text: Republican Scott Franklin, who has represented the district since 2021, was elected with 55% of the vote in 2020. Franklin is running for re-election.


title: 2022 United States House of Representatives elections in Florida

text: The boundaries of the district have been redrawn from 2020 determined by the 2020 redistricting cycle.


text: Republican Byron Donalds, who has represented the district since 2021, was elected with 61% of the vote in 2020. Donalds is running for re-election.


text: Democrat Alcee Hastings, who represented the district since 1993, was re-elected with 78% of the vote in 2020. Hastings died on April 6, 2021. A special election was held on January 11, 2022, to succeed him, which was won by Sheila Cherfilus-McCormick.


text: Republican Brian Mast, who has represented the district since 2017, was re-elected with 56% of the vote in 2020. Mast is running for re-election.


text: Democrat Lois Frankel, who has represented the district since 2013, was re-elected with 59% of the vote in 2020. Frankel is running for re-election.


text: Democrat Ted Deutch, who has represented the district since 2010, was re-elected with 58% of the vote in 2020. On February 28, 2022, Deutch announced he would leave Congress to become CEO of the American Jewish Committee.


text: Democrat Frederica Wilson, who has represented the district since 2011, was re-elected with 76% of the vote in 2020. Wilson is running for re-election.


text: Democrat Debbie Wasserman Schultz, who has represented the district since 2005, was re-elected with 58% of the vote in 2020. Wasserman Schultz is running for re-election.


text: Republican Mario Díaz-Balart, who has represented the district since 2003, was unopposed in 2020. Díaz-Balart is running for re-election.


text: Republican Maria Elvira Salazar, who has represented the district since 2021, flipped the district and was elected with 51% of the vote in 2020. Salazar is running for re-election.


text: This district is included on the list of Republican-held seats the Democratic Congressional Campaign Committee is targeting in 2022.


text: Republican Carlos Giménez, who has represented the 26th district since 2021, flipped that district and was elected with 52% of the vote in 2020. Giménez is running for re-election in the new 28th district.


title: Hydropower

text: Hydropower (from , "water"), also known as water power, is the use of falling or fast-running water to produce electricity or to power machines. This is achieved by converting the gravitational potential or kinetic energy of a water source to produce power. Hydropower is a method of sustainable energy production. Hydropower is now used principally for hydroelectric power generation, and is also applied as one half of an energy storage system known as pumped-storage hydroelectricity. Hydropower is an attractive alternative to fossil fuels as it does not directly produce carbon dioxide or other atmospheric pollutants and it provides a relatively consistent source of power. Nonetheless, it has economic, sociological, and environmental downsides and requires a sufficiently energetic source of water, such as a river or elevated lake. International institutions such as the World Bank view hydropower as a low-carbon means for economic development.


title: Hydropower

text: Since ancient times, hydropower from watermills has been used as a renewable energy source for irrigation and the operation of mechanical devices, such as gristmills, sawmills, textile mills, trip hammers, dock cranes, domestic lifts, and ore mills. A trompe, which produces compressed air from falling water, is sometimes used to power other machinery at a distance.


title: Hydropower

text: A hydropower resource can be evaluated by its available power. Power is a function of the hydraulic head and volumetric flow rate. The head is the energy per unit weight (or unit mass) of water. The static head is proportional to the difference in height through which the water falls. Dynamic head is related to the velocity of moving water. Each unit of water can do an amount of work equal to its weight times the head.


title: Hydropower

text: The power available from falling water can be calculated from the flow rate and density of water, the height of fall, and the local acceleration due to gravity:


title: Hydropower

text: To illustrate, the power output of a turbine that is 85% efficient, with a flow rate of 80 cubic metres per second (2800 cubic feet per second) and a head of 145 metres (480 feet), is 97 megawatts:


title: Hydropower

text: Operators of hydroelectric stations compare the total electrical energy produced with the theoretical potential energy of the water passing through the turbine to calculate efficiency. Procedures and definitions for calculation of efficiency are given in test codes such as ASME PTC 18 and IEC 60041. Field testing of turbines is used to validate the manufacturer's efficiency guarantee. Detailed calculation of the efficiency of a hydropower turbine accounts for the head lost due to flow friction in the power canal or penstock, rise in tailwater level due to flow, the location of the station and effect of varying gravity, the air temperature and barometric pressure, the density of the water at ambient temperature, and the relative altitudes of the forebay and tailbay. For precise calculations, errors due to rounding and the number of significant digits of constants must be considered.


title: Hydropower

text: Some hydropower systems such as water wheels can draw power from the flow of a body of water without necessarily changing its height. In this case, the available power is the kinetic energy of the flowing water. Over-shot water wheels can efficiently capture both types of energy. The flow in a stream can vary widely from season to season. The development of a hydropower site requires analysis of flow records, sometimes spanning decades, to assess the reliable annual energy supply. Dams and reservoirs provide a more dependable source of power by smoothing seasonal changes in water flow. However, reservoirs have a significant environmental impact, as does alteration of naturally occurring streamflow. Dam design must account for the worst-case, "probable maximum flood" that can be expected at the site; a spillway is often included to route flood flows around the dam. A computer model of the hydraulic basin and rainfall and snowfall records are used to predict the maximum flood.


title: Hydropower

text: Some disadvantages of hydropower have been identified. Dam failures can have catastrophic effects, including loss of life, property and pollution of land..


title: Hydropower

text: Dams and reservoirs can have major negative impacts on river ecosystems such as preventing some animals traveling upstream, cooling and de-oxygenating of water released downstream, and loss of nutrients due to settling of particulates. River sediment builds river deltas and dams prevent them from restoring what is lost from erosion. Furthermore, studies found that the construction of dams and reservoirs can result in habitat loss for some aquatic species.


title: Hydropower

text: Large and deep dam and reservoir plants cover large areas of land which causes greenhouse gas emissions from underwater rotting vegetation. Furthermore, although at lower levels than other renewable energy sources, it was found that hydropower produces methane gas which is a greenhouse gas. This occurs when organic matters accumulate at the bottom of the reservoir because of the deoxygenation of water which triggers anaerobic digestion.


title: Hydropower

text: People who live near a hydro plant site are displaced during construction or when reservoir banks become unstable. Another potential disadvantage is cultural or religious sites may block construction.


title: Hydropower

text: A plentiful head of water can be made to generate compressed air directly without moving parts. In these designs, a falling column of water is deliberately mixed with air bubbles generated through turbulence or a venturi pressure reducer at the high-level intake. This allows it to fall down a shaft into a subterranean, high-roofed chamber where the now-compressed air separates from the water and becomes trapped. The height of the falling water column maintains compression of the air in the top of the chamber, while an outlet, submerged below the water level in the chamber allows water to flow back to the surface at a lower level than the intake. A separate outlet in the roof of the chamber supplies the compressed air. A facility on this principle was built on the Montreal River at Ragged Shutes near Cobalt, Ontario in 1910 and supplied 5,000 horsepower to nearby mines.


title: Hydropower

text: Hydroelectricity is the biggest hydropower application. Hydroelectricity generates about 15% of global electricity and provides at least 50% of the total electricity supply for more than 35 countries.


title: Hydropower

text: Hydroelectricity generation starts with converting either the potential energy of water that is present due to the site's elevation or the kinetic energy of moving water into electrical energy.


title: Hydropower

text: Hydroelectric power plants vary in terms of the way they harvest energy. One type involves a dam and a reservoir. The water in the reservoir is available on demand to be used to generate electricity by passing through channels that connect the dam to the reservoir. The water spins a turbine, which is connected to the generator that produces electricity.


title: Hydropower

text: The other type is called a run-of-river plant. In this case, a barrage is built to control the flow of water, absent a reservoir. The run-of river power plant needs continuous water flow and therefore has less ability to provide power on demand. The kinetic energy of flowing water is the main source of energy.


title: Hydropower

text: Both designs have limitations. For example, dam construction can result in discomfort to nearby residents. The dam and reservoirs occupy a relatively large amount of space that may be opposed by nearby communities. Moreover, reservoirs can potentially have major environmental consequences such as harming downstream habitats. On the other hand, the limitation of the run-of-river project is the decreased efficiency of electricity generation because the process depends on the speed of the seasonal river flow. This means that the rainy season increases electricity generation compared to the dry season.


title: Hydropower

text: The size of hydroelectric plants can vary from small plants called micro hydro, to large plants supply that power to a whole country. As of 2019, the five largest power stations in the world are conventional hydroelectric power stations with dams.


title: Hydropower

text: Hydroelectricity can also be used to store energy in the form of potential energy between two reservoirs at different heights with pumped-storage. Water is pumped uphill into reservoirs during periods of low demand to be released for generation when demand is high or system generation is low.


title: Hydropower

text: Other forms of electricity generation with hydropower include tidal stream generators using energy from tidal power generated from oceans, rivers, and human-made canal systems to generating electricity.


title: Hydropower

text: Rain has been referred to as "one of the last unexploited energy sources in nature. When it rains, billions of litres of water can fall, which have enormous electric potential if used in the right way." Research is being done into the different methods of generating power from rain, such as by using the energy in the impact of raindrops. This is in its very early stages with new and emerging technologies being tested, prototyped and created. Such power has been called rain power. One method in which this has been attempted is by using hybrid solar panels called "all-weather solar panels" that can generate electricity from both the sun and the rain.


title: Hydropower

text: According to zoologist and science and technology educator, Luis Villazon, "A 2008 French study estimated that you could use piezoelectric devices, which generate power when they move, to extract 12 milliwatts from a raindrop. Over a year, this would amount to less than 0.001kWh per square metre – enough to power a remote sensor." Villazon suggested a better application would be to collect the water from fallen rain and use it to drive a turbine, with an estimated energy generation of 3 kWh of energy per year for a 185 m roof. A microturbine-based system created by three students from the Technological University of Mexico has been used to generate electricity. The Pluvia system "uses the stream of rainwater runoff from houses' rooftop rain gutters to spin a microturbine in a cylindrical housing. Electricity generated by that turbine is used to charge 12-volt batteries."


title: Hydropower

text: The term rain power has also been applied to hydropower systems which include the process of capturing the rain.


