could be used at home, thereby enabling lower-income people to copy the style of their idols.


title: Jheri curl

text: The Jheri curl was worn by Michael Jackson on the cover of his hit album "Thriller", which was released in 1982. Jackson also grew out his Jheri curl in 1986, which is shown on the cover of his 1987 album "Bad".


title: Jheri curl

text: Edmund Sylvers was the first African-American artist to have the Jheri curl on an album cover, on his 1980 Casablanca release "Have You Heard".


title: Jheri curl

text: Other notable wearers of the style in the 1980s and early 1990s include rappers MC Eiht, DJ Quik, Eazy-E, Ice Cube, Hi-C, Arabian Prince and B.G. Knocc Out.


title: Jheri curl

text: Singer and songwriter India Arie referenced Jheri curls in her song I Am Not My Hair, released in 2005.


title: Jheri curl

text: The 1988 comedy "Coming to America" features Eriq La Salle as Darryl Jenks, heir to the dynasty of a fictional product named "SoulGlo", which gave the wearer a style reminiscent of a Jheri curl while leaving the infamous greasy residue on soft furnishings.


title: Jheri curl

text: Keenen Ivory Wayans played a character entitled "Jeri Curl" in the 1987 Robert Townsend film "Hollywood Shuffle". One of Wayans' recurring characters on "In Living Color", Frenchy, also sported a Jheri curl. When attending an Alcoholics Anonymous meeting and hearing others testify to how much they used to drink, Frenchy claimed he was previously "up to three and a half bottles of TCB Lite a day; I switched over to Afro Sheen, and I'm never dry!"


title: Jheri curl

text: The character Jules Winnfield (played by Samuel L. Jackson) wore a Jheri curl in the 1994 drama "Pulp Fiction".


title: Jheri curl

text: In Samuel L. Jackson's opening monologue in the 1989 film "Do the Right Thing", his character (DJ) explains that there is a "Jheri Curl alert" in effect for the day: "If you have a Jheri Curl, stay in the house or you'll end up with a permanent plastic helmet on your head forever."


title: Jheri curl

text: Los Angeles Lakers basketball player Billy Ray Bates was reported to be unpopular with other players "because he had a really moist Jheri curl, and the ball would get all slippery."


title: DeShone Kizer

text: DeShone Allen Kizer (born January 3, 1996) is an American football quarterback who has played in the National Football League (NFL) for four seasons. He played college football at Notre Dame and was selected by the Cleveland Browns in the second round of the 2017 NFL Draft. Kizer served as the Browns' starter during his rookie season, but his tenure lasted only one year after he went winless and led the league in interceptions. Traded to the Green Bay Packers, he spent one season as a backup in 2018 and also held backup roles with the Las Vegas Raiders and Tennessee Titans.


title: DeShone Kizer

text: Kizer attended Central Catholic High School in Toledo, Ohio. Kizer was named the AP Ohio Division III co-offensive player of the year as a senior in 2013. A three-year starter, Kizer helped lead the Fighting Irish high school football team to a combined 34–6 overall record in 2011–13 (8–2 in playoff games), including a 14–1 record and Ohio Division II state title in 2012. In his career, Kizer's totals included 5,684 passing yards and 56 touchdowns to go with 1,211 rushing yards and 17 touchdowns.


title: DeShone Kizer

text: Considered a four-star recruit by "Rivals.com", he was rated as the ninth best dual-threat quarterback prospect of his class. On June 11, 2013, Kizer announced his commitment to play college football at the University of Notre Dame.


title: DeShone Kizer

text: Kizer redshirted his first year at Notre Dame in 2014 behind quarterbacks Everett Golson and Malik Zaire.


title: DeShone Kizer

text: Kizer started 2015 as a backup to Zaire. On September 5, in the season opener, he made his collegiate debut against Texas in relief of Zaire in the 38–3 victory. During the second game of the season against Virginia, Kizer replaced an injured Zaire and helped lead Notre Dame to a victory. With 12 seconds left, Kizer completed a 39-yard touchdown pass to wide receiver Will Fuller to give Notre Dame the lead. After it was announced that Zaire would miss the rest of the season, Kizer was named the starter. On October 3, in a 24–22 loss to Clemson, he passed for a season-high 321 yards, two touchdowns, and one interception while having 15 carries for 60 yards and a rushing touchdown. Against Pitt, Kizer accounted for all six touchdowns (five passing and one rushing) helping Notre Dame to a 42–30 victory. On Halloween, in a 24–20 win over Temple, he recorded 299 passing yards, one touchdown, and two interceptions, and had a stellar night on the ground with 143 rushing yards and two rushing touchdowns. Kizer and the Fighting Irish finished the 2015 regular season with a 10–2 record. On New Year's Day, Kizer and the Fighting Irish closed out their 2015 season with a 44–28 loss to Ohio State in the Fiesta Bowl. In the loss, he had 284 passing yards, two touchdowns, one interception while adding 21 rushing yards and a rushing touchdown on the ground. Overall in 2015, Kizer finished his redshirt first year with 2,880 passing yards, 525 rushing yards, and 31 total touchdowns in 13 games.


title: DeShone Kizer

text: Kizer started off the 2016 season with 215 passing yards, five passing touchdowns, 77 rushing yards, and a rushing touchdown in a 2OT 50–47 loss to Texas at Darrell K Royal–Texas Memorial Stadium. After a victory over Nevada, he had 344 passing yards, two passing touchdowns, 14 rushing yards, and two rushing touchdowns in a 36–28 loss to Michigan State. After a loss to Duke, he had a career day through the air with 471 yards and three touchdowns in a 50–33 win over Syracuse. He put together some solid performances over the rest of the season, but the team faltered and ended up with a 4–8 record. Kizer played 12 games with 2,925 passing yards, 472 rushing yards, and 34 total touchdowns. After the 2016 season, Kizer decided to forgo the remaining two years of eligibility and enter the 2017 NFL Draft.


