title: Merced, California

text: Merced is ranked as the sixth-top producing county in California. In 2019, Merced County generated $3.271 billion in total value of production. The top five commodities from 2019 in Merced are:


title: Merced, California

text: Merced is home to a community college, Merced College and the University of California Merced. UC Merced now enrolls 8,321 undergraduate and 772 graduate students for a total of 9,093 students, as reported in the university's fall 2021 census. Of the 2021-2022 undergraduate degrees awarded, the top degrees were: 19% Biological Sciences, 16% Psychology, 11% Management, and 10% Computer Science Engineering. The University of California, Merced campus opened in late 2005 northeast of the city limits. UC Merced enrolled about 7,967 students during the 2017–2018 academic year. Merced is served by the Merced City School District, which has five main middle schools, Cruickshank Middle School, Herbert Hoover Middle School, Rivera Middle School, Weaver Middle School and Tenaya Middle School. There are also 14 elementary schools in this district. Merced Union High School District has three major public high school campuses, Merced High School, Golden Valley High School, and El Capitan High School as well as a few smaller campuses offering alternative education. Merced's community college, Merced College, has an enrollment of 8,996 students as of January 2021.


title: Merced, California

text: Mercy Medical Center Merced. A 2016 Community Health Assessment prepared by the Merced County Department of Public Health (MCDPH), determined that top health topics that affect Merced and Merced county are heart disease and stroke; diabetes; access to health care; and drug and alcohol abuse. In 2017 the MCDPH published the Merced County Community Health Improvement Plan in an effort to "address health disparities and to promote health equity with the goal of health and wellness for all county residents."


title: Merced, California

text: The Decennial Census of Population and Housing reported that the population in 2021 was 89,308. In 2021, the average income of an individual was $21,518, and for a household $49,973.


title: Merced, California

text: The 2010 United States Census reported that Merced had a population of 78,959. The population density was 3,386.4 people per square mile. (1,307.5/km). The racial makeup of Merced was 41,177 (52.1%) White, 4,958 (6.3%) African American, 1,153 (1.5%) Native American, 9,342 (11.8%) Asian, 174 (0.2%) Pacific Islander, 17,804 (22.5%) from other races, and 4,350 (5.5%) from two or more races. Hispanic or Latino of any race were 39,140 persons (49.6%).


title: Merced, California

text: The Census reported that 77,878 people (98.6% of the population) lived in households, 492 (0.6%) lived in non-institutionalized group quarters, and 588 (0.7%) were institutionalized.


title: Merced, California

text: There were 24,899 households, out of which 11,484 (46.1%) had children under the age of 18 living in them, 10,958 (44.0%) were opposite-sex married couples living together, 4,921 (19.8%) had a female householder with no husband present, 1,941 (7.8%) had a male householder with no wife present. There were 2,156 (8.7%) unmarried opposite-sex partnerships, and 167 (0.7%) same-sex married couples or partnerships. 5,356 households (21.5%) were made up of individuals, and 1,823 (7.3%) had someone living alone who was 65 years of age or older. The average household size was 3.13. There were 17,820 families (71.6% of all households); the average family size was 3.65.


title: Merced, California

text: The population was spread out, with 25,091 people (31.8%) under the age of 18, 10,475 people (13.3%) aged 18 to 24, 20,986 people (26.6%) aged 25 to 44, 15,484 people (19.6%) aged 45 to 64, and 6,922 people (8.8%) who were 65 years of age or older. The median age was 28.1 years. For every 100 females, there were 96.3 males. For every 100 females age 18 and over, there were 93.6 males.


title: Merced, California

text: There were 27,446 housing units at an average density of , of which 10,637 (42.7%) were owner-occupied, and 14,262 (57.3%) were occupied by renters. The homeowner vacancy rate was 3.5%; the rental vacancy rate was 8.5%. 31,690 people (40.1% of the population) lived in owner-occupied housing units and 46,188 people (58.5%) lived in rental housing units.


title: Merced, California

text: As of the census of 2000, there were 63,893 people, 20,435 households, and 14,631 families residing in the city. The population density was . There were 21,532 housing units at an average density of . The racial makeup of the city was 57.4% White, 6.3% African American, 1.3% Native American, 12.4% Asian (mostly Hmong), 0.2% Pacific Islander, 23.2% from other races, and 5.2% from two or more races. Hispanic or Latino of any race were 26.4% of the population.


title: Merced, California

text: There were 20,435 households, out of which 42.9% had children under the age of 18 living with them, 47.2% contained married couples living together, 18.2% had a female householder with no husband present, and 28.4% were "nonfamilies." 22.6% of all households were made up of individuals, and 8.5% had someone living alone who was 65 years of age or older. The average household size was 3.06 and the average family size was 3.62.


title: Merced, California

text: In the city, the population was spread out, with 34.7% under the age of 18, 11.4% from 18 to 24, 27.4% from 25 to 44, 17.1% from 45 to 64, and 9.4% who were 65 years of age or older. The median age was 28 years. For every 100 females, there were 95.6 males. For every 100 females age 18 and over, there were 92.3 males.


title: Merced, California

text: The median income for a household in the city was $30,429, and the median income for a family was $32,470. Males had a median income of $31,725 versus $24,492 for females. The per capita income for the city was $13,115. About 22.4% of families and 27.9% of the population were below the poverty line, including 36.9% of those under age 18 and 10.1% of those age 65 or over.


title: Merced, California

text: Escaping persecution from Communist forces after the Laotian Civil War, Hmong refugees from Laos moved to the United States in the 1970s and '80s, first settling in Merced and other areas in the Central Valley of California. The Hmong could not initially take part in farming like they had expected, as the land was owned by other people. They could not get high end agricultural jobs because they did not speak sufficient English and Mexican migrants already held low end agricultural jobs. As such, a great many of Merced's Hmong collected social services and Hmong gangs arose, prompting other residents to perceive them as being the cause of economic troubles. As the Hmong settlement matured and the Hmong children gained English language skills, the town's overall attitude began to be more accepting of the Hmong community.


title: Merced, California

text: This acceptance is reflected in various services provided to the Hmong community. This includes the Merced Lao Family Community Inc., a nonprofit organization that provides social services to Hmong people, the Merced Department of Public Health's MATCH (Multidisciplinary Approach to Cross-Cultural Health) program, intending to draw Hmong patients into the health care system, a body of Hmong-speaking faculty and paraprofessionals (including college classes on Hmong culture and language), and media outlets for the Hmong community—cable television channel Channel 11 broadcasts programming to the Hmong community twice per week and radio station KBIF 900 AM airs programming oriented towards Hmong people.


title: Merced, California

text: While Merced has historically had a proportionally large portion of Hmong (in 1997, 12,000 of Merced's 61,000 residents were Hmong), demographic shifts have reduced this. The Personal Responsibility and Work Opportunity Act of 1996 prompted a move of some Hmong to Minnesota, North Carolina, and Wisconsin. More recently, many Hmong have gone to Alaska to work in crabbing and fishing industries that require little proficiency in English.


title: Merced, California

text: In 2010, Latinos became a majority population in Merced and Merced County as the agricultural industry brought in migrant farm laborers. The area's affordable housing prices attracted both Latino and Asian immigrants. Merced has large Asian-American (e.g. Hmong, followed by Chinese, Vietnamese, Laotian, Cambodian, Filipino, Thai, Korean and Asian Indian) populations relative to the city and county's population size.


title: Merced, California

text: In 2021, Merced, California had approximately 4,000 violent crimes occur within the city. This means that with a population of 89,303 people in 2021 you had approximately a 4.5% chance of being a victim of crime while living in Merced. Of the crimes that occurred roughly 1200 of the crimes where crimes against people and 2500 crimes were crimes against property. The crimes occurring in 2021 resulted in 13 fatalities. With the high crime rate occurring Merced, Merced is considered one of the 50 most dangerous cities to live in California.


title: Merced, California

text: Merced has a history of minor league baseball including the California League Merced Bears (1940s) and Atwater Angels (1970s) in nearby Atwater, California. There were the defunct Merced Black Bears of the Horizon Air Summer Series and the current Atwater Aviators of the Golden State Collegiate Baseball League.


title: Fort Campbell

text: Fort Campbell is a United States Army installation located astride the Kentucky–Tennessee border between Hopkinsville, Kentucky and Clarksville, Tennessee (post address is located in Kentucky). Fort Campbell is home to the 101st Airborne Division and the 160th Special Operations Aviation Regiment. The fort is named in honor of Union Army Brigadier General William Bowen Campbell, the last Whig Governor of Tennessee.


title: Fort Campbell

text: The site for Mid-Campbell was selected on September 9, 1941, and the Title I Survey was completed November 15, 1941, coincidentally the same time the Japanese Imperial Fleet was leaving Japanese home waters for the attack on Pearl Harbor. Construction of Camp Campbell began on January 12, 1942. Within a year, the reservation designated as Camp Campbell was developed to accommodate one armored division and various support troops, with a total size of , and billets for 2,422 officers and 45,198 enlisted personnel.


title: Fort Campbell

text: Due to its close proximity to Nashville, the War Department on March 7, 1941, designated Tennessee as the official address of the new camp. This caused a great deal of confusion. While the headquarters and a great majority of the base's acreage was in Tennessee, the base's post office was in Kentucky. After many months of mail delivery problems, Colonel Guy W. Chipman requested that the address be changed to Camp Campbell, Kentucky. The War Department officially changed the address on September 23, 1942.


title: Fort Campbell

text: Early in the summer of 1942, the post's initial cadre, one officer and 19 enlisted men, arrived from Fort Knox, Kentucky. From that time until the end of World War II, Camp Campbell was the training ground for the 12th, 14th and 20th Armored divisions, Headquarters IV Armored Corps and the 26th Infantry Division. Several formations were sent to Camp Campbell after the war and deactivated, one being the 5th Infantry Division in September 1946.


title: Fort Campbell

text: In the spring of 1949, the 11th Airborne Division arrived at Campbell following occupation duty in Japan. The 11th was in residence there until early 1956.


title: Fort Campbell

text: By April 1950, the post had evolved from a wartime training camp to a permanent installation and was renamed Fort Campbell.


title: Fort Campbell

text: From 1950 to 1962, the post operated an Airborne Course which trained nearly 30,000 soldiers as paratroopers before its inactivation.


