title: Hydroxide

text: In the higher oxidation states of the pnictogens, chalcogens, halogens, and noble gases there are oxoacids in which the central atom is attached to oxide ions and hydroxide ions. Examples include phosphoric acid HPO, and sulfuric acid HSO. In these compounds one or more hydroxide groups can dissociate with the liberation of hydrogen cations as in a standard Brønsted–Lowry acid. Many oxoacids of sulfur are known and all feature OH groups that can dissociate.


title: Hydroxide

text: Telluric acid is often written with the formula HTeO·2HO but is better described structurally as Te(OH).


title: Hydroxide

text: "Ortho"-periodic acid can lose all its protons, eventually forming the periodate ion [IO]. It can also be protonated in strongly acidic conditions to give the octahedral ion [I(OH)], completing the isoelectronic series, [E(OH)], E = Sn, Sb, Te, I; "z" = −2, −1, 0, +1. Other acids of iodine(VII) that contain hydroxide groups are known, in particular in salts such as the "meso"periodate ion that occurs in K[IO(OH)]·8HO.


title: Hydroxide

text: As is common outside of the alkali metals, hydroxides of the elements in lower oxidation states are complicated. For example, phosphorous acid HPO predominantly has the structure OP(H)(OH), in equilibrium with a small amount of P(OH).


title: Hydroxide

text: The oxoacids of chlorine, bromine, and iodine have the formula OA(OH), where "n" is the oxidation number: +1, +3, +5, or +7, and A = Cl, Br, or I. The only oxoacid of fluorine is F(OH), hypofluorous acid. When these acids are neutralized the hydrogen atom is removed from the hydroxide group.


title: Hydroxide

text: The hydroxides of the transition metals and post-transition metals usually have the metal in the +2 (M = Mn, Fe, Co, Ni, Cu, Zn) or +3 (M = Fe, Ru, Rh, Ir) oxidation state. None are soluble in water, and many are poorly defined. One complicating feature of the hydroxides is their tendency to undergo further condensation to the oxides, a process called olation. Hydroxides of metals in the +1 oxidation state are also poorly defined or unstable. For example, silver hydroxide Ag(OH) decomposes spontaneously to the oxide (AgO). Copper(I) and gold(I) hydroxides are also unstable, although stable adducts of CuOH and AuOH are known. The polymeric compounds M(OH) and M(OH) are in general prepared by increasing the pH of an aqueous solutions of the corresponding metal cations until the hydroxide precipitates out of solution. On the converse, the hydroxides dissolve in acidic solution. Zinc hydroxide Zn(OH) is amphoteric, forming the tetrahydroxidozincate ion in strongly alkaline solution.


title: Hydroxide

text: Numerous mixed ligand complexes of these metals with the hydroxide ion exist. In fact, these are in general better defined than the simpler derivatives. Many can be made by deprotonation of the corresponding metal aquo complex.


title: Hydroxide

text: Vanadic acid HVO shows similarities with phosphoric acid HPO though it has a much more complex vanadate oxoanion chemistry. Chromic acid HCrO, has similarities with sulfuric acid HSO; for example, both form acid salts A[HMO]. Some metals, e.g. V, Cr, Nb, Ta, Mo, W, tend to exist in high oxidation states. Rather than forming hydroxides in aqueous solution, they convert to oxo clusters by the process of olation, forming polyoxometalates.


title: Hydroxide

text: In some cases, the products of partial hydrolysis of metal ion, described above, can be found in crystalline compounds. A striking example is found with zirconium(IV). Because of the high oxidation state, salts of Zr are extensively hydrolyzed in water even at low pH. The compound originally formulated as ZrOCl·8HO was found to be the chloride salt of a tetrameric cation [Zr(OH)(HO)] in which there is a square of Zr ions with two hydroxide groups bridging between Zr atoms on each side of the square and with four water molecules attached to each Zr atom.


title: Hydroxide

text: The mineral malachite is a typical example of a basic carbonate. The formula, CuCO(OH) shows that it is halfway between copper carbonate and copper hydroxide. Indeed, in the past the formula was written as CuCO·Cu(OH). The crystal structure is made up of copper, carbonate and hydroxide ions. The mineral atacamite is an example of a basic chloride. It has the formula, CuCl(OH). In this case the composition is nearer to that of the hydroxide than that of the chloride CuCl·3Cu(OH). Copper forms hydroxyphosphate (libethenite), arsenate (olivenite), sulfate (brochantite), and nitrate compounds. White lead is a basic lead carbonate, (PbCO)·Pb(OH), which has been used as a white pigment because of its opaque quality, though its use is now restricted because it can be a source for lead poisoning.


title: Hydroxide

text: The hydroxide ion appears to rotate freely in crystals of the heavier alkali metal hydroxides at higher temperatures so as to present itself as a spherical ion, with an effective ionic radius of about 153 pm. Thus, the high-temperature forms of KOH and NaOH have the sodium chloride structure, which gradually freezes in a monoclinically distorted sodium chloride structure at temperatures below about 300 °C. The OH groups still rotate even at room temperature around their symmetry axes and, therefore, cannot be detected by X-ray diffraction. The room-temperature form of NaOH has the thallium iodide structure. LiOH, however, has a layered structure, made up of tetrahedral Li(OH) and (OH)Li units. This is consistent with the weakly basic character of LiOH in solution, indicating that the Li–OH bond has much covalent character.


title: Hydroxide

text: The hydroxide ion displays cylindrical symmetry in hydroxides of divalent metals Ca, Cd, Mn, Fe, and Co. For example, magnesium hydroxide Mg(OH) (brucite) crystallizes with the cadmium iodide layer structure, with a kind of close-packing of magnesium and hydroxide ions.


title: Hydroxide

text: The amphoteric hydroxide Al(OH) has four major crystalline forms: gibbsite (most stable), bayerite, nordstrandite, and doyleite.


title: Hydroxide

text: All these polymorphs are built up of double layers of hydroxide ions – the aluminium atoms on two-thirds of the octahedral holes between the two layers – and differ only in the stacking sequence of the layers. The structures are similar to the brucite structure. However, whereas the brucite structure can be described as a close-packed structure in gibbsite the OH groups on the underside of one layer rest on the groups of the layer below. This arrangement led to the suggestion that there are directional bonds between OH groups in adjacent layers. This is an unusual form of hydrogen bonding since the two hydroxide ion involved would be expected to point away from each other. The hydrogen atoms have been located by neutron diffraction experiments on α-AlO(OH) (diaspore). The O–H–O distance is very short, at 265 pm; the hydrogen is not equidistant between the oxygen atoms and the short OH bond makes an angle of 12° with the O–O line. A similar type of hydrogen bond has been proposed for other amphoteric hydroxides, including Be(OH), Zn(OH), and Fe(OH).


title: Hydroxide

text: A number of mixed hydroxides are known with stoichiometry AM(OH), AM(OH), and AM(OH). As the formula suggests these substances contain M(OH) octahedral structural units. Layered double hydroxides may be represented by the formula . Most commonly, "z" = 2, and M = Ca, Mg, Mn, Fe, Co, Ni, Cu, or Zn; hence "q" = "x".


title: Hydroxide

text: The hydroxide ion may act as a base catalyst. The base abstracts a proton from a weak acid to give an intermediate that goes on to react with another reagent. Common substrates for proton abstraction are alcohols, phenols, amines, and carbon acids. The p"K" value for dissociation of a C–H bond is extremely high, but the pK alpha hydrogens of a carbonyl compound are about 3 log units lower. Typical p"K" values are 16.7 for acetaldehyde and 19 for acetone. Dissociation can occur in the presence of a suitable base.


title: Hydroxide

text: The base should have a p"K" value not less than about 4 log units smaller, or the equilibrium will lie almost completely to the left.


title: Hydroxide

text: The hydroxide ion by itself is not a strong enough base, but it can be converted in one by adding sodium hydroxide to ethanol


title: Hydroxide

text: to produce the ethoxide ion. The pK for self-dissociation of ethanol is about 16, so the alkoxide ion is a strong enough base. The addition of an alcohol to an aldehyde to form a hemiacetal is an example of a reaction that can be catalyzed by the presence of hydroxide. Hydroxide can also act as a Lewis-base catalyst.


title: Hydroxide

text: The hydroxide ion is intermediate in nucleophilicity between the fluoride ion F, and the amide ion . The hydrolysis of an ester


title: Hydroxide

text: also known as saponification is an example of a nucleophilic acyl substitution with the hydroxide ion acting as a nucleophile. In this case the leaving group is an alkoxide ion, which immediately removes a proton from a water molecule to form an alcohol. In the manufacture of soap, sodium chloride is added to salt out the sodium salt of the carboxylic acid; this is an example of the application of the common ion effect.


title: Hydroxide

text: Other cases where hydroxide can act as a nucleophilic reagent are amide hydrolysis, the Cannizzaro reaction, nucleophilic aliphatic substitution, nucleophilic aromatic substitution, and in elimination reactions. The reaction medium for KOH and NaOH is usually water but with a phase-transfer catalyst the hydroxide anion can be shuttled into an organic solvent as well, for example in the generation of the reactive intermediate dichlorocarbene.


title: Nicole Randall Johnson

text: Nicole Randall Johnson (born December 9, 1973) is an American actress, writer and producer. Johnson is most notable for her membership in the recurring cast of performers on the sketch comedy series "MADtv".


title: Nicole Randall Johnson

text: Johnson was born in Los Angeles, California. When she turned seven, Johnson's family left LA and she split the rest of her time growing up in Phoenix, Arizona, and later, Portland, Oregon. She attended the University of Arizona, where she majored in theatre. While pursuing her degree, she performed in a number of dramatic plays and was a member of the school's sketch and improv group, Comedy Corner.


title: Nicole Randall Johnson

text: After college, Johnson moved back to Los Angeles and began studying at The Groundlings School and Theatre, whose alumni include fellow "MADtv" cast members Phil LaMarr, Michael McDonald and Daniele Gaither. There she became a member of the Sunday Company, where she wrote and performed for a year before becoming a Series Regular on the acclaimed Bravo comedy series, "Significant Others".