title: DeShone Kizer

text: Kizer received an invitation to the NFL Combine and completed all of the combine drills except for the bench press. He also performed positional drills, but had a disappointing performance. He also participated at Notre Dame's Pro Day and only ran positional drills in front of team scouts and representatives, including San Francisco 49ers general manager John Lynch and Pittsburgh Steelers offensive coordinator Todd Haley. Kizer completed 50/60 pass attempts and showed significantly better accuracy and footwork at his pro day. NFL draft experts and analysts projected him to be a first or second round pick. He was ranked the second best quarterback in the draft by NFL analyst Bucky Brooks, the third best quarterback by NFLDraftScout.com and "Sports Illustrated", and was ranked the fourth best quarterback by NFL Network analyst Mike Mayock.


title: DeShone Kizer

text: The Cleveland Browns selected Kizer in the second round (52nd overall) of the 2017 NFL Draft. He was the fourth quarterback selected and first taken in the second round. On June 14, 2017, the Browns signed Kizer to a four-year, $4.94 million contract that includes $2.42 million guaranteed and a signing bonus of $1.73 million. On August 27, 2017, following the team's third preseason game, the Browns named Kizer as the starting quarterback to begin the 2017 regular season, beating out veteran trade acquisition Brock Osweiler and second-year quarterbacks Cody Kessler and Kevin Hogan.


title: DeShone Kizer

text: Making his NFL debut on September 10, 2017, Kizer finished with 222 passing yards with a touchdown and an interception. He also rushed for 17 yards and a one-yard rushing touchdown, but the Browns lost by a score 21–18 at home to the Pittsburgh Steelers. He orchestrated a 12-play drive that ended when he scored on a 1-yard touchdown run. Kizer's first career passing touchdown was a three-yard pass to wide receiver Corey Coleman in the fourth quarter. He started the next four games for the Browns, which were all losses. During the Week 5 game against the New York Jets, Kizer was benched in favor of Kevin Hogan to begin the third quarter. Hogan was later named the starter for the team's Week 6 game against the Houston Texans. After Hogan's struggles in Week 6, Kizer was renamed the starter for the Week 7. Against the Tennessee Titans in Week 7, Kizer threw for 114 yards and two interceptions before being benched in favor of Cody Kessler in the third quarter. The Browns lost 12–9 in overtime. Following the game, reports surfaced Kizer was out late the Friday before the Titans game, which caused some controversy. During Week 14 against the Green Bay Packers, Kizer threw for 214 yards and a season-high three touchdowns, but also threw two interceptions, including one in overtime that gave the Packers excellent field position. The Browns lost by a score of 27–21. During the season finale against the Steelers in Week 17, Kizer finished with a season-high 314 passing yards, two touchdowns, and an interception as the Browns lost 24–28. The Browns finished the year with an 0–16 record, only the second team in NFL history to have that record.


title: DeShone Kizer

text: In 15 starts of his rookie season, Kizer completed 53.6 percent of his passes for 2,894 yards, 11 touchdowns, and a league-leading 22 interceptions. He also rushed for 419 yards and five touchdowns.


title: DeShone Kizer

text: On March 14, 2018, Kizer was traded to the Green Bay Packers in exchange for Damarious Randall and a swap of both fourth and fifth-round draft picks.


title: DeShone Kizer

text: On September 9, 2018, in Week 1, Kizer played in place of an injured Aaron Rodgers in the first and second quarters against the Chicago Bears. He threw for 55 yards and an interception, which was returned for a touchdown. Rodgers returned in the third quarter and led the Packers to a 24–23 victory. In the season finale against the Detroit Lions, Kizer played in relief of Rodgers, who had suffered a concussion, and threw for 132 yards and an interception as the Packers were shut-out by a score of 31–0.


title: DeShone Kizer

text: On September 1, 2019, Kizer was claimed off waivers by the Oakland Raiders. On May 5, 2020, Kizer was waived by the relocated Las Vegas Raiders. He was re-signed to the Raiders practice squad on September 7, 2020, and was released on September 30.


title: DeShone Kizer

text: On November 24, 2020, Kizer was signed to the Tennessee Titans practice squad. He was signed to a futures contract on January 11, 2021.


title: DeShone Kizer

text: Kizer entered the 2021 offseason as the third string quarterback competing with backup Logan Woodside for the No. 2 spot behind starter Ryan Tannehill. Kizer was released on August 5, 2021, after the Titans signed quarterback Matt Barkley. He was re-signed to the practice squad on November 26, 2021, but was released three days later.


title: Kewpie

text: Kewpie is a brand of dolls and figurines that were conceived as comic strip characters by cartoonist Rose O'Neill. The illustrated cartoons, appearing as baby cupid characters, began to gain popularity after the publication of O'Neill's comic strips in 1909, and O'Neill began to illustrate and sell paper doll versions of the Kewpies. The characters were first produced as bisque dolls in Waltershausen, Germany, beginning in 1912, and became extremely popular in the early 20th century.


title: Kewpie

text: The Kewpie dolls were initially made out of bisque exclusively, but composition versions were introduced in the 1920s, and celluloid versions were manufactured in the following decades. In 1949, Effanbee created the first hard plastic versions of the dolls, and soft rubber and vinyl versions were produced by Cameo Co. and Jesco between the 1960s and 1990s.


title: Kewpie

text: The earlier bisque and composition versions of Kewpie dolls are widely sought-after by antique and doll collectors, who especially want those hand-signed by O'Neill. Kewpies should not be confused with the baby-like Billiken figures that debuted in 1908.


title: Kewpie

text: Rose O'Neill, an American Midwest native who had worked as a writer and illustrator in New York City, initially conceptualized the Kewpie as a cartoon intended for a comic strip in 1909. According to O'Neill, the idea for the Kewpies came to her in a dream. The comic, featuring the cherub-faced characters, was first printed in "Ladies' Home Journal" in the December 1909 issue. O'Neill described the characters as "a sort of little round fairy whose one idea is to teach people to be merry and kind at the same time."