title: Fort Campbell

text: On September 21, 1956, Secretary of the Army Wilber M. Brucker and the Army Chief of Staff, General Maxwell D. Taylor, presented the colors of the 101st Airborne Division to MG T.L. Sherbourne, the first commander of the new, previously experimental, ROTAD (Reorganization Of The Airborne Division) division. This ceremony officially reactivated the famed "Screaming Eagles" of World War II.


title: Fort Campbell

text: On May 2, 1966, Third Army General Order 161 directed the activation of a Basic Combat Training Center at Fort Campbell. On July 6, barely two months after its activation, Fort Campbell's Army Training Center received its first 220 newly inducted soldiers. Basic Combat Training began on schedule July 11 with a full complement of 1,100 trainees. The Training Center operated until April 15, 1972, when it was deactivated.


title: Fort Campbell

text: The 1st Brigade was sent for duty in Vietnam in July 1965. Soon thereafter, upon the escalation of hostilities in Southeast Asia, the rest of the division arrived. Also in response to the military buildup, the 6th Infantry Division was reactivated at Fort Campbell on November 24, 1966, and inactivated July 25, 1968.


title: Fort Campbell

text: In September 1971, the 173rd Airborne Brigade returned to Fort Campbell and conducted its official homecoming ceremonies, which were presided over by Secretary of Defense Melvin Laird. The 173rd was then inactivated on 14 January 1972 and its personnel and the equipment used to rebuild the 3rd Brigade, 101st Airborne Division (Airmobile). The 3rd Brigade remained on jump status until April 1974, when its jump status was terminated and the division became entirely airmobile. On April 6, 1972, the 101st Airborne Division (Airmobile) was officially welcomed back to its home station after the cessation of hostilities in Vietnam. The ceremonies were attended by Vice President Spiro T. Agnew and General William C. Westmoreland, Army Chief of Staff.


title: Fort Campbell

text: On December 12, 1985, 246 servicemembers died with eight aircrews shortly after takeoff from Gander, Newfoundland, Canada, during a return from peacekeeping duties in Egypt. A memorial grove of trees and monument are near the post museum.


title: Fort Campbell

text: On July 5, 1999, Private First Class Barry Winchell, 21, of 2nd Battalion, 502nd Infantry Regiment, was bludgeoned to death with a baseball bat in his barracks. The murder was committed by Private Calvin Glover, who was egged on by Specialist Justin Fisher. Apparently the motive was punishing Winchell for falling in love with Calpernia Addams, a transsexual showgirl. Winchell died at Vanderbilt University Medical Center in Nashville. Glover was later convicted for the murder, while Fisher was convicted of lesser crimes. Fisher was released to a halfway house in August 2006 and was later released from all custody. Glover received a life sentence and is eligible for parole after 15 years.


title: Fort Campbell

text: On October 13, 2005, Fort Campbell made international headlines when Private Nicholas Mikel opened fire on a group of soldiers training at the base. Private Mikel was arrested soon thereafter and charged with attempted murder. In April 2006 he was convicted of attempted premeditated murder and sentenced to 25 years imprisonment.


title: Fort Campbell

text: Early on April 26, 2011, a strong tornado struck the Campbell Army Airfield at Fort Campbell, destroying one building and causing heavy damage to several others, all of which were large and well-constructed. Large doors were blown in on these buildings as well. Several other smaller buildings received minor to major damage, and numerous heavy vehicles were damaged, with at least three being flipped over. Immediately north of the airfield, across farmland, several dozen trees were downed, two barns were heavily damaged, three power poles were blown down, and some shingles were blown off of a house. The tornado was rated EF3 on the Enhanced Fujita scale.


title: Fort Campbell

text: The Sabalauski Air Assault School, named after Command Sergeant Major Walter James Sabalauski is located on Fort Campbell. Courses taught include Air Assault, Pathfinder, Pre-Ranger, Jumpmaster Refresher, and Rappel Master. FRIES/SPIES Master courses are also taught. The school is also home to the Division's Parachute Demonstration Team.


title: Fort Campbell

text: Kentucky has limited rights to taxation: Individuals performing services on the Kentucky portion of Fort Campbell only pay taxes to the state where they are residents, refer to US Code Title 4, Chapter 4, §115. Tennessee has no state income tax on wages but a higher retail sales tax than Kentucky.


title: Fort Campbell

text: The Fort Campbell parachute demonstration team was established in 1958 during the infancy of precision freefall as the Army's first such team—pre-dating the Golden Knights, United States Army Parachute Team, by one year. Early team members were soldiers who volunteered their free time in order to perform quality parachute demonstrations. In 1984, the 101st command group opted to form a full-time parachute team, known as the "Screaming Eagles".


title: Fort Campbell

text: The "Screaming Eagles" perform more than 60 parachute demonstrations each year in front of an average viewing audience of 5,000 spectators. The team has a diverse background of Army Military Occupational Specialties (MOS) and at this time has seven members. The team has one Light Wheeled Mechanic, two Combat Medics, three Infantrymen, and one Parachute Rigger most of whom have combat experience. Collectively, the 2009 team has more than 40 years of skydiving experience and more than 6,000 skydives.


title: Fort Campbell

text: Other facilities include Blanchfield Army Community Hospital, Sabalauski Air Assault School and the SSG John W. Kreckel NCO Academy.


title: Fort Campbell

text: Hammond Heights is divided among several elementary schools: Barkley and Marshall schools as well as Collins, Gorgas, and Hollis elementary schools.


title: Fort Campbell

text: Mahaffey Middle School and Wassom Middle School serve separate areas. Mahaffey Middle's boundary includes Cole Park, Drennan Park, Gardner Hills, Harper Village, New Drennan, Stryker Village, Turner Loop, Werner Park, and Woodlands. Wassom's boundary includes Barker Court, Hammond Heights, LaPointe, Lee Park, McAuliffe Park, New Hammond Heights, Pierce Village, Summer Park, Taylor Village, and Zahn Park.


title: Fort Campbell

text: The high school first opened in 1962. The current high school building was dedicated in 2018. Of the students, the percentage who attend for all four years total at FCHS is 10.


title: Fort Campbell

text: There were plans for a new middle school, but in 2019 the funds were instead designated for a wall along the Mexico-United States border.


Julie Montagu, Viscountess Hinchingbrooke (born Julie Jean Fisher; February 17, 1972) is an American entrepreneur, yoga instructor, blogger, writer and television personality. She is married to Luke Montagu, Viscount Hinchingbrooke, who is the son and heir to John Montagu, 11th Earl of Sandwich. Montagu began her television career as a cast member on the British reality series "Ladies of London" before hosting her own series on the "Smithsonian Channel" called "An American Aristocrat's Guide to Great Estates". Since 2021 she has run her own series, "American Viscountess", on YouTube.


title: Julie Montagu, Viscountess Hinchingbrooke

text: Julie Fisher was born on 17 February 1972 to Thomas Fisher, and was brought up in Sugar Grove, Illinois, as one of five siblings. She went on to study computer science at Indiana University. Fisher moved to London to work for an internet-based company, and was working at a digital agency when she met Luke Montagu in 2003. She was a single mother at the time with two children, and had assumed he was not interested in her.


text: Three months after they began dating, the couple spent a weekend on the Isle of Wight and she noticed that his credit cards read ‘Viscount Hinchingbrooke’. Only then did he explain that he was a member of the aristocracy and his father was John Montagu, 11th Earl of Sandwich. A year after they first met, they were married at Mapperton House, Dorset, the country estate of the Earl of Sandwich.


text: When Luke Montagu suffered years of side effects from being removed from prescription medication by an addiction clinic (and was later awarded £1.35 million in compensation), Julie Montagu began running yoga classes in nearby church halls in order to bring some money into the household. By that time, Luke was unable to continue in his position as director of the Met Film School so Julie became the sole supporter.


text: According to a June 2020 magazine article, Julie Montagu is a "qualified yoga teacher, nutritionist and mindfulness guru".


text: Julie Montagu started a blog, called the "Flexi Foodie" and wrote a successful cookbook, "Superfoods: The Flexible Approach to Eating More Superfoods & Superfoods Superfast". She founded the charity Council for Evidence-Based Psychiatry after Luke's recovery, based on their experiences.


text: She was then offered a position on the reality television series "Ladies of London" as her husband was recovering. She later said of the series, "We thought long and hard before accepting as it offered financial support for a while. But it was not fun to do. I was expected to behave in a way I wasn't, like an It girl or socialite, when I'm not. They edit you... You have to go along with things or you get fired. But you know it was a job. I was acting". She celebrated when it was cancelled after three seasons. In 2016, the couple took over the running of the Mapperton Estate. By that time, "Far from the Madding Crowd" had recorded some scenes at the estate.


text: The series brought financial stability which allowed the couple to invest further in the Mapperton Estate, turning an old stable block into a wedding venue. Julie also opened her own school of yoga on the grounds, but continues to practice yoga elsewhere, headlining an act at the Wanderlust yoga festival in Victoria Park, London. During the lead-up to the wedding of Prince Harry and Meghan Markle, Julie Montagu was interviewed on a number of occasions because she is a US citizen who married into British aristocracy; she was also an on-site commentator on the wedding for the BBC. She was also interviewed following such events as Markle's father selling a private letter his daughter had sent him, and the royal couple's break from the monarchy in 2020.


text: In a 2017 interview, the couple were working to increase the business: "by attracting more visitors and more weddings. At the moment we host 12 a year but we are hoping to build that up to 40". The cost of operating the Mapperton estate was £200,000 per annum at that time. Because of the restrictions due to the COVID-19 pandemic, Luke estimated that they lost £200,000 that year.


text: After appearing on their "Million Dollar American Princess" documentary series, she was asked by the "Smithsonian Channel" to host a new series to air in 2020, "An American Aristocrat's Guide to Great Estates", which was also streaming on Amazon Prime Video in North America by March 2021.


text: She is married to Luke Montagu, Viscount Hinchingbrooke, and has four children, two of whom are from her first marriage and two with Luke. She supported her husband through his recovery from a dependency of prescription drugs and now campaigns for greater awareness of the issue.


text: In 2021, she enrolled at the University of Buckingham to work towards a Master's of Arts in Country House Studies.


title: Carmel, Indiana

text: Carmel is a suburban city in Indiana immediately north of Indianapolis. With a population of 100,777, the city spans across Clay Township in Hamilton County, Indiana, and is bordered by the White River to the east; the Hamilton-Boone county line to the west; 96th Street to the south and 146th Street to the north. Although Carmel was home to one of the first electronic automated traffic signals in the state, the city has constructed 141 roundabouts between 1988 and 2022.


