title: Conditional expectation

text: Suppose we have daily rainfall data (mm of rain each day) collected by a weather station on every day of the ten–year (3652–day) period from January 1, 1990 to December 31, 1999. The unconditional expectation of rainfall for an unspecified day is the average of the rainfall amounts for those 3652 days. The "conditional" expectation of rainfall for an otherwise unspecified day known to be (conditional on being) in the month of March, is the average of daily rainfall over all 310 days of the ten–year period that falls in March. And the conditional expectation of rainfall conditional on days dated March 2 is the average of the rainfall amounts that occurred on the ten days with that specific date.


title: Conditional expectation

text: The related concept of conditional probability dates back at least to Laplace, who calculated conditional distributions. It was Andrey Kolmogorov who, in 1933, formalized it using the Radon–Nikodym theorem. In works of Paul Halmos and Joseph L. Doob from 1953, conditional expectation was generalized to its modern definition using sub-σ-algebras.


title: Conditional expectation

text: where formula_14 is the joint probability mass function of and . The sum is taken over all possible outcomes of .


title: Conditional expectation

text: Note that conditioning on a discrete random variable is the same as conditioning on the corresponding event:


title: Conditional expectation

text: Note that conditioning on a continuous random variable is not the same as conditioning on the event formula_16 as it was in the discrete case. For a discussion, see Conditioning on an event of probability zero. Not respecting this distinction can lead to contradictory conclusions as illustrated by the Borel-Kolmogorov paradox.


title: Conditional expectation

text: In its full generality, conditional expectation is developed without this assumption, see below under Conditional expectation with respect to a sub-σ-algebra. The formula_29 theory is, however, considered more intuitive and admits important generalizations.


title: Conditional expectation

text: formula_35, the result will be a function formula_40. Let formula_41 be a random vector. The conditional expectation formula_42 is a measurable function such that


title: Conditional expectation

text: Note that unlike formula_35, the conditional expectation formula_45 is not generally unique: there may be multiple minimizers of the mean squared error.


title: Conditional expectation

text: but in terms of functions it can be expressed as formula_49 or formula_50 or infinitely many other ways. In the context of linear regression, this lack of uniqueness is called multicollinearity.


title: Conditional expectation

text: Conditional expectation is unique up to a set of measure zero in formula_51. The measure used is the pushforward measure induced by .


title: Conditional expectation

text: In the first example, the pushforward measure is a Dirac distribution at 1. In the second it is concentrated on the "diagonal" formula_52, so that any set not intersecting it has measure 0.


title: Conditional expectation

text: In words, this equation says that the residual formula_59 is orthogonal to the space of all functions of .


title: Conditional expectation

text: is used below to extend conditional expectation to the case that and are not necessarily in formula_29.


title: Conditional expectation

text: The conditional expectation is often approximated in applied mathematics and statistics due to the difficulties in analytically calculating it, and for interpolation.


title: Conditional expectation

text: defined above is replaced with subsets thereof by restricting the functional form of , rather than allowing any measureable function. Examples of this are decision tree regression when is required to be a simple function, linear regression when is required to be affine, etc.


title: Conditional expectation

text: These generalizations of conditional expectation come at the cost of many of its properties no longer holding.


title: Conditional expectation

text: be the space of all linear functions of and let formula_63 denote this generalized conditional expectation/formula_29 projection. If formula_65 does not contain the constant functions, the tower property


title: Conditional expectation

text: Since formula_73 is a sub formula_74-algebra of formula_10, the function formula_70 is usually not formula_73-measurable, thus the existence of the integrals of the form formula_78, where formula_79 and formula_80 is the restriction of formula_81 to formula_73, cannot be stated in general. However, the local averages formula_83 can be recovered in formula_84 with the help of the conditional expectation.


title: Conditional expectation

text: A conditional expectation of "X" given formula_73, denoted as formula_86, is any formula_73-measurable function formula_88 which satisfies:


title: Conditional expectation

text: As noted in the formula_29 discussion, this condition is equivalent to saying that the residual formula_92 is orthogonal to the indicator functions formula_93:


title: Conditional expectation

text: The existence of formula_86 can be established by noting that formula_96 for formula_97 is a finite measure on formula_98 that is absolutely continuous with respect to formula_81. If formula_100 is the natural injection from formula_73 to formula_10, then formula_103 is the restriction of formula_104 to formula_73 and formula_106 is the restriction of formula_81 to formula_73. Furthermore, formula_109 is absolutely continuous with respect to formula_110, because the condition


title: Conditional expectation

text: The conditional expectation of given is defined by applying the above construction on the σ-algebra generated by :


title: Conditional expectation

text: All the following formulas are to be understood in an almost sure sense. The σ-algebra formula_73 could be replaced by a random variable formula_136, i.e. formula_137.


title: Conditional expectation

text: Thus the definition of conditional expectation is satisfied by the constant random variable formula_145, as desired.


title: Gunnery sergeant

text: Gunnery Sergeant (GySgt) is the seventh enlisted rank in the United States Marine Corps, above staff sergeant and below master sergeant and first sergeant, and is a staff non-commissioned officer (SNCO). It has a pay grade of E-7.


title: Gunnery sergeant

text: The gunnery sergeant insignia consists of two M1 Garands centered vertically between three chevrons and two rockers.


title: Gunnery sergeant

text: Gunnery sergeants in infantry units typically serve in the billet of "company gunnery sergeant" or as the platoon sergeant of 23–69 Marines in a reconnaissance platoon or a crew-served weapons platoon (i.e., machine guns, mortars, assault weapons/rockets, and anti-tank missiles). In artillery batteries, gunnery sergeants serve as the "battery gunnery sergeant" in the headquarters section of the firing battery's 94-member firing platoon. In tank and assault amphibian units gunnery sergeants may serve as a platoon sergeant of a 16-member platoon of four tanks or a 39-member platoon of 12 amphibious assault vehicles (AAVs), respectively. Tank and assault amphibian gunnery sergeants are also assigned as section leaders, in charge of either two tanks and 8 Marines or three AAVs and 9 Marines. Gunnery sergeants serving as platoon sergeants perform essentially the same duties as staff sergeant platoon sergeants, with the additional responsibility of supervising other staff non-commissioned officers (i.e., the gunnery/staff sergeants leading the organic sections of the platoon).


title: Gunnery sergeant

text: The company/battery gunnery sergeant serves as the unit's operations chief and works with the executive officer to plan and coordinate unit training and operations. In combat, as a member of the unit's command group, he/she serves as a tactical adviser to the commanding officer/battery commander regarding employment of the unit and assists in operating the command post or tactical operations center. In garrison, he/she is responsible to the company/battery commander for supervising and coordinating individual training for the enlisted members of the company or battery and may assist the company/battery first sergeant in the administration and non-tactical leadership of the unit and by supervising the property (logistics) NCO, advising the officers, mentoring subordinate ranking Marines, and performing other duties as assigned. The company/battery gunnery sergeant has been described as a "hands on disciplinarian". An approximate former equivalent in the United States Army would have been "field first sergeant".


title: Gunnery sergeant

text: Gunnery sergeants also serve as senior staff non-commissioned officers in military staff sections and headquarters and service companies and headquarters batteries at battalion/squadron, regiment/group, and division/wing headquarters levels. Typical gunnery sergeant billets in combat support companies and battalion, regiment, and division headquarters are: Personnel Administration Chief, Staff Secretary Personnel/Administration Clerk, Administration Assistance Chief, Division Reproduction NCO, Equal Opportunity Advisor, Human Affairs NCO, Career Planner, Intelligence Chief, Operations Chief, Operations Assistant, Watch Team NCOIC, Schools Coordinator, MAGTF Plans Chief, Cinematography Specialist, Logistics Chief, Embarkation Chief, Infantry Weapons Chief, Analyst and Review Fiscal Chief, Information Systems Maintenance Chief, Public Affairs Chief, Communications-Electronics Maintenance Section Chief, Radio Chief, Wire Chief, Motor Transport Chief, Battery Motor Transport Chief, Roadmaster, Assistant Roadmaster, Maintenance Chief, Assistant Maintenance Chief, Management Team Inspector, Engineer Equipment Chief, and Mess Manager.


title: Gunnery sergeant

text: In Command Element, Combat Logistics Element, and Aviation Combat Element organizations, gunnery sergeants serve in basically similar positions of responsibility, authority, and accountability as their Ground Combat Element counterparts, with perhaps slightly different titles, such as Division/Branch Chief/NCOIC or Department SNCOIC (Staff Non-Commissioned Officer-In-Charge) in the aircraft maintenance department of a Marine aircraft squadron. Non Fleet Marine Force (or other operating forces) assignments may include supervisory or staff positions in recruiting, drill instructor, Marine Security Guard, Naval ROTC instructor or service school instructor, and major/joint/combined headquarters commands.


title: Gunnery sergeant

text: The rank of gunnery sergeant in the Marine Corps was established by the Navy personnel act of March 3, 1899 () reflecting the duties of Marines in ship's detachments. The original insignia was three chevrons point up with three straight "ties" with an insignia of a bursting bomb over a crossed rifle and naval gun. From 1904 to 1929 the insignia went to three stripes only over a bursting bomb on top of crossed rifles. In 1929, like the rank of first sergeant, two "rockers" were added beneath the stripes with the same insignia in the middle. In 1937 the middle insignia was dropped. The rank was replaced by technical sergeant in 1946 until restored in 1959, when the crossed rifles insignia were added to Marine chevrons.