title: Kewpie

text: The name Kewpies is derived from Cupid, the Roman god of erotic love. After the characters gained popularity among both adults and children, O'Neill began illustrating paper dolls of them, called Kewpie Kutouts.


title: Kewpie

text: O'Neill produced a Sunday comic strip for newspapers starting December 2, 1917, syndicated by the McClure Syndicate. The strip ended nine months later, on July 28, 1918. She produced a second Sunday strip starting November 25, 1934, and that version lasted until February 6, 1937.


title: Kewpie

text: As demand for the Kewpie characters increased, Geo. Borgfeldt & Co. in New York contacted O'Neill in 1912 about developing a line of dolls and figurines. O'Neill agreed, and J.D. Kestner, a German toy company located in Waltershausen, set forth to manufacture small bisque dolls of the Kewpies. After the company manufactured the first run of dolls, they sent samples to O'Neill, who disapproved of the design because she felt they "did not look like her characters."


title: Kewpie

text: O'Neill traveled to Germany and had the company destroy the moulds of the dolls, and oversaw the final redesign of them, working with a 17-year-old art student named Joseph Kallus. The dolls were then released in nine different sizes, ranging from in height. These early Kewpies wore a heart-shaped decal on their chests, which read "Kewpie, Germany", and some had jointed arms. Many of these original German Kewpies were signed by O'Neill herself, and some were featured in various poses.


title: Kewpie

text: The small dolls became an international hit, and by 1914, O'Neill had become the highest-paid female illustrator in the country, garnering a small fortune from the wild popularity of the dolls. The Kewpie brand soon became a household name, and was used widely in product advertising, including promotion for Jell-O, Colgate, Kellogg's Corn Flakes, and Sears. The Kewpies also appeared as a brand on a multitude of household items and other memorabilia, such as dishware, rattles, soap, pepper shakers, coloring books, poetry collections, and stationery.


title: Kewpie

text: O'Neill also famously used the characters to promote the women's suffrage movement, using the illustrations in slogans and cartoons.


title: Kewpie

text: After World War I began in Europe, production of the bisque Kewpie dolls moved from Germany to France and Belgium, due to rising tensions after the assassination of Archduke Franz Ferdinand. Around this time, the dolls also began to be produced in the United States, made of composition material rather than bisque, due to bisque's fragility. The manufacturers also began to increase the sizes of the dolls, producing versions in addition to the versions. The American composition dolls also had the distinctive heart-shaped decal on the chest, reading "Kewpies, des. & copyright by Rose O'Neill." Like the original bisque models, some of the composition Kewpies were also hand-signed by O'Neill, and they all included jointed arms.


title: Kewpie

text: In the mid-1920s, small-sized celluloid versions of Kewpies appeared, and were often given out as prizes at carnivals. Many of the celluloid versions were mainly manufactured in Japan, unlicensed, and were of a lower quality than other Kewpies. During this time, many Kewpies were sold with clothing, as well.


title: Kewpie

text: As photographs became more commonplace in advertising, the prominence of Kewpies in the marketing circuit began to wane. O'Neill returned to Missouri, where she died purportedly impoverished of complications from a series of strokes in 1944. Despite the lessening in popularity, Kewpies continued to be manufactured for the majority of the century, including hard plastic versions, as well as all-bisque replicas of the original Kewpies, produced by Jesco and Cameo Co. in the 1960s until the 1990s. These reproduction Kewpies lack the heart-shaped decal that distinguishes the original, older versions.


title: Kewpie

text: According to "200 Years of Dolls" (fourth edition), a 10-inch Kewpie with a bisque head, composition body, and glass eyes today is worth $6,500, while a doll is valued at $20,000. Many of the original, small-sized German-produced bisque Kewpies (c. 1912-1915) range from $200–$500 among collectors. Composition Kewpies range from $100–$300, while celluloid versions (especially unlicensed Japanese reproductions) are worth considerably less. Kewpies that were hand-signed by Rose O'Neill (most often etched on their arms or feet) are much rarer than unsigned Kewpies.


title: Yannick Bolasie

text: Yannick Bolasie (born 24 May 1989) is a professional footballer who plays as a winger for TFF First League club Çaykur Rizespor. He has played in the Football League for Plymouth Argyle, Barnet, Bristol City, Crystal Palace, Everton and Aston Villa. Born in France, he represents the DR Congo national team.


title: Yannick Bolasie

text: Bolasie began his career with Rushden & Diamonds at age 16. He spent four months as a member of their youth team and then had a spell with Hillingdon Borough in the Southern Football League before moving across Europe to play for Floriana in the Maltese Premier League. He returned to England in 2008 after being offered a trial with Plymouth Argyle and impressed enough to be offered a two-year contract. He joined Dagenham & Redbridge on trial with a view to a loan move before returning to Rushden & Diamonds on loan near the end of the year. He made his debut against Eastbourne Borough on 29 November, and made seven appearances in the Conference before returning to Argyle in January 2009. Bolasie then joined Barnet on loan, making his Football League debut against Accrington Stanley on 24 January 2009. He scored his first goal two weeks later, opening the scoring in a 3–3 draw against Grimsby Town.


title: Yannick Bolasie

text: Bolasie returned to Argyle at the end of the 2008–09 season having made 20 league appearances for Barnet, scoring three goals. The club's manager, Ian Hendon, was keen to bring Bolasie back, but dismissed the chances of signing him permanently. Hendon said, "Yannick is still under contract at Plymouth, so it is likely that he will return there at the end of the season." He rejoined the Barnet squad in July 2009 ahead of the new season on a six-month loan, and hoped it would act as a springboard to winning a place in the Argyle first team. Bolasie scored against Grimsby again in October 2009, capping a fine display with a fierce shot from 30 yards Bolasie scored his second goal of the season three weeks later against Darlington, as Hendon's side maintained a place in the top half of the League Two table.