title: Carmel, Indiana

text: Carmel was originally called "Bethlehem". It was platted and recorded in 1837 by Daniel Warren, Alexander Mills, John Phelps, and Seth Green. The original settlers were predominantly Quakers. Today, the plot first established in Bethlehem, located at the intersection of Rangeline Road and Main Street, is marked by a clock tower, donated by the local Rotary Club in 2002. A post office was established as "Carmel" in 1846 because Indiana already had a post office called Bethlehem. The town of Bethlehem was renamed "Carmel" in 1874, due to the need of a post office, at which time it was incorporated.


title: Carmel, Indiana

text: In 1924, one of the first automatic traffic signals in the U.S. was installed at the intersection of Main Street and Rangeline Road. The signal was the invention of Leslie Haines and is currently in the old train station on the Monon Trail.


title: Carmel, Indiana

text: The Carmel Monon Depot, John Kinzer House, and Thornhurst Addition are listed on the National Register of Historic Places.


title: Carmel, Indiana

text: Carmel occupies the southwestern part of Hamilton County, adjacent to Indianapolis and, with the annexation of Home Place in 2018, is now entirely coextensive with Clay Township. It is bordered to the north by Westfield, to the northeast by Noblesville, to the east by Fishers, to the south by Indianapolis in Marion County, and to the west by Zionsville in Boone County. The center of Carmel is north of the center of Indianapolis.


title: Carmel, Indiana

text: According to the 2010 census, Carmel has a total area of , of which (or 97.76%) is land and (or 2.24%) is water.


title: Carmel, Indiana

text: Major east–west streets in Carmel generally end in a 6 and include 96th Street (the southern border), 106th, 116th, 126th, 131st, 136th, and 146th (which marks the northern border). The numbering system is aligned to that of Marion and Hamilton counties. Main Street (131st) runs east–west through Carmel's Art & Design District; Carmel Drive runs generally east–west through the main shopping area, and City Center Drive runs east–west near Carmel's City Center project.


title: Carmel, Indiana

text: North–south streets are not numbered and include (west to east) Michigan, Shelborne, Towne, Ditch, Spring Mill, Meridian, Guilford, Rangeline, Keystone, Carey, Gray, Hazel Dell, and River. Some of these roads are continuations of corresponding streets in Indianapolis. Towne Road replaces the name Township Line Road at 96th Street, while Westfield Boulevard becomes Rangeline north of 116th Street. Meridian Street (US 31) and Keystone Parkway (formerly Keystone Avenue/SR 431) are the major thoroughfares, extending from 96th Street in the south and merging just south of 146th Street. The City of Carmel is nationally noted for having well over 100 roundabouts within its borders, with even more presently under construction or planned.


title: Carmel, Indiana

text: As of the census of 2010, there were 79,191 people, 28,997 households, and 21,855 families residing in the city. The population density was . There were 30,738 housing units at an average density of . The racial makeup of the city was 85.4% White, 3.0% African American, 0.2% Native American, 8.9% Asian, 0.7% from other races, and 1.8% from two or more races. Hispanic or Latino people of any race were 2.5% of the population.


title: Carmel, Indiana

text: There were 28,997 households, of which 41.7% had children under the age of 18 living with them, 66.6% were married couples living together, 6.3% had a female householder with no partner present, 2.4% had a male householder with no partner present, and 24.6% were non-families. 20.8% of all households were made up of individuals, and 6.7% had someone living alone who was 65 years of age or older. The average household size was 2.71 and the average family size was 3.18.


title: Carmel, Indiana

text: The median age in the city was 39.2 years. 29.4% of residents were under the age of 18; 5.3% were between the ages of 18 and 24; 25.2% were from 25 to 44; 29.7% were from 45 to 64; and 10.4% were 65 years of age or older. The gender makeup of the city was 48.7% male and 51.3% female.


title: Carmel, Indiana

text: The Meridian Corridor serves as a large concentration of corporate office space within the city. It is home to more than 40 corporate headquarters and many more regional offices. Several large companies reside in Carmel, and it serves as the national headquarters for Allegion, CNO Financial Group, MISO, KAR Global and Delta Faucet.


title: Carmel, Indiana

text: Indiana's only Gran Fondo, this cycling event attracts professional cyclists as well as recreational riders. In 2019, the event is the World Championship for the Gran Fondo World Tour. Each route is fully supported with food, drinks, and mechanical support.


title: Carmel, Indiana

text: Founded in 1998, the Carmel Farmers Market is one of the largest in the state of Indiana, with over 60 vendors of Indiana-grown and/or produced edible products. The market, which is managed by an all-volunteer committee, is held each Saturday morning from mid-May through the first weekend of October on Center Green at the Palladium, the farmers market attracts over 60,000 people a year.


title: Carmel, Indiana

text: A $24.5 million water park and fitness center is the centerpiece of Carmel's $55 million Central Park, which opened in 2007. The Outdoor Water Park consists of two water slides, a drop slide, a rock-climbing wall, a lazy river, a kiddie pool, a large zero depth activity pool, Flowrider, and a lap pool. The fitness center consists of an indoor lap pool, a recreation pool with its own set of water slides and a snack bar, gymnasium, indoor running track, and the Kids Zone childcare. The building housing the Carmel Clay Parks Department offices is connected by an elevated walkway over the Monon Trail.


title: Carmel, Indiana

text: The Monon Greenway is a multi-use trail that is part of the Rails-to-Trails movement. It runs from 10th Street near downtown Indianapolis through Broad Ripple and then crosses into Carmel at 96th Street and continues north through 146th Street into Westfield and continues to Sheridan. The trail ends in Sheridan near the intersection of Opel and 236th streets. In January 2006, speed limit signs of were added to sections of the trail in Hamilton County.


title: Carmel, Indiana

text: Designed to promote small businesses and local artisans, Carmel's Arts and Design District and City Center is in Old Town Carmel and flanked by Carmel High School on the east and the Monon Greenway on the west, with the state goal of celebrating the creativity and craftsmanship of the miniature art form.. The district includes the Carmel Clay Public Library, the Hamilton County Convention & Visitor's Bureau and Welcome Center, and a collection of art galleries, boutiques, interior designers, cafes, and restaurants. Lifelike sculptures by John Seward Johnson II ornament the streets of the district.


title: Carmel, Indiana

text: The district hosts several annual events and festivals. The Carmel Artomobilia Collector Car Show showcases classic, vintage, exotic and rare cars, along with art inspired by automobile design. Every September, the Carmel International Arts Festival features a juried art exhibit of artists from around the world, concerts, dance performances, and hands-on activities for children.


title: Carmel, Indiana

text: In the heart of the district stands the Museum of Miniature Houses, open since 1993. The museum has seven exhibit rooms of fully furnished houses, room displays, and collections of miniature glassware, clocks, tools, and dolls.


title: Carmel, Indiana

text: Carmel City Center is a , $300 million, mixed-use development located in the heart of Carmel. Carmel City Center is home to The Palladium at the Center for the Performing Arts, which includes a 1,600-seat concert hall, 500-seat theater, and 200-seat black box theater. This pedestrian-based master plan development is located at the southwest corner of City Center Drive (126th Street) and Range Line Road. The Monon Greenway runs directly through the project. Carmel City Center was developed as a public/private partnership.


title: Carmel, Indiana

text: Clay Terrace is one of the largest retail centers in Carmel. Other shopping areas include Carmel City Center, Mohawk Trails Plaza, and Merchants' Square. The Carmel Arts & Design District has a number of retail establishments along Main Street, Range Line Road, 3rd Avenue, and 2nd Street.


title: Carmel, Indiana

text: Ground was broken for the Japanese Garden south of City Hall in 2007. The garden was dedicated in 2009 as the 15th anniversary of Carmel's Sister City relationship with Kawachinagano, Japan, was celebrated. An Azumaya-style tea gazebo was constructed in 2011 and dedicated on May 2 of that year.


title: Carmel, Indiana

text: The Great American Songbook Foundation is the nation's only foundation and museum dedicated to preserving the music of the early to mid 1900s. The foundation is led by Michael Feinstein, who is also the artistic director of the Center for the Performing Arts.


title: Carmel, Indiana

text: The government consists of a mayor and a city council. The current mayor is James Brainard, who has served since 1996. The city council consists of nine members. Six are elected from individual districts and three are elected at-large.


title: Carmel, Indiana

text: In mid-2017, the city council was considering a multimillion-dollar bond issue that would cover the cost of roundabouts, paths, roadwork, land acquisition by the Carmel Redevelopment Commission and would include the purchase of an antique carousel from a Canadian amusement park for an estimated purchase price of CAD $3 million, approximately US$2.25 million. However, a citizen led petition drive against the purchase caused the city counsel to remove it from the bond issue.


title: Carmel, Indiana

text: According to the Indiana Department of Local Government Finance, as of 2019 the City of Carmel had an overall debt load of $1.3 billion.


title: Carmel, Indiana

text: The Carmel Clay Schools district has 11 elementary schools (Kindergarten - Grade 5), three middle schools (Grades 6–8), and one high school (Grades 9–12). Student enrollment for the district is above 14,500.


title: Lincoln College, Oxford

text: Lincoln College (formally, The College of the Blessed Mary and All Saints, Lincoln) is one of the constituent colleges of the University of Oxford, situated on Turl Street in central Oxford. Lincoln was founded in 1427 by Richard Fleming, the then Bishop of Lincoln.


title: Lincoln College, Oxford

text: Notable alumni include the physician John Radcliffe, the founder of Methodism John Wesley, antibiotics scientists Howard Florey, Edward Abraham, and Norman Heatley, writers Theodor Seuss Geisel (Dr. Seuss) and David John Moore Cornwell (John le Carré), the journalist Rachel Maddow, and the current British Prime Minister Rishi Sunak. Mensa was founded at Lincoln College in 1946. Lincoln College has one of the oldest working medieval kitchens in the UK.


title: Lincoln College, Oxford

text: Richard Fleming, the then Bishop of Lincoln, founded the College in order to combat the Lollard teachings of John Wyclif. He intended it to be "a little college of true students of theology who would defend the mysteries of Scripture against those ignorant laymen who profaned with swinish snouts its most holy pearls".. To this end, he obtained a charter for the College from King Henry VI, which combined the parishes of All Saints, St Michael at the North Gate, and St Mildred's within the College under a rector. The College now uses All Saints Church as its library and has strong ties with St Michael's Church at the North Gate, having used it as a stand-in for the College chapel when necessary.