title: Hydropower

text: Evidence suggests that the fundamentals of hydropower date to ancient Greek civilization. Other evidence indicates that the waterwheel independently emerged in China around the same period. Evidence of water wheels and watermills date to the ancient Near East in the 4th century BC. Moreover, evidence indicates the use of hydropower using irrigation machines to ancient civilizations such as Sumer and Babylonia. Studies suggest that the water wheel was the initial form of water power and it was driven by either humans or animals.


title: Hydropower

text: In the Roman Empire, water-powered mills were described by Vitruvius by the first century BC. The Barbegal mill, located in modern-day France, had 16 water wheels processing up to 28 tons of grain per day. Roman waterwheels were also used for sawing marble such as the Hierapolis sawmill of the late 3rd century AD. Such sawmills had a waterwheel that drove two crank-and-connecting rods to power two saws. It also appears in two 6th century Eastern Roman sawmills excavated at Ephesus and Gerasa respectively. The crank and connecting rod mechanism of these Roman watermills converted the rotary motion of the waterwheel into the linear movement of the saw blades.


title: Hydropower

text: Water-powered trip hammers and bellows in China, during the Han dynasty (202 BC - 220 AD), were initially thought to be powered by water scoops. However, some historians suggested that they were powered by waterwheels. This is since it was theorized that water scoops would not have had the motive force to operate their blast furnace bellows. Many texts describe the Hun waterwheel; some of the earliest ones are the "Jijiupian" dictionary of 40 BC, Yang Xiong's text known as the "Fangyan" of 15 BC, as well as "Xin Lun," written by Huan Tan about 20 AD. It was also during this time that the engineer Du Shi (c. AD 31) applied the power of waterwheels to piston-bellows in forging cast iron.


title: Hydropower

text: Another example of the early use of hydropower is seen in hushing. Hushing is the use of the power of a wave of water released from a tank in the extraction of metal ores. The method was first used at the Dolaucothi Gold Mines in Wales from 75 AD onwards. This method was further developed in Spain in mines such as Las Médulas. Hushing was also widely used in Britain in the Medieval and later periods to extract lead and tin ores. It later evolved into hydraulic mining when used during the California Gold Rush in the 19th century.


title: Hydropower

text: The Islamic Empire spanned a large region, mainly in Asia and Africa, along with other surrounding areas. During the Islamic Golden Age and the Arab Agricultural Revolution (8th–13th centuries), hydropower was widely used and developed. Early uses of tidal power emerged along with large hydraulic factory complexes. A wide range of water-powered industrial mills were used in the region including fulling mills, gristmills, paper mills, hullers, sawmills, ship mills, stamp mills, steel mills, sugar mills, and tide mills. By the 11th century, every province throughout the Islamic Empire had these industrial mills in operation, from Al-Andalus and North Africa to the Middle East and Central Asia. Muslim engineers also used water turbines while employing gears in watermills and water-raising machines. They also pioneered the use of dams as a source of water power, used to provide additional power to watermills and water-raising machines.


title: Hydropower

text: Furthermore, in his book, "The Book of Knowledge of Ingenious Mechanical Devices", the Muslim mechanical engineer, Al-Jazari (1136–1206) described designs for 50 devices. Many of these devices were water-powered, including clocks, a device to serve wine, and five devices to lift water from rivers or pools, where three of them are animal-powered and one can be powered by animal or water. Moreover, they included an endless belt with jugs attached, a cow-powered shadoof (a crane-like irrigation tool), and a reciprocating device with hinged valves.


title: Hydropower

text: In the 19th century, French engineer Benoît Fourneyron developed the first hydropower turbine. This device was implemented in the commercial plant of Niagara Falls in 1895 and it is still operating. In the early 20th century, English engineer William Armstrong built and operated the first private electrical power station which was located in his house in Cragside in Northumberland, England. In 1753, the French engineer Bernard Forest de Bélidor published his book, "Architecture Hydraulique", which described vertical-axis and horizontal-axis hydraulic machines.


title: Hydropower

text: The growing demand for the Industrial Revolution would drive development as well. At the beginning of the Industrial Revolution in Britain, water was the main power source for new inventions such as Richard Arkwright's water frame. Although water power gave way to steam power in many of the larger mills and factories, it was still used during the 18th and 19th centuries for many smaller operations, such as driving the bellows in small blast furnaces (e.g. the Dyfi Furnace) and gristmills, such as those built at Saint Anthony Falls, which uses the 50-foot (15 m) drop in the Mississippi River.


title: Hydropower

text: Technological advances moved the open water wheel into an enclosed turbine or water motor. In 1848, the British-American engineer James B. Francis, head engineer of Lowell's Locks and Canals company, improved on these designs to create a turbine with 90% efficiency. He applied scientific principles and testing methods to the problem of turbine design. His mathematical and graphical calculation methods allowed the confident design of high-efficiency turbines to exactly match a site's specific flow conditions. The Francis reaction turbine is still in use. In the 1870s, deriving from uses in the California mining industry, Lester Allan Pelton developed the high-efficiency Pelton wheel impulse turbine, which used hydropower from the high head streams characteristic of the Sierra Nevada.


title: Abigail Disney

text: Abigail Edna Disney (born January 24, 1960) is an American documentary film producer, philanthropist, and social activist. She produced the 2008 documentary "Pray the Devil Back to Hell". Disney and Kathleen Hughes are producers and directors of "Outstanding Social Issue Documentary" Emmy Award winning "The Armor of Light" (2015)<ref name="RT/armor_of_light"></ref> and "The American Dream and Other Fairy Tales" (2022, her brother, Tim Disney, executive producing).<ref name="RT/american_dream_fairy_tales"></ref>


title: Abigail Disney

text: Abigail Disney is the daughter of Patricia Ann ("née" Dailey) and Roy E. Disney. She is the granddaughter of Roy O. Disney, who co-founded The Walt Disney Company with her great-uncle Walt Disney.


title: Abigail Disney

text: She was raised in North Hollywood, California where she attended the Buckley School. She received a Bachelor of Arts in English Literature from Yale University in 1982. She would go on to complete a Master of Arts in English Literature from Stanford University, and PhD in philosophy from Columbia University in 1994. While pursuing her PhD, Disney taught English and American literature at Iona College in New Rochelle, New York, and wrote a dissertation on the role of romanticized violence in American life: "Shadows of doubt: The American historical war novels of James Fenimore Cooper, Stephen Crane and Thomas Pynchon."


title: Abigail Disney

text: She turned to the family business of film production with a documentary film, "Pray the Devil Back to Hell", directed by Gini Reticker. "Pray the Devil Back to Hell" brought to light the work of Liberian peace activist Leymah Gbowee by telling the story about the critical role women played in bringing peace to war torn Liberia. "Pray the Devil Back to Hell" won Best Documentary at the Tribeca Film Festival in 2008, and screened in 60 countries around the world on all seven continents. It had cumulative gross worldwide of $90,066.


title: Abigail Disney

text: In 2007, she and Gini Reticker founded Fork Films, a New York-based production company. She is the president and CEO, and Reticker is the chief creative officer. In 2009, Fork Films and Film Sprout partnered together to create "Pray the Devil Back to Hell" Global Peace Tour, a nine-month grassroots screening tour that culminated on the United Nations' International Day of Peace on September 21, 2009. The tour brought the film to 31 foreign countries and 235 U.S. cities in 45 different states. The film highlights the bravery and sacrifice of its lead figure, Leymah Gbowee, who received a Nobel Peace Prize in 2011.


title: Abigail Disney

text: The response to "Pray the Devil Back to Hell" led Disney to work on the five-part special series for PBS, "Women, War & Peace", which aired in 2011 and was the winner of the Overseas Press Club's Edward R. Murrow Award, a Gracie Award, a Television Academy Honor and the America Bar Association's Silver Gavel Award (for "I Came to Testify"). This series created and executive produced by Abigail Disney, Pamela Hogan, and Gini Reticker, and looked at the role of women in war in the modern age, not just as victims of conflict, but as active agents for peace in their communities. Also in 2011, Disney received an Athena Film Festival Award for her extraordinary use of film for social change.


title: Abigail Disney

text: Disney executive produced "The Trials of Spring" (2015), which includes a feature-length documentary and six short films.


title: Abigail Disney

text: Disney made her directorial debut with "The Armor of Light," which follows anti-abortion evangelical minister Rob Schenck, Lucy McBath, the mother of teenager Jordan Davis, and John Michael Phillips. Jordan Davis was gunned down in Jacksonville, Florida on November 23, 2012. Davis was unarmed at the time of his death, and his story has cast a spotlight on stand-your-ground laws in the United States. The film follows Schenck as he meets McBath, a pro-choice Christian, and her attorney John Phillips. "The Armor of Light" premiered at the Tribeca Film Festival in April 2015 before opening theatrically on October 30, 2015. In 2017, it won an Emmy Award for Outstanding Social Issue Documentary.


title: Abigail Disney

text: In 2018, Disney partnered with Killer Content and launched Level Forward, a new breed film, television and theater production company focused on projects that extend the influence and opportunity of creative excellence and supports new voices. In October 2022, Fork Films shut down.


title: Abigail Disney

text: Disney and her husband Pierre Hauser created The Daphne Foundation in 1991 in order to fund programs that confront the causes and consequences of poverty in the five boroughs of New York City.


title: Abigail Disney

text: In 2008, Disney launched Peace is Loud, a nonprofit organization that uses media and live events to spotlight women leaders who build a culture of peace. Disney is the founder and president.


title: Abigail Disney

text: In 2011, Disney traveled with Nobel laureate Leymah Gbowee to the Congo to spend a week working with other women peace activists and to explore ideas for building peace in their country. The following year, they visited Sri Lanka, where women activists launched the Sri Lankan Women's Agenda on Peace, Security and Development, inspired by Gbowee's legacy.


title: Abigail Disney

text: In 2012, she renounced her share of the profits from the Disney family investment in the Ahava cosmetics company whose factory is located in a West Bank settlement. She stated "I cannot in good conscience profit from what is technically the 'plunder' or 'pillage' of occupied natural resources." For legal reasons, she could not withdraw her investments, and therefore donated the investments and profits "to organizations working to end this illegal exploitation."


title: Abigail Disney

text: In May 2015, Disney joined Gbowee and 28 other international women peacebuilders to cross the 2-mile wide De-Militarized Zone (DMZ) separating North and South Korea in an act of solidarity with Korean women and to call for an end to the Korean War. The peacebuilders headed international peace symposia in Pyongyang and Seoul, where they listened to Korean women and shared experiences of mobilizing women to end conflict.


title: Abigail Disney

text: She is part of the group The Patriotic Millionaires. This is a group of wealthy people who support hiking taxes on the rich. They sent a clear demand for higher tax rates at the World Economic Forum in Davos in January 2020.


title: Abigail Disney

text: In June 2021, Disney published an opinion piece in "The Atlantic" criticising practices by wealthy individuals who reduce their tax burden and protect their wealth across generations through practices such as "offsetting income with losses in unrelated businesses; structuring assets to grow rather than generate income, then borrowing against those growing assets for cash needs; and deducting interest payments and state taxes from taxable income".


title: Abigail Disney

text: On April 21, 2019, Disney, through several tweets, criticized Disney CEO Bob Iger's compensation. In 2018, Iger earned a $66 million package, while in 2019, his compensation package was estimated to be approximately $35 million. One month before this statement, she had claimed that CEOs are generally "paid far too much," saying that "there is nobody on Earth [who is] worth 500 times his median workers' pay." On April 22, the Disney Corporation responded in a statement that the company has made "historic investments" in its workers' pay and benefits, and defended the CEO's compensation, which it said is "90% performance-based." The company stated that Iger "has delivered exceptional value for shareholders." On April 23, "The Washington Post" published an op-ed by Abigail Disney where she again criticized the "never [before] so profitable" Disney corporation and called for pay equity reform.


title: Abigail Disney

text: In July 2019, Abigail Disney criticized working conditions at Disneyland after a meeting with employees at their union office. She stated that the Disneyland employees she talked to have to forage for food in other people's garbage.


title: Abigail Disney

text: Again turning to Twitter in 2020, Disney publicly criticized the corporation for furloughing hundreds of thousands of low paid workers during the coronavirus pandemic.


title: Abigail Disney

text: In May 2020, Disney gave a TED talk in which she criticized the pay rates of employees at Disney theme parks. Disney said that when she was growing up, a custodian at Disneyland could make enough money to feed a family, own a modest home, and access decent health care. Today, "three out of four of the people who smile when you walk in, who help you comfort that crying baby, who maybe help you have the best vacation you ever have, can't consistently put food on the table." She added, "Disney has turned a pretty profit on the idea that families are a kind of magic, that love is important, that imaginations matter. That's why it turns your stomach a little bit when I tell you that Cinderella might be sleeping in her car."


title: Abigail Disney

text: In 2022, Disney joined current and past Disney employees in criticizing Bob Chapek for refusing to make a statement concerning Florida House Bill 1557, which is officially named the Parental Rights in Education Bill and was passed in February of that same year. The law prohibits the teaching of gender identity in schools prior to 4th grade.


title: Velvet

text: Velvet is a type of woven tufted fabric in which the cut threads are evenly distributed, with a short pile, giving it a distinctive soft feel. By extension, the word "velvety" means "smooth like velvet". In the past, velvet was typically made from silk. Today, velvet can be made from linen, cotton, wool and synthetic fibers.


title: Velvet

text: Velvet is woven on a special loom that weaves two thicknesses of the material at the same time. The two pieces are then cut apart to create the pile effect, and the two lengths of fabric are wound on separate take-up rolls. This complicated process meant that velvet was expensive to make before industrial power looms became available, and well-made velvet remains a fairly costly fabric. Velvet is difficult to clean because of its pile, but modern dry cleaning methods make cleaning more feasible. Velvet pile is created by warp or vertical yarns and velveteen pile is created by weft or fill yarns.


title: Velvet

text: Velvet can be made from several different kinds of fibers, traditionally, the most expensive of which is silk. Much of the velvet sold today as "silk velvet" is actually a mix of rayon and silk. Velvet made entirely from silk is rare and usually has market prices of several hundred US dollars per yard. Cotton is also used to make velvet, though this often results in a less luxurious fabric. Velvet can also be made from fibers such as linen, mohair, and wool. A cloth made by the Kuba people of the Democratic Republic of Congo from the raffia palm is often referred to as "Kuba velvet". More recently, synthetic velvets have been developed, mostly from polyester, nylon, viscose, acetate, and from either mixtures of different synthetics or from combined synthetics and natural fibers (for example viscose mixed with silk produces a very soft, reflective fabric). A small percentage of spandex is sometimes added to give the final material a certain amount of stretch (hence "stretch velvet").


title: Velvet

text: Because of its unusual softness and appearance as well as its high cost of production, velvet has often been associated with nobility. Velvet was introduced to Baghdad during the rule of Harun al-Rashid (786–809) by Kashmiri merchants and to Al-Andalus by Ziryab. In the Mamluk era, Cairo was the world's largest producer of velvet. Much of it was exported to Venice (whence it spread to most of Europe), Iberia and the Mali Empire. Mansa Musa, the ruler of the Mali Empire, visited Cairo on his pilgrimage to Mecca. Many Arab velvet makers accompanied him back to Timbuktu. Later Ibn Battuta mentions how Suleyman, the ruler of Mali, wore a locally produced complete crimson velvet kaftan on Eid. During the reign of Mehmed II, assistant cooks wore blue dresses (), conical hats (, ) and baggy trousers (, ) made from Bursa velvet.


title: Malt liquor

text: Malt liquor is a type of mass market beer with high alcohol content, most closely associated with North America. Legally, it often includes any alcoholic beverage with 5% or more alcohol by volume made with malted barley. In common usage, it refers to beers containing a high alcohol content, generally above 6%, which are made with ingredients and processes resembling those for American-style lagers.


title: Malt liquor

text: Malt liquor is a strong lager or ale in which sugar, corn or other adjuncts are added to the malted barley to boost the total amount of fermentable sugars in the wort. This gives a boost to the final alcohol concentration without creating a heavier or sweeter taste. Also, they are not heavily hopped, so they are not very bitter.


title: Malt liquor

text: Malt liquor is typically straw to pale amber in color. While traditional premium lager is made primarily from barley, water, and hops, malt liquors tend to make much greater use of inexpensive adjuncts such as corn, rice, or dextrose. Use of these adjuncts, along with the addition of special enzymes, results in a higher percentage of alcohol than an average beer. Higher alcohol versions, sometimes called "high-gravity" or just "HG", may contain high levels of fusel alcohols, which gives off solvent- or fuel-like aromas and flavors.


title: Malt liquor

text: Owing to inconsistencies in American alcoholic beverage regulations, which can vary from state to state, the term "malt liquor" lacks a stable definition. In some states, malt liquor refers to any alcoholic beverage made by fermenting grain and water; in these states a non-alcoholic beer may also be called a non-alcoholic or non-intoxicating malt liquor. In some states, products labeled "beer" must fall below a certain alcohol content, and beers that exceed the mark must be labeled as "malt liquor". While ordinary beers in the United States average around 4-5% alcohol by volume, malt liquors typically range from 6% up to 9% alcohol by volume. A typical legal definition is Colorado's Rev. Stat. ss. 12-47-103(19), which provides that:


title: Malt liquor

text: "Malt Liquors" includes beer and shall be construed to mean any beverage obtained by the alcoholic fermentation of any infusion or decoction of barley, malt, hops or any other similar products, or any combination thereof, in water containing more than three and one fifth percent of alcohol by weight.


title: Malt liquor

text: Alcohol percentages measured by weight translate into larger figures when re-expressed as alcohol percentages by volume, because ethanol is less dense than water.


title: Malt liquor

text: The term "malt liquor" is documented in England in 1690 as a general term encompassing both beer and ale. The first mention of the term in North America appears in a patent issued by the Canadian government on July 6, 1842, to one G. Riley for "an improved method of brewing ale, beer, porter, and other maltliquors."


title: Malt liquor

text: The Clix brand is often credited as the first malt liquor made in the United States, granted a patent in 1948. The first widely successful malt liquor brand in America was Country Club, which was produced in the early 1950s by the M. K. Goetz Brewing Company in St. Joseph, Missouri.


title: Malt liquor

text: Other popular contemporary brands include Colt 45, St. Ides, Mickey's, Steel Reserve, King Cobra, and Olde English 800.


title: Malt liquor

text: The core market for malt liquor brewers in the United States in recent decades has been the Black and Hispanic populations. Brewers' use of target marketing in advertising malt liquor primarily to young, inner-city, black males has been controversial, due to the drink's higher alcohol content and the perceived vulnerability of the target audience. Brewers and advertisers have stated that they simply advertise to those who already buy their products. Critics have objected to the targeting of a segment of the population suffering disproportionately from alcohol-related disease and poor access to medical care.


title: Malt liquor

text: In order to highlight the potency of malt liquor, brand names have stressed powerful imagery such as Colt 45, Big Bear, and Power Master, and used slogans such as "It's got more" or "The Real Power". Power and sexual dominance have been common themes in advertising. Ads for Power Master were eventually banned in the United States due to regulations against advertising the strength of alcoholic beverages.


title: Malt liquor

text: The National Institute on Alcohol Abuse and Alcoholism (NIAAA) has reported that African Americans suffer disproportionate rates of cirrhosis of the liver and other alcohol-related health problems. In light of such statistics, African-American community leaders and some health officials have concluded that targeting high-alcohol beverage ads at this segment of the population is unethical and socially irresponsible. In 1991, U.S. Surgeon General Antonia Novello criticized all alcoholic beverage companies for "unabashedly targeting teenagers" with "sexual imagery, cartoons, and rock and rap music" in television and print ads.


title: Malt liquor

text: In the American vernacular, a forty-ounce or simply a forty is a glass or plastic bottle that holds of malt liquor. Malt liquors are commonly sold in 40 fluid ounce bottles, among other sizes, as opposed to the standard bottle that contains a single serving of beer, although many malt liquors are offered in various volumes.


title: Malt liquor

text: After the introduction of 40-ounce containers, which contain roughly five Standard drinks, "40s" became a favorite high of many youth in inner-city areas.


title: Malt liquor

text: Examples of malt liquors sold in forty ounce bottles include Olde English 800, Colt 45, Mickey's, Camo 40, Black Fist, Country Club, Black Bull, Labatt Blue Dry 6.1/7.1/8.1/9.1/10.1, WildCat, Molson Dry 6.5/7.5/8.5/10.1, Private Stock, Big Bear, St. Ides, Steel Reserve 211, B40 Bull Max, King Cobra, and Hurricane. Dogfish Head Brewery has sporadically produced a high-end bottle-conditioned forty called "Liquor de Malt".


title: Malt liquor

text: Forties are often mentioned in hip-hop and rap culture by rap stars endorsing the "40" Ounce tradition. A similar trend was common around the late 1990s' and early 2000s' punk scene, with such songs as "40.oz Casualty" by The Casualties, "Rock the 40. Oz." by Leftöver Crack, and "40oz. to Freedom" by Sublime.


title: Malt liquor

text: At least for a brief period in the mid-1990s, some brands of malt liquor, including Olde English 800, Colt 45, and Mickey's, were available in even larger, 64-ounce glass bottles. Forty-ounce bottles are not permitted in some US states, including Florida, where the largest container that a malt beverage may be sold at retail is .


title: Malt liquor

text: American-style malt liquors were made in Britain in the late 1970s and early 1980s. Some were American brands brewed under license, notably Colt 45; some were not. They were generally 5% ABV. They were heavily marketed but failed in the market.


title: Malt liquor

text: In Italy, beers with more than 14.5 Plato degrees fall into a distinct tax rate known as "Birra doppio malto". Brewing companies often state this classification on the label. Therefore, the "doppio malto" indication nearly always identifies a beer that is the rough equivalent strength of a North American malt liquor.


title: Cailey Fleming

text: Cailey Presley Fleming is an American actress. She is known for her role as Judith Grimes on the AMC horror-drama television series "The Walking Dead" (2018–2022), and as young versions of Rey and Sylvie in "" (2015) and "Loki" (2021) respectively.


title: Cailey Fleming

text: Fleming was born in Picayune, Mississippi. At age 8, she began acting professionally first gaining attention in "", portraying a young Rey. Fleming began to portray Judith Grimes in "The Walking Dead" during season nine and became a series regular beginning with season ten. She briefly appeared in "Loki" episode four as young Sylvie. On January 25, 2022, Fleming was cast as John Krasinski's imaginary friend in the comedy "IF".


title: Marcia Lucas

text: Marcia Lou Lucas (née Griffin; born October 4, 1945) is an American film editor and film producer. She is best known for her work editing Martin Scorsese's "Alice Doesn't Live Here Anymore" (1973), "Taxi Driver" (1976), and "New York, New York" (1977) and her then-husband George Lucas's "THX-1138" (1971), "American Graffiti" (1973), and the "Star Wars" trilogy (1977–1983).


title: Marcia Lucas

text: She won the Academy Award for Best Film Editing in 1977 for "Star Wars" (1977). She was previously nominated for an Academy Award for her film editing on "American Graffiti" and for a BAFTA Award for Best Editing for her work on "Taxi Driver". After a career gap while raising her family, Lucas produced two films in the 1990s.


title: Marcia Lucas

text: Lucas was born in Modesto, California. Her father was an Air Force officer stationed in Stockton, California, during World War II. Her parents divorced when she was two. Her mother, Mae Griffin, relocated the family to North Hollywood, California, to live with her parents. When Marcia's grandfather died, her mother moved to an apartment nearby, and she found work as a clerk at an insurance agency. When she was a teenager, her father reentered her life, but he had remarried and was stationed in Florida. Marcia lived with her stepfamily for two years and moved back to Hollywood. She returned to North Hollywood to finish high school, and enrolled in chemistry courses at Los Angeles City College while working in a mortgage banking firm.


title: Marcia Lucas

text: In 1964, Marcia's then-boyfriend worked for a Hollywood museum and wanted to hire her as a librarian to catalog all the donated movie memorabilia. They sent her to apply for the job at a California State Employment office. Since she had no experience, the Employment office sent her to Sandler Films who needed an apprentice film librarian with no experience. Marcia was eventually promoted up to being an assistant editor by the time she was twenty. She was in a Motion Picture Editors Guild apprenticeship of eight years, leading to becoming a Guild film editor. She edited promotional films and trailers.


title: Marcia Lucas

text: In 1967, Verna Fields, one of the few respected female film editors in the industry at that time, asked Sandler Films to send her an assistant editor to help on a United States Information Agency documentary, about Lyndon B. Johnsons 21–23 December 1967 Asia trip, later titled "Journey to the Pacific" (1968). Fields had also hired University of Southern California students as assistant editors, including George Lucas. The following spring, the newly engaged Marcia moved in with Lucas at his hilltop apartment on Portola Drive in Beverly Hills and returned to editing commercials as George Lucas accompanied Francis Ford Coppola to scout filming locations for "The Rain People" (1968) at Long Island, New York. When principal photography begun on "The Rain People", Lucas simultaneously begun shooting a behind-the-scenes documentary short titled "Filmmaker" (1968).


title: Marcia Lucas

text: Back in California, Marcia had accepted an offer to work on "Medium Cool" (1969) when George had recommended her as an assistant editor for Barry Malkin on "The Rain People". Fortunately, the shooting schedule for "Medium Cool" was delayed, which allowed for her to work on both films. Following this assignment, she and George returned to their Portola Drive residence to edit "Filmmaker". Shortly after, Coppola had established a multi-picture deal with his production company American Zoetrope and Warner Bros. Their first project was "THX 1138" (1971) for which Marcia served as an assistant editor. Reflecting on the film's commercial failure, Marcia stated "I never cared for "THX" because it left me cold. When the studio didn't like the film, I wasn't surprised. But George just said to me I was stupid and knew nothing. Because I was just a Valley Girl. He was the intellectual."


title: Marcia Lucas

text: When principal photography had wrapped on "American Graffiti" (1973), George had wanted Marcia to edit the film, but Universal Pictures executive Ned Tanen insisted on hiring Verna Fields, who had just finished editing Steven Spielberg's "The Sugarland Express" (1974). However, Fields worked on the rough cut of the film and then left to resume work on "What's Up, Doc?" (1972). For the next six months, Marcia edited "American Graffiti" alongside her husband and sound editor Walter Murch to its contractual runtime of 110 minutes. In 1974, Marcia Lucas and Fields were nominated for the Academy Award for Best Film Editing for their work on "American Graffiti".


title: Marcia Lucas

text: After "American Graffiti" was released, Martin Scorsese asked Marcia to edit "Alice Doesn't Live Here Anymore" (1974), his first studio film. Sandra Weintraub recalled "We knew her, and we liked her, and she was in the union. It was good for her to get away from George and his house. Here she was, a wonderful editor working on her husband's films. I don't think she got taken seriously." As Marcia was editing the film in Los Angeles, George joined her and sequestered himself in a hotel room as he wrote the first draft for "Star Wars" (1977). In his fourth draft of "Star Wars", George originally had written for Obi-Wan Kenobi to survive his lightsaber duel with Darth Vader by retreating through a blast door that would slam shut behind him. However, Marcia suggested to her husband that he should kill off Kenobi and have him act as a spiritual guide to Luke.


title: Marcia Lucas

text: Before "Star Wars" entered post-production, George did not consider that Marcia would work on it as she expected to give birth after editing "Taxi Driver" (1976), but the pregnancy was unsuccessful. Instead, George hired British union editor John Jympson to cut the film while they were in England. Horrified by the first rough cut, George fired Jympson and replaced him with Marcia. She was tasked to edit the Battle of Yavin sequence, in which she drastically diverted from the originally scripted shot sequence. George estimated that "it took her eight weeks to cut that battle. It was extremely complex, and we had 40,000 feet of dialogue footage of pilots saying this and that. And she had to cull through all that, and put in all the fighting as well." While editing the sequence, she warned George: "If the audience doesn't cheer when Han Solo comes in at the last second in the "Millennium Falcon" to help Luke when he's being chased by Darth Vader, the picture doesn't work."


title: Marcia Lucas

text: As Marcia edited the Death Star assault, Lucas brought in editor Richard Chew to restructure the rough cut. As the workload grew too burdensome, Lucas hired Paul Hirsch as the film's third editor. Shortly after Christmas 1976, Marcia left "Star Wars" to work on Scorsese's musical drama "New York, New York" (1977) because Irving Lerner had died before he finished editing the film. At the 50th Academy Awards, Lucas won the 1977 Academy Award for Best Film Editing with Chew and Hirsch.


title: Marcia Lucas

text: Following the success of "Star Wars", Marcia decided to place her career on hold in order to raise a family. In the meantime, she supervised the completion of the interior design and decoration of Skywalker Ranch. After viewing the rough cut of "Raiders of the Lost Ark" (1981), she stated that there was no emotional closure because Marion did not appear at the ending. As a result, Spielberg shot the final scene with her and Indiana Jones. In 1982, Marcia came on board "Return of the Jedi" as the film's third editor alongside Duwayne Dunham and Sean Barton. When asked of her contributions to the film, George described the scenes in which she helped edit as the emotional "dying and crying" scenes. Marcia's last film credit was as producer of 1996's "No Easy Way."


title: Marcia Lucas

text: In 1967, Marcia met George Lucas while he was attending film school at the University of Southern California, when they both served as apprentice editors on "Journey to the Pacific" under Verna Fields. On February 22, 1969, they were married. They adopted one daughter, Amanda Lucas, who was born in 1981. Due to her husband's commitments to the "Star Wars" films and "Raiders of the Lost Ark", Marcia grew impatient in her marriage as she blamed his workaholism and emotional blockage. In mid-1982, she asked for a divorce, but in order to maintain a positive public image, George asked her to wait until after the release of "Return of the Jedi" to go public with the decision. On June 13, 1983, George formally announced at Skywalker Ranch that he and Marcia were divorcing; the couple would share custody of their daughter while Marcia would relocate to Los Angeles. When the divorce was finalized, she reportedly received $50 million from the settlement.