title: Gunnery sergeant

text: The qualifications and selection of gunnery sergeants in the "Old Corps" was explained in congressional testimony in 1912:


title: Gunnery sergeant

text: A candidate for appointment as gunnery sergeant in the United States Marine Corps should be sufficiently proficient in the drill regulations to thoroughly drill recruits and to drill the squad and company. They should be thoroughly conversant with the nomenclature of the rapid-fire and machine guns used in the naval service and be sufficiently acquainted with their drill to be able to act as gun captains and to instruct the enlisted in their duties at such guns. They should have knowledge of the kinds and quantities of ammunition used in those guns. They should have a thorough knowledge of the instructions pertaining to target practice. They should have sufficient knowledge of the system of accountability of the United States Marine Corps to take charge of and properly render the accounts of a guard aboard ship, and should be competent in all respects to perform the duties of a first sergeant in charge of a guard on ship to which no marine officer is attached; also a knowledge of the duties involved in the subsistence of Marines ordered on detached duty, as well as the duties of an officer in command of a part of a landing party on shore.


title: Gunnery sergeant

text: Gunnery sergeants are selected from the sergeants of the corps on account of superior intelligence, reliability, and mechanical knowledge. The grade was provided with the idea that they should be somewhat higher in standard than first sergeants; that their knowledge of ordnance and of gunnery should be such that they would be able to make minor repairs to guns—to supervise all work in connection with guns; to command detachments which were of such size as not to warrant a commissioned officer being assigned to them. They are at present in command of marine detachments at naval magazines; are performing duty as first sergeants of regularly organized companies at various posts; in connection with the repair of guns at various Marine Corps stations; in connection with the training of recruits; and, in general, performing duties that require the utmost reliability. For a number of years candidates for promotion to this grade were required to take a special course of instruction before receiving their warrants, but recently, because of the lack of first sergeants and the numerous small detachments organized, it has been necessary to detail many of them for duty as first sergeants. As soon as there are a sufficient number of first sergeants available, it is intended to reestablish the school and to give gunnery sergeants a thorough course of instruction prior to their permanent appointment to this grade, in order that they may be experts in all matters pertaining to the care and preservation of naval ordnance.


title: Gunnery sergeant

text: Gunnery sergeants are commonly referred to by the informal abbreviation "Gunny" or "Guns". These nicknames, which are usually regarded as titles of both esteem and camaraderie, are generally acceptable for use in all but formal and ceremonial situations. Use of the term by lower-ranking personnel, however, remains at the gunnery sergeant's discretion.


title: David Malpass

text: David Robert Malpass (born March 8, 1956) is an American economic analyst and former government official serving as President of the World Bank Group since 2019. Malpass previously served as Under Secretary of the Treasury for International Affairs under Donald Trump, Deputy Assistant Treasury Secretary under Ronald Reagan, Deputy Assistant Secretary of State under George H. W. Bush. He served as Chief Economist at Bear Stearns for the six years preceding its collapse.


title: David Malpass

text: During the 2016 U.S. presidential election, Malpass served as an economic advisor to Donald Trump, and in 2017, he was nominated and confirmed as Under Secretary of the Treasury for International Affairs at the Treasury Department. Malpass was elected President of the World Bank on April 4, 2019, having been nominated to the position in February 2019 by the Trump administration. He formally took office on April 9, 2019.


title: David Malpass

text: Malpass earned a B.A. in physics at Colorado College and an MBA at the University of Denver. He studied international economics at Georgetown University's School of Foreign Service. He speaks Spanish, Russian, and French. From 1977 to 1983, he worked in Portland, Oregon for Esco Corporation and Arthur Andersen's systems consulting group, where he became a licensed CPA.


title: David Malpass

text: During the administrations of Ronald Reagan and George H. W. Bush, Malpass worked on an array of economic, budget, and foreign policy issues including small business promotion throughout Latin America and the 1986 tax cut. Malpass served as the Republican staff director of the United States Congress Joint Economic Committee from 1989 to 1990, and as a member of Congress's blue-ribbon panel on budget scoring from 2002 to 2003.


title: David Malpass

text: Malpass was chief economist at Bear Stearns from 1993 to 2008. As a result of the global financial crisis and under the prodding of the Federal Reserve and United States Department of the Treasury, Bear Sterns was sold to JPMorgan Chase in March 2008 for 6% of its value twelve months prior.


title: David Malpass

text: In June 2008, Malpass founded Encima Global, a New York City firm providing daily analysis of global economic and political trends relevant to institutional investors. In 2010, Malpass ran for the Republican nomination for United States Senate in that year's special election in New York. He placed second in the three-way primary with 38% of the vote after former Congressman Joe DioGuardi's 42%. In 2012, he wrote a chapter entitled 'Sound Money, Sound Policy' in "", published by the George W. Bush Presidential Center.


title: David Malpass

text: Malpass writes a column for "Forbes" and is a contributor to the op-ed section of "The Wall Street Journal". He is also a frequent television commentator.


title: David Malpass

text: Malpass sits on the boards of UBS Funds, the New Mountain Financial Corporation, and the Gary Klinsky Children's Center. He is also a former director of the National Committee on United States–China Relations, the Council of the Americas, and the Economic Club of New York, and a former member of the board of trustees of the Manhattan Institute.


title: David Malpass

text: Malpass has been noted for his forecasts before the financial crisis of 2007–2008 and in the time period following the Great Recession. In 2007, before the housing market collapse, Malpass wrote for "The Wall Street Journal" that "Housing and debt markets are not that big a part of the U.S. economy, or of job creation...the housing- and debt-market corrections will probably add to the length of the U.S. economic expansion." He also called for the raising of interest rates in 2011 at a time when others believed this would be harmful to the economy. Bruce Bartlett cited Malpass's 2008 forecast of economic growth and his 2012 forecast of recession as specific examples of partisan bias in economic forecasts.


title: David Malpass

text: Malpass joined Donald Trump's presidential campaign in May 2016 as Senior Economic Advisor. He appeared frequently on television and radio to support Trump's message of faster growth through policy reforms. Four of his pre-election "Forbes" columns discussed the need for political upheaval to upend the status quo. On August 5, the campaign announced an economic round-table including Malpass. His September 1, 2016, "The New York Times" op-ed essay described fast growth through a policy upheaval covering taxes, trade, regulations and energy ("Why Our Economy Needs Trump"). Throughout the election time period, Malpass was heading the transition team's work on economic agencies including Treasury, Commerce, the Federal Reserve, USTR and independent regulatory agencies as Trump prepared to become president.


title: David Malpass

text: In March 2017, the White House announced that Malpass would be President Trump's nominee for Under Secretary of the Treasury for International Affairs. Malpass was confirmed for the position by the United States Senate on August 3, 2017.


title: David Malpass

text: Malpass took a critical position on China during his tenure. He was described as "a champion of President Donald Trump's protectionist message."


title: David Malpass

text: In February 2019, President Trump announced Malpass as the nominee for President of the World Bank, succeeding Jim Yong Kim, who had announced in January 2019 that he would be stepping down three years prior to the end of his five-year term in 2022. Malpass was unanimously approved by the executive board on April 5, 2019, and began his term on April 9.


title: David Malpass

text: During the start of his tenure, Malpass rarely mentioned climate change and was considered a supporter of Trump's environmental policies. After inauguration of Joe Biden in early 2021, American policy shifted towards prioritizing fighting climate change, and Malpass increasingly began working and speaking on climate policy. In April 2021, the World Bank released a five year, 100 billion USD Climate Change Action Plan that would devote 35% of all financing to climate co-benefits, 50% of climate financing to climate change adaptation, and harmonize its financing goals with the Paris Agreement by 2023. The plan faced criticism that 35% was too low and that it did not move the World Bank towards fossil fuel divestment.


title: David Malpass

text: During the COVID-19 pandemic, Malpass won praise for supporting developing countries' recovery efforts and being able to quickly use World Bank financing.


title: David Malpass

text: On September 20, 2022, former US Vice President and environmentalist Al Gore labelled Malpass a climate denier and called for Biden to replace him during an event focusing on climate change hosted by "The New York Times". Later during the event, Malpass was given an opportunity to respond to Gore and was asked three times if he accepted the scientific consensus on climate change that human fossil fuel consumption was a leading cause. Malpass did not answer, and said "I'm not a scientist." This answer prompted criticism from climate policy makers such as Rachel Kyte and Mark Carney, and calls for his resignation from the Rocky Mountain Institute and Christiana Figueres, among others. On September 21, the United States Department of the Treasury issued a statement that it expected World Bank leadership to take a leading role on climate issues. On September 22, Malpass said in both an internal memo to World Bank staff and on an interview with CNN International that he accepted the scientific consensus on human activity causing climate change and that he was not a "denier."


title: David Malpass

text: Malpass and his wife, Adele, daughter of Herman Obermayer and granddaughter of Neville Levy, live in New York City. Adele Malpass was appointed as the Chairwoman of the Manhattan Republican Party in January 2015 and was elected to a two-year term in September 2015. She was succeeded in the role by Andrea Catsimatidis after resigning to move to Washington when Malpass was appointed to his role in the Treasury Department under President Trump. , Adele Malpass was the president of The Daily Caller News Foundation, a non-profit organization linked with the eponymous news organization.


title: Confidential Assignment

text: Confidential Assignment (; lit. "Cooperation") is a 2017 South Korean action comedy film directed by Kim Sung-hoon. It stars Hyun Bin, Yoo Hae-jin and Kim Joo-hyuk. In the film, a North Korean officer and a Seoul detective team up to track down a dangerous fugitive, who is running a gang of counterfeiters.


title: Confidential Assignment

text: Im Cheol-ryung, an officer of a special investigation team in North Korea, barges at a warehouse that prints counterfeit money, where he learns that his superior Cha Ki-seong and his own team are there to steal the master plates to print the counterfeit money. A shootout ensues where Cheol-ryung's wife Hwa-ryung and his team are killed, while Cheol-ryung is gravely injured.