title: Lincoln College, Oxford

text: Despite insufficient endowment and trouble from the Wars of the Roses (for their charter was from the deposed Lancastrian), the College has survived and flourished thanks to the efforts of its fellows and the munificence of a second Bishop of Lincoln, Thomas Rotherham. Richard Fleming died in 1431, and the first rector, William Chamberleyn, in 1434, leaving the College with few buildings and little money. The second rector, John Beke, secured the College's safety by attracting donors. By 1436, the College had seven fellows. John Forest, Dean of Wells and a close friend of Beke's, donated such an amount that the College promised to recognise him as a co-founder; it did not keep this promise. His gifts saw the construction of a chapel, a library, hall and kitchen. After a pointed sermon from the incumbent rector, Thomas Rotherham was compelled to give his support and effectively re-founded it in 1478, with a new charter from King Edward IV.


title: Lincoln College, Oxford

text: In the 18th century, Lincoln became the cradle of Methodism when John Wesley, a fellow there from 1726, held religious meetings with his brother Charles and the rest of Wesley's 'Holy Club', whom the rest of the university took to calling 'Bible-moths'. His appearances at College became less frequent after he departed for Georgia as a missionary chaplain in 1735. Indeed, he took to signing his publications as "John Wesley, Sometime Fellow of Lincoln College". A portrait of him hangs in the Hall, and a bust overlooks the front quad. The room where he is believed to have worked is also named after him, and was renovated by American Methodists at the beginning of the 20th century.


title: Lincoln College, Oxford

text: As is common with Oxford colleges, the College has a long-standing rivalry with neighbour Brasenose College (which was founded by a later Bishop of Lincoln, William Smyth). The two colleges share a tradition revived annually on Ascension Day. The story goes that, centuries ago, as a mob chased students at the University through the town, the Lincoln porter allowed in the Lincoln students but refused entry to the Brasenose member, leaving him to the mercy of the mob. An alternative is that a Lincoln man bested a Brasenose man in a duel. Either episode resulted in the Brasenose student's death, and ever since, on Ascension Day, Lincoln College has invited in members of Brasenose College every year through the one door connecting the two colleges, for free beer as penance. Since the nineteenth century, the beer has been flavoured with ivy so as to discourage excessive consumption.


title: Lincoln College, Oxford

text: Academically, Lincoln was one of the top ten in the Norrington Table each year from 2006 to 2015 (excluding 2010 and 2011). In 2021, Lincoln ranked third in the Norrington Table, with a score of 79.6.


title: Lincoln College, Oxford

text: The College is associated with the Goblin Club, an exclusive all-male dining society founded in 1902. In May 2019, the JCR voted to extend a ban on the society on the grounds that it was perceived to be both elitist and racist.


title: Lincoln College, Oxford

text: In 1958, the College was the first in Oxford or Cambridge to provide a Middle Common Room exclusively for the use of graduate students. Like many of Oxford's colleges, Lincoln admitted its first mixed-sex cohort in 1979, after more than half a millennium as a men-only institution. The MCR is now located in the Berrow Foundation Building, which was inaugurated in 2014.


title: Lincoln College, Oxford

text: In 2007, the College took the rare step of unveiling a commissioned portrait of two members of staff who were not fellows or benefactors of the College, in commemoration of their work. Chef Jim Murden and Butler Kevin Egleston have worked in the College's Kitchen and Buttery for 33 and 28 years respectively, as of 2010. Artist Daphne Todd was commissioned for the painting, who has had such previous sitters as the Grand Duke of Luxembourg and Spike Milligan.


title: Lincoln College, Oxford

text: According to Nikolaus Pevsner, Lincoln College preserves "more of the character of a 15th century college than any other in Oxford". This is mainly because both the façade to Turl Street and the front quad are still of only two storeys (although the parapets and battlements are of the 19th century). The College also owns most of the buildings across Turl Street from the college proper, in whole or in part, which chiefly contain student accommodation. The creeper that covers the College's front quad walls is Virginia creeper ("Parthenocissus quinquefolia"), dark green in the summer, through to scarlet in autumn, whilst being bare in winter.


title: Lincoln College, Oxford

text: There are three quads: the Front Quad (15th century), the Chapel Quad (1608–1631) and The Grove (19th century), as well as a number of irregular spaces. Unlike many other colleges, all of the architecture of the college proper is stone and there is no modern accommodation annexe. To quote the Lincoln College Freshers' Handbook, "Unlike most colleges, we have no grotty sixties annexe to spoil all the pretty bits". The college bar, Deep Hall (or "Deepers"), is immediately below the great hall and used to be the college beer cellar. It is one of the oldest parts of the college, and the pillars inside it are perhaps the oldest feature of the college. The wine cellar is accessed through Deep Hall, and extends completely beneath the Grove.


title: Lincoln College, Oxford

text: The Rector's lodgings in Turl Street are neo-Georgian and were built in 1929–1930; they are reached from within college through a gate in Chapel Quad, but have a main door on Turl Street.


title: Lincoln College, Oxford

text: The College is known as being the setting for many literary works. C.P. Snow was inspired for his novel "The Masters" by the story of Mark Pattison, a fellow at Lincoln, whose enthusiastic hopes for Lincoln were frustrated by older, more conservative fellows of the college; Snow's story transposes the story to a Cambridge College. It was the setting for three episodes of "Inspector Morse". Later, "Lewis" has used Turl Street in front of the College for filming. Lincoln College is the setting for much of the plot in "Heresy" by S.J. Parris (pseudonym for the literary critic Stephanie Merritt), a historical crime novel.


title: Lincoln College, Oxford

text: The college chapel was built in late perpendicular style between 1629 and 1631; its windows are enamelled rather than stained, which is a process of painting the windows then firing them, a complicated procedure. They are the work of Abraham van Linge, who was an expert in this technique. The east window of the chapel depicts twelve biblical scenes: the top six depict scenes from Jesus' life (including the Last Supper), whilst the six below depict corresponding scenes from the Old Testament (including Adam and Eve at Creation and the whale spitting out Jonah). The north windows show the Twelve Prophets, and the south windows the Twelve Apostles. The screen separating the ante-chapel (containing the organ) from the chapel proper is made of cedar, and reportedly filled the chapel with the strong scent of cedar for around the first one hundred years of its existence.


title: Lincoln College, Oxford

text: Much of the chapel was restored in a project beginning in 1999, having been deemed to be in unacceptable disrepair in the early 1990s, when a funding campaign began. The black slate and white marble tiles were repaired, cleaned and replaced where necessary, whilst most of the age damage was to be found in the woodwork, which was suffering greatly from poor ventilation and having been laid directly on to earth, resulting in worm and wet rot. Cracks in the enamel of the windows were also repaired where most obvious and disfiguring. The renovations were made with the intention of preserving the chapel's 17th-century character as much as possible. The chapel has remained much unchanged since the wooden figurines (of Saint Peter, Saint Paul, Moses and Aaron) were placed on the front pews and the carved ceiling was installed in the 1680s.


title: Lincoln College, Oxford

text: Perhaps the college's most striking feature, its library, is located in the converted 18th-century All Saints Church handed over to the college in 1971. All Saints church tower is a feature of Oxford's skyline, one of the city's "dreaming spires". After the church spire collapsed in 1700, amateur architect and Dean of Christ Church Henry Aldrich designed a new church. It is believed, however, that on some of the later features of the church, particularly on the tower and spire, the work of Nicholas Hawksmoor, the Baroque architects, is to be found. The tower has a full peal of eight bells, which are regularly rung.


title: Lincoln College, Oxford

text: Its library holds some 60,000 books. Graduates and undergraduates are able to work in the building until 2.00 a.m. most nights; the Bodleian and faculty libraries have earlier closing times. It is kept up-to-date by regular purchases, and welcomes suggestions for books pertinent to studies. The upper reading room, or Cohen Room, has an elaborate plastered ceiling and the Senior Library (downstairs) holds some of the college's older books, including pamphlets from the English Civil War, Wesleyana, and plays dating from the late 17th and early 18th centuries, as well as a small collection of manuscripts. The science library is also to be found downstairs. Access to the library is generally restricted to current students and staff at the college, although alumni may use the library if acceptable justification is provided.


title: Lincoln College, Oxford

text: Lincoln College has visiting undergraduate student arrangements with Middlebury College, Simon's Rock College of Bard, Drew University, and National Taiwan University. The College also has ties to Middlebury College's "Bread Loaf School of English", which runs a summer graduate course using Lincoln's facilities during the University of Oxford's long summer vacation. A clock donated by Middlebury stands in the Porters' Lodge.


title: Lincoln College, Oxford

text: The College grace is read aloud at every formal hall, usually by a student. To encourage readers, students who read the grace twice in a term receive a bottle of wine. The College grace is in Latin:


title: Lincoln College, Oxford

text: The College arms incorporate (1) the arms of Bishop Richard Fleming, the founder; (2) the arms of the See of Lincoln; (3) the arms of Bishop Thomas Rotherham, the second founder.


title: Lincoln College, Oxford

text: The college guarantees all undergraduates three years of college-owned accommodation. Similarly, virtually all graduate students are provided housing for the duration of their studies. The college's housing stock is extensive and centrally located. About 80 students live on the three quads described above, with over 100 more living in rooms above the shops on the other side of Turl Street. These include the Mitre rooms, formerly guest rooms of the Mitre Inn, which has been owned by the college since the 15th century. The accommodation was incorporated into the college in 1969, but the restaurants were left to the inn. Lincoln House, directly across from the college, was constructed in 1939 as an annexe. There were at one point vague plans for a bridge over Turl Street connecting the annexe to the college proper; these never materialised. Further accommodation is provided at Bear Lane (across High Street). Donors Emily and John Carr gave to the college numbers 113 and 114 on the High Street, with land extending back to Bear Lane, which the college still owns and constitutes the Bear Lane accommodation.


title: Lincoln College, Oxford

text: On Museum Road near Keble College is a further accommodation complex. 12 terraced houses are officially called Lincoln Hall, but most commonly referred to as simply 'Mus Road'. The EPA Science Centre, named after Edward Abraham, was constructed behind them in the early 21st century and contains apartment-style accommodation, teaching facilities and the college's archives. A number of outlying houses make up the remainder of the housing stock.