title: Marcia Lucas

text: Marcia later married Tom Rodrigues, a stained glass artist who worked as a production manager at Skywalker Ranch from 1980 to 1983, whom she met before divorcing George. In 1985, the couple had a daughter, Amy Rodrigues. Lucas and Rodrigues divorced in 1993.


title: Marcia Lucas

text: In an interview, Mark Hamill cited Marcia for her contributions to "Star Wars". In "Mythmaker: The Life and Work of George Lucas," filmmaker John Milius described Marcia's contributions to Milius's own films and those of George Lucas, Steven Spielberg, and Martin Scorsese, calling her one of the best editors he knew. In 2021, "SFGate" published an article calling Marcia the "secret weapon of 'Star Wars'", further stating that:Considering the reaction to the "Star Wars" prequels and George's distance from the franchise now, it's not a stretch to say that Marcia was actually the glue that kept the galaxy far, far away together. Or, at the very least, helped repair it when it needed to be fixed.


title: Marcia Lucas

text: In J. W. Rinzler's posthumous final book, "Howard Kazanjian: A Producer's Life", Lucas criticized the later "Star Wars" films. She revealed that upon seeing "The Phantom Menace", she "cried because [she] didn't think it was very good," particularly criticizing the age gap between romantic leads Anakin Skywalker and Padmé Amidala. On the sequel trilogy, she stated that Kathleen Kennedy and J. J. Abrams "don't get it", saying she was furious at the deaths of Han Solo and Luke Skywalker, as well as the lack of an explanation for Rey's powers.


title: Moorland

text: Moorland or moor is a type of habitat found in upland areas in temperate grasslands, savannas, and shrublands and montane grasslands and shrublands biomes, characterised by low-growing vegetation on acidic soils. Moorland, nowadays, generally means uncultivated hill land (such as Dartmoor in South West England), but also includes low-lying wetlands (such as Sedgemoor, also South West England). It is closely related to heath, although experts disagree on what precisely distinguishes these types of vegetation. Generally, moor refers to highland and high rainfall zones, whereas heath refers to lowland zones which are more likely to be the result of human activity.


title: Moorland

text: Moorland habitats mostly occur in tropical Africa, northern and western Europe, and neotropical South America. Most of the world's moorlands are diverse ecosystems. In the extensive moorlands of the tropics, biodiversity can be extremely high. Moorland also bears a relationship to tundra (where the subsoil is permafrost or permanently frozen soil), appearing as the tundra and the natural tree zone. The boundary between tundra and moorland constantly shifts with climatic change.


title: Moorland

text: Heathland and moorland are the most extensive areas of semi-natural vegetation in the British Isles. The eastern British moorlands are similar to heaths but are differentiated by having a covering of peat. On western moors, the peat layer may be several metres thick. Scottish "muirs" are generally heather moors, but also have extensive covering of grass, cotton-grass, mosses, bracken and under-shrubs such as crowberry, with the wetter moorland having sphagnum moss merging into bog-land.


title: Moorland

text: There is uncertainty about how many moors were created by human activity. Oliver Rackham writes that pollen analysis shows that some moorland, such as in the islands and extreme north of Scotland, are clearly natural, never having had trees, whereas much of the Pennine moorland area was forested in Mesolithic times. How much the deforestation was caused by climatic changes and how much by human activity is uncertain.


title: Moorland

text: A variety of distinct habitat types are found in different world regions of moorland. The wildlife and vegetation forms often lead to high endemism because of the severe soil and microclimate characteristics. An example of this is the Exmoor Pony, a rare horse breed which has adapted to the harsh conditions in England's Exmoor.


title: Moorland

text: In Europe, the associated fauna consists of bird species such as red grouse, hen harrier, merlin, golden plover, curlew, skylark, meadow pipit, whinchat, ring ouzel, and twite. Other species dominate in moorlands elsewhere. Reptiles are few due to the cooler conditions. In Europe, only the common viper is frequent, though in other regions moorlands are commonly home to dozens of reptile species. Amphibians such as frogs are well represented in moorlands. When moorland is overgrazed, woody vegetation is often lost, being replaced by coarse, unpalatable grasses and bracken, with a greatly reduced fauna.


title: Moorland

text: Some hill sheep breeds, such as Scottish Blackface and the Lonk, thrive on the austere conditions of heather moors.


title: Moorland

text: Burning of moorland has been practised for a number of reasons, for example, when grazing is insufficient to control growth. This is recorded in Britain in the fourteenth century. Uncontrolled burning frequently caused (and causes) problems and was forbidden by statute in 1609. With the rise of sheep and grouse management in the nineteenth century, it again became common practice. Heather is burnt at about 10 or 12 years old when it will regenerate easily. Left longer, the woodier stems will burn more aggressively and will hinder regrowth. Burning of moorland vegetation needs to be very carefully controlled, as the peat itself can catch fire, and this can be difficult if not impossible to extinguish. In addition, uncontrolled burning of heather can promote alternative bracken and rough grass growth, which ultimately produces poorer grazing. As a result, burning is now a controversial practice; Rackham calls it "second-best land management".


title: Moorland

text: Mechanical cutting of the heather has been used in Europe, but it is important for the material to be removed to avoid smothering regrowth. If heather and other vegetation are left for too long, a large volume of dry and combustible material builds up. This may result in a wildfire burning out a large area, although it has been found that heather seeds germinate better if subject to the brief heat of controlled burning.


title: Moorland

text: In terms of managing moorlands for wildlife, in the UK, vegetation characteristics are important for passerine abundance, whilst predator control benefits red grouse, golden plover, and curlew abundances. To benefit multiple species, many management options are required. However, management needs to be carried out in locations that are also suitable for species in terms of physical characteristics such as topography, climate and soil.


title: Moorland

text: The development of a sensitivity to nature and one's physical surroundings grew with the rise of interest in landscape painting, and particularly the works of artists that favoured wide and deep prospects, and rugged scenery. To the English Romantic imagination, moorlands fitted this image perfectly, enhancing the emotional impact of the story by placing it within a heightened and evocative landscape. Moorland forms the setting of various works of late Romantic English literature, ranging from the Yorkshire moorland in Emily Brontë's "Wuthering Heights" and "The Secret Garden" by Frances Hodgson Burnett to Dartmoor in Arthur Conan Doyle's Holmesian mystery "The Hound of the Baskervilles". They are also featured in Charlotte Bronte's "Jane Eyre" representing the heroine's desolation and loneliness after leaving Mr Rochester.


title: Moorland

text: Enid Blyton's Famous Five series featured the young protagonists adventuring across various moorlands where they confronted criminals or other individuals of interest. Such a setting enhanced the plot as the drama unfolded away from the functioning world where the children could solve their own problems and face greater danger. Moorland in the Forest of Bowland in Lancashire is the setting for Walter Bennett's "The Pendle Witches", the true story of some of England's most infamous witch trials. In Erin Hunter's "Warriors" series, one of the four Clans, WindClan, lives in the moorland alone.


title: Moorland

text: Michael Jecks, author of Knights Templar Mysteries, sets his books in and around Dartmoor, England. Paul Kingsnorth’s "Beast" is also set on a western English moor, using the barren landscape and fields of heather to communicate themes of timelessness and distance from civilization.


title: Moorland

text: Great Britain is home to an estimated 10–15% of the world's moors. Notable areas of upland moorland in Britain include the Lake District, the Pennines (including the Dark Peak and Forest of Bowland), Mid Wales, the Southern Uplands of Scotland, the Scottish Highlands, and a few pockets in the West Country.


title: Moorland

text: Moorlands are called "páramos" in Spanish. They are particularly common in Northern Spain and the Meseta Central.


title: Moorland

text: Colombia is one of only three countries in the world to be home to páramo (tropical moorland) and more than 60% of the paramo regions are found on its soil.


title: Candyman (character)

text: Daniel Robitaille, colloquially known as Candyman, is a fictional character and the main antagonist of the "Candyman" film series. The character originated in Clive Barker's 1985 short story, "The Forbidden". In the film series, he is depicted as an African-American man who was brutally murdered for a forbidden 19th-century interracial love affair; he returns as an urban legend, and kills anyone who summons him by saying his name five times in front of a mirror. The character is played by Tony Todd in "Candyman" (1992), "" (1995), and "" (1999); Todd reprises the role in "Candyman" (2021), a sequel of the original 1992 film, with additional formssouls brought into the Candyman "hive"Sherman Fields (played by Michael Hargrove), William Bell, Samuel Evans, George Stinney, James Byrd Jr., Gil Cartwright (played by Cedric Mays), and Anthony McCoy (played by Yahya Abdul-Mateen II).


title: Candyman (character)

text: The character originated in Clive Barker's short story, "The Forbidden", published in volume five of Barker's six-volume "Books of Blood" anthology collection. Fantasy Tales artist John Stewart's own image in the book's illustration deviates from the author's words – giving us a beastly man in silhouette with wild hair and a far more elaborate hook hand than was shown in the later films; but in the pages, Candyman is described thus:


title: Candyman (character)

text: He was bright to the point of gaudiness: His flesh was a waxy yellow. His thin lips are pale blue. His wild eyes are glittering as if their irises are set with rubies. His jacket was patchwork and his trousers are the same. He looked, [Helen] thought, almost ridiculous with his bloodstained motley and the hint of rouge on his cheeks.


title: Candyman (character)

text: The Candyman's iconic hook and bees are introduced in the story with Helen and other characters. Although Candyman was described as a mysterious Caucasian male with long blonde hair, incredibly pale skin, and a brightly colored patchwork suit; his race, name, place of origin, and backstory are never mentioned; doubting his existence is enough to summon him.


title: Candyman (character)

text: Candyman's first film appearance was in "Candyman" (1992). Set in the present, the film follows Helen Lyle, a graduate student in Chicago, who investigates him as the central figure of an urban legend connected to a series of murders at the Cabrini–Green Homes.


title: Candyman (character)

text: Helen writes a thesis about how Cabrini–Green's residents attribute their hardships to this apparently-mythical figure. When she discredits the legend, analyzing examples of his history and participating in the arrest of a criminal using the Candyman legend to intimidate the locals, Candyman appears and frames her for another series of murders to perpetuate the public's fear of him.


title: Candyman (character)

text: It is hinted that Helen is the reincarnation of Candyman's lover. He plots to have himself, Helen, and kidnapped baby Anthony McCoy immolated in a bonfire, but Helen escapes him and sacrifices herself to rescue Anthony. With Candyman apparently destroyed, Helen becomes a vengeful spirit and continues his behavior.


title: Candyman (character)

text: In "", set three years after "Candyman" in 1995, he appears in New Orleans. Candyman encounters Annie Tarrant (a descendant of his and Caroline's daughter Isabel) after she summons him. The movie explores how he meets Caroline Sullivan during his lifetime (as the artist Daniel Robitaille) before he is murdered and becomes Candyman.


title: Candyman (character)

text: In "", set twenty-five years after "Farewell to the Flesh", in 2020, Candyman appears in Los Angeles during Day of the Dead celebrations, encountering Annie's adult daughter Caroline.


title: Candyman (character)

text: In "Candyman" (2021), set twenty-seven years after "Candyman" (1992), in 2019, Candyman is summoned once more by a now adult Anthony McCoy. It is revealed that the legend of Candyman has survived and evolved by being recontextualized throughout the years around similar tragic murders of African-Americans killed by racist authorities in ways that resemble his (Daniel Robitaille's) death, and that these figures become part of "the hive" of Candyman. The Candyman before Anthony was a mentally disabled man named Sherman Fields, who was accused of placing razor blades in children's candy before being beaten to death by the police for it, although he turned out to be innocent. Eventually, a disfigured and catatonic Anthony is gunned down by the police, thereby enabling Candyman to assimilate Anthony and renew his legend. Other characters depicted as part of the Candyman hive include Anthony Crawford, William Bell, Samuel Evans, George Stinney, Helen Lyle, James Byrd, Jr., and Gil Cartwright (in deleted scenes).


title: Candyman (character)

text: When Tony Todd and co-star Virginia Madsen were cast as Candyman and Helen, original "Candyman" director Bernard Rose gave them free rein to flesh out their characters' backstories as part of the creative process. Rose said, "The Candyman is not black in Clive's story. In fact, the whole back story of the interracial love affair that went wrong is not in the book. Everything that's in the book is in the film, but it's been amplified." Todd came up with the character's backstory during rehearsals with Madsen. He called his character "Granville T. Candyman", who has a forbidden love affair with a white woman whose portrait he paints (leading to his lynching). The name "Granville" is never used, and the character's name ultimately becomes Daniel Robitaille.


title: Candyman (character)

text: The Candyman is largely driven by a need to sustain his legacy, killing those who doubt his existence. He has been described as a "ghoul fueled by the 'faith' of his believers. He is forced to deal with his followers to make them believe again and punish the interloper who leads them astray." In "Draculas, Vampires and Other Undead Forms: Essays on Gender, Race and Culture", the character is compared to a vampire: "[Candyman] possesses the capacity to hypnotize his prey such that they appear to desire their victimizations."


title: Candyman (character)

text: Tony Todd compared his ability to invoke fear, suggestion and seduction to the DC Comics villain Scarecrow. Todd also compared his character to the Phantom of the Opera and the Hunchback of Notre Dame; all are "monsters", who use tenderness and terror in an unsuccessful attempt to win the love of a female protagonist. Virginia Madsen confirmed that the Candyman was intended to be an "African-American Dracula", "appealing to the African-American community because they finally had their own Dracula".


title: Candyman (character)

text: In "Day of the Dead," the lynch mob chants "Candyman" five times before he dies. Summoning a specter by chanting his name repeatedly in front of a mirror may be traced back to Bloody Mary. In the short story, the character describes his existence as an urban legend: "I am rumor. It's a blessed condition, believe me. To live in people's dreams; to be whispered at street-corners; but not have to be". According to the film version, "I am the writing on the wall, the whisper in the classroom. Without these things, I am nothing".


title: Candyman (character)

text: The Candyman physical appearance is often seen by the subject who summoned him and those who believe in him. His image is not able to be captured by individuals who don't believe as well as not seen physically to the naked eye through surveillance systems but may be seen through reflections to the affected subject. He often uses the ability to possess an individual by hypnosis placing them in a trance with his dark poetic voice, making attempts at mind control on his subjects to surrender to him and become immortal. As with the "2021 film", the spirit of Candyman through Sherman Fields doesn't speak but rather makes painful eerie breathing sounds. In the film series, he can make his murders seem as if his subjects committed them themselves as his existence is played on by their mind. Candyman in supernatural form has the ability to levitate into the air. In "Candyman" (1992), the Candyman is seen by Helen Lyle floating horizontally as well as swiftly flying out of a window backwards. As with both standalone sequels he is seen by Annie Tarrant in "" rising from water into the air, landing on top of water. In "," he appears to Caroline McKeever levitating towards her with bees surrounding him. In "Candyman" (2021), he appears both in standing form and floating levitation with bees following him, it is also in this film that he is able to be a vessel within his main subject in the reflection. In the film series, Candyman has the ability to swiftly disappear and instantly change positions around the subject. Daniel Robitaille's physical body appear to be rotting away with his chest cavity exposed (hidden by his Trench coat) with bees swarming in the flesh, as with Sherman Fields appearance is displayed by his rotten affected beaten face. Anthony McCoy becomes a Candyman with his entire body going through a fleshy transformation and accumulate a bee-hive like appearance throughout his skin.


title: Candyman (character)

text: The Candyman was ninth on Fandango and Bloody Disgusting's list of top 10 slasher icons, and eighth on an older Bloody Disgusting list. Based on a readers' poll, "Rolling Stone" ranked him tenth among horror villains. JoBlo.com ranked the Candyman fifth on its list of horror boogeymen, and ComingSoon.net ranked him seventh on its list of slasher villains.


title: Candyman (character)

text: Candyman is sometimes referenced in songs, most notably Tupac Shakur song ""Troublesome '96"" with him urging listeners to ""say my name three times like Candyman...Bet I roll on yo' ass like an avalanche"", which often confused many people to this present day with debates if the summoning was three or five, however the actual times to summon is five. It was in fact Bloody Mary who is summoned three times. Kayne West also gave mention in his song titled "" Breathe In, Breathe Out"" rapping, ""So, say my name like Candyman, and I'ma come and fix you up like the handyman"."


title: Candyman (character)

text: The character was often parodied or mentioned in many television, movies and media ranging from Family Guy, The Simpsons, South Park, The Chappelle Show and Key & Peele. Social media also parodied Candyman various ways with mock trailers or appearances in their videos/short. A meme created with a picture of Terrance Howard circulated in the late 2010s with the spelling caption of Candyman as "'CANDY-MAYNE' )" due to his southern vocal accent and speaking annunciation of how he pronounces the word "man". It was then followed by mock VHS/DVDs/Bluray with Howard as the Candyman with the accent spelling in the title, also followed by edited parodied video/bits that went viral of what would the movie be like if Terrance Howard starred in the movie, it featured the impersonation of Howards' voice and likeness saying "CANDY-MAYNE" in the mirror and others correcting him to pronounce the name right otherwise he wont come out.


title: Candyman (character)

text: McFarlane Toys released a Candyman action figure as part of its Movie Maniacs Series 4 in 2001. More action figures were scheduled for release in November 2019 by NECA.


title: Candyman (character)

text: Yayha Abdul-Mateen II version of the Anthony McCoy's Candyman was released from Funko Pop merchandising in 2022. It features him dressed in his painter's overall jumpsuit wearing the honey colored Trench coat with bees surrounding his honeycomb like face.


title: Party

text: A party is a gathering of people who have been invited by a host for the purposes of socializing, conversation, recreation, or as part of a festival or other commemoration or celebration of a special occasion. A party will often feature food and beverages, and often conversation, music, dancing, or other forms of entertainment.


title: Party

text: Some parties are held in honor of a specific person, day, or event, such as a birthday party, a Super Bowl party, or a St. Patrick’s Day party. Parties of this kind are often called celebrations. A party is not necessarily a private occasion. Public parties are sometimes held in restaurants, pubs, beer gardens, nightclubs, or bars, and people attending such parties may be charged an admission fee by the host. Large parties in public streets may celebrate events such as Mardi Gras or the signing of a peace treaty ending a long war.


title: Party

text: A birthday party is a celebration of the anniversary of the birth of the person who is being honored. While there is historical precedent for birthday parties for the rich and powerful throughout history, the tradition extended to middle-class Americans around the nineteenth century, and took on more modern norms and traditions in the twentieth century. Birthday parties are now a feature of many cultures.


title: Party

text: In Western cultures, birthday parties include a number of common rituals. The guests may be asked to bring a gift for the honored person. Party locations are often decorated with colorful decorations, such as balloons and streamers. A birthday cake is usually served with lit candles that are to be blown out after a "birthday wish" has been made. The person being honored will be given the first piece of cake. While the birthday cake is being brought to the table, the song "Happy Birthday to You" or some other birthday song is sung by the guests.


title: Party

text: At parties for children, time is often taken for the "gift opening" wherein the individual whose birthday is celebrated opens each of the gifts brought. It is also common at children's parties for the host to give parting gifts to the attendees in the form of "goodie bags". Children and even adults sometimes wear colorful cone-shaped party hats.


title: Party

text: Birthday parties are often larger and more extravagant if they celebrate someone who has reached what is regarded in the culture as a milestone age, such as transition from childhood to adulthood. Examples of traditional coming of age celebrations include the North American sweet sixteen party and the Latin American quinceañera.


title: Party

text: A surprise party is a party that is not made known beforehand to the person in whose honor it is being held.


title: Party

text: Birthday surprise parties are the most common kind of surprise party. At most such parties, the guests will arrive an hour or so before the honored person arrives. Often, a friend in on the surprise will lead the honored person to the location of the party without letting on anything.