title: Confidential Assignment

text: Meanwhile, the North Korean officials learn that Cha Ki-seong has fled to South Korea, where Cheol-ryung is ordered to capture Ki-seong and retrieve the stolen master plates, and is given only three days to complete his mission. However, the South Korean officials suspects whether Ki-seong is really a killer, where they assign Detective Kang Jin-tae from Seoul to watch over Cheol-ryung tightly as they suspect him to kill Ki-seong for vengeance. Jin-tae receives Cheol-ryung from the airport, where they head for Myeong-Dong to check on one of Ki-seong's men Park Myung-ho, but Cheol-ryong escapes after learning about Jin-tae's mission. Cheol-ryung arrives at Myeong-Dong to Jongro where Jin-tae also reaches there and interrogates Park, but the latter escapes. After the orders from his superior, Jin-tae takes Cheol-ryung to his home to spy on him.


title: Confidential Assignment

text: Having guessed the latter's plan, Cheol-ryung removes the SIM card which Jin-tae had inserted in his phone to track his location anytime. The duo learns about the location where Park was supplying drugs and a fight ensues where Cheol-ryung takes one of the men's phone and gives it to Jin-tae. Cheol-ryung learns about Park's location after secretly bugging Jin-tae's phone. The duo heads to the restaurant where they find that Park is conversing with one of Ki-seong's comrades (who was present at the warehouse). The comrade learns that Park plans to settle in South Korea, where he kills him under Ki-seong's orders. Cheol-ryung arrives and warns Ki-seong of his impending death, where he fights the comrade, who escapes. After checking Park's belongings, the officials learn about Cheol-ryung's mission.


title: Confidential Assignment

text: Meanwhile, Jin-tae learns about Cheol-ryung's past and decide to help him. They reach the place where Ki-seong has arranged a deal to sell the plates, but Ki-seong kills the buyer where Cheol-ryung arrives and kills the henchmen where he is about Ki-seong, but Jin-tae stops him which gives time for Ki-seong to escape. Cheol-ryung takes the master plates and leaves. However, Ki-seong kidnaps Jin-tae's family and demands the plates. A frightened Jin-tae tells Cheol-ryung, where he takes the plates and heads to the location. Jin-tae and Cheol-ryung arrives and gives the plates to Ki-seong, who leaves Jin-tae's family where Jin-tae takes his family to a safe place. A battle ensues where Cheol-ryung and Jin-tae manages to kill Ki-seong. One year later, Cheol-ryung and Jin-tae receive their next mission.


title: Confidential Assignment

text: "Confidential Assignment" opened in second place at the box office on January 18. It rose to first place in its second week selling an accumulative four million tickets by January 30 and surpassed the five million mark two days later.


title: Confidential Assignment

text: The movie became the most viewed Korean movie during the first half of 2017 by attracting 7.8 million audience domestically. However, this record was surpassed in August by "A Taxi Driver".


title: Confidential Assignment

text: "Confidential Assignment" was sold to 42 territories, including the U.S. and several countries in Asia.


title: Confidential Assignment

text: "", a sequel was announced on August 24, 2020. Filming started on February 18, 2021 and was released on September 7, 2022.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip of Sweden, Duke of Värmland (Carl Philip Edmund Bertil; born 13 May 1979) is the only son and the second of three children of King Carl XVI Gustaf and Queen Silvia. , Prince Carl Philip is fourth in the line of succession, after his older sister, Crown Princess Victoria, his niece and goddaughter Princess Estelle, and his nephew Prince Oscar. He lives with his wife, Princess Sofia, and three sons, Prince Alexander, Prince Gabriel and Prince Julian in Villa Solbacken in Djurgården, Stockholm.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip was born on 13 May 1979 at Stockholm Palace, Sweden. He was baptised at the Royal Chapel on 31 August 1979. His mother is of half German and half Brazilian descent.


title: Prince Carl Philip, Duke of Värmland

text: Carl Philip was heir apparent to the throne of Sweden (and thus held the title Crown Prince) for seven months, until 1 January 1980 when a change in the constitution came into effect which made natural birth order the basis for succession to the throne, replacing the principle of agnatic primogeniture. His elder sister Victoria became heir apparent and Crown Princess, with Carl Philip becoming second in line.


title: Prince Carl Philip, Duke of Värmland

text: During 1984–1986, Prince Carl Philip attended the Västerled parish preschool. In the autumn of 1986, he started school at Smedslättsskolan in Bromma which he attended at junior level. For the intermediate level, he attended Ålstensskolan in Bromma, proceeding from there, in the autumn of 1992, to senior level at Enskilda Gymnasiet in Stockholm. In the autumn of 1994, Carl Philip enrolled at Kent School. He then continued his studies in a science programme at Lundsbergs upper secondary school. He graduated in the spring of 1999. In 2007–2008, he studied graphic design at the Rhode Island School of Design for one year. In 2011, Prince Carl Philip finished his studies in Agricultural and Rural Management at the Swedish University of Agricultural Sciences in Alnarp.


title: Prince Carl Philip, Duke of Värmland

text: Carl Philip has dyslexia, as do his father King Carl XVI Gustaf and his sister Crown Princess Victoria.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip has been a scout and is fond of outdoor life. He is keen on sport and athletics, especially football, swimming, sailing and skiing. In 2003, he completed the historic Swedish "Vasaloppet", the longest cross country ski race in the world. Carl Philip also enjoys car racing, a passion he inherited from his great-uncle and godfather, Prince Bertil, and has a licence to compete. Prince Carl Philip has taken part in the racing series Porsche Carrera Cup Scandinavia in a Porsche 911 GT3. Since 2013 he has raced in the Scandinavian Touring Car Championship.


title: Prince Carl Philip, Duke of Värmland

text: The prince completed his military service at the Amphibious Battalion at Vaxholm Coastal Artillery Regiment as a combat boat commander (Combat Boat 90) in the autumn of 2000. In December 2002, the Prince was promoted to second lieutenant, and in 2004 to the rank of lieutenant in the Swedish Amphibious Corps. In 2007 and 2008 he went to the Swedish National Defense College. The course was divided in three weeks autumn 2007 and three weeks spring 2008. After that course he was appointed captain. On 1 October 2014, Prince Carl Philip achieved the rank of major.


title: Prince Carl Philip, Duke of Värmland

text: With a great interest for design and drawing, the prince began studying graphic design in Stockholm in 2003, studies which he continues still.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip and Princess Sofia's Foundation was established to mark the occasion of the couple's marriage in 2015. The foundation's purpose is to counteract bullying.


title: Prince Carl Philip, Duke of Värmland

text: In 2013, the Prince Carl Philip Racing Cup was founded. The racing cup aims to help young people with karting talents progress within the sport. The Prince with the Royal Swedish Academy of Engineering Sciences conducts a range of visits to companies, with focus on the companies' creative work.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip is a patron of several organizations such as The Swedish National Dyslexia Association, The Swedish Rural Economy and Agricultural Societies, The International Union for Conservation of Nature, The Royal Swedish Motorboat Club and others.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip dated Emma Pernald from 1999 to 2009. Pernald worked at a PR firm for several years. However, the prince and Pernald broke off their relationship in March 2009. She revealed in the Swedish newspaper "Expressen" that she and the prince mutually decided to go their separate ways. Pernald made no further comment as to the reason for the break-up.


title: Prince Carl Philip, Duke of Värmland

text: In April 2010, Carl Philip was linked in the press with former glamour model Sofia Hellqvist. In August 2010, Royal Court spokesperson Nina Eldh confirmed the relationship between Carl Philip and Hellqvist in a statement released by the palace. On 27 June 2014, it was announced that Carl Philip and Hellqvist were engaged.


title: Prince Carl Philip, Duke of Värmland

text: They married on 13 June 2015 in Stockholm's Royal Palace chapel, and thousands of people lined the streets for the occasion. In an interview he criticized the press for suggesting that Hellqvist was not welcome in the royal family. He told the press that the opposite was true and that his family easily accepted her into the family. He compared the "bullying" of her past to that of himself being bullied for having dyslexia.


title: Prince Carl Philip, Duke of Värmland

text: The couple was due to move into the Villa Solbacken which had been vacant since the death of Princess Lilian, and while it was being renovated, they lived in Rosendal Palace until 2017.


title: Prince Carl Philip, Duke of Värmland

text: On 7 October 2019, Carl Philip's father, the king, issued a statement rescinding the royal status of Prince Alexander and Prince Gabriel in an effort to more strictly associate Swedish royalty to the office of the head of state; they are still to be styled as princes and dukes of their provinces, and they remain in the line of succession to the throne. Carl Philip and his wife commented that their sons now will have more freedom of choice for their future lives.


title: Prince Carl Philip, Duke of Värmland

text: Prince Carl Philip's coat of arms is based on the greater coat of arms of Sweden. It features in the first and fourth quarters, the Three Crowns; in the second, the lion of the House of Bjelbo; and in the third, the eagle of the arms of Värmland, representing the titular designation of his dukedom. In the centre, on an inescutcheon, is the dynastic arms of the House of Bernadotte. Surrounding the shield is the chain of the Order of the Seraphim.


title: The Man with the Iron Heart (film)

text: The Man with the Iron Heart (released as HHhH in France and Killing Heydrich in Canada) is a 2017 biographical action-thriller film directed by Cédric Jimenez and written by David Farr, Audrey Diwan, and Jimenez. An English-language French-Belgian production, it is based on French writer Laurent Binet's 2010 novel "HHhH", and focuses on "Operation Anthropoid", the assassination of Nazi leader Reinhard Heydrich in Prague during World War II.


title: The Man with the Iron Heart (film)

text: The film stars Jason Clarke, Rosamund Pike, Jack O'Connell, Jack Reynor, and Mia Wasikowska. It was shot in Prague and Budapest from September 2015 until February 2016.