title: Lincoln College, Oxford

text: Due to Lincoln's small numbers and tight-knit community, its Junior Common Room (JCR) plays a greater role in student life than do the JCRs of most other colleges. JCR elections, held in Trinity and Michaelmas Terms, attract one of the highest turnouts of any Oxford college. The JCR, like all JCRs in Oxford, is both a communal room for undergraduates (with a television, kitchen, vending machine, daily newspapers, a DVD library and sofas) as well as the name of the body that represents said undergraduates to the senior members of College and on a university-wide basis. All undergraduate members of the College are automatically members of the JCR, unless they specifically express a desire not to be a part of it. Honorary membership to others is sometimes extended, but have limited rights compared to other members. Every year, Lincoln JCR collaborates with the JCRs of the other Turl Street Colleges (Exeter and Jesus) in holding the Turl Street Arts Festival, a week-long event consisting of music, plays, comedy nights, hall-swaps, and talks.


title: Lincoln College, Oxford

text: The JCR is run by an Executive of seven officers, headed by the President, which is ultimately responsible for the JCR, whilst the JCR Committee comprises thirty-four members and fulfils a wide range of duties, all aimed at the general improvement of the lives of and facilities available to the undergraduate body of the College. Members of the JCR Committee are elected by popular vote. Shabana Mahmood, the MP for Birmingham Ladywood, served as JCR president in 2000–2001. JCR meetings are held three times a term, in 2nd week, 5th week and 8th week of each.


title: Lincoln College, Oxford

text: The JCR was founded in 1854 as the Lincoln College Debating Society but was renamed in 1919 (although it continued to be referred to by its former name for some time after). From 1886, the society provided members of the Common Room with tobacco and cigarettes from its funds, as well as tea and coffee; however, "The President shall have the power to stop smoking while the Torpid "[a rowing eight entering a regatta in Hilary Term]" and the Eight "[an eight entering a regatta in Trinity Term]" are in training." Tobacco and cigarettes are no longer available from the JCR, but tea and coffee are to be found in the JCR kitchen, along with a vending machine.


title: Lincoln College, Oxford

text: The Lincoln MCR is the oldest (founded in 1960) of the Oxford MCRs. With around 350 graduate students in residence each year, the MCR organises a full and varied programme of meetings, social events and sporting activities during term time and vacations. The MCR is located in the Berrow Foundation Building.


title: Lincoln College, Oxford

text: Notable former students of the college have progressed to careers in academia, business, politics and sports. Alumni include; John Radcliffe (renowned physician after whom the Radcliffe Camera, Radcliffe Infirmary, Radcliffe Observatory and John Radcliffe Hospital are named), Howard Florey (who was awarded the Nobel Prize in Physiology or Medicine in 1945 for his role in large scale production of penicillin), Edward Abraham and Norman Heatley (biochemists also instrumental in the development of penicillin), Philip May (husband of former Prime Minister Theresa May), Steph Cook (Olympic gold medalist), William Davenant (poet), John Hobson (economist and influential theorist of imperialism), John le Carré (author), Rachel Maddow (political commentator and author), Dr. Seuss (author and illustrator), Nevil Sidgwick (chemist), Rishi Sunak (British Prime Minister), Adebayo Ogunlesi (lawyer and investment banker), Deborah Bowman (medical ethicist), Edward Thomas (poet) and John Wesley (theologian).


title: Lincoln College, Oxford

text: From 1954 to 1972, the Rector of the college was Walter Fraser Oakeshott, most famous for discovering the Winchester Manuscript of Sir Thomas Malory's Le Morte d'Arthur in 1934 while an Assistant Master at Winchester College, and after whom Lincoln College's largest performance space is named.


title: Lincoln College, Oxford

text: The academic Mark Pattison, elected as Rector of the College in 1861, is thought to have been the inspiration for the character of Dr. Casaubon in George Eliot's novel Middlemarch.


title: Lincoln College, Oxford

text: Lincoln was the first college in Oxford (or Cambridge) to admit a Jewish Fellow, the Australian-born philosopher Samuel Alexander (appointed 1882).


title: Lincoln College, Oxford

text: Years after the success of his Cold War spy novels, novelist and Lincoln graduate John le Carré, himself a one-time spy, revealed that fictional spymaster George Smiley was partly modelled on former Lincoln rector Vivian H. H. Green. At least one other recent Lincoln Rector, Sir Maurice Shock, enjoyed a prior career in British intelligence, although there is little evidence to substantiate the college's reputation as a recruiting ground for spies.


title: Lincoln College, Oxford

text: In 1955, Paul Shuffrey, the civil servant and editor, and a former Lincoln student, endowed a fellowship in memory of his father, the leading architect and architectural designer, Leonard Shuffrey.


title: Lincoln College, Oxford

text: Princess Elisabeth of Belgium, heir apparent to King Philippe, started to read history and politics in 2021.


title: Lillehammer

text: Lillehammer () is a municipality in Innlandet county, Norway. It is located in the traditional district of Gudbrandsdal. The administrative centre of the municipality is the town of Lillehammer. Some of the more notable villages in the municipality include Fåberg, Hunderfossen, Jørstadmoen, Vingnes, and Vingrom.


title: Lillehammer

text: The municipality is the 211th largest by area out of the 356 municipalities in Norway. Lillehammer is the 38th most populous municipality in Norway with a population of 28,425. The municipality's population density is and its population has increased by 6.2% over the previous 10-year period.


title: Lillehammer

text: The town of Lillehammer is the largest urban centre in the municipality. It lies in the central part of the municipality and it is surrounded by more rural areas. The town centre is a late nineteenth-century concentration of wooden houses, which enjoys a picturesque location overlooking the northern part of lake Mjøsa and the river Lågen, surrounded by mountains. Lillehammer hosted the 1994 Winter Olympics and 2016 Winter Youth Olympics.


title: Lillehammer

text: The municipality was established on 1 January 1838 (see formannskapsdistrikt law). On 1 January 1906, a small adjacent area of the neighboring municipality of Fåberg (population: 140) was annexed by Lillehammer to make room for more expansion as the town grew. During the 1960s, there were many municipal mergers across Norway due to the work of the Schei Committee. On 1 January 1964, the town of Lillehammer (population: 5,905) was merged with Fåberg Municipality (population: 13,381) to form a new, larger Lillehammer Municipality.


title: Lillehammer

text: The municipality (originally the parish) was named after the old "Hamar" farm (), since the first Lillehammer Church was built there. The name is identical with the word "hamarr" which means "rocky hill". To distinguish it from the nearby town of Hamar and Diocese of Hamar, it began to be called "little Hamar": "Lilþlæ Hamar" and "Litlihamarr", and finally Lillehammer. It is also mentioned in the Old Norse sagas as "Litlikaupangr" ("Little Trading Place").


title: Lillehammer

text: The coat of arms was granted on 4 April 1898. The arms depict a birkebeiner, carrying a spear and a shield, who is skiing down a silver/white mountainside under a blue sky. The design symbolizes the historical importance of when the Birkebeiners carried the future King Haakon from Lillehammer to Rena on skis.


title: Lillehammer

text: The Church of Norway has six parishes () within the municipality of Lillehammer. It is part of the Sør-Gudbrandsdal prosti (deanery) in the Diocese of Hamar.


title: Lillehammer

text: The village of Lillehammer is located at the northern end of Norway's largest lake, Mjøsa. There have likely been settlements here since the Iron Age and the market here was mentioned in Håkon Håkonson's saga in 1390. It is also mentioned as a site for Thing assembly in 1390. Tradition states that it was here in Lillehammer where the birkebeiners Torstein Skjevla and Skjervald Skrukka joined up with the King's son (and future King), Haakon, in 1205 before they traveled to Østerdalen (an event which is commemorated in March every year to this day). Since medieval times, the Lillehammer Church has been located here.


title: Lillehammer

text: The village was granted market town rights on 7 August 1827. At that time, 50 people lived within the boundaries of the newly established town. This site was chosen because there were no other towns in all of Christians amt (county) and this site was located along the Gudbrandsdalslågen river and the whole Gudbrandsdal valley was a major transportation route from the capital to northern Norway. Within two years of the establishment of the town, the population had risen to 360 people. The merchant Ludvig Wiese has been counted as the founder of the town (a statue of him was erected in the town in connection with the town's 100th anniversary in 1927). The laying of the main railway line from the capital in Christiania to Eidsvoll was completed in 1852. This railway line was connected with steamships along the lake Mjøsa which travelled to Lillehammer and from there a newly laid road made connections further up into the Gudbrandsdalen valley. This transport system made the transit of timber and agricultural goods from all over the county to the capital possible, and it contributed to the growth of the town of Lillehammer.


title: Lillehammer

text: In 1973, Mossad killed a Moroccan waiter, having mistaken him for Palestinian terrorist Ali Hassan Salameh, which became known as the "Lillehammer affair".


title: Lillehammer

text: Lillehammer is known as a typical venue for winter sporting events; it was host city of the 1994 Winter Olympics, and the 2016 Winter Youth Olympics, and was part of a joint bid with applicant host city Oslo to host events part of the 2022 Winter Olympics until Oslo withdrew its bid on 1 October 2014.


title: Lillehammer

text: Lillehammer is home to the largest literature festival in the Nordic countries and, in 2017, was designated as a UNESCO City of Literature.


title: Lillehammer

text: A number of schools are located in Lillehammer, including the Hammartun Primary and Lower Secondary School, Søre Ål Primary School and Kringsjå Primary and Lower Secondary School. Lillehammer Upper Secondary School consists of two branches, North and South, both situated near the city center. The private high school Norwegian College of Elite Sports, NTG, also has a branch in Lillehammer. The Lillehammer campus of Inland Norway University of Applied Sciences is situated just north of the town itself.


title: Lillehammer

text: Lillehammer is also the home of the Nansen Academy - the Norwegian Humanistic Academy. The Nansen Academy is an educational institution for adult students with varied political, religious, and cultural backgrounds. The Academy was founded on the core principles of humanism and aims at strengthening the knowledge of these principles.


title: Lillehammer

text: The 14th World Scout Jamboree was held from 29 July to 7 August 1975 and was hosted by Norway at Lillehammer.