title: Nicole Randall Johnson

text: Johnson has had recurring roles on "Key & Peele", "Reno 911!" and "Andy Barker, P.I.". A few of her other television credits include guest-starring roles on "Single Parents", "Prime Suspect", "Weeds", "Curb Your Enthusiasm", "Monk", "", "The Shield", "Hannah Montana" and "Hot in Cleveland".


title: Nicole Randall Johnson

text: Johnson had supporting roles in such films as "Murder Mystery", "Role Models, The 40 Year Old Virgin, Transformers" and "In Her Shoes".


title: Nicole Randall Johnson

text: Johnson joined the cast of "MADtv" in 2005 as a feature performer and writer in the show's eleventh season. She became the third black female cast member in the show's history (Debra Wilson and Daniele Gaither were the first two respectively). She was promoted to repertory status for the show's twelfth season. Frequently recurring characters include Ka-Son and Darell, while her impersonations include Condoleezza Rice, Oprah Winfrey, Queen Latifah and Randy Jackson.


title: Squad

text: In military terminology, a squad is among the smallest of military organizations and is led by a non-commissioned officer. NATO and US doctrine define a squad as an organization "larger than a team, but smaller than a section." while US Army doctrine further defines a squad as a "small military unit typically containing two or more fire teams." In US usage, a squad consists of eight to fourteen soldiers, and may be further subdivided into fireteams.


title: Squad

text: The standard NATO symbol for a "squad" consists of one single dot (●) placed above a framed unit icon.


title: Squad

text: Historically, a "squad" in the US Army was a sub-unit of a section, consisting of from as few as two soldiers to as many as 12 and was originally used primarily for drill and administrative purposes (e.g., billeting, messing, working parties, etc.). The smallest tactical sub-unit being the section, which was also known as a half-platoon (the platoon itself being a half company).


title: Squad

text: Depending upon the time period, the squad "leader" (not an official position title until 1891) could be a sergeant (the sergeant, in sections with only one corporal, led the section's first squad, while the lone corporal served as assistant section leader and led the section's second squad), a corporal (in sections with two corporals), a lance corporal (a rank the Army had in varying numbers and conditions from at least 1821 until 1920), a private first class (PFC) (the rank existing since 1846 but not earning its one chevron – taken from the abolished lance corporal rank – until 1920). or even a "senior" private (there being many long-service, or "professional," privates until the post-WWII era).


title: Squad

text: In 1891, the US Army officially defined a rifle "squad" as consisting of "seven privates and one corporal." The US Army employed the eight-man rifle squad through WWI and until the late 1930s under the Square Division organizational plan, in which sergeants continued to lead sections consisting of two squads.


title: Squad

text: Under the Triangular Division organization plan in 1939 rifle squads were no longer organized into sections. Instead, the squads were reorganized into a 12-man unit of three elements, or teams, Able, Baker, and Charlie, reporting directly to the platoon commander (an officer, usually a second lieutenant), assisted by a sergeant assigned as the "assistant to platoon commander" (re-designated as "platoon leader" in 1940 and as "platoon sergeant" in 1943 with the officer then re-designated as "platoon leader".) The squad leader was still only a corporal but the squad was also assigned a PFC (one of the scout riflemen) as the assistant to the squad leader. This soldier could serve as either the squad leader's messenger to the platoon commander or could be used to relay orders to other squad elements, as needed. While not a noncommissioned officer (NCO) the PFC was an experienced soldier, as prior to WWII the majority of enlisted men remained privates for the entire term of their enlistment since promotion opportunity was scarce. However, the obvious command (viz., leadership and supervision) weakness of so large a squad under one NCO rapidly became obvious in light of the pre-war mobilization and was corrected in 1940 when a second NCO was added to the squad.


title: Squad

text: This adjustment raised the squad leader to a sergeant (grade 4) and the assistant squad leader to a corporal (grade 5). The "platoon leader" (with the officer still being the "platoon commander") now became a staff sergeant, (grade 3). (In 1920 the enlisted rank structure was simplified and seven grades were established ranging from master sergeant as grade 1 to private as grade 7; staff sergeant being one of the new rank titles then established by combining several intermediate sergeant grades ranking above section leaders but below the company first sergeant.) This squad organization included two men serving as “scout (rifleman),” who along with the squad leader, formed the security element (i.e., reconnaissance and overwatch actions), designated as “Able.” The second element was a three-man Browning Automatic Rifle (BAR) team consisting of an automatic rifleman, an assistant automatic rifleman and an ammunition bearer. This element formed the “base of fire” (viz., fire support in providing suppressive fires in the attack and protective fires in the defense) and was designated as “Baker.” Lastly, there were five riflemen and the assistant squad leader, who formed the “maneuver element” (e.g., flanking and assault movements in the attack and repelling and reinforcing actions in the defense), designated as “Charlie.”


title: Squad

text: In 1942, the Army had a massive restructuring of its Tables of Organization & Equipment (TO&Es) and increased the rank of the squad leader and assistant squad leader to staff sergeant and sergeant, respectively. (Platoon leaders now became technical sergeants, as grade 2, and first sergeants became equal in pay grade to master sergeants as grade 1.) The BAR man (automatic rifleman) and the senior rifleman of the Charlie element became corporals (grade 5) and de facto team leaders, even though not officially designated as such. (In 1943 NCO platoon leaders were re-designated as platoon sergeants and officer platoon commanders became platoon leaders.)


title: Squad

text: After WWII, in 1948, the Army decided to "downsize” the rifle squad to a nine-man organization (as well as realign its enlisted grade structure), as post-war analysis had shown that the 12-man squad was too large and unwieldy in combat. The squad leader was again called a sergeant (but retained the grade 3 pay grade and insignia of the rank of a staff sergeant, which was then eliminated.) The two scouts of the Able element were eliminated with the idea that all of the riflemen should be able to perform the scouting duties and would therefore all share in the associated inherent risk of that position. The Baker element's ammunition bearer was also eliminated, leaving the two-man BAR team as the base of fire, supervised by the assistant squad leader (again called a corporal), but remaining as a grade 4, since the rank of sergeant (three chevrons) was then eliminated. (PFC became grade 5, private was grade 6, and recruit was grade 7; PFCs wore one chevron and privates and recruits both wore none.) The five riflemen of the “Charlie” team, now led by the squad leader, remained as the maneuver element.


title: Squad

text: Also, in 1948, the rank title of the platoon sergeant changed from technical sergeant (which was eliminated) to sergeant first class (SFC) (grade 2) and the rank title of first sergeant was again eliminated, being retained only as an occupational title for the senior NCO of a company. In 1951 the pay grades were reversed, with master sergeant becoming E-7 (vice the previous grade 1) and sergeant first class becoming E-6, so that the squad leader became a sergeant (E-5) and the assistant squad leader, a corporal (E-4). (With PFC, PVT, and RCT being E-3, E-2, and E-1, respectively.)


title: Squad

text: In the 1956 the Army began reorganizing into its "Pentomic” plan under the ROCID (Reorganization of Current Infantry Divisions) TO&Es. The rifle squad was reorganized into an eleven-man organization with a sergeant (E-5) as squad leader and two five-man fire teams. Each fire team consisted of a corporal (E-4) team leader, an automatic rifleman, an assistant automatic rifleman, a grenadier, and a scout-rifleman. The assistant squad leader position was eliminated, with the senior fire team leader now filling this role as needed.


title: Squad

text: In 1958, with the addition of the E-8 and E-9 pay grades, the ranks of the squad and fire team leaders changed again, now to staff sergeant (E-6) and sergeant (E-5), respectively. The 1958 restructuring restored the traditional sergeant and staff sergeant rank insignia of three chevrons and three chevrons over an inverted arc, respectively. (Platoon sergeant became a separate rank title, and along with SFC, became E-7; first sergeants and master sergeants became pay grade E-8. Also, the rank of sergeant major was revived as E-9, with a new distinctive rank insignia consisting of the three chevrons and three inverted arcs of a master sergeant/first sergeant but replacing the first sergeant's lozenge with a star.)


title: Squad

text: Under the ROAD (Reorganization Objective Army Divisions) structure in 1963, the rifle squad was reduced to a ten-man organization. This iteration of the rifle squad retained the two fire teams but eliminated the two scouts (one in each fire team), instead providing the squad leader with one extra rifleman, who could be used to reinforce either fire team or assist the squad leader as required. An exception was in mechanized infantry units, where an additional rifleman (increasing the squad to eleven members) was assigned as the driver of the squad's M113 armored personnel carrier. (Also, in 1968, the separate rank title of platoon sergeant was eliminated, leaving SFC as the only E-7 rank.)


title: Squad

text: Currently, US Army rifle squads consist of nine soldiers, organized under a squad leader into two four-man fire teams. The squad leader is a staff sergeant (E-6) and the two fire team leaders are sergeants (E-5). Mechanized infantry and Stryker infantry units are equipped with M2A3 Bradley infantry fighting vehicles and M1126 Stryker infantry carrier vehicles, respectively. Unlike the ROAD era mechanized infantry units, none of the vehicle crewman (M2A3 – three, M1126 – two) are counted as part of the nine-man rifle squad transported by the vehicles. The term squad is also used in infantry crew-served weapons sections (number of members varies by weapon), military police (twelve soldiers including a squad leader divided into four three-man teams, with three team leaders), and combat engineer units.


title: Squad

text: In the United States Marine Corps, a rifle squad is usually composed of three fireteams of four Marines each and a squad leader who is typically a sergeant or corporal, Other types of USMC infantry squads include: machinegun (7.62mm), heavy machinegun (12.7 mm (.50 cal.) and 40mm), LWCMS mortar (60-mm), 81-mm mortar, assault weapon (SMAW), antiarmor (Javelin missile), and anti-tank (TOW missile). These squads range from as few as three Marines (60mm LWCM squad) to as many as eight (Javelin Missile squad), depending upon the weapon system with which the squad is equipped. Squads are also used in reconnaissance, light armored reconnaissance (scout dismounts), combat engineer, law enforcement (i.e., military police), Marine Security Force Regiment (MSFR), and Fleet Antiterrorism Security Team (FAST) companies. On 9 May 2018, it was announced that a USMC squad would be reduced to 12 Marines, with three fire teams of three Marines each with two new positions: an assistant squad leader and a squad systems operator. As of 2020, the structure has been changed to 15 men; assistant automatic riflemen are replaced with grenadiers and a new addition to Marine fireteams, anti mechanized infantry. All M16A4 rifles and M4A1 carbines are to be replaced with the M27 Infantry Automatic Rifle. Depending on the mission, automatic rifleman may use the M249 light machine gun instead of the M27 IAR.


title: Squad

text: In the US Air Force Security Forces, a squad is made up of three fire teams of four members, each led by a senior airman, staff sergeant, or tech sergeant.


title: Squad

text: A squad is a term used in the US Fire and EMS services to describe several types of units and emergency apparatus. Oftentimes, the names "squad" and "rescue squad" are used interchangeably, however the function of the squad is different from department to department. In some departments, a "squad" and a "rescue" are two distinct units. This is the case in New York City, where the FDNY operates eight squad companies. These special "enhanced" engine companies perform both "truck" and "engine" company tasks, as well as hazardous materials (Hazmat) mitigation and other specialty rescue functions. FDNY's five "rescue" companies primarily mitigate technical and heavy rescue incidents, and operate as a pure special rescue unit. Squads and rescues within the FDNY are part of the departments specialty operations command (SOC).


title: Squad

text: In other departments, a squad is a name given to a type of apparatus that delivers EMS and rescue services, and is staffed by firefighter/EMTs or firefighter/paramedics. This type of service delivery is common in the greater Los Angeles area of California, and was made famous in the 1970s show "Emergency!", where the fictional Squad 51 highlighted the lives of two firefighter/paramedics of the LACoFD.


title: Squad

text: In the Soviet Armed Forces a motorised rifle squad was mounted in either a BTR armoured personnel carrier or BMP infantry fighting vehicle, with the former being more numerous by the late 1980s. BTR rifle squads consisted of a squad leader/BTR commander, senior rifleman/assistant squad leader, a machine gunner armed with an RPK-74, a grenadier armed with an RPG-7, a rifleman/assistant grenadier, a rifleman/medic, a rifleman, a BTR driver/mechanic and a BTR machine gunner.


title: Squad

text: BMP rifle squads consisted of a squad leader/BMP commander, assistant squad leader/BMP gunner, a BMP driver/mechanic, a machine gunner armed with an RPK-74, a grenadier armed with an RPG-7, a rifleman/assistant grenadier, a rifleman/medic, a senior rifleman and a rifleman all armed with AKMs or AK-74s. Within a platoon the rifleman in one of the squads was armed with an SVD sniper rifle. In both BTR and BMP squads the vehicle's gunner and driver stayed with the vehicle while the rest of the squad dismounted.


title: Squad

text: The squad (班), or section was the basic unit of the National Revolutionary Army (of the National Government of the Republic of China), and would usually be 14 men strong. An infantry squad from an elite German-trained division would ideally have one light machine gun and 10 rifles, but only one of the three squads in a non-elite Central Army division would have a light machine gun. Furthermore, the regular provincial army divisions often had no machine guns at all.


title: Squad

text: The squad, "grupp", in the Swedish army is organized as follows during offensive missions, according to "Markstridsreglemente 3 Grupp" (Ground combat regulation 3 Squad):


title: Squad

text: During defensive missions, the two soldiers with anti-tank launchers are armed with the "Granatgevär m/48" or "m/86" instead, where one is gunner and the second loader.


title: Squad

text: In accordance with "Brigadreglemente Armén Pansar-/Mekskyttepluton/-grupp 90" (Army Brigade Regulation Armor-/Mechanized Rifle Platoon/Squad 90) from 2002:


title: Squad

text: A Danish mechanized infantry squad (gruppe) consists of 9 privates and a sergent, subdivided into 5 pairs, or “buddies”.


title: Squad

text: A squad is led by a non-commissioned officer known as a Squad Leader. His/her second in command is known as an Assistant Squad Leader. In Britain and in the Commonwealth, these appointments are known as Section Commander and Section 2IC ("second in command"), respectively. In the US military, a squad leader is a non-commissioned officer who leads a squad of typically 9 soldiers (US Army: squad leader and two fireteams of 4 men each) or 13 Marines (US Marine Corps: squad leader and three fireteams of 4 men each) in a rifle squad, or 3 to 8 men in a crew-served weapons squad. In the United States Army the TO&E rank of a rifle squad leader is staff sergeant (E-6, or OR-6) and in the United States Marine Corps the TO rank is sergeant (E-5, or OR-5), though a corporal may also act as a squad leader in the absence of sufficient numbers of sergeants. Squad leaders of crew-served weapons squads range from corporal through staff sergeant, depending upon the branch of service and type of squad. In some armies, notably those of the British Commonwealth, in which the term section is used for units of this size, the NCO in charge, which in the British Army and Royal Marines is normally a Corporal (OR-4), is termed a "section commander".


title: Squad

text: The Canadian Forces Manual of Drill and Ceremonial defines a squad as "a small military formation of less than platoon size which is adopted to teach drill movements. (escouade)".


title: Harold Gould

text: Harold Vernon Goldstein (December 10, 1923 – September 11, 2010), better known as Harold Gould, was an American character actor. He appeared as Martin Morgenstern on the sitcom "Rhoda" (1974–78) and Miles Webber on the sitcom "The Golden Girls" (1989–92). A five-time Emmy Award nominee, Gould acted in film and television for nearly 50 years, appearing in more than 300 television shows, 20 major motion pictures, and over 100 stage plays. He was known for playing elegant, well-dressed men (as in "The Sting"), and he regularly played Jewish characters and grandfather-type figures on television and in film.


title: Harold Gould

text: Gould was born to a Jewish family in Schenectady, New York. He was the son of Louis Goldstein, a postal worker, and Lillian, a homemaker who did part-time work for the state health department. Gould was raised in Colonie, New York, and was valedictorian of his high school class. He enrolled at Albany Teachers College upon graduation (now known as University at Albany, SUNY) and studied to become a social studies or English teacher.


title: Harold Gould

text: After two years in college, Gould enlisted in the United States Army during World War II and saw combat in France in a mortar battalion. He developed trench foot and was sent to England to recover. After convalescence, Gould served in a rail transport unit in France.


title: Harold Gould

text: After the war Gould returned to Albany Teachers College to study drama and graduated with a bachelor's degree in 1947. He performed in summer stock theatre on Cape Cod and then decided to enroll at Cornell University to study drama and speech. Gould earned an M.A. degree in 1948 and a Ph.D. in theatre in 1953 from Cornell and also met his future wife, Lea Vernon.


title: Harold Gould

text: Upon graduation, Gould accepted a position at Randolph-Macon Woman's College in Lynchburg, Virginia, where he spent three years teaching and doing stage work. He made his professional theatre debut in 1955 as Thomas Jefferson in "The Common Glory" in Williamsburg.


title: Harold Gould

text: In 1956, Gould was offered a professorship in the drama department at the University of California, Riverside, which he accepted. He taught there until 1960 when he decided to try professional acting himself. He had difficulty finding acting jobs at first and had to take work as a security guard and as a part-time acting teacher at UCLA.


title: Harold Gould

text: Gould made his film debut in an uncredited role in "Two for the Seesaw" (1962). His first credited role was a small part in "The Coach" (also 1962). That same year he appeared as Prosecutor Tom Finney on the TV western "The Virginian" in the episode titled "The Accomplice." After uncredited appearances in Alfred Hitchcock's "Marnie" (1964) and "The Satan Bug" (1965), Gould gradually found more work with credited roles in "The Yellow Canary" (1964), a Rod Serling film starring Pat Boone, Jack Klugman, and Barbara Eden, "Inside Daisy Clover" (1965), and "Harper" (1966) starring Paul Newman.


title: Harold Gould

text: Gould appeared regularly in television in the 1960s and 1970s, including roles in "Dennis the Menace", "Dr. Kildare", "Hazel", "The Twilight Zone", "The Donna Reed Show", "Get Smart", "Hogan's Heroes", "Gunsmoke", "I Dream Of Jeannie", "The F.B.I.", "The Big Valley", "", "The Man from U.N.C.L.E.", "Cannon", and "Hawaii Five-O" where he made multiple appearances as Honore Vashon, one of that series' most memorable villains. Gould originated the role of Marlo Thomas's father in the 1965 pilot for "That Girl", but the series role was recast with Lew Parker. Gould appeared in "The Long, Hot Summer" and "He & She", two short-lived television series. He also appeared in a pilot later broadcast as a 1972 episode of "Love, American Style" titled "Love and the Happy Days" as Howard Cunningham, the frustrated father of a young man named Richie Cunningham (played by Ron Howard).


title: Harold Gould

text: When ABC turned that episode into a series called "Happy Days", Gould agreed to reprise the role of Howard Cunningham; however, when production of "Happy Days"


title: Harold Gould

text: was delayed, he went abroad to perform in a play. Midway through the play's run, after learning the series was ready to begin shooting, he decided to honor his commitment to the stage production and passed on "Happy Days", which led to the role of Howard Cunningham being recast with Tom Bosley. Gould would later state that a requirement to shave the beard he wore at the time was another factor in his decision to decline the role.


title: Harold Gould

text: Gould had worked steadily in television and film for nearly fifteen years before his career began to gain momentum with his portrayal of Kid Twist in "The Sting" (1973), winner of seven Academy Awards, including Best Picture. He appeared in the Woody Allen film "Love and Death" (1975). He was "Engulf", the villainous head of a conglomerate, in "Silent Movie" (1976), directed by Mel Brooks, and made guest appearances on television shows such as "Petrocelli", "The Love Boat" and "Soap" where he played the hospital roommate of Jody Dallas (Billy Crystal).


title: Harold Gould

text: In 1972, Gould was cast as Martin Morgenstern, the father of Mary's best friend Rhoda, in an episode of "The Mary Tyler Moore Show". He reprised the role the following year and was hired as a regular when "Rhoda" became a spin-off in 1974. Gould appeared in the short-lived 1977 series "The Feather and Father Gang", starring as Harry Danton, a smooth-talking ex-con man, with Stefanie Powers as Toni "Feather" Danton, his daughter and a hard-working, successful lawyer. The show was canceled after 13 episodes, and Gould returned to "Rhoda" for the remainder of its run.


title: Harold Gould

text: Gould also appeared in the miniseries "". In the 1980 NBC miniseries "The Scarlett O'Hara War", he portrayed MGM mogul Louis B. Mayer which gained him an Emmy nomination. He appeared as Chad Lowe's grandfather in "Spencer" and played a Jewish widower wooing the Christian Katharine Hepburn in "Mrs. Delafield Wants to Marry". Other roles included a married man having an affair with another member of his Yiddish-speaking club in an episode of the PBS series "The Sunset Years" and as the owner of a deli grooming two African-American men to inherit his business in "Singer & Sons". Gould received Emmy nominations for his roles in "Rhoda", "Mrs. Delafield Wants to Marry", and "Moviola".


title: Harold Gould

text: Gould played Miles Webber, the steadfast suitor of Rose Nylund (Betty White), on the NBC series "The Golden Girls" (he also played another of Rose's boyfriends, Arnie, in the show's first season). He portrayed the father of a villain called The Prankster on "" and made guest appearances on television series such as "Felicity", "The King of Queens", "Touched by an Angel", and "Judging Amy". Gould's film roles in the 1990s and 2000s include appearances in "Stuart Little", "Patch Adams", "The Master of Disguise", the 2003 remake of "Freaky Friday", "Nobody's Perfect", and "Whisper of the Heart".


title: Harold Gould

text: His stage credits include Broadway theatre plays such as Jules Feiffer's "Grown Ups", Neil Simon's "Fools", Richard Baer's "Mixed Emotions", and Tom Stoppard's "Artist Descending a Staircase". Gould won an Obie Award in 1969 for his work in "The Increased Difficulty of Concentration", written by Václav Havel, and reprised the role for a 1988 PBS version of the play. Gould was an early and longtime (48 years) member of Theatre West, the oldest membership theatre company in Los Angeles. He played Mr. Green in Jeff Baron's "Visiting Mr. Green" at the Pasadena Playhouse.


title: Harold Gould

text: Gould died from prostate cancer on September 11, 2010. He had two sons, Joshua and Lowell, and a daughter, Deborah. He and Lea were married for 60 years.


title: Extended family

text: An extended family is a family that extends beyond the nuclear family of parents and their children to include aunts, uncles, grandparents, cousins or other relatives, all living nearby or in the same household. Particular forms include the stem and joint families.


title: Extended family

text: In some circumstances, the extended family comes to live either with or in place of a member of the immediate family. These families include, in one household or close proximity, relatives in addition to an immediate family. An example would be an elderly parent who moves in with his or her children due to old age. In modern Western cultures dominated by immediate family constructs, the term has come to be used generically to refer to grandparents, uncles, aunts, and cousins, whether they live together within the same household or not. However, it may also refer to a family unit in which several generations live together within a single household. In some cultures, the term is used synonymously with consanguineous family.


title: Extended family

text: A stem family, a kind of extended family, first discussed by Frédéric Le Play, parents will live with one child and his/her spouse, as well as the children of both, while other children will leave the house or remain in it, unmarried. The stem family is sometimes associated with inegalitarian inheritance practices, as in Japan and Korea, but the term has also been used in some contexts to describe a family type where parents live with a married child and his or her spouse and children, but the transfer of land and moveable property is more or less egalitarian, as in the case of traditional Romania, northeastern Thailand or Mesoamerican indigenous peoples. In these cases, the child who cares for the parents usually receives the house in addition to his or her own share of land and moveable property.


title: Extended family

text: In an extended family, parents and their children's families may often live under a single roof. This type of joint family often includes multiple generations in the family. Three to four generations stay together under a single roof. The joint family form a coherent group, follow common culture, have equal rights over property and celebrate all the festivals and functions of the family together. From culture to culture, the variance of the term may have different meanings. With globalization, increasing urbanization people have become more individualistic and consider family secondary.


title: Extended family

text: Often, it has been presumed that extended family groups sharing a single household enjoy specific advantages, such as a greater sense of security and belonging due to sharing a wider pool of members to serve as resources during a crisis, and more role models to help perpetuate desired behavior and cultural values. However, even in cultures in which adults are expected to leave home after marriage to begin their own nuclear-based households, the extended family often forms an important support network offering similar advantages. Particularly in working-class communities, grown children tend to establish their own households within the same general area as their parents, aunts, uncles, and grandparents. These extended family members tend to gather often for family events and to feel responsible for helping and supporting one another, both emotionally and financially.


title: Extended family

text: While contemporary families may be considered more mobile in general than in the past, sociologists find that this has not necessarily resulted in the disintegration of extended family networks. Rather, technological aids such as the Internet and social networking sites such as Facebook are now commonly used to retain contact and maintain these family ties.


title: Extended family

text: Particularly in the case of single-parent households, it can be helpful for extended family members to share a single household in order to share the burden of meeting expenses. On the other hand, sharing a household can present a disadvantage depending on the sizes and number of families involved, particularly when only a few members shoulder most of the responsibility to meet expenses for the family's basic needs.


title: Extended family

text: An estimated 49 million Americans (16.1% of the total population) live in homes comprising three or more generations, up from 42 million in 2000. This situation is similar in Western Europe. Another 34 percent live within a kilometer of their children.


title: Extended family

text: In many cultures, such as in those of Asians,<ref name="Pritchard 2006 https://archive.org/details/practisingmental00prit/page/n125 111"></ref> Middle Easterners, Africans, Indigenous peoples like Native Americans and Pacific Islanders, and Latin Americans and Caribbeans, even for Eastern Europeans and Southern Europeans (Orthodox/Catholic countries), extended families are the basic family unit. That is to say the modern western nuclear family is not the norm. Even in Western Europe, extended families (mostly of the stem type) were also clearly prevalent, England being a rare exception. In Britain and the United States, during the Industrial Revolution (approximately 1750 to 1900), more people lived in extended families than at any time before or since.


title: Extended family

text: It is common for today's world to have older children in nuclear families to reach walking up to driving age ranges before meeting extended family members. Geographical isolation is common for middle-class families who move based on occupational opportunities while family branches "retain [their] basic independence". Some extended families hold family reunions or opportunities for gathering regularly, normally around holiday time frames, to reestablish and integrate a stronger family connection. This allows individual nuclear families to connect with extended family members.


title: Extended family

text: Australian Aborigines are another group for whom the concept of family extends well beyond the nuclear model. Aboriginal immediate families include aunts, uncles and a number of other relatives who would be considered "distant relations" in the context of the nuclear family. Aboriginal families have strict social rules regarding whom they can marry. Their family structure incorporates a shared responsibility for all tasks.


title: Extended family

text: Where families consist of multiple generations living together, the family is usually headed by the elders. More often than not, it consists of grandparents, their sons, and their sons' families in patriarchal and especially patrilineal societies. Extended families make discussions together and solve the problem.


title: Extended family

text: Historically, for generations South Asia had a prevailing tradition of the "joint family system" or "undivided family". The joint family system is an extended family arrangement prevalent throughout the Indian subcontinent, particularly in India, consisting of many generations living in the same home, all bound by the common relationship. A patrilineal joint family consists of an older man and his wife, his sons and unmarried daughters, his sons’ wives and children. The family is headed by a patriarch, usually the oldest male, who makes decisions on economic and social matters on behalf of the entire family. The patriarch's wife generally exerts control over the household, minor religious practices and often wields considerable influence in domestic matters. Family income flows into a common pool, from which resources are drawn to meet the needs of all members, which are regulated by the heads of the family.


title: Extended family

text: In the early stages of the twentieth century, it was not very common to find many families with extended kin in their household, which may have been due to the idea that the young people in these times typically waited to establish themselves and start a household before they married and filled a home. As life expectancy becomes older and programs such as Social Security benefit the elderly, the old are now beginning to live longer than prior generations, which then may lead to generations mixing together. According to results of a study by Pew Research Center in 2010, approximately 50 million (nearly one in six) Americans, including rising numbers of seniors, live in households with at least two adult generations, and often three. It has become an ongoing trend for elderly generations to move in and live with their children, as they can give them support and help with everyday living. The main reasons cited for this shift are an increase in unemployment and slumped housing prices and arrival of new immigrants from Asian and South American countries. According to the U.S. Census Bureau, there were 2.7 million grandparents raising their grandchildren in 2009. The dramatic increase in grandparent-headed households has been attributed to many factors including parental substance abuse. In 2003, the number of U.S. "family groups" where one or more subfamilies live in a household (e.g. a householder's daughter has a child. The mother-child is a subfamily) was 79 million. Two-point-six million of U.S. multigenerational family households in 2000 had a householder, the householder's children, and the householder's grandchildren. That's 65 percent of multigenerational family households in the U.S. So it is twice as common for a grandparent to be the householder than for adult children to bring parents into their home. The increase in the number of multigenerational households has created complex legal issues, such as who in the household has authority to consent to police searches of the family home or private bedrooms.


title: Extended family

text: Besides the legal issues that multigenerational households could create, there are issues that may arise from households where the grandparents are the sole guardians. The Supporting Grandparents Raising Grandchildren Act was signed into law on July 7, 2018 after unanimously passing the U.S. House and Senate. It was first introduced in the Senate on May 10, 2017 by Senators Susan Collins (R-ME) and Bob Casey Jr. (D-PA). Out of this came The Supporting Grandparents Raising Grandchildren Advisory Council which will identify, promote, coordinate, and disseminate to the public information, resources, and the best practices available to help grandparents and other older relatives both meet the needs of the children in their care and maintain their own physical and mental health and emotional well-being.


title: Extended family

text: Mexican society is composed of three-generational units consisting of grandparents, children, and grandchildren. Further close relationships are maintained with the progenitors of these families and are known as kin or "cousins". When one is born, they are born into two extended families, a kinship group of sometimes 70 people. The group traditionally acts as a cohesive unit, pooling resources and influence. The extended family also consists of spouses and siblings. This is in contrast to the two generational American nuclear family.


title: Extended family

text: Some scholars have used the term "grand-family" to describe the close relationship between grandparents, children, and grandchildren in Mexican society. Larissa A. Lomnitz and Marisol Perez-Lizaur, for example, describe the grand-family as "the basic unit of family solidarity in Mexico", where basic family obligations between grandparents, children, and grandchildren include "economic support, participation in family rituals, and social recognition".


title: Extended family

text: The relative economic deprivation of racial and ethnic minorities leads to higher levels of extended family involvement; primarily because blacks and Latinos have less money and education than whites, they are more likely to give and receive help from kin. Having family on which one can rely is very important in times of economic hardship especially if there are children involved. Living in an extended family provides constant care for children and support for other members of the family as well. Analysis of the National Survey of Families and Households suggests there are differences between whites and other ethnic groups because of economic differences among racial groups: blacks and Latinos less often have the economic resources that allow the kind of privatization that the nuclear family entails. Extended kinship, then, is a survival strategy in the face of economic difficulties. Being able to rely on not only two parents but grandparents, aunts, uncles, brothers, and sisters helps to create a support system which in turn brings families closer together. Living in an extended family provides many things that a nuclear family does not.


title: Extended family

text: The number of multigenerational households has been steadily rising because of the economic hardships people are experiencing today. According to the AARP, multigenerational households have increased from 5 million in 2000 to 6.2 million in 2008. "There's no question that with some ethnicities that are growing in America, it is more mainstream and traditional to have multigenerational households. We're going to see that increasing in the general population as well," says AARP's Ginzler. While high unemployment and housing foreclosures of the recession have played a key role in the trend, Pew Research Center exec VP and co-author of its multigenerational household study Paul Taylor said it has been growing over several decades, fueled by demographic and cultural shifts such as the rising number of immigrants and the rising average age of young-adult marriages. The importance of an extended family is one that many people may not realize, but having a support system and many forms of income may help people today because of the difficulties in finding a job and bringing in enough money.


title: Water treatment

text: Water treatment is any process that improves the quality of water to make it appropriate for a specific end-use. The end use may be drinking, industrial water supply, irrigation, river flow maintenance, water recreation or many other uses, including being safely returned to the environment. Water treatment removes contaminants and undesirable components, or reduces their concentration so that the water becomes fit for its desired end-use. This treatment is crucial to human health and allows humans to benefit from both drinking and irrigation use.


title: Water treatment

text: Water is the most crucial compound for life on Earth, and having drinkable water is a key worldwide concern for the twenty-first century. All living things require clean, uncontaminated water as a basic requirement. Water covers more than 71 percent of the earth’s surface, but only around 1% of it is drinkable according to international standards due to various contaminations . Waste water discharge from industries, agricultural pollution, municipal wastewater, environmental and global changes are the main sources of water contamination. Even trace levels of heavy metals, dyes, and microbes are hazardous to human health, aquatic systems, and the environment. According to a United Nations Sustainable Development Group report from 2021, 2.3 billion people now live in water-stressed countries, and 733 million people live in high and critically water-stressed countries.


title: Water treatment

text: To address water scarcity issues, it is becoming increasingly important to recover water from current wastewater or develop alternate water sources for human consumption.


title: Water treatment

text: Domestic and industrial wastewater are the two types of wastewater. Domestic wastewater contains sewage, bacteria, viruses, hazardous and non-toxic organisms, sanitary outputs, rubbish, detergents, and other solid and liquid discharges from non-manufacturing processes.


title: Water treatment

text: Water contamination is primarily caused by the discharge of untreated wastewater from enterprises. The effluent from various enterprises, which contains varying levels of contaminants, is dumped into rivers or other water resources. The wastewater may have a high proportion of organic and inorganic contaminants at the initial discharge. Industries generate wastewater as a result of fabrication processes, processes dealing with paper and pulp, textiles, chemicals, and from various streams such as cooling towers, boilers, and production lines.


title: Water treatment

text: Treatment for drinking water production involves the removal of contaminants and/or inactivation of any potentially harmful microbes from raw water to produce water that is pure enough for human consumption without any short term or long term risk of any adverse health effect. In general terms, the greatest microbial risks are associated with ingestion of water that is contaminated with human or animal (including bird) faeces. Faeces can be a source of pathogenic bacteria, viruses, protozoa and helminths. The removal or destruction of microbial pathogens is essential, and commonly involves the use of reactive chemical agents such as suspended solids, to remove bacteria, algae, viruses, fungi, and minerals including iron and manganese. Research including Professor Linda Lawton's group at Robert Gordon University, Aberdeen is working to improve detection of cyanobacteria. These substances continue to cause great harm to several less developed countries who do not have access to effective water purification systems.


title: Water treatment

text: Measures taken to ensure water quality not only relate to the treatment of the water, but to its conveyance and distribution after treatment. It is therefore common practice to keep residual disinfectants in the treated water to kill bacteriological contamination during distribution and to keep the pipes clean.


title: Water treatment

text: Water supplied to domestic properties such as for tap water or other uses, may be further treated before use, often using an in-line treatment process. Such treatments can include water softening or ion exchange. Many proprietary systems also claim to remove residual disinfectants and heavy metal ions.


title: Water treatment

text: Heavy metals in wastewater have become a serious environmental issue in recent years, owing to the high damage they pose to ecosystems and human health even at extremely low concentrations. Heavy metal pollution is a substantial environmental burden due to its flexibility, accumulation, non-biodegradability, and persistence. Its effluent is discharged into the environment by industries such as paper, Insecticides, tanneries, metal plating, mining operations, and so on. This effluent is non-biodegradable and poisonous or damaging to human physiology and other biological systems.


title: Water treatment

text: Organic and inorganic pollutants are two types of pollutants found in wastewater, each with a different spectrum of dangerous values.


title: Water treatment

text: In the treatment of organic pollutants, biological, physical, and chemical methods are commonly used. However, these approaches are ineffective against inorganic pollutants such as heavy metals. Heavy metal decomposition is a serious concern due to properties such as solubility, oxidation-reduction characteristics, and complex formation. Heavy metal is defined as an element with an atomic weight of between 63.5 and 200.6 and a specific gravity larger than 5.0.


title: Water treatment

text: Heavy metals in open waters cause aquatic life to perish, oxygen deficiency, and algae blooms. When heavy metals are discharged into rivers, they are transformed into hydrated ions, which are far more hazardous than metal atoms. The enzymatical processes is disrupted by these hydrated ions, and absorption is accelerated. As a result, heavy metals must be removed in order to reduce public risk.


title: Water treatment

text: Elimination of hazardous chemicals from the water, many treatment procedures have been applied. The selection of wastewater treatment systems is contingent on a number of factors: (1)The degree to which a method is necessary to raise the waste water quality to a permissible level; (2) The control method's flexibility; (3) The process's cost; and (4) The process's environmental compatibility.


title: Water treatment

text: The processes involved in removing the contaminants include physical processes such as settling and filtration, chemical processes such as disinfection and coagulation, and biological processes such as slow sand filtration.


title: Water treatment

text: A combination selected from the following processes (depending on the season and contaminants and chemicals present in the raw water) is used for municipal drinking water treatment worldwide.


title: Water treatment

text: Chemical approaches are used in addition to physical and biological measures to reduce the discharge of pollutants and waste water into water bodies. Different chemical procedures for the conversion into final products or the removal of pollutants are used for the safe disposal of contaminants.


title: Water treatment

text: Physical techniques of water/waste water treatment rely on physical phenomena to complete the removal process, rather than biological or chemical changes.


title: Water treatment

text: Chemical precipitation is a common process used to reduce heavy metals concentrations in wastewater. The dissolved metal ions are transformed to an insoluble phase by a chemical interaction with a precipitant agent such as lime. In industrial applications stronger alkalis may be used to effect complete precipitation. In drinking water treatment, the common-ion effect is often used to help reduce water hardness.


title: Water treatment

text: Membrane filtration has gotten a lot of attention for inorganic effluent treatment since it can remove not only suspended solids and organic components, but also inorganic pollutants such heavy metals. For heavy metal removal, several forms of membrane filtration, such as ultrafiltration, nanofiltration, and reverse osmosis, can be used depending on the particle size that can be maintained.


title: Water treatment

text: Ion exchange is a reversible ion exchange process in which an insoluble substance (resin) takes ions from an electrolytic solution and releases additional ions of the same charge in a chemically comparable amount without changing the resin's structure.


title: Water treatment

text: Adsorption is a mass transfer process in which a substance is transported from the liquid phase to the surface of a solid/liquid (adsorbent) and becomes physically and chemically bonded (adsorbate). Adsorption can be classified into two forms based on the type of attraction between the adsorbate and the adsorbent: physical and chemical adsorption, commonly known as physisorption and chemisorptions.


title: Water treatment

text: Activated carbons (ACs) or biological-activated carbon (BAC) are effective adsorbents for a wide variety of contaminants. The adsorptive removal of color, aroma, taste, and other harmful organics and inorganics from drinking water and wastewater is one of their industrial applications.


title: Water treatment

text: Both a high surface area and a large pore size can improve the efficiency of activated carbon. Activated carbon was utilized by a number of studies to remove heavy metals and other types of contaminants from wastewater. The cost of activated carbon is rising due to a shortage of commercial activated carbon (AC). Because of its high surface area, porosity, and flexibility, activated carbon has a lot of potential in wastewater treatment.


title: Water treatment

text: This is the method by which dissolved and suspended organic chemical components are eliminated through biodegradation, in which an optimal amount of microorganism is given to re-enact the same natural self-purification process. Through two distinct biological process, such as biological oxidation and biosynthesis, microorganisms can degrade organic materials in wastewater. Microorganisms involved in wastewater treatment produce end products such as minerals, carbon dioxide, and ammonia during the biological oxidation process. The minerals (products) remained in the wastewater and were discharged with the effluent. Microorganisms use organic materials in wastewater to generate new microbial cells with dense biomass that is eliminated by sedimentation throughout the biosynthesis process.


title: Water treatment

text: Phytoremediation, Rhizofiltration, Bioaugmentation, and Biostimulation are all biological treatment method in which microorganisms breakdown or transform hazardous contaminants in wastewater to a less toxic or non-toxic state. Both autotrophs and heterotrophs may be involved. Autotrophs can fix carbon and use inorganic chemicals in wastewater to make organic compounds such as fats, proteins, and carbohydrates. Heterotrophs feed on the soluble and emulsified organic organic substances present in the wastewater to develop and reproduce.


title: Water treatment

text: The sewage treatment processes of trickling filters and activated sludge both depend on maintained populations of heterotrophic organisms to do much of the work in removing contaminants.


title: Water treatment

text: In potable water production, the hypogeal zone (the Schmutzdecke) of Slow sand filtration is a naturally developed biofilm that metabolizes organic matter, adsorbs soluble components and entraps particulates.


title: Water treatment

text: Technologies for potable water and other uses are well-developed, and generalized designs are available from which treatment processes can be selected for pilot testing on the specific source water. In addition, a number of private companies provide patented technological solutions for the treatment of specific contaminants. Automation of water treatment is common in the developed world. Source water quality through the seasons, scale, and environmental impact can dictate capital costs and operating costs. End use of the treated water dictates the necessary quality monitoring technologies, and locally available skills typically dictate the level of automation adopted.


title: Water treatment

text: Saline water can be treated to yield fresh water. Two main processes are used, reverse osmosis or distillation. Both methods require more energy than water treatment of local surface waters, and are usually only used in coastal areas or where water such as groundwater has high salinity.


title: Water treatment

text: Living away from drinking water supplies often requires some form of portable water treatment process. These can vary in complexity from the simple addition of a disinfectant tablet in a hiker's water bottle through to complex multi-stage processes carried by boat or plane to disaster areas.


title: Water treatment

text: Many developed countries specify standards to be applied in their own country. In Europe, this includes the European Drinking Water Directive and in the United States the United States Environmental Protection Agency (EPA) establishes standards as required by the Safe Drinking Water Act. For countries without a legislative or administrative framework for such standards, the World Health Organization publishes guidelines on the standards that should be achieved. China adopted its own drinking water standard GB3838-2002 (Type II) enacted by Ministry of Environmental Protection in 2002.


title: Water treatment

text: Where drinking water quality standards do exist, most are expressed as guidelines or targets rather than requirements, and very few water standards have any legal basis or, are subject to enforcement. Two exceptions are the European Drinking Water Directive and the Safe Drinking Water Act in the United States, which require legal compliance with specific standards.


title: Water treatment

text: Two of the main processes of industrial water treatment are "boiler water treatment" and "cooling water treatment". A large amount of proper water treatment can lead to the reaction of solids and bacteria within pipe work and boiler housing. Steam boilers can suffer from scale or corrosion when left untreated. Scale deposits can lead to weak and dangerous machinery, while additional fuel is required to heat the same level of water because of the rise in thermal resistance. Poor quality dirty water can become a breeding ground for bacteria such as "Legionella" causing a risk to public health.


title: Water treatment

text: Corrosion in low pressure boilers can be caused by dissolved oxygen, acidity and excessive alkalinity. Water treatment therefore should remove the dissolved oxygen and maintain the boiler water with the appropriate pH and alkalinity levels.


title: Water treatment

text: Without effective water treatment, a cooling water system can suffer from scale formation, corrosion and fouling and may become a breeding ground for harmful bacteria. This reduces efficiency, shortens plant life and makes operations unreliable and unsafe.


title: Water treatment

text: Boiler water treatment is a type of industrial water treatment focused on removal or chemical modification of substances potentially damaging to the boiler. Varying types of treatment are used at different locations to avoid scale, corrosion, or foaming. External treatment of raw water supplies intended for use within a boiler is focused on removal of impurities before they reach the boiler. Internal treatment within the boiler is focused on limiting the tendency of water to dissolve the boiler, and maintaining impurities in forms least likely to cause trouble before they can be removed from the boiler in boiler blowdown.


title: Water treatment

text: Water cooling is a method of heat removal from components of machinery and industrial equipment. Water may be a more efficient heat transfer fluid where air cooling is ineffective. In most occupied climates water offers the thermal conductivity advantages of a liquid with unusually high specific heat capacity and the option that of evaporative cooling. Low cost often allows rejection as waste after a single use, but recycling coolant loops may be pressurized to eliminate evaporative loss and offer greater portability and improved cleanliness. Unpressurized recycling coolant loops using evaporative cooling require a blowdown waste stream to remove impurities concentrated by evaporation. Disadvantages of water cooling systems include accelerated corrosion and maintenance requirements to prevent heat transfer reductions from biofouling or scale formation. Chemical additives to reduce these disadvantages may introduce toxicity to wastewater. Water cooling is commonly used for cooling automobile internal combustion engines and large industrial facilities such as nuclear and steam electric power plants, hydroelectric generators, petroleum refineries and chemical plants.


title: Water treatment

text: Chemical treatments utilizes the additive of chemicals to make industrial water suitable for use or discharge. These includes processes like chemical precipitation, chemical disinfection, Advanced oxidation process (AOP), ion exchange, and chemical neutralization. AOPs are attractive in the treatment of hazardous wastewater due to its high oxidation potential and degradation performance. In AOPs, oxidants like Fenton's reagent, Ozone or Hydrogen peroxide are introduced in the wastewater to degrade harmful substances in industrial water for discharge.


title: Water treatment

text: Physical treatment involves the separation of solids form industrial wastewater either through Filtration or Dissolved air flotation. Filtration involves the use of Membrane or filters such as mechanical filters like sand filtration etc to achieve solid-liquid separation. Whereas for Dissolved air flotation,


title: Water treatment

text: pressurized air is pumped into the wastewater. The pressurized air then forms small bubbles which adhere to the suspended matter causing them to float to the surface of the water where they can be removed by a skimming device or an overflow.


title: Water treatment

text: Biological treatment is needed to treat wastewater containing biodegradable elements. It is commonly used in municipal and industrial wastewater management facilities and usually consists in adding common bacteria and other microbes, mostly environmentally friendly, to treat the water. It is a sustainable practice that has been successful for over a century.


title: Water treatment

text: Slow sand filters use a biological process to purify raw water to produce potable water. They work by using a complex biological film that grows naturally on the surface of sand. This gelatinous biofilm called the hypogeal layer or Schmutzdecke is located in the upper few millimetres of the sand layer. The surface biofilm purifies the water as it flows through the layer, the underlying sand provides a support medium for the biological treatment layer. The Schmutzdecke consists of bacteria, fungi, protozoa, rotifera and a range of aquatic insect larvae. As the biofilm ages, more algae may develop and larger aquatic organisms including bryozoa, snails and Annelid worms may be present. As water passes through the hypogeal layer, particles of matter are trapped in the mucilaginous matrix and soluble organic material is adsorbed. The contaminants are metabolised by the bacteria, fungi and protozoa.


title: Water treatment

text: Slow sand filters are typically 1–2 metres deep, and have a hydraulic loading rate of 0.2–0.4 cubic metres per square metre per hour. Filters lose their performance as the biofilm thickens and reduces the rate of flow. The filter is refurbished by removing the biofilm and a thin upper layer of sand. Water is decanted back into the filter and re-circulated to enable a new biofilm to develop. Alternatively wet harrowing involves stirring the sand and flushing the biolayer through for disposal.


title: Water treatment

text: (Also referred to as 'conventional treatment'.) Chemical flocculants are used to generate a floc in the water that traps suspended solids. Chemical polyelectrolytes are used to increase coagulation of suspended solids to improve removal.


title: Water treatment

text: Appropriate technology options in water treatment include both community-scale and household-scale point-of-use (POU) or self-supply designs. Such designs may employ solar water disinfection methods, using solar irradiation to inactivate harmful waterborne microorganisms directly, mainly by the UV-A component of the solar spectrum, or indirectly through the presence of an oxide photocatalyst, typically supported TiO in its anatase or rutile phases. Despite progress in SODIS technology, military surplus water treatment units like the ERDLator are still frequently used in developing countries. Newer military style Reverse Osmosis Water Purification Units (ROWPU) are portable, self-contained water treatment plants are becoming more available for public use.


title: Water treatment

text: For waterborne disease reduction to last, water treatment programs that research and development groups start in developing countries must be sustainable by the citizens of those countries. This can ensure the efficiency of such programs after the departure of the research team, as monitoring is difficult because of the remoteness of many locations.


title: Water treatment

text: Energy Consumption: Water treatment plants can be significant consumers of energy. In California, more than 4% of the state's electricity consumption goes towards transporting moderate quality water over long distances, treating that water to a high standard. In areas with high quality water sources which flow by gravity to the point of consumption, costs will be much lower.


title: Water treatment

text: Much of the energy requirements are in pumping. Processes that avoid the need for pumping tend to have overall low energy demands. Those water treatment technologies that have very low energy requirements including trickling filters, slow sand filters, gravity aqueducts.


title: Water treatment

text: A 2021 study found that a large-scale water chlorination program in urban areas of Mexico massively reduced childhood diarrheal disease mortality rates.


title: Water treatment

text: The Water Services Act 2021 brought Taumata Arowai' into existence as the new regulator of drinking water and waste water treatment in New Zealand. Initial activities including the establishment of a national register of water suppliers and establishing a network of accredited laboratories for drinking water and waste water analysis


title: Water treatment

text: Singapore is a significant importer of water from neighbouring Malaysia but also has a made great efforts to reclaim as much used water as possible to enure adequate provision for the very crowded city/state. Their reclaimed water is marketed as NEWater. Singapore updated its water quality regulation in 2019 setting standards consistent with WHO recommended standards. Monitoring is undertaken by the Environmental Public Health Department of the Singaporean Government


title: Water treatment

text: In the United Kingdom regulation of water supplies is a devolved matter to the Welsh and Scottish Parliaments and the Northern Ireland Assembly.


title: Water treatment

text: The functions and duties of the bodies are formally defined in the Water Industry Act 1991 (1991 c. 56) as amended by the Water Act 2003 (2003 c. 37) and the Water Act 2014 (2014 c. 21).


title: Water treatment

text: In Scotland water quality is the responsibility of independent Drinking Water Quality Regulator (DWQR).


title: Water treatment

text: In Northern Ireland the Drinking Water Inspectorate (DWI) regulates drinking water quality of public and private supplies. The current standards of water quality are defined in the Water Supply (Water Quality) Regulations (Northern Ireland) 2017.


title: Water treatment

text: The Safe Drinking Water Act requires the U.S. Environmental Protection Agency (EPA) to set standards for drinking water quality in public water systems (entities that provide water for human consumption to at least 25 people for at least 60 days a year). Enforcement of the standards is mostly carried out by state health agencies. States may set standards that are more stringent than the federal standards.


title: Water treatment

text: EPA has set standards for over 90 contaminants organized into six groups: microorganisms, disinfectants, disinfection byproducts, inorganic chemicals, organic chemicals and radionuclides.


title: Water treatment

text: EPA also identifies and lists unregulated contaminants which may require regulation. The "Contaminant Candidate List" is published every five years, and EPA is required to decide whether to regulate at least five or more listed contaminants.


title: Water treatment

text: Local drinking water utilities may apply for low interest loans, to make facility improvements, through the Drinking Water State Revolving Fund.


title: Cinéma vérité

text: Cinéma vérité (, , ; "truthful cinema") is a style of documentary filmmaking developed by Edgar Morin and Jean Rouch, inspired by Dziga Vertov's theory about Kino-Pravda. It combines improvisation with use of the camera to unveil truth or highlight subjects hidden behind reality.


title: Cinéma vérité

text: It is sometimes called observational cinema, if understood as pure direct cinema: mainly without a narrator's voice-over. There are subtle, yet important, differences between terms expressing similar concepts. Direct Cinema is largely concerned with the recording of events in which the subject and audience become unaware of the camera's presence: operating within what Bill Nichols, an American historian and theoretician of documentary film, calls the "observational mode", a fly on the wall. Many therefore see a paradox in drawing attention away from the presence of the camera and simultaneously interfering in the reality it registers when attempting to discover a cinematic truth.


title: Cinéma vérité

text: Cinéma vérité can involve stylized set-ups and interaction between the filmmaker and the subject, even to the point of provocation. Some argue that the obvious presence of the filmmaker and camera was seen by most cinéma vérité filmmakers as the best way to reveal the truth. The camera is always acknowledged, for it performs the act of filming real objects, people, and events in a confrontational way. The filmmaker's intention was to represent the truth as objectively as possible, freeing the viewer from deceptions in how those aspects of life were formerly presented to them. From this perspective, the filmmaker should be the catalyst of a situation. Few agree on the meanings of these terms, even the filmmakers whose films are being described.


title: Cinéma vérité

text: Pierre Perrault sets situations up and then films them, for example in "Pour la suite du monde" (1963) where he asked old people to fish for whale. The result is not a documentary about whale fishing; it is about memory and lineage. In this sense cinéma vérité is concerned with anthropological cinema, and with the social and political implications of what is captured on film. How a filmmaker shoots a film, what is being filmed, what to do with what was filmed, and how that film will be presented to an audience, all were very important for filmmakers of the time.


title: Cinéma vérité

text: In all cases, the ethical and aesthetic analysis of documentary form (see docufiction) of the 1950s and 1960s has to be linked with a critical look at post-war propaganda analysis. This type of cinema is concerned with notions of truth and reality in film. Feminist documentary films of the 1970s often used cinéma-vérité techniques. This sort of "realism" was criticized for its deceptive pseudo-natural construction of reality.


title: Cinéma vérité

text: Edgar Morin coined the term around the time of such essential films as 1960's "Primary" and his own 1961 collaboration with Jean Rouch, "Chronicle of a Summer".


title: Cinéma vérité

text: Many film directors of the 1960s and later adopted use of handheld camera and other cinéma vérité aspects for their scripted, fiction filmshaving actors improvise to get a more spontaneous quality in their dialogue and action. Influential examples include director John Cassavetes, who broke ground with his film "Faces". The techniques of cinéma vérité can also be seen in fiction films from "The Blair Witch Project" to "Saving Private Ryan".


title: Cinéma vérité

text: Cinéma vérité was also adapted for use in scripted TV programs, such as "", "NYPD Blue", both the UK and American versions of "The Office", "Parks & Recreation" and "Modern Family". Documentary series are less common, but "COPS" is one famous non-fictional example.


title: Cinéma vérité

text: It has also been a subject ripe for parodies and spoofs such as the mockumentary film "This Is Spinal Tap" and Emmy-nominated TV series "Documentary Now" (the latter paying homage to the style of such CV classics as "Grey Gardens" and "The War Room").


title: Anatoli Boukreev

text: Anatoli Nikolaevich Boukreev (; January 16, 1958 – December 25, 1997) was a Soviet and Kazakhstani mountaineer who made ascents of 10 of the 14 eight-thousander peaks—those above —without supplemental oxygen. From 1989 through 1997, he made 18 successful ascents of peaks above 8000 m.


title: Anatoli Boukreev

text: Boukreev had a reputation as an elite mountaineer in international climbing circles for summiting K2 in 1993 and Mount Everest via the North Ridge route in 1995, and for his solo speed ascents of some of the world's highest mountains. He became even more widely known for saving the lives of climbers during the 1996 Mount Everest disaster.


title: Anatoli Boukreev

text: In 1997, Boukreev was killed in an avalanche during a winter ascent of Annapurna in Nepal. Boukreev's companion, Linda Wylie, edited his memoirs and published them in 2002 under the title, "Above the Clouds: The Diaries of a High-Altitude Mountaineer".


title: Anatoli Boukreev

text: Boukreev was born in Korkino, within the Soviet Union's Russian SFSR. He came from the "narod", the common people, and his parents were both poor. After completing high school in 1975, he attended Chelyabinsk University for Pedagogy, where he majored in physics and earned his Bachelor of Science degree in 1979. At the same time, he also completed a coaching program for cross-country skiing.


title: Anatoli Boukreev

text: After graduation, the 21-year-old dreamed of mountain climbing. Boukreev moved to Alma-Ata, the capital of the neighbouring Kazakh SSR (present day Kazakhstan) located in the Tian Shan mountain range. From 1985 he was part of a Kazakhstani mountaineering team, and he became a citizen of Kazakhstan in 1991 after the breakup of the Soviet Union.


title: Anatoli Boukreev

text: Boukreev worked as a commercial guide in the 1990s, and was working with Scott Fischer's adventure company Mountain Madness during the 1996 Mount Everest disaster. He managed to survive and was also instrumental in saving the lives of others, including New York socialite Sandy Hill Pittman.


title: Anatoli Boukreev

text: In May 1990, Boukreev was invited by an American climber to guide several clients to the summit of Denali in Alaska. Denali, previously known as Mount McKinley, has challenges such as hidden crevasses and unpredictably cold weather due to its proximity to the Arctic Circle and the ocean.


title: Anatoli Boukreev

text: The expedition was a success and the team reached the summit and returned without incident. During the climb there had been somewhat of a language barrier and Boukreev felt the sting of needing to borrow equipment due to his economic circumstances. After the team had returned home, Boukreev decided to attempt a solo speed ascent of Denali before returning to the Soviet Union.


title: Anatoli Boukreev

text: Boukreev's solo speed ascent of Denali in 1990 was completed in 10½ hours from the base to the summit. That season acclimatised climbers were normally taking three to four days and five camps to summit — Boukreev's feat was noted by "Climbing" magazine in a 1990 issue, and commented on by Denali Park rangers who described it as "unreal".


title: Anatoli Boukreev

text: In 1993, Boukreev reached the summit of K2 via the Abruzzi Spur, where he shared the peak with team members Peter Metzger of Germany and Andrew Lock of Australia. The other team members were German climbers Reinmar Joswig (the team leader) and Ernst Eberhardt. With a peak elevation of 8,611 metres (28,251 ft), K2 is the second-highest mountain on Earth after Mount Everest.


title: Anatoli Boukreev

text: As part of the Karakoram range, K2 is located on the border between Pakistan and China. K2 is referred to as the "Savage Mountain" — notable for its steep pyramidal relief, dropping quickly in almost all directions, and the inherent danger in climbing it.


title: Anatoli Boukreev

text: The danger facing Boukreev on K2 was that the summit felt like the finish line. Boukreev would later write that he did not feel the emotions of victory in that moment on top of K2's peak because he was physically and emotionally spent. Boukreev found himself in a dangerous position. He had expended too much energy placing fixed lines along a narrow, steep portion earlier that day. But since the team wanted to push on to the summit that same afternoon, rather than return to their tents to sleep and make a summit bid the next morning, Boukreev acquiesced. Boukreev would later write:


title: Anatoli Boukreev

text: Boukreev later described feeling like a "squeezed lemon". When Boukreev and the other two climbers began their descent just after sundown they met Reinmar Joswig ascending and near the peak. Relying heavily on intuition and his previous mountaineering experiences, Boukreev slowly made his way down the steep rock and ice of the mountain. A crampon kept coming off of his boot, and at one point he had to use his ice axe to arrest a fall, keeping himself from sliding into the abyss. Eventually he made his way to the tents at the highest elevation camp. However, teammates Peter Metzger and Reinmar Joswig never returned from the summit, both having fallen to their death during the descent.


title: Anatoli Boukreev

text: Boukreev became widely known as the lead climbing guide for the Mountain Madness expedition headed by Scott Fischer in May 1996. The expedition was one of several attempting to summit Everest on the same day (May 10). Soon after summiting on May 10 a disastrous blizzard struck, stranding many climbers above the South Col overnight, and by May 11, eight climbers from three different expeditions had perished. Boukreev rescued three climbers stranded in the disaster above 8000 m, and all six of the climbing clients on the Mountain Madness expedition survived the ordeal.


title: Anatoli Boukreev

text: Author Jon Krakauer was generally critical of Boukreev in his book, "Into Thin Air." Subsequently, Boukreev was contacted by various media for a response, and also wrote his own account of the events on Everest in "The Climb", a book co-written with Gary Weston DeWalt.