title: The Man with the Iron Heart (film)

text: Reinhard Heydrich is serving as an officer in the German Navy. After beginning a relationship with Lina, he is court-martialled for breaking his word to another woman he had been having sex with. He marries Lina and follows her in joining the Nazi Party and idolising Adolf Hitler. He meets Heinrich Himmler and is appointed head of SS counter-intelligence, working with Heinrich Müller to fight Communists in Weimar Germany. After Hitler is appointed Chancellor, Heydrich becomes Chief of the Gestapo.


title: The Man with the Iron Heart (film)

text: After the German Invasion of Poland and World War II breaks out, Heydrich is promoted to Chief of the Reich Security Main Office. His "Einsatzgruppen" mobile death squads follow the German Army, committing genocide across Eastern Europe. He blackmails General Eduard Wagner into sending the "Einzsatzgruppen" information to allow them to exterminate Jews and other "Untermenschen". In September 1941, Heydrich is appointed Acting Reich Protector of the Protectorate of Bohemia and Moravia, declaring that he will turn Prague into a "Jew-free" city. On 22 January 1942, Heydrich chairs the Wannsee Conference, to ensure there is a "Final Solution" for the genocide of Jews. In May 1942, Heydrich is attacked by Czech resistance fighters.


title: The Man with the Iron Heart (film)

text: The film is based on Laurent Binet's novel "HHhH" about Operation Anthropoid, the assassination of Nazi leader Reinhard Heydrich in Prague. The title is an acronym for "Himmlers Hirn heißt Heydrich" ("Himmler's brain is called Heydrich"), a quip about Heydrich said to have circulated in Nazi Germany. Cédric Jimenez directed the film based on the script he co-wrote with David Farr and Audrey Diwan, which was financed by Légende Films, Adama Pictures, Echo Lake Entertainment and FilmNation Entertainment. Alain Goldman and Simon Istolainen produced the film. On 28 October 2015, The Weinstein Company came on board to handle the United States distribution rights to the film. Principal photography on the film began on 14 September 2015 in Prague and Budapest, which ended on 1 February 2016.


title: The Man with the Iron Heart (film)

text: On Rotten Tomatoes, the film holds an approval rating of 67% based on , with an average rating of 5.83/10.


title: The Man with the Iron Heart (film)

text: Boyd van Hoeij of "The Hollywood Reporter" wrote: "Finally less a two-stories-for-the-price-of-one situation than essentially two films of about an hour each, this is nonetheless a visually impressive Hollywood calling card for Jimenez, who almost manages to overcome the material’s structural weaknesses with impressive directorial verve."


title: Ministry of Defence (Russia)

text: The Ministry of Defence of the Russian Federation (, informally abbreviated as МО, МО РФ or Minoboron) is the governing body of the Russian Armed Forces.


title: Ministry of Defence (Russia)

text: The President of Russia is the Commander-in-Chief of the Armed Forces of the Russian Federation and directs the activity of the Ministry. The Defence Minister exercises day-to-day administrative and operational authority over the armed forces. The General Staff executes the president's and the defence minister's instructions and orders.


title: Ministry of Defence (Russia)

text: The main building of the ministry, built in the 1940s, is located on Arbatskaya Square, near Arbat Street. Other buildings of the ministry are located throughout the city of Moscow. The supreme body responsible for the Ministry's management and supervision of the Armed Forces is The National Defense Management Center (Национальный центр управления обороной РФ) located on Frunzenskaya Embankment and responsible for the centralization of the Armed Forces' command.


title: Ministry of Defence (Russia)

text: The authors of the U.S. Library of Congress Country Studies' volume for Russia said in July 1996 that:


title: Ministry of Defence (Russia)

text: In May 1992, President of Russia Boris Yeltsin appointed General of the Army Pavel Grachev to the post of Minister of Defence. Grachev's decision to side with Yeltsin in the Russian constitutional crisis of 1993, when the president called up tanks to shell the Russian White House to blast his opponents out of parliament, effectively deprived the Supreme Soviet of Russia of its nominal an opportunity to overturn the president's authority. At least partly for that reason, Yeltsin retained his defence minister despite intense criticism of Grachev's management of the First Chechen War and the Russian military establishment in general. Finally, Yeltsin's victory in the first round of the 1996 Russian presidential election spurred Yeltsin to dismiss Grachev.


title: Ministry of Defence (Russia)

text: In March 2001, Sergei Ivanov, previously secretary of the Security Council of Russia was appointed defence minister by President Vladimir Putin, becoming Russia's first non-uniformed civilian defence minister.


title: Ministry of Defence (Russia)

text: Putin called the personnel changes in Russia's security structures coinciding with Ivanov's appointment as defence minister "a step toward demilitarizing public life." Putin also stressed Ivanov's responsibility for overseeing military reform as defence minister. What Putin did not emphasise was Ivanov's long service within the KGB and FSB and his then rank of General-Lieutenant within the FSB. Such military and security agency associated men are known as siloviki.


title: Ministry of Defence (Russia)

text: As of 2002 there were four living Marshals of the Soviet Union. Such men are automatically Advisors to the Defence Minister. The Marshals alive at that time were Viktor Kulikov, Vasily Petrov, Sergei Sokolov, a former Minister of Defence of the Soviet Union, and Dmitri Yazov. Yazov was listed by the American analysts Scott and Scott in 2002 as a consultant to the (former 10th) Directorate for International Military Cooperation


title: Ministry of Defence (Russia)

text: Perhaps the first 'real' non-uniformed Defence Minister was Anatoliy Serdyukov, appointed in February 2007. Serdyukov was a former Tax Minister with little siloviki or military associations beyond his two years' military service.


title: Ministry of Defence (Russia)

text: The Ministry of Defence is managed by a collegium chaired by the Defence Minister and including the deputy Defence Ministers, heads of Main Defence Ministry and General Staff Directorates, and the commanders of the Joint Strategic Commands/Military Districts, the three Services, and three branches, who together form the principal staff and advisory board of the Minister of Defence.


title: Ministry of Defence (Russia)

text: The executive body of the Ministry of Defence is the General Staff of the Armed Forces of the Russian Federation. It is commanded by the Chief of General Staff. U.S. expert William Odom said in 1998 that 'the Soviet General Staff without the MoD is conceivable, but the MoD without the General Staff is not.' Russian General Staff officers exercise command authority in their own right. In 1996 the General Staff included fifteen main directorates and an undetermined number of operating agencies. The staff is organized by functions, with each directorate and operating agency overseeing a functional area, generally indicated by the organization's title.


title: Ministry of Defence (Russia)

text: "Military Thought" is the military-theoretical journal of the Ministry of Defence, and Krasnaya Zvezda its daily newspaper.


title: Ministry of Defence (Russia)

text: The Office of Inspectors General of the Ministry of Defence was established in 2008, consisting of around thirty retired senior officers. The main task of the office is "to promote the organization of combat and operational training of troops, the construction and further development of the Armed Forces of the Russian Federation, the development of the theory and history of military art, and the education of personnel." It is the successor to the Soviet Armed Forces's Group of Inspectors General, which was dissolved in 1992.


title: Ministry of Defence (Russia)

text: An outline structure of the Ministry of Defence includes the groupings below, but this structure was in transition when it was recorded in 2004, with several deputy minister posts being abolished:


title: Simon of Cyrene

text: Simon of Cyrene (, Standard Hebrew "Šimʿon", Tiberian Hebrew "Šimʿôn"; , "Simōn Kyrēnaios"; ) was the man compelled by the Romans to carry the cross of Jesus of Nazareth as Jesus was taken to his crucifixion, according to all three Synoptic Gospels: He was also the father of the disciples Rufus and Alexander.


title: Simon of Cyrene

text: Cyrene was located in northern Africa in eastern Libya. A Greco-Egyptian city in the province of Cyrenaica, it had a Jewish community where 100,000 Judean Jews had been forced to settle during the reign of Ptolemy Soter (323–285 BC) and was an early center of Christianity.


title: Simon of Cyrene

text: Simon's act of carrying the cross, "patibulum" (crossbeam in Latin), for Jesus is the fifth or seventh of the Stations of the Cross. Some interpret the passage as indicating that Simon was chosen because he may have shown sympathy with Jesus. Others point out that the text itself says nothing, that he had no choice, and that there is no basis to consider the carrying of the cross an act of sympathetic generosity.


title: Simon of Cyrene

text: A burial cave in the Kidron Valley discovered in 1941 by E. L. Sukenik, belonging to Cyrenian Jews and dating before AD 70, was found to have an ossuary inscribed twice in Greek "Alexander son of Simon". It cannot, however, be certain that this refers to the same person.


title: Simon of Cyrene

text: According to some Gnostic traditions, Simon of Cyrene, by mistaken identity, suffered the events leading up to the crucifixion. This is the story presented in the Second Treatise of the Great Seth, although it is unclear whether Simon or another actually died on the cross. This is part of a belief held by some Gnostics that Jesus was not of flesh, but only took on the appearance of flesh (see also Basilides, and Swoon hypothesis).


title: Simon of Cyrene

text: Basilides, in his gospel of Basilides, is reported by Irenaeus as having taught a docetic doctrine of Christ's passion. He states the teaching that Christ, in Jesus, as a wholly divine being, could not suffer bodily pain and did not die on the cross; but that the person crucified was, in fact, Simon of Cyrene. Irenaeus quotes Basiledes:


title: Simon of Cyrene

text: He appeared on earth as a man and performed miracles. Thus he himself did not suffer. Rather, a certain Simon of Cyrene was compelled to carry his cross for him. It was he who was ignorantly and erroneously crucified, being transfigured by him, so that he might be thought to be Jesus. Moreover, Jesus assumed the form of Simon, and stood by laughing at them.Irenaeus, "Against Heresies"


title: Simon of Cyrene

text: According to the visions of Anne Catherine Emmerich, Simon was a pagan. The Romans recognized he was not a Jew by his clothes and then chose him to oblige him to help Jesus carry the cross.