title: Lillehammer

text: All municipalities in Norway, including Lillehammer, are responsible for primary education (through 10th grade), outpatient health services, senior citizen services, unemployment and other social services, zoning, economic development, and municipal roads. The municipality is governed by a municipal council of elected representatives, which in turn elects a mayor. The municipality falls under the Vestre Innlandet District Court and the Eidsivating Court of Appeal.


title: Lillehammer

text: The municipal council of Lillehammer is made up of 47 representatives that are elected to four year terms. The party breakdown of the council is as follows:


title: Lillehammer

text: Lillehammer is situated in the lower part of the Gudbrandsdal valley, at the northern end of lake Mjøsa. It is located to the south of Øyer Municipality, to the southeast of Gausdal Municipality, northeast of Nordre Land Municipality, to the north of Gjøvik Municipality, and to the southeast of Ringsaker Municipality. The mountain Nevelfjell lies in the northeast part of the municipality.


title: Lillehammer

text: Lillehammer has a humid continental climate (Köppen: "Dfb") and used to have a subarctic climate (Köppen: "Dfc"), with the Scandinavian mountain chain to the west and north limiting oceanic influences. The record high of was recorded in June 1970. The record low of was recorded in December 1978 and January 1979, and the same low was recorded in January 1987. There has been no overnight air frost in the month of August since 1978 with the record low for that month being (a sufficient temperature for air frost). The coldest recorded temperature after 2000 is in January 2010. The current weather station Lillehammer-Sætherengen became operational in 1982; extremes are also from two earlier weather stations in Lillehammer.


title: Lillehammer

text: Lillehammer Municipality is subdivided into the following populated places (i.e.: neighborhoods, quarters, villages, localities, settlements, communities, hamlets, etc.):


title: Lillehammer

text: The basis for the economy of the municipality is its position as the northernmost point of the lake Mjøsa and as the gateway for the Gudbrandsdal region, through which the historical highway from Oslo to Trondheim passes. The Mesna river has provided the basis for several small industries through the years, but Lillehammer is now all but industry-less.


title: Lillehammer

text: One of the major Norwegian rail lines, the Dovre Line, runs from Hamar to the north through Lillehammer on its way up the Gudbrandsdal valley, to terminate in the city of Trondheim. The European route E6 highway also passes through Lillehammer.


title: Nine Perfect Strangers (TV series)

text: Nine Perfect Strangers is an American drama streaming television miniseries based on the 2018 novel of the same name by Liane Moriarty. Created by David E. Kelley who also developed the series alongside John-Henry Butterworth, the series premiered on August 18, 2021, on Hulu.


title: Nine Perfect Strangers (TV series)

text: Nine strangers from the city gather for a 10-day retreat at Tranquillum House, a health and wellness resort in the fictional town of Cabrillo, California, which promises to transform and heal the guests who stay there. The resort is not what it seems to be, and the guests are about to discover many secrets about each other and the resort's host. One of the controversies arising between the guests and resort director Masha starts when she tells them during a meal conducted at a large table that they are all given a psychoactive drug, namely Psylocybin, in very small but relevant doses in their food without their prior consent or even knowledge, about which the guests are upset and assume it to be a crime.


title: Nine Perfect Strangers (TV series)

text: On May 1, 2019, it was reported that Hulu had given the production a straight-to-series order. The limited series was created by David E. Kelley who also developed the series alongside John-Henry Butterworth who also served as executive producers alongside Nicole Kidman, Per Saari, Bruna Papandrea, Steve Hutensky, and Casey Haver. Production companies involved with the limited series are Made Up Stories, Blossom Films, and Endeavor Content. On January 7, 2020, Melissa McCarthy joined the miniseries as an executive producer. On July 29, 2020, it was announced Jonathan Levine was set to direct all eight episodes of the limited series as well as serve as an executive producer, while Gillian Bohrer joined the series as producer. Yves Bélanger served as cinematographer.


title: Nine Perfect Strangers (TV series)

text: Alongside the initial series announcement, it was reported that Nicole Kidman was cast in a lead role. In addition to her executive producing announcement, Melissa McCarthy had also joined the cast in a starring role. On May 27, 2020, Manny Jacinto joined the main cast. In June 2020, Asher Keddie and Luke Evans were cast in starring roles. In July 2020, Melvin Gregg, Samara Weaving, Grace Van Patten, Tiffany Boone and Michael Shannon joined the main cast. In August 2020, Regina Hall and Bobby Cannavale were cast in starring roles. On October 22, 2020, Hal Cumpston joined the cast in a recurring role. On November 19, 2020, Zoe Terakes was cast in a recurring role.


title: Nine Perfect Strangers (TV series)

text: On July 8, 2020, Evans revealed that filming would take place in Australia. He also revealed that all actors were required to quarantine for fourteen days in the city of arrival in Australia, due to regulations imposed by the Australian government in response to the COVID-19 pandemic. Furthermore, all actors were required to be tested during the quarantine before filming could begin. Principal photography began on August 10, 2020, in Byron Bay, New South Wales. On December 21, 2020, Kidman announced that filming had wrapped.


title: Nine Perfect Strangers (TV series)

text: Kidman met most of the other nine actors right when filming their first scene together, and stayed in character as Masha during production.


title: Nine Perfect Strangers (TV series)

text: Hulu released a first-look trailer for the show during the 93rd Academy Awards airing on ABC on April 25, 2021. The miniseries premiered on Hulu on August 18, 2021, with the first three episodes released at once, and a new episode released weekly thereafter. The finale was released on September 22, 2021. Outside of the United States and China, the series was released on Prime Video. It was broadcast free-to-air in Australia on SBS TV in October/November 2022.


title: Nine Perfect Strangers (TV series)

text: The review aggregator website Rotten Tomatoes reports a 61% approval rating with an average rating of 6.1/10, based on 106 critic reviews. The critics consensus reads, "A meandering mystery may muddle its impact, but strong performances across the board from its eclectic ensemble mean "Nine Perfect Strangers" is never less than watchable." Metacritic, which uses a weighted average, assigned a score of 54 out of 100 based on 35 critics, indicating "mixed or average reviews".


title: Nine Perfect Strangers (TV series)

text: On August 24, 2021, it was reported that the limited series' premiere was the most-watched Hulu original at the time.


title: Nath

text: Nath, also called Natha, are a Shaiva sub-tradition within Hinduism in India and Nepal. A medieval movement, it combined ideas from Buddhism, Shaivism and Yoga traditions in India. The Naths have been a confederation of devotees who consider Shiva, as their first lord or guru, with varying lists of additional gurus. Of these, the 9th or 10th century Matsyendranath and the ideas and organization mainly developed by Gorakhnath are particularly important. Gorakhnath is considered the originator of the Nath Panth.


title: Nath

text: Nath tradition has extensive Shaivism-related theological literature of its own, most of which is traceable to 11th century CE or later. However, its roots are in far more ancient Siddha tradition. A notable aspect of Nath tradition practice have been its refinements and use of Yoga, particularly Hatha Yoga, to transform one's body into a "sahaja siddha" state of awakened self’s identity with absolute reality. An accomplished guru, that is, a yoga and spiritual guide, is considered essential, and they have historically been known for their esoteric and heterodox practices.


title: Nath

text: Their unconventional ways challenged all orthodox premises, exploring dark and shunned practices of society as a means to understanding theology and gaining inner powers. They formed monastic organizations, itinerant groups that walked great distances to sacred sites and festivals such as the Kumbh Mela as a part of their spiritual practice. The Nath also have a large settled householder tradition in parallel to its monastic groups. Some of them metamorphosed into warrior ascetics during the Islamic rule of the Indian subcontinent.


title: Nath

text: The Nath tradition was influenced by other Indian traditions such as Advaita Vedanta monism, and in turn influenced it as well as movements within Vaishnavism, Shaktism and Bhakti movement through saints such as Kabir and Namdev.


title: Nath

text: The Sanskrit word nātha नाथ literally means "lord, protector, master". The related Sanskrit term Adi Natha means first or original Lord, and is a synonym for Shiva, the founder of the Nāthas. Initiation into the Nātha sampradaya includes receiving a name ending in "-nath", "-yogi", or "-jogi".


title: Nath

text: According to the yoga scholar James Mallinson, the term "Nath" is a neologism for various groups previously known as "yogi" or "jogi" before the 18th century. Within the Natha tradition, however, it is said that the identifier Nath began with the figures of Matsyendranath in the 10th century and his guru Shiva, known as Adinath (first lord). During East India Company and later British Raj rule, itinerant yogis were suppressed and many were forced into householder life. Many of their practices were banned in an attempt to limit their political and military power in North India. During colonial rule the term "Yogi/Jogi" became a derisive word and they were classified by British India census as a "low status caste". In the 20th century, the community began to use the alternate term "Nath" instead in their public relations, while continuing to use their historical term of "yogi" or "jogi" to refer to each other within the community. The term "Nath" or "Natha", with the meaning of lord, is a generic Sanskrit theological term found in all the dharmic religions that utilize Sanskrit. It is found in Vaishnavism (e.g. Gopinath, Jagannath), Buddhism (e.g. Minanath), and in Jainism (Adinatha, Parsvanatha).


title: Nath

text: The term "yogi" or "jogi" is not limited to Natha subtradition, and has been widely used in Indian culture for anyone who is routinely devoted to yoga. Some memoirs by travelers such as those by the Italian traveler Varthema refer to the Nath Yogi people they met, phonetically as "Ioghes".


title: Nath

text: Nath are a sub-tradition within Shaivism, who trace their lineage to nine Nath gurus, starting with Shiva as the first, or ‘’Adinatha’’. The list of the remaining eight is somewhat inconsistent between the regions Nath sampradaya is found, but typically consists of c. 9th century Matsyendranatha and c. 12th century Gorakhshanatha along with six more. The other six vary between Buddhist texts such as "Abhyadattasri", and Hindu texts such as "Varnaratnakara" and "Hathapradipika". The most common remaining Nath gurus include Caurangi (Sarangadhara, Puran Bhagat), Jalandhara (Balnath, Hadipa), Carpatha, Kanhapa, Nagarjuna and Bhartrihari.


title: Nath

text: The Nath tradition was not a new movement, but one evolutionary phase of a very old Siddha tradition of India. The Siddha tradition explored Yoga, with the premise that human existence is a psycho-chemical process that can be perfected by a right combination of psychological, alchemy and physical techniques, thereby empowering one to a state of highest spirituality, living in prime condition "ad libitum", and dying when one so desires into a calm, blissful transcendental state. The term "siddha" means "perfected", and this premise was not limited to Siddha tradition but was shared by others such as the Rasayana school of Ayurveda.