title: Yannick Bolasie

text: Bolasie returned to Plymouth Argyle in January 2010, having made a further 22 league appearances for Barnet, scoring twice. He was given a chance to impress by Paul Mariner, who had succeeded Sturrock a month earlier, and included him in the squad to take on Barnsley on 13 February 2010. He made his debut for the club in that game, coming off the substitute bench to provide the momentum to turn a one nil deficit into a 3–1 win for the visitors. He scored his first goal for the club two weeks later at Sheffield United. The pacy winger, ended the season with 16 Championship appearances to his name, but could not prevent the club from being relegated to League One. Bolasie was offered a new contract by the club in April 2010, and Bolasie signed it in July after the arrival of Peter Reid as the club's new manager.


title: Yannick Bolasie

text: Bolasie was transferred to Bristol City on 6 June 2011 for an undisclosed fee and signed a two-year contract. He scored his first goal for the club in a 3–1 win against Coventry City on 9 April 2012. Prior to the match against Barnsley later that month, Bolasie was named Young Player of the Year by the Supporters Club and Trust after a fans vote. He submitted a written transfer request in August 2012 because he wanted to move back to London.


title: Yannick Bolasie

text: In August 2012, Bolasie signed a three-year contract with Crystal Palace for an undisclosed fee. He made his debut in a 2–1 defeat at Middlesbrough, and scored his first goal for Palace in a 5–0 home win against Ipswich Town. He was an unused substitute for Palace in the 2013 Football League Championship play-off Final as the "Eagles" defeated Watford 1–0 to gain promotion to the Premier League for the 2013–14 season.


title: Yannick Bolasie

text: Bolasie made his Premier League debut as a substitute against Liverpool at Anfield on 5 October 2013. He was sent-off in the 78th minute of a 1–0 win at Hull City on 23 November 2013, and scored his first Premier League goal in a 3–2 win over Everton at Goodison Park on 21 September 2014. On 11 April 2015, Bolasie scored an 11-minute hat-trick against Sunderland in a 4–1 win at the Stadium of Light, becoming the first Crystal Palace player to score a hat-trick in the Premier League. He signed a new three-and-a-half-year deal for Crystal Palace early in the 2015–16 season.


title: Yannick Bolasie

text: On 15 August 2016, Bolasie joined Everton for a reported £25 million transfer fee. He made his debut as a substitute in a 2–1 win away against West Bromwich Albion five days later, and three days after that made his first start for Everton, in a 4–0 EFL Cup win at home to Yeovil Town. Bolasie sustained an injury to his right anterior cruciate ligament in a 1–1 draw with Manchester United on 4 December 2016, and was out injured until 26 December 2017. On 2 October 2020, manager Carlo Ancelotti said that although Bolasie was training well, he was not in his plans and was free to leave the club. He left the club in June 2021.


title: Yannick Bolasie

text: Bolasie signed for Aston Villa on a season-long loan in August 2018, but returned, early, the following January, before being loaned to Belgian side Anderlecht for the remainder of the 2018–19 season. In September 2019 he joined Portuguese club Sporting CP on loan for the 2019–20 season. On 28 January 2021, Bolasie moved to EFL Championship club Middlesbrough, on a loan deal until the end of the season. He scored his first goal for Middlesbrough on 5 April 2021 in a 1–1 draw with Watford.


title: Yannick Bolasie

text: Bolasie was eligible to represent France, England and DR Congo internationally through birth, upbringing and heritage respectively. In January 2013 while playing in the Championship for Crystal Palace, Bolasie rejected the chance to represent the DR Congo in the 2013 Africa Cup of Nations claiming that he did not want to disrupt making progress in his club career. In March 2013, Bolasie was again called up to the Democratic Republic of Congo squad, and made his international debut in a 2014 World Cup qualification 0–0 draw with Libya.


title: Yannick Bolasie

text: Bolasie was selected in the Congolese squad for the 2015 Africa Cup of Nations in Equatorial Guinea. He scored the equaliser in their first group game, a 1–1 draw against Zambia at the Nuevo Estadio de Ebebiyín on 18 January. The team finished in third place.


title: Yannick Bolasie

text: His parents were born in Zaire, now the Democratic Republic of the Congo. Bolasie was born in the French city of Lyon, but moved to England when he was seven months old and grew up in the London borough of Brent. Lomana LuaLua, Kazenga LuaLua and Trésor Kandol are his cousins. His younger brother Ruddock Yala is a footballer, who played for Harrow Borough, Grays Athletic, Boreham Wood and Maldon & Tiptree.


title: Yannick Bolasie

text: Bolasie holds an active interest in grime music. In 2014, he filmed a rap battle with fellow professional footballer Bradley Wright-Phillips for the long running grime DVD series Lord of the Mics.


title: Wheeler Yuta

text: Paul Gruber (born October 26, 1996), is an American professional wrestler better known by his ring name Wheeler Yuta (sometimes stylized as Wheeler YUTA). He is currently signed to All Elite Wrestling (AEW), where he is the current ROH Pure Champion in his record-setting second reign and also member of the Blackpool Combat Club. He also makes appearances in Ring of Honor (ROH) and Japan's New Japan Pro-Wrestling (NJPW), where he was formerly a member of Chaos


title: Wheeler Yuta

text: Yuta debuted in 2014. He made his Combat Zone Wrestling (CZW) debut in late 2015 and consistently appeared for CZW until late 2016. On October 5, 2017, at One Shot, he made his debut for Major League Wrestling (MLW) in a losing effort to MJF. His last match for the promotion would be in 2019 against Low-Ki.


title: Wheeler Yuta

text: Yuta made his debut for Ring of Honor (ROH) in the first round of the ROH Pure Tournament, where he was defeated by Jonathan Gresham.