title: Simon of Cyrene

text: Poet Ridgely Torrence wrote a play about him titled "Simon the Cyrenian". A 1920 YWCA production of this play was directed by Dora Cole, sister of composer Bob Cole, and starred Paul Robeson.


title: Simon of Cyrene

text: Sidney Poitier was cast as Simon of Cyrene in "The Greatest Story Ever Told" that was directed by George Stevens and released in 1965.


title: Simon of Cyrene

text: The 1979 comedy film "Monty Python's Life of Brian" contains a vignette referencing the Simon of Cyrene episode. In this case, a seemingly pious and generous man offers to one of the condemned carrying a cross, "Brother, let me shoulder your burden." Upon doing so, the condemned man runs off, leaving the generous man stuck with the cross and future crucifixion.


title: Simon of Cyrene

text: The film "The Passion of the Christ" portrays Simon as a Jew who, having been forced by the Romans to carry the cross, is initially unwilling but comes to show compassion to Jesus and helps him.


title: Simon of Cyrene

text: Both the Simon Community, and the Cyrenian movement (which provides services to homeless and other disadvantaged groups in the UK) take their name from Simon of Cyrene.


title: Square metre

text: The square metre (international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m. It is the area of a square with sides one metre in length.


title: Square metre

text: Adding and subtracting SI prefixes creates multiples and submultiples; however, as the unit is exponentiated, the quantities grow exponentially by the corresponding power of 10. For example, 1 kilometre is 10 (one thousand) times the length of 1 metre, but 1 square kilometre is (10) (10, one million) times the area of 1 square metre, and 1 cubic kilometre is (10) (10, one billion) cubic metres.


title: Square metre

text: Unicode has several characters used to represent metric area units, but these are for compatibility with East Asian character encodings and are meant to be used in new documents.


title: Transfer function

text: In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used in electronics and control systems. In some simple cases, this function is a two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.


title: Transfer function

text: The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electrical current applied to the device; the transfer function of a photodetector might be the output voltage as a function of the luminous intensity of incident light of a given wavelength.


title: Transfer function

text: The term "transfer function" is also used in the frequency domain analysis of systems using transform methods such as the Laplace transform; here it means the amplitude of the output as a function of the frequency of the input signal. For example, the transfer function of an electronic filter is the voltage amplitude at the output as a function of the frequency of a constant amplitude sine wave applied to the input. For optical imaging devices, the optical transfer function is the Fourier transform of the point spread function (hence a function of spatial frequency).


title: Transfer function

text: Transfer functions are commonly used in the analysis of systems such as single-input single-output filters in the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear time-invariant (LTI) systems. Most real systems have non-linear input/output characteristics, but many systems, when operated within nominal parameters (not "over-driven") have behavior close enough to linear that LTI system theory is an acceptable representation of the input/output behavior.


title: Transfer function

text: The descriptions below are given in terms of a complex variable, formula_1, which bears a brief explanation. In many applications, it is sufficient to define formula_2 (thus formula_3), which reduces the Laplace transforms with complex arguments to Fourier transforms with real argument ω. The applications where this is common are ones where there is interest only in the steady-state response of an LTI system, not the fleeting turn-on and turn-off behaviors or stability issues. That is usually the case for signal processing and communication theory.


title: Transfer function

text: Thus, for continuous-time input signal formula_4 and output formula_5, the transfer function formula_6 is the linear mapping of the Laplace transform of the input, formula_7, to the Laplace transform of the output formula_8:


title: Transfer function

text: In discrete-time systems, the relation between an input signal formula_4 and output formula_5 is dealt with using the z-transform, and then the transfer function is similarly written as formula_13 and this is often referred to as the pulse-transfer function.


title: Transfer function

text: where "u" and "r" are suitably smooth functions of "t", and "L" is the operator defined on the relevant function space, that transforms "u" into "r". That kind of equation can be used to constrain the output function "u" in terms of the "forcing" function "r". The transfer function can be used to define an operator formula_15 that serves as a right inverse of "L", meaning that formula_16.


title: Transfer function

text: Solutions of the "homogeneous", constant-coefficient differential equation formula_17 can be found by trying formula_18. That substitution yields the characteristic polynomial


title: Transfer function

text: The inhomogeneous case can be easily solved if the input function "r" is also of the form formula_20. In that case, by substituting formula_21 one finds that formula_22 if we define


title: Transfer function

text: Taking that as the definition of the transfer function requires careful disambiguation between complex vs. real values, which is traditionally influenced by the interpretation of abs("H"("s")) as the gain and −atan("H"("s")) as the phase lag. Other definitions of the transfer function are used: for example formula_24


title: Transfer function

text: A general sinusoidal input to a system of frequency formula_25 may be written formula_26. The response of a system to a sinusoidal input beginning at time formula_27 will consist of the sum of the steady-state response and a transient response. The steady-state response is the output of the system in the limit of infinite time, and the transient response is the difference between the response and the steady state response (it corresponds to the homogeneous solution of the above differential equation). The transfer function for an LTI system may be written as the product:


title: Transfer function

text: where "s" are the "N" roots of the characteristic polynomial and will therefore be the poles of the transfer function. Consider the case of a transfer function with a single pole formula_29 where formula_30. The Laplace transform of a general sinusoid of unit amplitude will be formula_31. The Laplace transform of the output will be formula_32 and the temporal output will be the inverse Laplace transform of that function:


title: Transfer function

text: The second term in the numerator is the transient response, and in the limit of infinite time it will diverge to infinity if "σ" is positive. In order for a system to be stable, its transfer function must have no poles whose real parts are positive. If the transfer function is strictly stable, the real parts of all poles will be negative, and the transient behavior will tend to zero in the limit of infinite time. The steady-state output will be:


title: Transfer function

text: The frequency response (or "gain") "G" of the system is defined as the absolute value of the ratio of the output amplitude to the steady-state input amplitude:


title: Transfer function

text: which is just the absolute value of the transfer function formula_36 evaluated at formula_37. This result can be shown to be valid for any number of transfer function poles.


title: Transfer function

text: Let formula_38 be the input to a general linear time-invariant system, and formula_39 be the output, and the bilateral Laplace transform of formula_38 and formula_39 be


title: Transfer function

text: In particular, if a complex harmonic signal with a sinusoidal component with amplitude formula_46, angular frequency formula_47 and phase formula_48, where arg is the argument


title: Transfer function

text: Note that, in a linear time-invariant system, the input frequency formula_52 has not changed, only the amplitude and the phase angle of the sinusoid has been changed by the system. The frequency response formula_53 describes this change for every frequency formula_52 in terms of "gain":


title: Transfer function

text: The phase delay (i.e., the frequency-dependent amount of delay introduced to the sinusoid by the transfer function) is:


title: Transfer function

text: The group delay (i.e., the frequency-dependent amount of delay introduced to the envelope of the sinusoid by the transfer function) is found by computing the derivative of the phase shift with respect to angular frequency formula_52,


title: Transfer function

text: The transfer function can also be shown using the Fourier transform which is only a special case of the bilateral Laplace transform for the case where formula_60.


title: Transfer function

text: While any LTI system can be described by some transfer function or another, there are certain "families" of special transfer functions that are commonly used.


title: Transfer function

text: In control engineering and control theory the transfer function is derived using the Laplace transform.


title: Transfer function

text: The transfer function was the primary tool used in classical control engineering. However, it has proven to be unwieldy for the analysis of multiple-input multiple-output (MIMO) systems, and has been largely supplanted by state space representations for such systems. In spite of this, a transfer matrix can always be obtained for any linear system, in order to analyze its dynamics and other properties: each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.


title: Transfer function

text: A useful representation bridging state space and transfer function methods was proposed by Howard H. Rosenbrock and is referred to as Rosenbrock system matrix.


title: Transfer function

text: For example, when observing a series of black-white-light fringes drawn with a specific spatial frequency, the image quality may decay. White fringes fade while black ones turn brighter.


title: Transfer function

text: In imaging, transfer functions are used to describe the relationship between the scene light, the image signal and the displayed light.


title: Transfer function

text: Transfer functions do not properly exist for many non-linear systems. For example, they do not exist for relaxation oscillators; however, describing functions can sometimes be used to approximate such nonlinear time-invariant systems.


title: Cathode

text: A cathode is the electrode from which a conventional current leaves a polarized electrical device. This definition can be recalled by using the mnemonic "CCD" for "Cathode Current Departs". A conventional current describes the direction in which positive charges move. Electrons have a negative electrical charge, so the movement of electrons is opposite to that of the conventional current flow. Consequently, the mnemonic "cathode current departs" also means that electrons flow "into" the device's cathode from the external circuit. For example, the end of a household battery marked with a + (plus) is the cathode.


title: Cathode

text: The electrode through which conventional current flows the other way, into the device, is termed an anode.


title: Cathode

text: Conventional current flows from cathode to anode outside of the cell or device (with electrons moving in the opposite direction), regardless of the cell or device type and operating mode.


title: Cathode

text: Cathode polarity with respect to the anode can be positive or negative depending on how the device is being operated. Positively charged cations always move towards the cathode and negatively charged anions move towards the anode, although cathode polarity depends on the device type, and can even vary according to the operating mode. Whether the cathode is negatively polarized (such as recharging a battery) or positively polarized (such as a battery in use), the cathode will draw electrons into it as well as attract positively charged cations.


title: Cathode

text: A battery or galvanic cell in use has a cathode that is the positive terminal since that is where conventional current flows out of the device. This outward current is carried internally by positive ions moving from the electrolyte to the positive cathode (chemical energy is responsible for this "uphill" motion). It is continued externally by electrons moving into the battery which constitutes positive current flowing outwards. For example, the Daniell galvanic cell's copper electrode is the positive terminal and the cathode.