title: Nath

text: According to Mallinson, "the majority of the early textual and epigraphic references to Matsyendra and Goraksa are from the Deccan region and elsewhere in peninsular India; the others are from eastern India". The oldest iconography of Nath-like yogis is found in the Konkan region (near the coast of Maharashtra, Goa, Karnataka). The Vijayanagara Empire artworks include them, as do texts from a region now known as Maharashtra, northern Karnataka and Kerala. The Chinese traveller, named Ma Huan, visited a part of the western coast of India, wrote a memoir, and he mentions the Nath Yogis. The oldest texts of the Nath tradition that describe pilgrimage sites include predominantly sites in the Deccan region and the eastern states of India, with hardly any mention of north, northwest or south India. This community also can be found in some parts of Rajasthan but these are normal like other castes, considered as other backward castes.


title: Nath

text: Gorakhshanatha is traditionally credited with founding the tradition of renunciate ascetics, but the earliest textual references about the Nath ascetic order as an organized entity (sampradaya), that have survived into the modern era, are from the 17th century. Before the 17th century, while a mention of the Nath sampradaya as a monastic institution is missing, extensive isolated mentions about the Nath Shaiva people are found in inscriptions, texts and temple iconography from earlier centuries.


title: Nath

text: In the Deccan region, only since the 18th century according to Mallison, Dattatreya has been traditionally included as a Nath guru as a part of Vishnu-Shiva syncretism. According to others, Dattatreya has been the revered as the Adi-Guru (First Teacher) of the Adinath Sampradaya of the Nathas, the first "Lord of Yoga" with mastery of Tantra (techniques).


title: Nath

text: The number of Nath gurus also varies between texts, ranging from 4, 9, 18, 25 and so on. The earliest known text that mentions nine Nath gurus is the 15th century Telugu text "Navanatha Charitra". Individually, the names of Nath Gurus appear in much older texts. For example, Matsyendranatha is mentioned as a siddha in section 29.32 of the 10th century text "Tantraloka" of the Advaita and Shaivism scholar Abhinavagupta.


title: Nath

text: The mention of Nath gurus as siddhas in Buddhist texts found in Tibet and the Himalayan regions led early scholars to propose that Naths may have Buddhist origins, but the Nath doctrines and theology is unlike mainstream Buddhism. In the Tibetan tradition, Matsyendranath of Hinduism is identified with Luipa, one referred to as the first of Buddhist Siddhacharyas. In Nepal, he is a form of Buddhist Avalokiteshvara.


title: Nath

text: According to Deshpande, the Natha Sampradaya (Devanagari:नाथ संप्रदाय), is a development of the earlier Siddha or Avadhuta Sampradaya, an ancient lineage of spiritual masters. They may be linked to Kapalikas or Kalamukhas given they share their unorthodox lifestyle, though neither the doctrines nor the evidence that links them has been uncovered. The Nath Yogis were admired by Bhakti movement saint Kabir.


title: Nath

text: The Nath Sampradaya is traditionally divided into twelve streams or "Panths". According to David Gordon White, these "panth"s were not really a subdivision of a monolithic order, but rather an amalgamation of separate groups descended from either Matsyendranath, Gorakshanath or one of their students. However, there have always been many more Natha sects than will conveniently fit into the twelve formal "panths".


title: Nath

text: In Goa, the town called Madgaon may have been derived from Mathgram, a name it received from being a center of Nath Sampradaya Mathas (monasteries). Nath yogis practiced yoga and pursued their beliefs there, living inside caves. The Divar island and Pilar rock-cut caves were used for meditation by the Nath yogis. In the later half of the 16th century, they were persecuted for their religious beliefs and forced to convert by the Portuguese Christian missionaries. Except for few, the Nath yogi chose to abandon the village.


title: Nath

text: The Inchegeri Sampradaya, also known as Nimbargi Sampradaya, is a lineage of Hindu Navnath c.q. Lingayat teachers from Maharashtra which was started by Shri Bhausaheb Maharaj. It is inspired by Sant Mat teachers as Namdev, Raidas and Kabir. The Inchegeri Sampraday has become well-known through the popularity of Nisargadatta Maharaj.


title: Nath

text: The Nath tradition has two branches, one consisting of sadhus (celibate monks) and other married householder laypeople. The householders are significantly more in number than monks and have the characteristics of an endogamous caste. Both Nath sadhus and householders are found in Nepal and India, but more so in regions such as West Bengal, Nepal, Uttarakhand, Uttar Pradesh, Rajasthan and Karnataka. The ascetics created an oversight organization called the "Barah Panthi" Yogi Mahasabha in 1906, based in the Hindu sacred town of Haridwar. According to an estimate by Bouillier in 2008, there are about 10,000 ascetics (predominantly males) in the Nath ascetic order, distributed in about 500 monasteries across India but mostly in northern and western regions of India, along with a much larger householder Nath tradition. The oldest known monastery of the Naths that continues to be in use, is near Mangalore, in Karnataka. This monastery (Kadri matha) houses Shaiva iconography from the 10th century.


title: Nath

text: A notable feature of the monks is that most of them are itinerant, moving from one monastery or location to another, never staying in the same place for long. Many form a floating group of wanderers, where they participate in festivals together, share work and thus form a collective identity. They gather in certain places cyclically, particularly on festivals such as Navratri, Maha Shivaratri and Kumbh Mela. Many walk very long distances over a period of months from one sacred location to another, across India, in their spiritual pursuits.


title: Nath

text: The Nath monks wear loin cloths and "dhotis", little else. Typically they also cover themselves with ashes, tie up their hair in dreadlocks, and when they stop walking, they keep a sacred fire called dhuni. These ritual dressing, covering body with ash, and the body art are, however, uncommon with the householders. Both the Nath monks and householders wear a woolen thread around their necks with a small horn, rudraksha bead and a ring attached to the thread. This is called "Singnad Janeu". The small horn is important to their religious practice, is blown during certain festivals, rituals and before they eat. Many Nath monks and a few householders also wear notable earrings.


title: Nath

text: The Yogis and Shaiva sampradayas such as Nath metamorphosed into a warrior ascetic group in the late medieval era, with one group calling itself "shastra-dharis" (keepers of scriptures) and the other "astra-dharis" (keepers of weapons). The latter group grew and became particularly prominent during the Islamic period in South Asia, from about the 14th to 18th century.


title: Nath

text: The Nath tradition revere nine, twelve or more Nath gurus. For example, nine Naths are revered in the Navnath Sampradaya. The most revered teachers across its various subtraditions are:


title: Nath

text: The establishment of the Naths as a distinct historical sect purportedly began around the 8th or 9th century with a simple fisherman, Matsyendranath (sometimes called Minanath, who may be identified with or called the father of Matsyendranath in some sources).


title: Nath

text: One of earliest known Hatha text "Kaula Jnana Nirnaya" is attributed to Matsyendra, and dated to the last centuries of the 1st millennium CE. Other texts attributed to him include the "Akulavira tantra", "Kulananda tantra" and "Jnana karika".


title: Nath

text: Gorakshanath is considered a "Maha-yogi" (or great yogi) in the Hindu tradition. Within the Nath tradition, he has been a revered figure, with Nath hagiography describing him as a superhuman who appeared on earth several times. The matha and the city of Gorakhpur in Uttar Pradesh is named after him. The Gurkhas of Nepal and Indian Gorkha take their name after him, as does Gorkha, a historical district of Nepal. The monastery and the temple in Gorakhpur perform various cultural and social activities and serves as the cultural hub of the city, and publishes texts on the philosophy of Gorakhnath. Gorakshanath did not emphasize a specific metaphysical theory or a particular Truth, but emphasized that the search for Truth and spiritual life is valuable and a normal goal of man. Gorakshanath championed Yoga, spiritual discipline and an ethical life of self-determination as a means to reaching siddha state, samadhi and one's own spiritual truths. Gorakshanath, his ideas and yogis have been highly popular in rural India, with monasteries and temples dedicated to him found across the country, particularly in the eponymous city of Gorakhpur, whereas among urban elites, the movement founded by Gorakhnath has been ridiculed.


title: Nath

text: According to Muller-Ortega (1989: p. 37), the primary aim of the ancient Nath Siddhas was to achieve liberation or "jivan-mukti" while alive, and ultimately "paramukti" which it defined as the state of liberation in the current life and into a divine state upon death.


title: Nath

text: According to contemporary Nath Guru, Mahendranath, another aim is to avoid reincarnation. In "The Magick Path of Tantra", he wrote about several of the aims of the Naths:


title: Nath

text: Our aims in life are to enjoy peace, freedom, and happiness in this life, but also to avoid rebirth onto this Earth plane. All this depends not on divine benevolence, but on the way we ourselves think and act.


title: Nath

text: The earliest texts on Hatha yoga of the Naths, such as "Vivekamārtaṇḍa" and "Gorakhshasataka", are from Maharashtra, and these manuscripts are likely from the 13th century. These Nath texts, however, have an overlap with the 13th century Jnanadeva commentary on the Hindu scripture Bhagavada Gita, called the Jnanesvari. This may be because of mutual influence, as both the texts integrate the teachings of Yoga and Vedanta schools of Hinduism in a similar way.


title: Nath

text: Numerous technical treatises in the Hindu tradition, composed in Sanskrit about Hatha Yoga, are attributed to Gorakshanath.


title: Nath

text: The Hatha Yoga ideas that developed in the Nath tradition influenced and were adopted by Advaita Vedanta, though some esoteric practices such as "kechari-mudra" were omitted. Their yoga ideas were also influential on Vaishnavism traditions such as the Ramanandis, as well as Sufi fakirs in the Indian subcontinent. The Naths recruited devotees into their fold irrespective of their religion or caste, converting Muslim yogins to their fold.


title: Block matrix

text: In mathematics, a block matrix or a partitioned matrix is a matrix that is "interpreted" as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.


title: Block matrix

text: This notion can be made more precise for an formula_1 by formula_2 matrix formula_3 by partitioning formula_1 into a collection formula_5, and then partitioning formula_2 into a collection formula_7. The original matrix is then considered as the "total" of these groups, in the sense that the formula_8 entry of the original matrix corresponds in a 1-to-1 way with some formula_9 offset entry of some formula_10, where formula_11 and formula_12.