title: Wheeler Yuta

text: After Tony Khan's purchase of Ring of Honor, it was announced that Yuta would face Josh Woods at the revived Supercard of Honor XV for the ROH Pure Championship. At the event, Yuta defeated Woods to win the title. On the May 24, 2022 episode of "Dark", which aired almost two months after their bout at Supercard of Honor XV, Yuta would successfully defend the ROH Pure Championship against Woods in a rematch. Yuta once again defended the title on the June 29 episode of "Dark", defeating Tony Nese. After the match, Yuta was attacked by 2point0 and Daniel Garcia. This led to a match between Garcia and Yuta for the title at Death Before Dishonor, in which Yuta successfully retained the championship. Yuta lost the title on the September 7 episode of "Dynamite" to Garcia, ending his reign at 159 days. On December 10, 2022 Yuta regained the ROH Pure Championship during Ring of Honor Final Battle.


title: Wheeler Yuta

text: On the June 29, 2021 episode of "", Yuta made his debut for All Elite Wrestling (AEW) against Karl Anderson, and would consistently appear on AEW's YouTube shows throughout the coming months. Yuta also joined Best Friends, where he filled in for the injured Trent Beretta in trios matches. On the November 10 episode of "Dynamite", Rocky Romero announced that Best Friends would become a sub-group within NJPW stable Chaos, and they would represent the stable in AEW. On the March 30, 2022 episode of "Dynamite", after Yuta was defeated by Bryan Danielson, he teased to join the Blackpool Combat Club stable. The April 8 episode of "Rampage" saw Yuta lose in a hard-fought match to Jon Moxley, which led to him joining the BCC, after being welcomed by the leader William Regal.


title: Wheeler Yuta

text: In April 2021, Yuta made his debut for New Japan Pro-Wrestling (NJPW) with the promotion's American subsidiary, appearing on "NJPW Strong". On May 1, 2022, Yuta was announced to be competing in the 29th Best of the Super Juniors tournament as part of the B Block. Yuta finished with a record of five wins and four losses, resulting in 10 points, failing to advance to the finals. On the tournament finals day, Yuta, Ace Austin, Alex Zayne and El Lindaman defeated Robbie Eagles, Yoh, Clark Connors and Titán in a tag-team match.


title: Wheeler Yuta

text: In January 2022, Yuta made his debut for Pro Wrestling Guerrilla (PWG) at the Battle of Los Angeles. He defeated Blake Christian in the first round, but would lose the second round match to Mike Bailey.


title: Navier–Stokes existence and smoothness

text: The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering.


title: Navier–Stokes existence and smoothness

text: Even more basic (and seemingly intuitive) properties of the solutions to Navier–Stokes have never been proven. For the three-dimensional system of equations, and given some initial conditions, mathematicians have neither proved that smooth solutions always exist, nor found any counter-examples. This is called the "Navier–Stokes existence and smoothness" problem.


title: Navier–Stokes existence and smoothness

text: Since understanding the Navier–Stokes equations is considered to be the first step to understanding the elusive phenomenon of turbulence, the Clay Mathematics Institute in May 2000 made this problem one of its seven Millennium Prize problems in mathematics. It offered a US$1,000,000 prize to the first person providing a solution for a specific statement of the problem:


title: Navier–Stokes existence and smoothness

text: In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using continuum mechanics. The equations are a statement of Newton's second law, with the forces modeled according to those in a viscous Newtonian fluid—as the sum of contributions by pressure, viscous stress and an external body force. Since the setting of the problem proposed by the Clay Mathematics Institute is in three dimensions, for an incompressible and homogeneous fluid, only that case is considered below.


title: Navier–Stokes existence and smoothness

text: Let formula_1 be a 3-dimensional vector field, the velocity of the fluid, and let formula_2 be the pressure of the fluid. The Navier–Stokes equations are:


title: Navier–Stokes existence and smoothness

text: where formula_4 is the kinematic viscosity, formula_5 the external volumetric force, formula_6 is the gradient operator and formula_7 is the Laplacian operator, which is also denoted by formula_8 or formula_9. Note that this is a vector equation, i.e. it has three scalar equations. Writing down the coordinates of the velocity and the external force


title: Navier–Stokes existence and smoothness

text: The unknowns are the velocity formula_1 and the pressure formula_2. Since in three dimensions, there are three equations and four unknowns (three scalar velocities and the pressure), then a supplementary equation is needed. This extra equation is the continuity equation for incompressible fluids that describes the conservation of mass of the fluid:


title: Navier–Stokes existence and smoothness

text: Due to this last property, the solutions for the Navier–Stokes equations are searched in the set of solenoidal ("divergence-free") functions. For this flow of a homogeneous medium, density and viscosity are constants.


title: Navier–Stokes existence and smoothness

text: Since only its gradient appears, the pressure "p" can be eliminated by taking the curl of both sides of the Navier–Stokes equations. In this case the Navier–Stokes equations reduce to the vorticity-transport equations.


title: Navier–Stokes existence and smoothness

text: The Navier-Stokes equations are nonlinear because the terms in the equations do not have a simple linear relationship with each other. This means that the equations cannot be solved using traditional linear techniques, and more advanced methods must be used instead. Nonlinearity is important in the Navier-Stokes equations because it allows the equations to describe a wide range of fluid dynamics phenomena, including the formation of shock waves and other complex flow patterns. However, the nonlinearity of the Navier-Stokes equations also makes them more difficult to solve, as traditional linear methods may not work.


title: Navier–Stokes existence and smoothness

text: One way to understand the nonlinearity of the Navier-Stokes equations is to consider the term (v · ∇)v in the equations. This term represents the acceleration of the fluid, and it is a product of the velocity vector v and the gradient operator ∇. Because the gradient operator is a linear operator, the term (v · ∇)v is nonlinear in the velocity vector v. This means that the acceleration of the fluid depends on the magnitude and direction of the velocity, as well as the spatial distribution of the velocity within the fluid.


title: Navier–Stokes existence and smoothness

text: The nonlinear nature of the Navier-Stokes equations can be seen in the term formula_16, which represents the acceleration of the fluid due to its own velocity. This term is nonlinear because it involves the product of two velocity vectors, and the resulting acceleration is therefore dependent on the magnitude and direction of both vectors.