title: Cathode

text: A battery that is recharging or an electrolytic cell performing electrolysis has its cathode as the negative terminal, from which current exits the device and returns to the external generator as charge enters the battery/ cell. For example, reversing the current direction in a Daniell galvanic cell converts it into an electrolytic cell where the copper electrode is the positive terminal and also the anode.


title: Cathode

text: In a diode, the cathode is the negative terminal at the pointed end of the arrow symbol, where current flows out of the device. Note: electrode naming for diodes is always based on the direction of the forward current (that of the arrow, in which the current flows "most easily"), even for types such as Zener diodes or solar cells where the current of interest is the reverse current.


title: Cathode

text: In vacuum tubes (including cathode-ray tubes) it is the negative terminal where electrons enter the device from the external circuit and proceed into the tube's near-vacuum, constituting a positive current flowing out of the device.


title: Cathode

text: The word was coined in 1834 from the Greek κάθοδος ("kathodos"), 'descent' or 'way down', by William Whewell, who had been consulted by Michael Faraday over some new names needed to complete a paper on the recently discovered process of electrolysis. In that paper Faraday explained that when an electrolytic cell is oriented so that electric current traverses the "decomposing body" (electrolyte) in a direction "from East to West, or, which will strengthen this help to the memory, that in which the sun appears to move", the cathode is where the current leaves the electrolyte, on the West side: ""kata" downwards, "`odos" a way ; the way which the sun sets".


title: Cathode

text: The use of 'West' to mean the 'out' direction (actually 'out' → 'West' → 'sunset' → 'down', i.e. 'out of view') may appear unnecessarily contrived. Previously, as related in the first reference cited above, Faraday had used the more straightforward term "exode" (the doorway where the current exits). His motivation for changing it to something meaning 'the West electrode' (other candidates had been "westode", "occiode" and "dysiode") was to make it immune to a possible later change in the direction convention for current, whose exact nature was not known at the time. The reference he used to this effect was the Earth's magnetic field direction, which at that time was believed to be invariant. He fundamentally defined his arbitrary orientation for the cell as being that in which the internal current would run parallel to and in the same direction as a hypothetical magnetizing current loop around the local line of latitude which would induce a magnetic dipole field oriented like the Earth's. This made the internal current East to West as previously mentioned, but in the event of a later convention change it would have become West to East, so that the West electrode would not have been the 'way out' any more. Therefore, "exode" would have become inappropriate, whereas "cathode" meaning 'West electrode' would have remained correct with respect to the unchanged direction of the actual phenomenon underlying the current, then unknown but, he thought, unambiguously defined by the magnetic reference. In retrospect the name change was unfortunate, not only because the Greek roots alone do not reveal the cathode's function any more, but more importantly because, as we now know, the Earth's magnetic field direction on which the "cathode" term is based is subject to reversals whereas the current direction convention on which the "exode" term was based has no reason to change in the future.


title: Cathode

text: Since the later discovery of the electron, an easier to remember, and more durably technically correct (although historically false), etymology has been suggested: cathode, from the Greek "kathodos", 'way down', 'the way (down) into the cell (or other device) for electrons'.


title: Cathode

text: In chemistry, a cathode is the electrode of an electrochemical cell at which reduction occurs. The cathode can be negative like when the cell is electrolytic (where electrical energy provided to the cell is being used for decomposing chemical compounds); or positive as when the cell is galvanic (where chemical reactions are used for generating electrical energy). The cathode supplies electrons to the positively charged cations which flow to it from the electrolyte (even if the cell is galvanic, i.e., when the cathode is positive and therefore would be expected to repel the positively charged cations; this is due to electrode potential relative to the electrolyte solution being different for the anode and cathode metal/electrolyte systems in a galvanic cell).


title: Cathode

text: The cathodic current, in electrochemistry, is the flow of electrons from the cathode interface to a species in solution. The anodic current is the flow of electrons into the anode from a species in solution.


title: Cathode

text: In an electrolytic cell, the cathode is where the negative polarity is applied to drive the cell. Common results of reduction at the cathode are hydrogen gas or pure metal from metal ions. When discussing the relative reducing power of two redox agents, the couple for generating the more reducing species is said to be more "cathodic" with respect to the more easily reduced reagent.


title: Cathode

text: In a galvanic cell, the cathode is where the positive pole is connected to allow the circuit to be completed: as the anode of the galvanic cell gives off electrons, they return from the circuit into the cell through the cathode.


title: Cathode

text: When metal ions are reduced from ionic solution, they form a pure metal surface on the cathode. Items to be plated with pure metal are attached to and become part of the cathode in the electrolytic solution.


title: Cathode

text: In a vacuum tube or electronic vacuum system, the cathode is a metal surface which emits free electrons into the evacuated space. Since the electrons are attracted to the positive nuclei of the metal atoms, they normally stay inside the metal and require energy to leave it; this is called the "work function" of the metal. Cathodes are induced to emit electrons by several mechanisms:


title: Cathode

text: A hot cathode is a cathode that is heated by a filament to produce electrons by thermionic emission. The filament is a thin wire of a refractory metal like tungsten heated red-hot by an electric current passing through it. Before the advent of transistors in the 1960s, virtually all electronic equipment used hot-cathode vacuum tubes. Today hot cathodes are used in vacuum tubes in radio transmitters and microwave ovens, to produce the electron beams in older cathode-ray tube (CRT) type televisions and computer monitors, in x-ray generators, electron microscopes, and fluorescent tubes.


title: Cathode

text: In order to improve electron emission, cathodes are treated with chemicals, usually compounds of metals with a low work function. Treated cathodes require less surface area, lower temperatures and less power to supply the same cathode current. The untreated tungsten filaments used in early tubes (called "bright emitters") had to be heated to 1400 °C (~2500 °F), white-hot, to produce sufficient thermionic emission for use, while modern coated cathodes produce far more electrons at a given temperature so they only have to be heated to 425–600 °C (~800–1100 °F) () There are two main types of treated cathodes:


title: Cathode

text: This is a cathode that is not heated by a filament. They may emit electrons by field electron emission, and in gas-filled tubes by secondary emission. Some examples are electrodes in neon lights, cold-cathode fluorescent lamps (CCFLs) used as backlights in laptops, thyratron tubes, and Crookes tubes. They do not necessarily operate at room temperature; in some devices the cathode is heated by the electron current flowing through it to a temperature at which thermionic emission occurs. For example, in some fluorescent tubes a momentary high voltage is applied to the electrodes to start the current through the tube; after starting the electrodes are heated enough by the current to keep emitting electrons to sustain the discharge.


title: Cathode

text: Cold cathodes may also emit electrons by photoelectric emission. These are often called "photocathodes" and are used in phototubes used in scientific instruments and image intensifier tubes used in night vision goggles.


title: Cathode

text: In a semiconductor diode, the cathode is the N–doped layer of the PN junction with a high density of free electrons due to doping, and an equal density of fixed positive charges, which are the dopants that have been thermally ionized. In the anode, the converse applies: It features a high density of free "holes" and consequently fixed negative dopants which have captured an electron (hence the origin of the holes).


title: Cathode

text: When P and N-doped layers are created adjacent to each other, diffusion ensures that electrons flow from high to low density areas: That is, from the N to the P side. They leave behind the fixed positively charged dopants near the junction. Similarly, holes diffuse from P to N leaving behind fixed negative ionised dopants near the junction. These layers of fixed positive and negative charges are collectively known as the depletion layer because they are depleted of free electrons and holes. The depletion layer at the junction is at the origin of the diode's rectifying properties. This is due to the resulting internal field and corresponding potential barrier which inhibit current flow in reverse applied bias which increases the internal depletion layer field. Conversely, they allow it in forwards applied bias where the applied bias reduces the built in potential barrier.


title: Cathode

text: Electrons which diffuse from the cathode into the P-doped layer, or anode, become what are termed "minority carriers" and tend to recombine there with the majority carriers, which are holes, on a timescale characteristic of the material which is the p-type minority carrier lifetime. Similarly, holes diffusing into the N-doped layer become minority carriers and tend to recombine with electrons. In equilibrium, with no applied bias, thermally assisted diffusion of electrons and holes in opposite directions across the depletion layer ensure a zero net current with electrons flowing from cathode to anode and recombining, and holes flowing from anode to cathode across the junction or depletion layer and recombining.


title: Cathode

text: Like a typical diode, there is a fixed anode and cathode in a Zener diode, but it will conduct current in the reverse direction (electrons flow from anode to cathode) if its breakdown voltage or "Zener voltage" is exceeded.


title: Address

text: An address is a collection of information, presented in a mostly fixed format, used to give the location of a building, apartment, or other structure or a plot of land, generally using political boundaries and street names as references, along with other identifiers such as house or apartment numbers and organization name. Some addresses also contain special codes, such as a postal code, to make identification easier and aid in the routing of mail.


title: Address

text: Addresses provide a means of physically locating a building. They are used in identifying buildings as the end points of a postal system and as parameters in statistics collection, especially in census-taking and the insurance industry.


title: Address

text: Address formats are different in different places, and unlike latitude and longitude coordinates, there is no simple mapping from an address to a location.


title: Address

text: Street naming and numbering began under the age of Enlightenment, also as part of campaigns for census and military conscription, such as in the dominions of Maria Theresa in the mid 18th century.


title: Address

text: Numbering allowed the efficient delivery of mail, as the postal system evolved in the 18th and 19th centuries to reach widespread usage.


title: Address

text: Comprehensive addressing of all buildings is still not complete, even in developed countries. For example, the Navajo Nation in the United States was still assigning rural addresses as of 2015 and the lack of addresses can be used for voter disenfranchisement in the USA. In many cities in Asia, most minor streets were never named, and this is still the case today in much of Japan. A third of houses in Ireland lacked unique numbers until the introduction of Eircode in 2014.


title: Address

text: In most English-speaking countries, the usual method of house numbering is an alternating numbering scheme progressing in each direction along a street, with odd numbers on one side (often west or south or the left-hand side leading away from a main road) and even numbers on the other side, although there is significant variation on this basic pattern. Many older towns and cities in the UK have "up and down" numbering where the numbers progress sequentially along one side of the road, and then sequentially back down the other side. Cities in North America, particularly those planned on a grid plan, often incorporate block numbers, quadrants (explained below), and cardinal directions into their street numbers, so that in many such cities, addresses roughly follow a Cartesian coordinate system. Some other cities around the world have their own schemes.


title: Address

text: Although house numbering is the principal identification scheme in many parts of the world, it is also common for houses in the United Kingdom and Ireland to be identified by name, rather than number, especially in villages. In these cases, the street name will usually follow the house name. Such an address might read: "Smith Cottage, Frog Lane, Barchester, Barsetshire, BZ9 9BA" or "Dunroamin, Emo, Co. Laois, Ireland" (fictional examples).


title: Address

text: In cities with Cartesian-coordinate-based addressing systems, the streets that form the north–south and east–west dividing lines constitute the "x" and "y" axes of a Cartesian coordinate plane and thus divide the city into quadrants. The quadrants are typically identified in the street names, although the manner of doing so varies from city to city. For example, in one city, all streets in the northeast quadrant may have "NE" prefixed or suffixed to their street names, while in another, the intersection of "North" Calvert Street and "East" 27th Street can be only in the northeast quadrant.


title: Address

text: Street names may follow a variety of themes. In many North American cities, such as San Francisco, USA, and Edmonton, Alberta and Vancouver, British Columbia, streets are simply numbered sequentially across the street grid. Numbered streets originated in the United States in Philadelphia by Thomas Holme who laid out the original plan for the city in 1683. Washington, D.C. has its numbered streets running north–south and lettered or alphabetically named streets running east–west, while diagonal avenues are typically named after states. In Salt Lake City, and many other Utah cities, streets are in a large grid and are numbered in increments of 100 based on their location relative to the center of the city in blocks. A similar system is in use in Detroit with the Mile Road System. In some housing developments in North America and elsewhere, street names may all follow the same theme (for example, bird species), or start with the same letter. Streets in Continental Europe, the Middle East, and Latin America are often named after famous people or significant dates.


title: Address

text: Postal codes are a relatively recent development in addressing, designed to speed the sorting and processing of mail by assigning unique numeric or alphanumeric codes to each geographical locality.


title: Address

text: For privacy and other purposes, postal services have made it possible to receive mail without revealing one's physical address or even having a fixed physical address. Examples are post office boxes, service addresses and poste restante (general delivery).


title: Address

text: In most of the world, addresses are written in order from most specific to general, i.e. finest to coarsest information, starting with the addressee and ending with the largest geographical unit. For example:


title: Address

text: In English-speaking countries, the postal code usually comes last. In much of Europe, the code precedes the town name, thus: "1010 Lausanne". Sometimes, the ISO 3166 country code is placed in front of the postal code: "CH-1010 Lausanne".


title: Address

text: If a house number is provided, it is written on the same line as the street name; a house name is written on the previous line. When addresses are written inline, line breaks are replaced by commas. Conventions on the placing of house numbers differ: either before or after the street name. Similarly, there are differences in the placement of postal codes: in the UK, they are written on a separate line at the end of the address; in Australia, Canada and the United States, they usually appear immediately after the state or province, on the same line; in Austria, Belgium, France, Germany and The Netherlands they appear before the city, on the same line.


title: Address

text: East Asian addressing systems, including Chinese, Japanese, Korean, and Taiwanese addressing systems, when written in their native scripts, use the opposite ordering, starting with the province/prefecture, ending with the addressee. However both have the same order as western countries when written in the Latin alphabet. The Hungarian system also goes from large to small units, except that the name of the addressee is put into the first line.


title: Address

text: The postal code has been changed from a four digit format to an eight digit format, which is shown in the example. The new format adds a district or province letter code at the beginning, which allows it to be identified. As the system has been changed recently, the four digit format can still be used: in that case it is necessary to add the name of the province or district.


title: Address

text: In common with the rest of the English-speaking world, addresses in Australia put the street number—which may be a range—before the street name, and the placename before the postcode. Unlike addresses in most other comparable places, the city is not included in the address, but rather a much more fine-grained locality is used, usually referred to in Australia as a suburb or locality – although these words are understood in a different way than in other countries. Because the suburb or town serves to locate the street or delivery type, the postcode serves only as routing information rather than to distinguish previous other parts of an address. As an example, there are around 8000 localities in Victoria (cf. List of localities in Victoria (Australia) and List of Melbourne suburbs), yet around 700 unique geographic postcodes. For certain large volume receivers or post offices, the "locality" may be an institution or street name. It is always considered incorrect to include the city or metropolis name in an address (unless this happens to be the name of the suburb), and doing so may delay delivery.


title: Address

text: Australia Post recommends that the last line of the address should be set in capital letters. In Australia, subunits are essential and should be separated from the street by two spaces; apartments, flats and units are typically separated with a forward slash (/) instead.


title: Address

text: Apartment, flat and unit numbers, if necessary, are shown immediately prior to the street number (which might be a range), and, as noted above, are separated from the street number by a forward slash. These conventions can cause confusion. To clarify, "3/17 Adam Street" would mean Apartment 3 (before the slash) at 17 Adam Street (in the case of a residential address) or Unit 3 at 17 Adam St (in the case of a business park). On the other hand, "3–17 Adam Street" would specify a large building (or cluster of related buildings) occupying the lots spanning street numbers 3 to 17 on one side of Adam St (without specifying any particular place within the buildings). These forms can be combined, so "3/5–9 Eve Street" signifies Apartment 3 (before the slash) in a building which spans street numbers 5 to 9 on one side of Eve Street.


title: Address

text: As in the US, the state/territory is crucial information as many placenames are reused in different states/territories; it is usually separated from the suburb with two spaces and abbreviated. In printed matter, the postcode follows after two spaces; in handwritten matter, the postcode should be written in the boxes provided.


title: Address

text: In rural areas, "Property numbers are worked out based on the distance from the start of the road to the entrance of the property. That distance (in metres) is divided by ten. Even numbers are on the right and odd numbers are on the left. For example: the entrance to a property 5,080 metres from the start of the road on the right hand side becomes number 508. The start of the road is determined as the fastest and safest road accessed from the nearest major road or town. Rural road maps are being drawn up to define the name, the start point and direction of every rural road."


title: Address

text: In Belarus, Some neighbourhoods may be planned in such a way that some, or most, apartment buildings don't face a named street. In this case, a number of expedients can be used. In older neighbourhoods, a "main" building may have the same number as one or more "subsidiary" buildings accessible via driveways behind the main building. They will be addressed as "vul. Lenina, d. 123" ("123 Lenin St") An address may also cover one or more "subsidiary buildings" behind the main building, addressed as "vul. Lenina, d. 123, bud. 2" ("123 Lenin St, unit 2", where "bud." (abbreviation for ) means a '(subsidiary) building'). In newer areas with more regular street plans, apartment buildings that do not face a named street may be designated with Cyrillic letters appended to the building number, e.g. "123-а", "123-б", etc., in Cyrillic alphabetical order.


title: Address

text: In some "microraion" neighbourhoods, with few, if any, buildings facing named streets, the name (or more likely number of the "microraion" (planned housing development)) would be used instead of the street name; thus someone may live at "4-th microrayon, d. 123, kv. 56", i.e. "123 - 4th Microraion, apt. 56".


title: Address

text: In Belgium, the address starts with the most specific information (addressee individual identification) and ends with the most general information (postcode and town for domestic mail or country for cross border mail.)


title: Address

text: Spatial information of a physical address (including building, wing, stairwell, floor and door) may be useful for internal path of delivery, but is not allowed in the delivery point location line (i.e. the line containing street, number and box number). If needed, this information will appear on a line above the delivery point location line.


title: Address

text: The street number is placed after the thoroughfare name (unlike in France), separated by a space. Separators such as punctuation (point, comma or other signs) or "nº", or "nr" are not allowed. Extension designation (box numbers), if present, appears in the delivery point location line, preceded by the word for "box" ( in Dutch, in French). Symbols such as "b", "Bt", "#", "-", "/" are not allowed as separators between the street number element and the box number element.


title: Address

text: The Belgian addressing guidelines are registered with the Universal Postal Union (UPU and see the link Universal Postal Union – Postal addressing systems in member countries). These guidelines indicate exactly how to combine the various address components in order to obtain a correctly formatted postal address.


title: Address

text: The complete set of addressing guidelines can be found on the website of the Belgian postal operator (bpost). The correct representation of an address is not limited to the correct structure of address components but also relates to the content of addresses and their position on envelopes (see bpost - Lettres & cartes - Envoi - Comment addresser ? (in French)).


title: Address

text: It is also possible to validate a Belgian postal address on bpost's website and to receive feedback on the content and the format of an address.


title: Address

text: States can have their name written in full, abbreviated in some way, or totally abbreviated to two letters (SP = São Paulo, RJ = Rio de Janeiro, etc.).


title: Address

text: Only towns with 60,000 inhabitants and above have postal codes individualized for streets, roads, avenues, etc. One street can have several postal codes (by odd/even numbers side or by segment). These postcodes range from -000 to -899. Other towns have only a generic postcode with the suffix -000. Recipients of bulk mail (large companies, condos, etc.) have specific postcodes, with a suffix ranging from -900 to -959. P.O. boxes are mailed to offices, with suffixes ranging from -970 to -979. Some rural settlements have community postboxes with suffix -990.


title: Address

text: Similar to Belgium and most other European countries, in Bulgaria the address starts with the most specific information (addressee individual identification) and ends with the most general information (town and postcode for domestic mail or country for cross border (international) mail.)