title: Party

text: The guests might even conceal themselves from view, and when the honored person enters the room, they leap from hiding and all shout, "Surprise!" For some surprise birthday parties, it is considered to be a good tactic to shock the honored person. Streamers, silly string, and balloons may be used for this purpose. Evidence of a party, such as decorations and balloons, are not made visible from the exterior of the home, so that the person honored will suspect nothing.


title: Party

text: A dinner party is a social gathering at which people eat dinner together, usually in the host's home. At the most formal dinner parties, the dinner is served on a dining table with place settings. Dinner parties are often preceded by a cocktail hour in a living room or bar, where guests drink cocktails while mingling and conversing. Wine is usually served throughout the meal, often with a different wine accompanying each course.


title: Party

text: At less formal dinner parties, a buffet is provided. Guests choose food from the buffet and eat while standing up and conversing. Women guests may wear cocktail dresses; men may wear blazers.


title: Party

text: At some informal dinner parties, the host may ask guests to bring food or beverages (a main dish, a side dish, a dessert, or appetizers). A party of this type is called a potluck or potluck dinner. In the United States, potlucks are very often held in churches and community centers.


title: Party

text: A garden party is a party in a park or a garden. An event described as a garden party is usually more formal than other outdoor gatherings, which may be called simply parties, picnics, barbecues, etc. A garden party can be a prestigious event. For example, invitations by the British Sovereign to garden parties at Buckingham Palace or at the Palace of Holyroodhouse (in Scotland) are considered an honor. The President of France holds a garden party at the Palais de l'Elysée in Paris on Bastille Day.


title: Party

text: A cocktail party is a party at which cocktails are served. It is sometimes called a "cocktail reception". Women who attend a cocktail party may wear a cocktail dress. A cocktail hat is sometimes worn as a fashion statement.


title: Party

text: In Anglo-American culture, a tea party is a formal gathering for afternoon tea. These parties were traditionally attended only by women, but men may also be invited. Tea parties are often characterized by the use of prestigious tableware, such as bone china and silver. The table, whatever its size or cost, is made to look its prettiest, with cloth napkins and matching cups and plates.


title: Party

text: In addition to tea, larger parties may serve punch or, in cold weather, hot chocolate. The tea is accompanied by a variety of easily managed foods. Thin sandwiches such as cucumber or tomato, bananas, cake slices, buns, and cookies are all common choices.


title: Party

text: Formal receptions are parties that are designed to receive a large number of guests, often at prestigious venues such as Buckingham Palace, the White House, or Government Houses of the British Empire and Commonwealth. The hosts and any guests of honor form a receiving line in order of precedence near the entrance. Each guest is announced to the host who greets each one in turn as he or she arrives. Each guest properly speaks little more than his name (if necessary) and a conventional greeting or congratulation to each person in the receiving line. In this way, the line of guests progresses steadily without unnecessary delay. After formally receiving each guest in this fashion, the hosts may mingle with the guests.


title: Party

text: Somewhat less formal receptions are common in academic settings, sometimes to honor a guest lecturer, or to celebrate a special occasion such as retirement of a respected member of staff. Receptions are also common in symposium or academic conference settings, as an environment for attendees to mingle and interact informally. These gatherings may be accompanied by a sit-down dinner, or more commonly, a stand-up informal buffet meal.


title: Party

text: Receptions are also held to celebrate exhibition openings at art galleries or museums. The featured artist or artists are often present, as well as the curators who organized the exhibition. In addition or instead, a celebratory reception may be held partway through or at the end of an exhibition run. This alternative scheduling allows guests more time to see the exhibition in depth at their own pace, before meeting the featured guests. Some food is often served, as in academic gatherings.


title: Party

text: Refreshments at a reception may be as minimal, such as coffee or lemonade, or as elaborate as those at a state dinner.


title: Party

text: In the 18th century, in France and England, it became fashionable for wealthy, well married ladies who had a residence "in town" to invite accomplished guests to visit their home in the evening, to partake of refreshments and cultural conversation. Soirées often included refined musical entertainment, and the term is still sometimes used to define a certain sophisticated type of evening party.


title: Party

text: Society hostesses included actresses or other women with a larger-than-life reputation. The character of the hostess obviously determined the character of the soirée and the choice of guests.


title: Party

text: A dance is a social gathering at which the guests dance. It may be a casual, informal affair, or a structured event, such as a school dance or a charity ball. Dances usually take place during the evening. An afternoon dance is formally known as a tea dance. Some dances feature specific kinds of dancing, such as square dancing.


title: Party

text: A ball is a large formal party that features ballroom dancing. Women guests wear ball gowns; men wear evening dress.


title: Party

text: A block party is a public party that is attended by the residents of a specific city block or neighborhood. These parties are typically held in a city street that has been closed to traffic to accommodate the party. At some block parties, attendees are free to pass from house to house, socializing, and often drinking alcoholic beverages.


title: Party

text: At a masquerade ball, guests wear masks to conceal their identities. Guests at a costume party or a fancy dress party wear costumes. These parties are sometimes associated with holiday events, such as Halloween and Mardi Gras.


title: Party

text: In English and American culture during the Christmas season, it is traditional to have a Christmas caroling party. People go from door to door in a neighborhood and sing Christmas carols. Some popular Christmas carols are "We Wish You a Merry Christmas", "Deck the Halls", "The Twelve Days of Christmas", "Frosty the Snowman", "Jingle Bells", "Silver Bells", "Santa Claus Is Coming to Town", and "O Holy Night".


title: Party

text: In Spain, this type of party is called "El Aguinaldo". It is the same as in England and the United States, but the only difference is that the children who sing the carols are given tips. Christmas songs are called "villancicos" in Spain; they are mainly sung by children at small parties.


title: Party

text: Dance parties are gatherings in bars or community centers where the guests dance to house music, techno music, or disco. The music for dance parties is usually selected and played by a disc jockey.


title: Party

text: A spin-off of dance parties, the rave involves dancing to loud house music, techno music, or industrial music. Rave parties may be attended by as few as a score of people in a basement or, more likely, by a few hundred people in a club, to as many as thousands in a large warehouse, field, or even tens of thousands in a sporting arena, amusement park, or other large space. Raves are associated with illegal drugs such as ecstasy and psychedelic drugs.


title: Party

text: A house party is a party where a large group of people get together at a private home to socialize. House parties that involve the drinking of beer pumped from a keg are called keg parties or "keggers." These parties are popular in North America, the United Kingdom, and Australia and are often attended by people under the legal drinking age. Sometimes, even older party-goers run afoul of the law for having provided alcoholic beverages to minors. Arrests may also be made for violating a noise ordinance, for disorderly conduct, and even for operating a "blind pig", an establishment that illegally sells alcoholic beverages.


title: Party

text: Outdoor parties include bush parties and beach parties. Bush parties (also called "field parties") are held in a secluded area of a forest ("bush"), where friends gather to drink and talk. These parties are often held around a bonfire. Beach parties are held on a sandy shoreline of a lake, river, or sea, and also often feature a bonfire.


title: Party

text: School-related parties for teenagers and young adults include proms and graduation parties, which are held in honor of someone who has recently graduated from a school or university.


title: Party

text: A singles dance party and mixer is a party which is organized for people who are not married and who want to find a partner for friendship, dating, or sex.


title: Party

text: Usually a "mixer game" is played, to make it easy for people to meet each other. For example, each guest may be given a card with an inspiring quotation on it. The game is to find a potential partner who has the same quotation. Couples who have matching cards may be given a small prize.


title: Party

text: A fundraising party, or fundraiser, is a party that is held for the purpose of collecting money that will be given to some person or to some institution, such as a school, charity, business, or political campaign. These parties are usually formal and consist of a dinner followed by speeches or by a presentation extolling whatever the money is being raised for.


title: Party

text: It is very common to charge an admission fee for parties of this kind. This fee may be as high as several thousand dollars, especially if money is being raised for a political campaign.


title: Party

text: In some places, parties to celebrate graduation from school, college, or university are popular. A graduation party may be held on campus or external, and transportation is provided when location is far away.


title: Party

text: A shower is a party whose primary purpose is to give gifts to the guest of honor. Traditionally, a bridal shower is a way for an engaged woman to be "showered" with gifts for her upcoming married life (see hope chest). Guests are expected to bring a small gift related to the upcoming life event. Themed games are a frequent sight at this sort of party. A new twist on the baby shower for a pregnant woman is the gender reveal party, made possible by modern ultrasound technology.


title: Party

text: A housewarming party may be held when a family, couple, or person moves into a new house or apartment. It is an occasion for the hosts to show their new home to their friends. Housewarming parties are typically informal and do not include any planned activities other than a tour of the new house or apartment. Invited family members and friends may bring gifts for the new home.


title: Party

text: A welcome party is held for the purpose of welcoming a newcomer, such as a new club member, a new employee, or a family's new baby.


title: Party

text: In many cultures, it is customary to throw a farewell party in honor of someone who is moving away or departing on a long trip (sometimes called a "bon voyage" party). Retirement parties for departing co-workers fall into this category. Several are described in Japan in Shusaku Endo's 1974 novel "When I Whistle".


title: Party

text: A cast party is a celebration following the final performance of a theatrical event, such as a play, a musical, or an opera. A party of this kind may also be held following the end of shooting for a motion picture (called a "wrap party") or after the season's final episode of a television series. Cast parties are traditionally held for most theater performances, both professional and amateur.


title: Party

text: Invited guests are usually restricted to performers, crew members, and a few others who did not participate in the performance, such as sponsors and donors who have helped fund the production.


title: Party

text: A pre-party is a party that is held immediately before a school dance, a wedding, a birthday party, and a bar mitzvah. These parties are usually of short duration and sometimes involve getting ready for the event (e.g., the guests may put on makeup or costumes). Guests usually leave at the same time and arrive at the event together. Often people engage in pregaming or drinking before an event or a night out, especially if the event lacks access to alcohol.


title: Party

text: An after-party is a party that is held after a wedding, school dance, or other more formal event. Guests are usually limited to friends of the host.


title: 2021–22 2. Bundesliga

text: The 2021–22 2. Bundesliga was the 48th season of the 2. Bundesliga. It began on 23 July 2021 and concluded on 15 May 2022.


title: Laplace's equation

text: In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as


title: Laplace's equation

text: where formula_3 is the Laplace operator, formula_4 is the divergence operator (also symbolized "div"), formula_5 is the gradient operator (also symbolized "grad"), and formula_6 is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function.


title: Laplace's equation

text: This is called Poisson's equation, a generalization of Laplace's equation. Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations. Laplace's equation is also a special case of the Helmholtz equation.


title: Laplace's equation

text: The general theory of solutions to Laplace's equation is known as potential theory. The twice continuously differentiable solutions of Laplace's equation are the harmonic functions, which are important in multiple branches of physics, notably electrostatics, gravitation, and fluid dynamics. In the study of heat conduction, the Laplace equation is the steady-state heat equation. In general, Laplace's equation describes situations of equilibrium, or those that do not depend explicitly on time.


title: Laplace's equation

text: where is the Euclidean metric tensor relative to the new coordinates and denotes its Christoffel symbols.


title: Laplace's equation

text: The Dirichlet problem for Laplace's equation consists of finding a solution on some domain such that on the boundary of is equal to some given function. Since the Laplace operator appears in the heat equation, one physical interpretation of this problem is as follows: fix the temperature on the boundary of the domain according to the given specification of the boundary condition. Allow heat to flow until a stationary state is reached in which the temperature at each point on the domain doesn't change anymore. The temperature distribution in the interior will then be given by the solution to the corresponding Dirichlet problem.


title: Laplace's equation

text: The Neumann boundary conditions for Laplace's equation specify not the function itself on the boundary of but its normal derivative. Physically, this corresponds to the construction of a potential for a vector field whose effect is known at the boundary of alone. For the example of the heat equation it amounts to prescribing the heat flux through the boundary. In particular, at an adiabatic boundary, the normal derivative of is zero.


title: Laplace's equation

text: Solutions of Laplace's equation are called harmonic functions; they are all analytic within the domain where the equation is satisfied. If any two functions are solutions to Laplace's equation (or any linear homogeneous differential equation), their sum (or any linear combination) is also a solution. This property, called the principle of superposition, is very useful. For example, solutions to complex problems can be constructed by summing simple solutions.


title: Laplace's equation

text: The real and imaginary parts of a complex analytic function both satisfy the Laplace equation. That is, if , and if


title: Laplace's equation

text: then the necessary condition that be analytic is that and be differentiable and that the Cauchy–Riemann equations be satisfied:


title: Laplace's equation

text: Therefore satisfies the Laplace equation. A similar calculation shows that also satisfies the Laplace equation.


title: Laplace's equation

text: Conversely, given a harmonic function, it is the real part of an analytic function, (at least locally). If a trial form is


title: Laplace's equation

text: and thus may be defined by a line integral. The integrability condition and Stokes' theorem implies that the value of the line integral connecting two points is independent of the path. The resulting pair of solutions of the Laplace equation are called conjugate harmonic functions. This construction is only valid locally, or provided that the path does not loop around a singularity. For example, if and are polar coordinates and


title: Laplace's equation

text: The close connection between the Laplace equation and analytic functions implies that any solution of the Laplace equation has derivatives of all orders, and can be expanded in a power series, at least inside a circle that does not enclose a singularity. This is in sharp contrast to solutions of the wave equation, which generally have less regularity.


title: Laplace's equation

text: There is an intimate connection between power series and Fourier series. If we expand a function in a power series inside a circle of radius , this means that


title: Laplace's equation

text: which is a Fourier series for . These trigonometric functions can themselves be expanded, using multiple angle formulae.


title: Laplace's equation

text: Let the quantities and be the horizontal and vertical components of the velocity field of a steady incompressible, irrotational flow in two dimensions. The continuity condition for an incompressible flow is that


title: Laplace's equation

text: then the continuity condition is the integrability condition for this differential: the resulting function is called the stream function because it is constant along flow lines. The first derivatives of are given by


title: Laplace's equation

text: and the irrotationality condition implies that satisfies the Laplace equation. The harmonic function that is conjugate to is called the velocity potential. The Cauchy–Riemann equations imply that


title: Laplace's equation

text: Thus every analytic function corresponds to a steady incompressible, irrotational, inviscid fluid flow in the plane. The real part is the velocity potential, and the imaginary part is the stream function.


title: Laplace's equation

text: According to Maxwell's equations, an electric field in two space dimensions that is independent of time satisfies


title: Laplace's equation

text: where is the charge density. The first Maxwell equation is the integrability condition for the differential


title: Laplace's equation

text: which is the Poisson equation. The Laplace equation can be used in three-dimensional problems in electrostatics and fluid flow just as in two dimensions.


title: Laplace's equation

text: where the Dirac delta function denotes a unit source concentrated at the point . No function has this property: in fact it is a distribution rather than a function; but it can be thought of as a limit of functions whose integrals over space are unity, and whose support (the region where the function is non-zero) shrinks to a point (see weak solution). It is common to take a different sign convention for this equation than one typically does when defining fundamental solutions. This choice of sign is often convenient to work with because −Δ is a positive operator. The definition of the fundamental solution thus implies that, if the Laplacian of is integrated over any volume that encloses the source point, then


title: Laplace's equation

text: The Laplace equation is unchanged under a rotation of coordinates, and hence we can expect that a fundamental solution may be obtained among solutions that only depend upon the distance from the source point. If we choose the volume to be a ball of radius around the source point, then Gauss' divergence theorem implies that


title: Laplace's equation

text: Note that, with the opposite sign convention (used in physics), this is the potential generated by a point particle, for an inverse-square law force, arising in the solution of Poisson equation. A similar argument shows that in two dimensions


title: Laplace's equation

text: where denotes the natural logarithm. Note that, with the opposite sign convention, this is the potential generated by a pointlike sink (see point particle), which is the solution of the Euler equations in two-dimensional incompressible flow.


title: Laplace's equation

text: A Green's function is a fundamental solution that also satisfies a suitable condition on the boundary of a volume . For instance,


title: Laplace's equation

text: and assumes the boundary values on , then we may apply Green's identity, (a consequence of the divergence theorem) which states that


title: Laplace's equation

text: The notations "u" and "G" denote normal derivatives on . In view of the conditions satisfied by and , this result simplifies to


title: Laplace's equation

text: Thus the Green's function describes the influence at of the data and . For the case of the interior of a sphere of radius , the Green's function may be obtained by means of a reflection : the source point at distance from the center of the sphere is reflected along its radial line to a point "P"' that is at a distance


title: Laplace's equation

text: Note that if is inside the sphere, then "P′" will be outside the sphere. The Green's function is then given by


title: Laplace's equation

text: where denotes the distance to the source point and denotes the distance to the reflected point "P"′. A consequence of this expression for the Green's function is the Poisson integral formula. Let , , and be spherical coordinates for the source point . Here denotes the angle with the vertical axis, which is contrary to the usual American mathematical notation, but agrees with standard European and physical practice. Then the solution of the Laplace equation with Dirichlet boundary values inside the sphere is given by


title: Laplace's equation

text: is the cosine of the angle between and . A simple consequence of this formula is that if is a harmonic function, then the value of at the center of the sphere is the mean value of its values on the sphere. This mean value property immediately implies that a non-constant harmonic function cannot assume its maximum value at an interior point.


title: Laplace's equation

text: Consider the problem of finding solutions of the form . By separation of variables, two differential equations result by imposing Laplace's equation:


title: Laplace's equation

text: The second equation can be simplified under the assumption that has the form . Applying separation of variables again to the second equation gives way to the pair of differential equations


title: Laplace's equation

text: for some number . A priori, is a complex constant, but because must be a periodic function whose period evenly divides , is necessarily an integer and is a linear combination of the complex exponentials . The solution function is regular at the poles of the sphere, where . Imposing this regularity in the solution of the second equation at the boundary points of the domain is a Sturm–Liouville problem that forces the parameter to be of the form for some non-negative integer with ; this is also explained below in terms of the orbital angular momentum. Furthermore, a change of variables transforms this equation into the Legendre equation, whose solution is a multiple of the associated Legendre polynomial . Finally, the equation for has solutions of the form ; requiring the solution to be regular throughout forces .


title: Laplace's equation

text: Here the solution was assumed to have the special form . For a given value of , there are independent solutions of this form, one for each integer with . These angular solutions are a product of trigonometric functions, here represented as a complex exponential, and associated Legendre polynomials:


title: Laplace's equation

text: Here is called a spherical harmonic function of degree and order , is an associated Legendre polynomial, is a normalization constant, and and represent colatitude and longitude, respectively. In particular, the colatitude , or polar angle, ranges from at the North Pole, to at the Equator, to at the South Pole, and the longitude , or azimuth, may assume all values with . For a fixed integer , every solution of the eigenvalue problem


title: Laplace's equation

text: is a linear combination of . In fact, for any such solution, is the expression in spherical coordinates of a homogeneous polynomial that is harmonic (see below), and so counting dimensions shows that there are linearly independent such polynomials.


title: Laplace's equation

text: The general solution to Laplace's equation in a ball centered at the origin is a linear combination of the spherical harmonic functions multiplied by the appropriate scale factor ,


title: Laplace's equation

text: where the are constants and the factors are known as solid harmonics. Such an expansion is valid in the ball


title: Laplace's equation

text: For formula_63, the solid harmonics with negative powers of formula_64 are chosen instead. In that case, one needs to expand the solution of known regions in Laurent series (about formula_65), instead of Taylor series (about formula_66), to match the terms and find formula_67.


title: Laplace's equation

text: Let formula_68 be the electric field, formula_69 be the electric charge density, and formula_70 be the permittivity of free space. Then Gauss's law for electricity (Maxwell's first equation) in differential form states


title: Laplace's equation

text: Now, the electric field can be expressed as the negative gradient of the electric potential formula_72,


title: Laplace's equation

text: if the field is irrotational, formula_74. The irrotationality of formula_68 is also known as the electrostatic condition.