title: Navier–Stokes existence and smoothness

text: Another source of nonlinearity in the Navier-Stokes equations is the pressure term formula_17. The pressure in a fluid depends on the density and the gradient of the pressure, and this term is therefore nonlinear in the pressure.


title: Navier–Stokes existence and smoothness

text: One example of the nonlinear nature of the Navier-Stokes equations can be seen in the case of a fluid flowing around a circular obstacle. In this case, the velocity of the fluid near the obstacle will be higher than the velocity of the fluid farther away from the obstacle. This results in a pressure gradient, with higher pressure near the obstacle and lower pressure farther away.


title: Navier–Stokes existence and smoothness

text: To see this more explicitly, consider the case of a circular obstacle of radius formula_18 placed in a uniform flow with velocity formula_19 and density formula_20. Let formula_21 be the velocity of the fluid at position formula_22 and time formula_23, and let formula_24 be the pressure at the same position and time.


title: Navier–Stokes existence and smoothness

text: Assuming that the flow is steady (meaning that the velocity and pressure do not vary with time), we can set the time derivative terms equal to zero:


title: Navier–Stokes existence and smoothness

text: We can now consider the flow near the circular obstacle. In this region, the velocity of the fluid will be higher than the uniform flow velocity formula_19 due to the presence of the obstacle. This results in a nonlinear term formula_31 in the Navier-Stokes equations that is proportional to the velocity of the fluid.


title: Navier–Stokes existence and smoothness

text: At the same time, the presence of the obstacle will also result in a pressure gradient, with higher pressure near the obstacle and lower pressure farther away. This can be seen by considering the continuity equation, which states that the mass flow rate through any surface must be constant. Since the velocity is higher near the obstacle, the mass flow rate through a surface near the obstacle will be higher than the mass flow rate through a surface farther away from the obstacle. This can be compensated for by a pressure gradient, with higher pressure near the obstacle and lower pressure farther away.


title: Navier–Stokes existence and smoothness

text: As a result of these nonlinear effects, the Navier-Stokes equations in this case become difficult to solve, and approximations or numerical methods must be used to find the velocity and pressure fields in the flow.


title: Navier–Stokes existence and smoothness

text: Another example would be For example, consider the case of a two-dimensional fluid flow in a rectangular domain, with a velocity field formula_32 and a pressure field formula_33. We can use a finite element method to solve the Navier-Stokes equation for the velocity field:


title: Navier–Stokes existence and smoothness

text: To do this, we divide the domain into a series of smaller elements, and represent the velocity field as:


title: Navier–Stokes existence and smoothness

text: where formula_36 is the number of elements, and formula_37 are the shape functions associated with each element. Substituting this expression into the Navier-Stokes equation and applying the finite element method, we can derive a system of ordinary differential equations:


title: Navier–Stokes existence and smoothness

text: where formula_39 is the domain, and the integrals are over the domain. This system of ordinary differential equations can be solved using techniques such as the finite element method or spectral methods.


title: Navier–Stokes existence and smoothness

text: One common approach is to use a finite difference method, which involves approximating the derivative terms in the equation using finite differences. To do this, we can divide the time interval formula_40 into a series of smaller time steps, and approximate the derivative at each time step using a finite difference formula:


title: Navier–Stokes existence and smoothness

text: where formula_42 is the size of the time step, and formula_43 and formula_44 are the values of formula_43 and formula_23 at time step formula_47.


title: Navier–Stokes existence and smoothness

text: Using this approximation, we can iterate through the time steps and compute the value of formula_43 at each time step. For example, starting at time step formula_47 and using the approximation above, we can compute the value of formula_43 at time step formula_51:


title: Navier–Stokes existence and smoothness

text: There are many other approaches to solving ordinary differential equations, each with its own advantages and disadvantages. The choice of approach depends on the specific equation being solved, and the desired accuracy and efficiency of the solution.


title: Navier–Stokes existence and smoothness

text: There are two different settings for the one-million-dollar-prize Navier–Stokes existence and smoothness problem. The original problem is in the whole space formula_54, which needs extra conditions on the growth behavior of the initial condition and the solutions. In order to rule out the problems at infinity, the Navier–Stokes equations can be set in a periodic framework, which implies that they are no longer working on the whole space formula_54 but in the 3-dimensional torus formula_56. Each case will be treated separately.


title: Navier–Stokes existence and smoothness

text: The initial condition formula_57 is assumed to be a smooth and divergence-free function (see smooth function) such that, for every multi-index formula_58 (see multi-index notation) and any formula_59, there exists a constant formula_60 such that


title: Navier–Stokes existence and smoothness

text: The external force formula_63 is assumed to be a smooth function as well, and satisfies a very analogous inequality (now the multi-index includes time derivatives as well):


title: Navier–Stokes existence and smoothness

text: For physically reasonable conditions, the type of solutions expected are smooth functions that do not grow large as formula_66. More precisely, the following assumptions are made:


title: Navier–Stokes existence and smoothness

text: Condition 1 implies that the functions are smooth and globally defined and condition 2 means that the kinetic energy of the solution is globally bounded.


title: Navier–Stokes existence and smoothness

text: Let formula_72. For any initial condition formula_57 satisfying the above hypotheses there exist smooth and globally defined solutions to the Navier–Stokes equations, i.e. there is a velocity vector formula_32 and a pressure formula_33 satisfying conditions 1 and 2 above.


title: Navier–Stokes existence and smoothness

text: There exists an initial condition formula_57 and an external force formula_63 such that there exists no solutions formula_32 and formula_33 satisfying conditions 1 and 2 above.


title: Navier–Stokes existence and smoothness

text: The Millennium Prize conjectures are two mathematical problems that were chosen by the Clay Mathematics Institute as the most important unsolved problems in mathematics. The first conjecture, which is known as the "smoothness" conjecture, states that there should always exist smooth and globally defined solutions to the Navier–Stokes equations in three-dimensional space. The second conjecture, known as the "breakdown" conjecture, states that there should be at least one set of initial conditions and external forces for which there are no smooth solutions to the Navier–Stokes equations.


title: Navier–Stokes existence and smoothness

text: The Navier-Stokes equations are a set of partial differential equations that describe the motion of fluids. They are given by:


title: Navier–Stokes existence and smoothness

text: where formula_32 is the velocity field of the fluid, formula_33 is the pressure, formula_20 is the density, formula_27 is the kinematic viscosity, and formula_63 is an external force. The first equation is known as the momentum equation, and the second equation is known as the continuity equation.


title: Navier–Stokes existence and smoothness

text: These equations are typically accompanied by boundary conditions, which describe the behavior of the fluid at the edges of the domain. For example, in the case of a fluid flowing through a pipe, the boundary conditions might specify that the velocity and pressure are fixed at the walls of the pipe.


title: Navier–Stokes existence and smoothness

text: The Navier-Stokes equations are nonlinear and highly coupled, making them difficult to solve in general. In particular, the difficulty of solving these equations lies in the term formula_88, which represents the nonlinear advection of the velocity field by itself. This term makes the Navier-Stokes equations highly sensitive to initial conditions, and it is the main reason why the Millennium Prize conjectures are so challenging.


title: Navier–Stokes existence and smoothness

text: In addition to the mathematical challenges of solving the Navier-Stokes equations, there are also many practical challenges in applying these equations to real-world situations. For example, the Navier-Stokes equations are often used to model fluid flows that are turbulent, which means that the fluid is highly chaotic and unpredictable. Turbulence is a difficult phenomenon to model and understand, and it adds another layer of complexity to the problem of solving the Navier-Stokes equations.


title: Navier–Stokes existence and smoothness

text: To solve the Navier-Stokes equations, we need to find a velocity field formula_32 and a pressure field formula_33 that satisfy the equations and the given boundary conditions. This can be done using a variety of numerical techniques, such as finite element methods, spectral methods, or finite difference methods.


title: Navier–Stokes existence and smoothness

text: For example, consider the case of a two-dimensional fluid flow in a rectangular domain, with velocity and pressure fields formula_32 and a pressure field formula_33,respectively. The Navier-Stokes equations can be written as:


title: Navier–Stokes existence and smoothness

text: where formula_20 is the density, formula_27 is the kinematic viscosity, and formula_98 is an external force. The boundary conditions might specify that the velocity is fixed at the walls of the domain, or that the pressure is fixed at certain points.


title: Navier–Stokes existence and smoothness

text: To solve these equations numerically, we can divide the domain into a series of smaller elements, and solve the equations locally within each element. For example, using a finite element method, we might represent the velocity and pressure fields as:


title: Navier–Stokes existence and smoothness

text: where formula_36 is the number of elements, and formula_37 are the shape functions associated with each element. Substituting these expressions into the Navier-Stokes equations and applying the finite element method, we can derive a system of ordinary differential equations


title: Navier–Stokes existence and smoothness

text: The functions sought now are periodic in the space variables of period 1. More precisely, let formula_104 be the unitary vector in the "i"- direction:


title: Navier–Stokes existence and smoothness

text: Notice that this is considering the coordinates mod 1. This allows working not on the whole space formula_54 but on the quotient space formula_110, which turns out to be the 3-dimensional torus:


title: Navier–Stokes existence and smoothness

text: Now the hypotheses can be stated properly. The initial condition formula_57 is assumed to be a smooth and divergence-free function and the external force formula_63 is assumed to be a smooth function as well. The type of solutions that are physically relevant are those who satisfy these conditions:


title: Navier–Stokes existence and smoothness

text: Just as in the previous case, condition 3 implies that the functions are smooth and globally defined and condition 4 means that the kinetic energy of the solution is globally bounded.


title: Navier–Stokes existence and smoothness

text: Let formula_72. For any initial condition formula_57 satisfying the above hypotheses there exist smooth and globally defined solutions to the Navier–Stokes equations, i.e. there is a velocity vector formula_32 and a pressure formula_33 satisfying conditions 3 and 4 above.


title: Navier–Stokes existence and smoothness

text: There exists an initial condition formula_57 and an external force formula_63 such that there exists no solutions formula_32 and formula_33 satisfying conditions 3 and 4 above.


title: Navier–Stokes existence and smoothness

text: Unsolved problems have been used to indicate a rare mathematical talent in fiction. The Navier-Stokes problem features in "The Mathematician's Shiva" (2014), a book about a prestigious, deceased, fictional mathematician named Rachela Karnokovitch taking the proof to her grave in protest of academia. The movie "Gifted" (2017) referenced the Millennium Prize problems and dealt with the potential for a 7-year-old girl and her deceased mathematician mother for solving the Navier–Stokes problem.


title: JJ Lin

text: Wayne Lin Junjie (; born 27 March 1981), better known by his stage name JJ Lin, is a Singaporean singer, songwriter, record producer and actor. Lin launched his musical career by releasing his debut album "Music Voyager" (2003).


title: JJ Lin

text: JJ Lin was born to a Kim-mûi Hokkien family in Singapore and studied at , Anglo-Chinese School (Independent) and Saint Andrew's Junior College before completing his National Service. Lin's family consists of his brother, father and mother who have a background in Chinese Classical Music, hence influencing the artist's music. Furthermore, his brother was a major influence in his career choice.


title: JJ Lin

text: In addition to Mandarin, Lin also sings in English, Hokkien (his native dialect) and Cantonese using romanized pronunciation system, and has released his songs in Cantonese. In Taiwan, he was awarded the Best New Artist award at the Golden Melody Awards.


title: JJ Lin

text: After completing his national service, Lin signed with Ocean Butterflies International, which launched the then 22-year-old Lin's debut album in 2003. In 2011, Lin signed a new contract with the record label Warner Music Taiwan.