title: Anatoli Boukreev

text: The core of the controversy was Boukreev's decision to attempt the summit without supplementary oxygen and to descend to the camp ahead of his clients in the face of approaching darkness and blizzard. He was one of the first to reach the summit on the day of the disaster and stayed at or near the summit for nearly 1.5 hours helping others with their summit efforts, before returning to his tent by 5 pm on May 10, well ahead of the later summiters on his team.


title: Anatoli Boukreev

text: Boukreev's supporters point to the fact that his return to camp allowed him enough rest that, when the blizzard had subsided around midnight, he was able to mount a rescue attempt and to lead several climbers still stranded on the mountain back to the safety of the camp. Boukreev's detractors say that had he simply stayed with the clients, he would have been in better position to assist them down the mountain, though every one of Boukreev's clients survived, including the three (Pittman, Fox, Madsen) that he rescued on May 11 after he had rested and overcome hypoxia. The only client deaths that day were suffered by the Adventure Consultants expedition, led by guide Rob Hall, who lost his own life when he chose to stay and help a client complete a late summit rather than helping the client descend. Reinhold Messner criticized Boukreev, saying "[n]o one should guide Everest without using bottled oxygen" while David Breashears pointed out that Boukreev, despite climbing down first, was "sitting in his tent unable to assist anyone" until the clients themselves staggered into the camp with the information vital to their rescue.


title: Anatoli Boukreev

text: According to Krakauer, Boukreev's "refusal or inability to play the role of a conventional guide" caused dissension between him and Scott Fischer (who later died while returning from the summit). On the way to the summit, Fischer had directed Boukreev to bring up the rear of the group and keep an eye on everybody, but he instead remained at Base Camp and followed the group some five hours later. When a client named Dale Kruse fell ill, Boukreev was nowhere to be found, forcing Fischer to descend from Camp II to Kruse and help him back to Base Camp. According to Krakauer, Fischer encountered Boukreev at the Khumbu Icefall and "harshly reprimanded the guide for shirking his responsibilities". Back at Base Camp, Fischer called his Seattle business partner Karen Dickinson and publicist Jane Bromet to complain about Boukreev's actions before resuming his ascent.


title: Anatoli Boukreev

text: Before returning to the U.S. after the events on Everest in 1996, Boukreev climbed the Lhotse, which is in proximity to Everest. He decided on a solo ascent because he hoped that in the process of climbing it he might find some inner clarity to what had just transpired on Everest.


title: Anatoli Boukreev

text: In 1997 Anatoli Boukreev was awarded the David A. Sowles Memorial Award by the American Alpine Club. The award recognizes people "who have distinguished themselves, with unselfish devotion at personal risk or sacrifice of a major objective, in going to the assistance of fellow climbers imperiled in the mountains. It is dedicated to the memory of David A. Sowles." It was presented to him by Jim Wickwire, the first American to summit K2. The award is the American Alpine Club's highest award for valor in recognition of his role in rescuing climbers in the 1996 Everest disaster.


title: Anatoli Boukreev

text: Three weeks after receiving the David A. Sowles Memorial Award, Boukreev began his attempt to climb the south face of Annapurna I () along with Simone Moro, an accomplished Italian mountaineer. They were accompanied by Dimitri Sobolev, a cinematographer from Kazakhstan who was documenting the attempt. On December 25 around noon, Boukreev and Moro were fixing ropes in a couloir at around the level.


title: Anatoli Boukreev

text: Suddenly, an enormous cornice broke loose from the heights of Annapurna's Western Wall and rumbled down the long couloir. The avalanche knocked Moro down the mountain where he landed just above their tent at Camp I . Fortuitously, Moro had somehow stayed near the top of the avalanche debris and managed to dig himself out after a few minutes. Unable to see or hear any signs of Boukreev or Sobolev (whom Moro had witnessed disappearing beneath "car-sized blocks of ice"), Moro descended to Annapurna base camp where he was flown by helicopter back to Kathmandu for surgery on his hands, which had been ripped down to the tendons during the fall.


title: Anatoli Boukreev

text: News of the accident reached New Mexico on December 26. Linda Wylie, Boukreev's girlfriend, left for Nepal on December 28. Several attempts were made to reach the avalanche site by helicopter but inclement weather in late December prevented search teams from reaching Camp I. On January 3, 1998, searchers were finally able to reach Camp I and an empty tent. Linda Wylie subsequently issued a somber statement from Kathmandu:


title: Anatoli Boukreev

text: Boukreev had dreamt in detail of dying in an avalanche nine months before his death. The only thing missing was the name of the mountain. When Boukreev's companion tried to convince him to take a different path in life to avoid a fate that Boukreev was convinced of, he responded, "Mountains are my life...my work. It is too late for me to take up another road."


title: Anatoli Boukreev

text: At the site of Annapurna base-camp there is a memorial chorten to Boukreev including one of his favorite quotes:"Mountains are not stadiums where I satisfy my ambition to achieve, they are the cathedrals where I practice my religion."


title: Anatoli Boukreev

text: Icelandic actor Ingvar Eggert Sigurðsson portrays Boukreev in the Baltasar Kormákur film, "Everest", about the 1996 Everest disaster.


title: Simplex algorithm

text: In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.


title: Simplex algorithm

text: The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial "cones", and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function.


title: Simplex algorithm

text: George Dantzig worked on planning methods for the US Army Air Force during World War II using a desk calculator. During 1946 his colleague challenged him to mechanize the planning process to distract him from taking another job. Dantzig formulated the problem as linear inequalities inspired by the work of Wassily Leontief, however, at that time he didn't include an objective as part of his formulation. Without an objective, a vast number of solutions can be feasible, and therefore to find the "best" feasible solution, military-specified "ground rules" must be used that describe how goals can be achieved as opposed to specifying a goal itself. Dantzig's core insight was to realize that most such ground rules can be translated into a linear objective function that needs to be maximized. Development of the simplex method was evolutionary and happened over a period of about a year.


title: Simplex algorithm

text: After Dantzig included an objective function as part of his formulation during mid-1947, the problem was mathematically more tractable. Dantzig realized that one of the unsolved problems that he had mistaken as homework in his professor Jerzy Neyman's class (and actually later solved), was applicable to finding an algorithm for linear programs. This problem involved finding the existence of Lagrange multipliers for general linear programs over a continuum of variables, each bounded between zero and one, and satisfying linear constraints expressed in the form of Lebesgue integrals. Dantzig later published his "homework" as a thesis to earn his doctorate. The column geometry used in this thesis gave Dantzig insight that made him believe that the Simplex method would be very efficient.


title: Simplex algorithm

text: with formula_4 the coefficients of the objective function, formula_5 is the matrix transpose, and formula_6 are the variables of the problem, formula_7 is a "p"×"n" matrix, and formula_8. There is a straightforward process to convert any linear program into one in standard form, so using this form of linear programs results in no loss of generality.


title: Simplex algorithm

text: In geometric terms, the feasible region defined by all values of formula_9 such that formula_10 and formula_11 is a (possibly unbounded) convex polytope. An extreme point or vertex of this polytope is known as "basic feasible solution" (BFS).


title: Simplex algorithm

text: It can be shown that for a linear program in standard form, if the objective function has a maximum value on the feasible region, then it has this value on (at least) one of the extreme points. This in itself reduces the problem to a finite computation since there is a finite number of extreme points, but the number of extreme points is unmanageably large for all but the smallest linear programs.


title: Simplex algorithm

text: It can also be shown that, if an extreme point is not a maximum point of the objective function, then there is an edge containing the point so that the value of the objective function is strictly increasing on the edge moving away from the point. If the edge is finite, then the edge connects to another extreme point where the objective function has a greater value, otherwise the objective function is unbounded above on the edge and the linear program has no solution. The simplex algorithm applies this insight by walking along edges of the polytope to extreme points with greater and greater objective values. This continues until the maximum value is reached, or an unbounded edge is visited (concluding that the problem has no solution). The algorithm always terminates because the number of vertices in the polytope is finite; moreover since we jump between vertices always in the same direction (that of the objective function), we hope that the number of vertices visited will be small.


title: Simplex algorithm

text: The solution of a linear program is accomplished in two steps. In the first step, known as Phase I, a starting extreme point is found. Depending on the nature of the program this may be trivial, but in general it can be solved by applying the simplex algorithm to a modified version of the original program. The possible results of Phase I are either that a basic feasible solution is found or that the feasible region is empty. In the latter case the linear program is called "infeasible". In the second step, Phase II, the simplex algorithm is applied using the basic feasible solution found in Phase I as a starting point. The possible results from Phase II are either an optimum basic feasible solution or an infinite edge on which the objective function is unbounded above.


title: Simplex algorithm

text: The transformation of a linear program to one in standard form may be accomplished as follows. First, for each variable with a lower bound other than 0, a new variable is introduced representing the difference between the variable and bound. The original variable can then be eliminated by substitution. For example, given the constraint


title: Simplex algorithm

text: The second equation may be used to eliminate formula_15 from the linear program. In this way, all lower bound constraints may be changed to non-negativity restrictions.


title: Simplex algorithm

text: Second, for each remaining inequality constraint, a new variable, called a "slack variable", is introduced to change the constraint to an equality constraint. This variable represents the difference between the two sides of the inequality and is assumed to be non-negative. For example, the inequalities


title: Simplex algorithm

text: It is much easier to perform algebraic manipulation on inequalities in this form. In inequalities where ≥ appears such as the second one, some authors refer to the variable introduced as a " surplus variable".


title: Simplex algorithm

text: Third, each unrestricted variable is eliminated from the linear program. This can be done in two ways, one is by solving for the variable in one of the equations in which it appears and then eliminating the variable by substitution. The other is to replace the variable with the difference of two restricted variables. For example, if formula_18 is unrestricted then write


title: Simplex algorithm

text: It is also useful to assume that the rank of formula_22 is the number of rows. This results in no loss of generality since otherwise either the system formula_23 has redundant equations which can be dropped, or the system is inconsistent and the linear program has no solution.