title: Address

text: The street number is placed after the thoroughfare name (unlike in France), separated by a space and the symbol 'No. '. Separators such as punctuation (point, comma or other signs) are allowed if needed. Extension designation (box numbers), if present, appears in the delivery point location line, preceded by the word for "box" (" {numeral}", " {numeral}", or " {numeral}"). Symbols such as "#", "-", "/" are not strictly disallowed as separators between the street number element and the box number element. Note that there may sometimes be a confusion between (, postal code (of the local post office)) and (, P.O. (post office box), the individual physical P.O. box of a specific address or a subscription-based physical P.O. box inside a post-office branch).


title: Address

text: The convention is that the addressee's information is written on the bottom right portion of the letter. The sender's information is written either on the top left portion of the letter or on the top reverse side of the letter (except for parcel packages).


title: Address

text: Domestic post letters, parcels and postal money transfers are written in Bulgarian Cyrillic while the international postal letters and parcels are written in the Latin script (usually in English due to its global usage) with Arabic numerals.


title: Address

text: Apart delivering mail and parcel packages to individual addresses, the Bulgarian Posts also delivers to local post offices (which then notify the recipient that he/she has mail to collect from the post office; so-called (letters on demand/request)) or to a subscription mailbox within a local post office.


title: Address

text: "Format for mail and parcel sending to an individual subscription mailbox within a local office of Bulgarian Posts (""):"


title: Address

text: The Bulgarian postal addressing guidelines are registered with the Universal Postal Union (UPU and see the link Universal Postal Union – Postal addressing systems in member countries). These guidelines indicate exactly how to combine the various address components in order to obtain a correctly formatted postal address.


title: Address

text: The complete set of addressing guidelines can be found on the website of the Bulgarian postal operator (Bulgarian Posts). The correct representation of an address is not limited to the correct structure of address components but also relates to the content of addresses and their position on envelopes (see Български пощи ( Български пощи ) (in Bulgarian)).


title: Address

text: It is also possible to validate a Bulgarian postal address on Bulgarian Posts' website and to receive feedback on the content and the format of an address. More information can be found at (see Български пощи (in Bulgarian)).


title: Address

text: Addressing guidelines can differ between English- and French-speaking populations in Canada. Here are some formatting rules that are used in common:


title: Address

text: Chilean urban addresses require only the street name, house number, apartment number (if necessary) and municipality; however, more information is frequently included, such as commune (neighbourhood or town) and region. Postal codes are rarely included by people. All postal codes have seven digits, the first three indicating the municipality, the next four identifying a block or in large and scarcely populated areas a quadrant within the municipal territory.


title: Address

text: The territories of most of the larger cities comprise several adjacent municipalities, so it is important to mention it.


title: Address

text: Smaller cities often consist of only one municipality with several unofficial comunes (neighborhoods) that are usually mentioned even for official addressing purposes.


title: Address

text: Several large and mostly rural municipalities contain more than one small town, in such cases, the recipient address must mention either the town, the postal code or both.


title: Address

text: In other towns or rural communities there are no house numbers and addresses are generally identified by company name followed by only a street name follow by some reference point.


title: Address

text: In China, the Postal area when written in Chinese characters (preferably Simplified Chinese characters), has the order of the largest unit first, ending with the addressee, i.e. country, province, municipality, town, street or road, building name, floor/level, house/flat number, company name, addressee. This is the most common language used when posting within mainland China.


title: Address

text: The whole address is commonly written as a string of characters with no particular format regarding where a new line would start, similar to one long sentence, with any new lines appearing depending on the space available on the envelope. Generally, the district is omitted when posting within China.


title: Address

text: In Colombia the address format uses a numeric format based on which increase the number from south to north and which increase the number from east to west.


title: Address

text: Croatia uses five-digit postal code numbers. The Croatian postal service recommends using 2-letter ISO country codes as prefixes before international and domestic postal codes, though the practice is not mandatory.


title: Address

text: Postal codes are in the format "### ##" (i.e. 158 00 = Prague 58) or "CZ-#####" (especially for international mail). On pre-printed Czech postcards and envelopes, the postal code is written on a separate last row in boxes for each number. If the envelope doesn't have pre-printed rows and boxes, the postal code should be before the town (or post office) name.


title: Address

text: On private letters, the first line is usually constituted by a courtesy title (...) For private mails addressed to the workplace, the order is (name + company), while in official mails it is (company + name).


title: Address

text: The basic system of house numbering uses conscription house numbers (). For a temporary or recreational house, an evidentional house number ( or , or distinguished by initial 0 or E prefix) is used instead. In most larger cities and also in some towns and large villages with street names, there is a double system of house numbering. The first number is the conscription or evidentional number (which corresponds to the chronological order of cadastral registration of the house), and the second number (after a slash) is the orientational number () which expresses the position in the street. Sometimes only one of the two numbers is used, or the numbers are used in reverse order, and it can be difficult to distinguish which number is which. Generally, orientation numbers (if they exist) are preferred for mail services.


title: Address

text: In Denmark, apartment buildings will usually have two or three apartments per floor. Thus, if the addressee lives in an apartment, the address should contain the floor they live on, and a side ( or , meaning "to the left", "in the middle" and "to the right", respectively) or an alphanumeric character (1, 2, 3... or A, B, C...= starting from left seen from the top most step just before the floor).


title: Address

text: In Finland, if a person's name is written before the company name in the address field of a letter, then that person is considered the recipient. In this case, no other employee is allowed to open the letter but the indicated recipient. If the company name is before the person's name, then the company is the recipient and any employee is allowed to open the letter.


title: Address

text: The apartment number can formatted as "" ( is an abbreviation for , apartment) or as "" (the letter indicates the correct staircase in apartment blocks with several entrances.)


title: Address

text: Finland uses a five-digit postal code. Note that some larger companies and organizations have their own postal codes.


title: Address

text: The postal code always consists of five digits. The is usually a town, but may be other territorial entities (up to a )


title: Address

text: Organisations, government agencies, and companies which receive large amounts of mail often have a special CEDEX address which goes after the last line (for instance, "75001 PARIS CEDEX").


title: Address

text: The most widespread format, shown above, gives on the last line the recipient's five-digit post code (with a single space between the third and fourth digits) and the name of the town or village that is the base of a post office, in capital letters and separated from the postcode by two spaces. When sending mail abroad, or when sending mail from abroad to Greece, Hellenic Post recommends the following format:


title: Address

text: As with domestic mail, mail sent from abroad must contain the postcode in the same manner, but the postcode must be preceded by the international prefix of the country of delivery (for Greece, GR). Below the destination, the country of delivery must be written in capital letters, either in English or French (for Greece, or GREECE).


title: Address

text: The official languages of Hong Kong are Chinese and English. For domestic mail within Hong Kong, the address may be written entirely in either Chinese or English. For overseas mail going out from Hong Kong, the address may be written in the language of the destination country, provided that the city name and the country name are in English. However, for an overseas mail from Hong Kong to Mainland China, Macao, Taiwan or Singapore, the address may be written entirely in Chinese. While traditional Chinese characters are commonly used in Hong Kong, simplified Chinese characters are also understood by Hong Kong's postmen. Note that Hong Kong does not use any postal codes, though many rural properties have a property identification code, e.g. HKT-12345.


title: Address

text: An address written in English should begin with the smallest unit and end with the largest unit, as in the following example for a domestic mail within Hong Kong.


title: Address

text: An address written in Chinese should begin with the largest unit and end with the smallest unit, as in the following example for a piece of domestic mail within Hong Kong. Traditional Chinese characters are used in this example.


title: Address

text: For mail to Hong Kong from overseas, "Hong Kong" should be added at the end of an address written in English, and should be added at the beginning of an address written in Chinese.


title: Address

text: In Hungarian mail addresses, the city/town name precedes the street address. The post code then comes after the street address.


title: Address

text: Various abbreviations might appear in the precise street/building address: for instance, specifying the street type (, etc.), or for (floor), or for (which means Land Registry number, or lot number), or for (ground floor) and so on.


title: Address

text: Generally or means 'street' and should be written before the street name, e.g. . For more about Indonesian administrative divisions, see administrative divisions of Indonesia.


title: Address

text: Postal addresses in Iran have a standard which should be used by mail or parcel senders. This standard is registered and qualified by the Universal Postal Union (UPU). According to the below table, Iran has 4 types of standard address:


title: Address

text: In July 2015, the Republic of Ireland introduced Eircodes, a seven digit alphanumeric code, consisting of a 3 character routing key and a 4 character unique identifier for the property. Example A65 F4E2. Up until the introduction of Eircodes Dublin was the only county with a form of postal district identifier; these have been incorporated into the Eircode scheme. For example, Dublin 2 is routing code D02.


title: Address

text: Rural addresses are specified by the county, nearest post town, and the townland. Urban addresses are specified by county, city or town name, street name, house number, and apartment or flat number where relevant. A house name may be used instead of a number. The Eircode is appended to the bottom of the address.


title: Address

text: In apartment buildings the building number should appear first and then the apartment number separated by a "/". In the below example, "16" is the building number while "20" is the apartment number:


title: Address

text: A seven digit postal code for all addresses was introduced in 2013 which can cover an entire locality for a small town or village. In bigger cities postal areas are divided along streets and neighbourhoods.


title: Address

text: A domestic address in Italy must be composed of three to five rows. Up to six rows can be used for international mail:


title: Address

text: A Japanese postal address, when written in Japanese phonetic and Chinese characters, starts with the largest geographical division, continues with progressively smaller subdivisions before ending with the addressee, i.e. country, prefecture, town, , , building number, building name, floor number, company name, addressee. This is the most common addressing format used when mailing within Japan. It is common practice to add the appropriate honorific to the addressee's name, e.g. for a private individual or for a company or institution.