title: JJ Lin

text: He is well known for his songwriting and singing skills. He wrote songs for various musical artists while he was still a trainee under Ocean Butterflies under his mentors, Billy Koh and Sunkist Ng. In total, he has written over a hundred songs for other artists. His notable compositions include "Remember" (记得) for Taiwanese singer A-Mei, A-Do's "Let Go" (放手), Harlem Yu's "What's Wrong With You?" (干嘛你看不爽我), Cyndi Wang's "When You" (当你), Vivian Hsu's "Smiling Eyes" (爱笑的眼睛), and Comic Boyz's "Heart of Superman" (超人心).


title: JJ Lin

text: In Singapore, he was selected to perform the remixed version of "Home", the theme song of the National Day Parade in 2004. Lin has sold 1 million copies in less than a week and is extremely successful throughout Asia.


title: JJ Lin

text: In July 2007, he broke a Guinness record by signing 3,052 CDs in 2 hours and 30 minutes. During the signing, he was not allowed to drink or eat. The average time for him to sign a CD was 2.7 seconds.


title: JJ Lin

text: In May 2008, he performed at the CCTV charity event "The Giving of Love", dedicated to helping victims of the 2008 Sichuan earthquake. Lin also donated a large sum of money to the rescue efforts and composed a song "Love and Hope" () commemorating the tragedy.


title: JJ Lin

text: In February 2008, Lin released a compilation album entitled "Waiting for Love" (). It has selected tracks from several of his albums spanning from his debut album to 2007's "West Side". Later in October of that year, his sixth album, "Sixology" (), was released, and it sold 280,000 copies in a week.


title: JJ Lin

text: His own fashion line, SMUDGE, was opened in Singapore during 2008 Christmas with an unofficial launch. The store's official launch was on 13 March 2009.


title: JJ Lin

text: In May 2009, Lin won three awards at the 14th annual Composers and Authors Society of the UK (Compass) Awards Presentations, a ceremony that honors performers in the music scene. It was held at the Royal Albert Hall, Hyde Park, Buckingham Palace and Raffles City Convention Centre, Singapore. He was honored with the Top Local Artiste of the Year award, which is given out to Singaporean artists who generated the highest royalty earnings for the year. In that same year, Lin won the Singapore Youth Award.


title: JJ Lin

text: In 2009, his singing career was put on hold due to his voice being damaged by acid reflux and flu, as well as his hectic touring and recording schedules. His poor health forced him to return to Singapore to recover and receive treatments. He released the seventh album, Hundred Days, on 18 December 2009.


title: JJ Lin

text: In May 2010, Lin performed in America for the first time at the Asian Pacific American Heritage Month Concert Tour (APAHM).


title: JJ Lin

text: In June 2010, Lin performed together with American singer Sean Kingston at the opening concert of the Marina Bay Sands to thousands of invited VIPs guests. But both were absent at the inaugural YOG Opening Ceremony. Lin's eighth album, "She Says" (她說), was released on 8 December 2010.


title: JJ Lin

text: Lin's ninth studio album, Lost N Found (学不会) was released on 31 December 2011. A preview of his 9th album was made available on 12 December 2011 on various Chinese internet radio channels.


title: JJ Lin

text: Lin's tenth anniversary album, Stories Untold (因你而在) was released on 13 March 2013. A compilation of micro films were released in conjunction with the album, serving to expand the stories behind the songs. He worked with a few notable people on the album, including Ashin, Harry Chang (张怀秋), and his older brother Eugene Lim (林俊峰). He also started his world tour "Timeline" in July 2013 in Taipei, Taiwan.


title: JJ Lin

text: Lin co-wrote the song "Dreams" with Goh Kheng Long and Corrinne May and performed the song live during the grand finale at the Chingay Parade on 27 and 28 February 2015.


title: JJ Lin

text: One of his recent ventures in the world of music was a duet with Ayumi Hamasaki, for the latter's music video, "The Gift" (and as of 27 April 2015, has about 1,882,459-page views).


title: JJ Lin

text: In 2015, he was selected to perform the National Day Theme Song, "Our Singapore", which was composed by Dick Lee. His experimental debut album "From M.E. to Myself" was released on 25 December 2015.


title: JJ Lin

text: On 7 July 2016, Lin released "If Miracles had a Sound", a 96-minute music documentary created over the course of 455 days, taking place throughout studios in the U.S., Singapore, Malaysia, Hong Kong, and Taiwan. The theme song of the documentary, "Infinity and Beyond" (超越无限) was released on 21 June 2016.


title: JJ Lin

text: On 19 December 2017, JJ Lin posted on his Instagram page that the past two years "had not been easy" and that he had been "searching constantly for a clear direction", needing a "shelter for the soul, a 'SANCTUARY'". He "penned songs and finished his Message in a Bottle album", which was released on 29 December 2017. At the same time, he and his team and "shared a common vision, starting on project "SANCTUARY" and built the space from ground zero." In early 2018, he announced his "Sanctuary" concert tour began in Shanghai on 17 March. In 2019, he released "The Story of Us" (), and actress Wu Jinyan starred in the music video.


title: JJ Lin

text: In January 2020, Lin released a song "I'll Stay With You" dedicated to the medical staff in Wuhan, China, who were working hard to save patients infected with COVID-19.


title: JJ Lin

text: Lin has appeared in various advertisements for brands such as Sprite, Durex, "Dota 2", Beats and Cornetto Royale.


title: JJ Lin

text: He is also a tourist ambassador for Singapore. He was also involved in an anti-drugs event as an ambassador, in Taiwan. The theme song for this event is "Baby Baby", which is from his album "Westside".


title: JJ Lin

text: On 14 August 2015, Lin was selected to be the advisor for Team Harlem Yu on "The Voice of China" (season 4).


title: JJ Lin

text: On 4 November 2016, Lin joined the variety show "Dream Voice" as one of the mentors alongside A-mei Zhang, Jam Hsiao, Hebe Tian, and Yu Quan. He stayed on as a mentor for the second season of the show, which was released in October 2017, and the third season, which was released in October 2018.