title: Block matrix

text: It is possible to use a block partitioned matrix product that involves only algebra on submatrices of the factors. The partitioning of the factors is not arbitrary, however, and requires "conformable partitions" between two matrices formula_16 and formula_17 such that all submatrix products that will be used are defined. Given an formula_18 matrix formula_19 with formula_20 row partitions and formula_21 column partitions


title: Block matrix

text: can be performed blockwise, yielding formula_30 as an formula_31 matrix with formula_20 row partitions and formula_26 column partitions. The matrices in the resulting matrix formula_30 are calculated by multiplying:


title: Block matrix

text: where A and D are square blocks of arbitrary size, and B and C are conformable with them for partitioning. Furthermore, A and the Schur complement of A in P: must be invertible.


title: Block matrix

text: By the Weinstein–Aronszajn identity, one of the two matrices in the block-diagonal matrix is invertible exactly when the other is.


title: Block matrix

text: The formula for the determinant of a formula_40-matrix above continues to hold, under appropriate further assumptions, for a matrix composed of four submatrices formula_41. The easiest such formula, which can be proven using either the Leibniz formula or a factorization involving the Schur complement, is


title: Block matrix

text: If the blocks are square matrices of the "same" size further formulas hold. For example, if formula_49 and formula_44 commute (i.e., formula_51), then


title: Block matrix

text: This formula has been generalized to matrices composed of more than formula_40 blocks, again under appropriate commutativity conditions among the individual blocks.


title: Block matrix

text: For formula_54 and formula_55, the following formula holds (even if formula_16 and formula_17 do not commute)


title: Block matrix

text: A block diagonal matrix is a block matrix that is a square matrix such that the main-diagonal blocks are square matrices and all off-diagonal blocks are zero matrices. That is, a block diagonal matrix A has the form


title: Block matrix

text: where A is a square matrix for all "k" = 1, ..., "n". In other words, matrix A is the direct sum of A, ..., A. It can also be indicated as A ⊕ A ⊕ ... ⊕ A or diag(A, A, ..., A)  (the latter being the same formalism used for a diagonal matrix). Any square matrix can trivially be considered a block diagonal matrix with only one block.


title: Block matrix

text: A block diagonal matrix is invertible if and only if each of its main-diagonal blocks are invertible, and in this case its inverse is another block diagonal matrix given by


title: Block matrix

text: A block tridiagonal matrix is another special block matrix, which is just like the block diagonal matrix a square matrix, having square matrices (blocks) in the lower diagonal, main diagonal and upper diagonal, with all other blocks being zero matrices. It is essentially a tridiagonal matrix but has submatrices in places of scalars. A block tridiagonal matrix A has the form


title: Block matrix

text: Block tridiagonal matrices are often encountered in numerical solutions of engineering problems (e.g., computational fluid dynamics). Optimized numerical methods for LU factorization are available and hence efficient solution algorithms for equation systems with a block tridiagonal matrix as coefficient matrix. The Thomas algorithm, used for efficient solution of equation systems involving a tridiagonal matrix can also be applied using matrix operations to block tridiagonal matrices (see also Block LU decomposition).


title: Block matrix

text: A block Toeplitz matrix is another special block matrix, which contains blocks that are repeated down the diagonals of the matrix, as a Toeplitz matrix has elements repeated down the diagonal.


title: Block matrix

text: A special form of matrix transpose can also be defined for block matrices, where individual blocks are reordered but not transposed. Let formula_66 be a formula_67 block matrix with formula_68 blocks formula_69, the block transpose of formula_16 is the formula_71 block matrix formula_72 with formula_68 blocks formula_74.


title: Block matrix

text: As with the conventional trace operator, the block transpose is a linear mapping such that formula_75. However, in general the property formula_76 does not hold unless the blocks of formula_16 and formula_49 commute.


title: Block matrix

text: For any arbitrary matrices A (of size "m" × "n") and B (of size "p" × "q"), we have the direct sum of A and B, denoted by A formula_79 B and defined as


title: Block matrix

text: This operation generalizes naturally to arbitrary dimensioned arrays (provided that A and B have the same number of dimensions).


title: Block matrix

text: Note that any element in the direct sum of two vector spaces of matrices could be represented as a direct sum of two matrices.


title: Block matrix

text: In linear algebra terms, the use of a block matrix corresponds to having a linear mapping thought of in terms of corresponding 'bunches' of basis vectors. That again matches the idea of having distinguished direct sum decompositions of the domain and range. It is always particularly significant if a block is the zero matrix; that carries the information that a summand maps into a sub-sum.


title: Block matrix

text: Given the interpretation "via" linear mappings and direct sums, there is a special type of block matrix that occurs for square matrices (the case "m" = "n"). For those we can assume an interpretation as an endomorphism of an "n"-dimensional space "V"; the block structure in which the bunching of rows and columns is the same is of importance because it corresponds to having a single direct sum decomposition on "V" (rather than two). In that case, for example, the diagonal blocks in the obvious sense are all square. This type of structure is required to describe the Jordan normal form.


title: Block matrix

text: This technique is used to cut down calculations of matrices, column-row expansions, and many computer science applications, including VLSI chip design. An example is the Strassen algorithm for fast matrix multiplication, as well as the Hamming(7,4) encoding for error detection and recovery in data transmissions.


title: Block matrix

text: The technique can also be used where the elements of the A,B,C, and D matrices do not all require the same field for their elements. For example, The matrix A can be over the field of complex numbers, while the matrix D can be over the field of real numbers. This can lead to valid operations involving the matrices, while simplifying the operations within one of the matrices. For example, if D has only real elements finding its inverse takes less calculations than if complex elements must be considered. But the reals is a subfield of the complex numbers (further it can be considered a projection), so the matrices operations can be well defined.


title: Theorem

text: In mathematics, a theorem is a statement that has been proved, or can be proved. The "proof" of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.


title: Theorem

text: In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as "theorems" only the most important results, and use the terms "lemma", "proposition" and "corollary" for less important theorems.


title: Theorem

text: In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them. In this context, statements become well-formed formulas of some formal language. A theory consists of some basis statements called "axioms", and some "deducing rules" (sometimes included in the axioms). The theorems of the theory are the statements that can be derived from the axioms by using the deducing rules. This formalization led to proof theory, which allows proving general theorems about theorems and proofs. In particular, Gödel's incompleteness theorems show that every consistent theory containing the natural numbers has true statements on natural numbers that are not theorems of the theory (that is they cannot be proved inside the theory).


title: Theorem

text: As the axioms are often abstractions of properties of the physical world, theorems may be considered as expressing some truth, but in contrast to the notion of a scientific law, which is "experimental", the justification of the truth of a theorem is purely deductive.


title: Theorem

text: Until the end of the 19th century and the foundational crisis of mathematics, all mathematical theories were built from a few basic properties that were considered as self-evident; for example, the facts that every natural number has a successor, and that there is exactly one line that passes through two given distinct points. These basic properties that were considered as absolutely evident were called postulates or axioms; for example Euclid's postulates. All theorems were proved by using implicitly or explicitly these basic properties, and, because of the evidence of these basic properties, a proved theorem was considered as a definitive truth, unless there was an error in the proof. For example, the sum of the interior angles of a triangle equals 180°, and this was considered as an undoubtful fact.


title: Theorem

text: One aspect of the foundational crisis of mathematics was the discovery of non-Euclidean geometries that do not lead to any contradiction, although, in such geometries, the sum of the angles of a triangle is different from 180°. So, the property ""the sum of the angles of a triangle equals 180°"" is either true or false, depending whether Euclid's fifth postulate is assumed or denied. Similarly, the use of "evident" basic properties of sets leads to the contradiction of Russel's paradox. This has been resolved by elaborating the rules that are allowed for manipulating sets.


title: Theorem

text: This crisis has been resolved by revisiting the foundations of mathematics to make them more rigorous. In these new foundations, a theorem is a well-formed formula of a mathematical theory that can be proved from the axioms and inference rules of the theory. So, the above theorem on the sum of the angles of a triangle becomes: "Under the axioms and inference rules of Euclidean geometry, the sum of the interior angles of a triangle equals 180°". Similarly, Russel's paradox disappears because, in an axiomatized set theory, the "set of all sets" cannot be expressed with a well-formed formula. More precisely, if the set of all sets can be expressed with a well-formed formula, this implies that the theory is inconsistent, and every well-formed assertion, as well as its negation, is a theorem.


title: Theorem

text: In this context, the validity of a theorem depends only on the correctness of its proof. It is independent from the truth, or even the significance of the axioms. This does not mean that the significance of the axioms is uninteresting, but only that the validity of a theorem is independent from the significance of the axioms. This independence may be useful by allowing the use of results of some area of mathematics in apparently unrelated areas.


title: Theorem

text: An important consequence of this way of thinking about mathematics is that it allows defining mathematical theories and theorems as mathematical objects, and to prove theorems about them. Examples are Gödel's incompleteness theorems. In particular, there are well-formed assertions than can be proved to not be a theorem of the ambient theory, although they can be proved in a wider theory. An example is Goodstein's theorem, which can be stated in Peano arithmetic, but is proved to be not provable in Peano arithmetic. However, it is provable in some more general theories, such as Zermelo–Fraenkel set theory.


title: Theorem

text: Many mathematical theorems are conditional statements, whose proofs deduce conclusions from conditions known as hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses. Namely, that the conclusion is true in case the hypotheses are true—without any further assumptions. However, the conditional could also be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol (e.g., non-classical logic).


title: Theorem

text: Although theorems can be written in a completely symbolic form (e.g., as propositions in propositional calculus), they are often expressed informally in a natural language such as English for better readability. The same is true of proofs, which are often expressed as logically organized and clearly worded informal arguments, intended to convince readers of the truth of the statement of the theorem beyond any doubt, and from which a formal symbolic proof can in principle be constructed.


title: Theorem

text: In addition to the better readability, informal arguments are typically easier to check than purely symbolic ones—indeed, many mathematicians would express a preference for a proof that not only demonstrates the validity of a theorem, but also explains in some way "why" it is obviously true. In some cases, one might even be able to substantiate a theorem by using a picture as its proof.


title: Theorem

text: Because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being "trivial", or "difficult", or "deep", or even "beautiful". These subjective judgments vary not only from person to person, but also with time and culture: for example, as a proof is obtained, simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a deep theorem may be stated simply, but its proof may involve surprising and subtle connections between disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem.