title: Lyles, Bissett, Carlisle, and Wolff

abstract: Lyles, Bissett, Carlisle, and Wolff (LBC&W), an architecture firm based in Columbia, South Carolina, was the region's most prominent firm from 1948 until 1975. While the roots of the firm stretch back to 1938, LBC&W was officially incorporated in 1948 as William G. Lyles, Thomas J. Bissett, William A. Carlisle, and Louis M. Wolff. LBC&W's streamlined operational structure, atypically high employment numbers, and varied portfolio contributed to the success of the firm. The firm had satellite offices in Richmond, Virginia; Washington, D.C.; Spartanburg, South Carolina; Raleigh, North Carolina; and Rockville, Maryland. At its height, over 350 architects, engineers, and other staff members were employed by LBC&W. The firm completed over 7,000 projects in its 30-year span, many of which were on the cutting edge of Modern architecture. From Clemson University's library that reflects the influence of Edward Durell Stone's Embassy at New Delhi to the Bankers Trust Tower in downtown Columbia that mimics the Seagram Building by Mies van der Rohe, LBC&W incorporated the methodologies and designs of the great architects of the twentieth century. LBC&W designed some of South Carolina's – and certainly Columbia's – most prominent commercial and private buildings, contributing greatly to the modern built environment of Columbia today.

text:
# Lyles, Bissett, Carlisle, and Wolff

**Lyles, Bissett, Carlisle, and Wolff** (LBC&W), an architecture firm based in Columbia, South Carolina, was the region's most prominent firm from 1948 until 1975. While the roots of the firm stretch back to 1938, LBC&W was officially incorporated in 1948 as William G. Lyles, Thomas J. Bissett, William A. Carlisle, and Louis M. Wolff. LBC&W's streamlined operational structure, atypically high employment numbers, and varied portfolio contributed to the success of the firm. The firm had satellite offices in Richmond, Virginia; Washington, D.C.; Spartanburg, South Carolina; Raleigh, North Carolina; and Rockville, Maryland. At its height, over 350 architects, engineers, and other staff members were employed by LBC&W. The firm completed over 7,000 projects in its 30-year span, many of which were on the cutting edge of Modern architecture. From Clemson University's library that reflects the influence of Edward Durell Stone's Embassy at New Delhi to the Bankers Trust Tower in downtown Columbia that mimics the Seagram Building by Mies van der Rohe, LBC&W incorporated the methodologies and designs of the great architects of the twentieth century. LBC&W designed some of South Carolina's – and certainly Columbia's – most prominent commercial and private buildings, contributing greatly to the modern built environment of Columbia today.

## History

### 1938-1948

In 1938, William Lyles and Robert Caughman Stork began the firm Stork & Lyles. Robert Stork suffered a severe cerebral hemorrhage a few years earlier, however, and did not recover enough to carry a full workload alongside Lyles. Bill Stork, the brother of Robert, returned to South Carolina from Washington D.C. where he had been working and continued with the firm Stork and Lyles. Bill Stork and Lyles, who were both graduates of Clemson University's architecture program, were interrupted by World War II. In February 1942, Lyles was transferred to Washington D.C. as a member of the General Staff of the War Department. He attained the rank of captain in April 1942, and by June of that year, Lyles was on his way to Europe as the chief of design for the chief engineer of the European Theater of Operations. He was responsible for the design of camps and hospitals in the European theater for forty-one months. On November 13, 1945, Lyles returned to Columbia and resumed his work with Stork. At this time, the firm was working in a small space above McGregor's Drug Store. Stork and Lyles began working in 1946 with T.J. Bissett, William Carlisle, and Louis Wolff as associates. Around 1948, Stork left the firm, and the firm became officially incorporated as William G. Lyles, Bissett, Carlisle, and Wolff, which was later shortened to Lyles, Bissett, Carlisle, and Wolff.

In 1948, LBC&W designed and began to build a new office complex at 1321 Bull Street to accommodate its continuously growing staff. The architects were relieved to leave the cramped conditions of the rooms above McGregor's Drug Store.

### 1948-1960

LBC&W's success in later years can be attributed in part to their early connections with the Federal Housing Administration through Bill Stork. The firm's projects during the late '40s and early '50s were primarily residential buildings insured under the FHA's section 608 policy, which was aimed at ensuring housing for veterans. LBC&W was by far the most active firm under the section 608 program in South Carolina. In tangent with this program, LBC&W completed 22 projects insured by the FHA at $16,836,400 by the end of the program in 1950. The closest competition was David Cevil of Spartanburg with a mere six projects insured at $3,492,500. Stork and Lyles completed only one FHA project of which $195,900 was insured by the FHA. Stork is reported to have completed three projects on his own, of which $1,381,500 was FHA insured.

By 1950, the firm had grown to 58 people. During this period, the architects worked to diversify their portfolio after the postwar housing boom began to subside. The architects were successful in their diversification, and by the end of the 1950s, could list many different types of buildings in the company's portfolio such as libraries, science laboratories, office buildings, schools, and military facilities.

### 1960-1970s

In 1960, the firm moved to a new larger office designed by the firm to accommodate a growing staff. The 1960s were a critical period for LBC&W as they solidified their design philosophy, which was centered around their concept of "Total Design." This design philosophy embodied modern ideals about functionality, beauty, and client satisfaction. During this decade, the firm began their expansion outside of South Carolina. Offices in Washington D.C. were opened in 1960, and in later years the firm opened offices in Virginia, Maryland, and North Carolina.

LBC&W entered the 1970s with continuing growth and merged with CE-TEC, a professional service division of Combustion Engineering. The firm continued to win many awards for their work. They received awards from the American Institute of Architects for the Carolina Coliseum in 1970 and the U.S. Post Office in Florence, South Carolina, 1976. In April 1974, the firm moved into four of the twenty-one floors of the Bankers Trust Tower they designed. In addition to LBC&W's geographic reach, the firm's design versatility was critical to their significant place in the history of Modern architecture.

By the late 1970s, the firm had been involved in more than 7,000 projects. Their buildings included elementary, middle, and high schools, collegiate dorms, libraries, student unions, government complexes, office buildings, post offices, military facilities, private homes, apartment complexes, factories, corporate headquarters, and at least one fallout shelter. The majority of these structures were built in a Modernist style. However, several buildings such as the Palmetto Club in Downtown Columbia and several single family residences were designed in the traditional Colonial Revival style that was also popular throughout the twentieth century. Even with projects for more conservative clients, the firm was able to adhere to its principles of design while taking into account the needs of their patrons.

LBC&W was dissolved in the late 1970s. Lyles’ retirement in 1974 followed by Bissett's in 1975 and the economic recession – compounded with LBC&W's illegal financial contribution to the Nixon campaign – most likely led to the breakup of the firm. Articles in *The State* newspaper report that LBC&W was still receiving bids in 1977, but by 1980, LBC&W was referred to as “the now-dissolved firm.”

LBC&W was able to transform the built environment of the South into a Modernist landscape. Its magnitude and versatility, coupled with its atypical organizational structure and breadth of work gave it the competitive edge needed to reshape the skyline of the South time and again.

## Principal architects

Each partner, except Bill Lyles, began his career outside of South Carolina. Therefore, the unified LBC&W had ties to existing corporations and firms across the United States. The senior partners were collectively licensed to practice architecture in South Carolina, North Carolina, Georgia, Washington DC, Kentucky, Mississippi, Alabama, Florida, Arkansas, Virginia, Maryland, New Jersey, Pennsylvania, Delaware, and Tennessee.

**William G. Lyles**  (1913-1981) was born in Whitmire, South Carolina, on October 23, 1913. He earned a Bachelor of Science degree in architecture from Clemson College in 1934. He was the lead designer and partner, with his brother-in-law Robert C. Stork, at Stork & Lyles from 1938 to 1942 and 1945 to 1948. From 1940 until 1945, he served on active duty with the U.S. Army. He was a constructing quartermaster at Fort Gordon, Georgia, and the head of the design and engineering section of the Office of the Chief Engineers in Europe. He served as the president, vice president, and secretary of the South Carolina chapter of the American Institute of Architects (AIA), as well as president of the Clemson Architectural Foundation. Lyles was also one of the founding members of the Richland County Historic Preservation Commission. He wrote several articles for professional journals discussing his architecture philosophy and the firm's projects. These articles included "Lift Slab Construction Saves Clemson Time and Money" in the *Consulting Engineer* in 1954, and "Principles of Economic Feasibility for Architectural Projects" in 1962 in the *AIA Journal*. Within LBC&W, he headed the administration and legal services.

**Thomas J. Bissett** (1909-1992) was born in Tampa, Florida, on December 30, 1909. He graduated from Clemson College with a Bachelor of Science degree in architecture in 1934. He was a member of the AIA and served as director of the South Carolina chapter for a number of years. Prior to his tenure at LBC&W he served as a draftsman for the firm of Frank Frimmer in Tampa, Florida, from 1935 to 1936. He was chief draftsman with the firm of Lester Avery in Miami, Florida, from 1936 to 1941. While on active duty in the U.S. Army from 1942 until 1946, he held the rank of major with the Transportation Corps. In addition to his role as senior partner in Columbia, he also acted as executive director and treasurer of the firm. Within the firm, he was in charge of production and engineering.

**William A. Carlisle** (1918-1999) was born in West Point, Georgia, on July 11, 1918. He earned a Bachelor of Science degree in architecture from Clemson College in 1939. Prior to LBC&W, he had 25 years of architecture experience practicing in Durham, North Carolina, and Fort Jackson, South Carolina. Carlisle was a second lieutenant with the 32nd Infantry Division and was a draftsman and engineer in the southwest Pacific during his active duty with the U.S. Army from 1942 to 1945. He served as president and vice president of the South Carolina chapter of the AIA and as president of the Clemson Architectural Foundation. At LBC&W, he acted as vice president and spent the majority of his time in the field in a supervisory capacity.

**Louis M. Wolff** (1910-1977) was born in Allendale, South Carolina, on December 25, 1910. He majored in architecture and engineering at Clemson College, earning a Bachelor of Science in architecture in 1931. Wolff continued his education at the University of Pennsylvania, earning a Bachelor of Arts in architecture in 1933. Prior to LBC&W, Wolff worked as a draftsman in Flint, Michigan, from 1933 until 1934, the senior foreman for the State Park Division in Myrtle Beach, South Carolina, from 1934 to 1936, and an associate with Buckler and Fenhagen in Baltimore, Maryland from 1936 until 1940. He served with the Corps of Engineering during World War II, 1940 through 1946. He was appointed the chief of Oise Military Labor Service near Reims, France in 1945, where he supervised over 227,000 German prisoners of war in the reconstruction of France. Wolff served as president, vice president, and secretary of the South Carolina chapter of the AIA, and was president of the Clemson Architectural Foundation. He wrote an article for the *South Carolina Magazine* in 1953, "Modern Architecture: Its Purposes and Aims," in which he discussed his personal design philosophy. Wolff served as secretary and head of design of LBC&W. He died in 1977 in Columbia.

## Organization

The sheer size and organizational structure of LBC&W was impressive. Each of the firm's senior partners functioned as the heads of four separate operational departments, which created an assembly line mechanism during the design process. This structure allowed LBC&W to take on multiple projects at one time. Bill Lyles oversaw administration and legal services. T.J. Bissett organized production and engineering. Bill Carlisle functioned as an on-site supervisory agent. Louis Wolff directed design. It was unusual for an architectural firm to be broken up this way. One source alludes to the fact that the divisions applied at the firm sprang from the senior partners’ days in the military. With each step of the process handled by a designated sector, LBC&W had the ability to address every detail in planning more fully than a smaller, more conglomerate firm could do.

## Design philosophy

By the 1960s, the firm began to articulate its design philosophy, called "Total Design," through promotional literature. Advertising its philosophy, LBC&W said: "Design means welding all conditions and influences into the most practical plan. Above all the plan must be functional, serving well the purpose for which the building is intended. It must be simple and sound from engineering and construction standpoints. It must be economical and come within budget limitations of the client. It must satisfy the personal likes and dislikes of the client. And, last but not least, it must be architecturally correct, a beautiful building." According to LBC&W, the philosophy of “Total Design” viewed man's environment holistically: the firm considered the buildings, neighborhoods, streets, parks, and additional facilities in the overall design of the structure.

The firm's Architecture, Engineering, and Planning departments coordinated efforts to devise the best design plan to respond to “the increasing complexities of modern living” that “have made it necessary to take a new approach toward achieving this age old goal.” Regarding architecture, what LBC&W heralded as “the guiding force of total design,” the firm paid close attention to the overall site of a project; its landscaping, exteriors, interiors, and furnishings. Engineering, meanwhile, was the science of total design that made the project feasible and produced “safe, serviceable, and practical structures and systems.” Planning, considered “the unifying force” of a project, “molds architectural and engineering ideas and creations into an orderly and efficient environmental pattern to meet the physical, social, and economic needs of man.” LBC&W also recognized the importance of forming an expert design team of electrical, mechanical, and structural engineers, as well as landscape architects, interior designers, and soil experts. A mandate was that these specialists have “a genuine appreciation of and basic understanding of one another’s problems – with a collective objective to produce excellence in an over-all solution rather than in its various components.”

## Style

### Residential architecture

The post-war housing needs in the mid-twentieth century prompted standardization in residential design. Mass production, cost efficiency, and functional layouts were not only necessary for the production of high volumes of residential architecture, but were also tenets of modern design. Modern architects designing residential properties reflective of the International Style developed innovative concrete systems that adapted to normative construction processes. This allowed for mass prototypes that streamlined housing architecture in the midcentury. Pre-fabrication became a way for architects to design economical buildings that could help Americans purchase their own home and achieve the “American Dream.” Lyles, Bissett, Carlisle, and Wolff all designed their own homes and demonstrated how architects employed the use of the international style for residential architecture.

Modern architecture not only emphasized style, but introduced good style on a large scale. LBC&W published several design books dedicated to different designs of residential homes. For example, “Small Homes” promoted their designs as “economical, efficient, and simple to build,” without compromising “attractiveness, durability, and livability of the finished product.” While not usually considered explicit expressions of Modern architecture, these other residential homes incorporated modern materials and overall design iterations from the modern movement and helped foster modern architecture for the masses. LBC&W did not design every residential building in the International Style. James F. Byrnes, who was a notable politician and statesman, commissioned his residence to be done in the Colonial Revival style.

LBC&W incorporated the Modernist movement ideas of urban planning into its work. A big concern with Modern architecture was thinking about how good design and planning could solve social problems. Several early Modernists looked for new ways to eliminate the congestion of cities, which many believed created unhealthy environments and social problems. The use of space was then reimagined to think about how people can interact differently with a city. Le Corbusier’s Towers in the Park was one of the ideas intended to cure social problems through designing planned landscapes. Le Corbusier's idea was that high-rise buildings could mitigate the effects of overcrowding and urban pollution. LBC&W integrated this theory into their work early in the firm's history when they designed Cornell Arms in 1949, a nineteen-story apartment building located in the heart of Columbia. Funded by the FHA and intended to cater to Columbia's post-war population boom, LBC&W built a cruciform high-rise tower to house hundreds of people in a crowded downtown.

### University architecture

LBC&W constructed buildings for colleges throughout the South, including libraries, student unions, dorms, and classroom buildings. Among their more significant works, the firm designed the Carolina Coliseum, 1968–1969, for the University of South Carolina. Built both to serve the academic needs of the student body and to house the university's basketball program, the Coliseum was an instrumental part of the university's expansion in the mid-sixties. William Lyles was active in Columbia's urban renewal policies and practices, and the Coliseum was a beacon of this social and economic force, as designed by LBC&W. Along with the Coliseum, the firm also constructed other buildings on the campus of the University of South Carolina. These buildings include the Russell House student union, constructed in 1955, the Engineering Laboratory (Sumwalt) in 1951–52, the Humanities Complex/Center in 1968, the President House in 1953, South Building in 1962, Tower Dormitory and Thomas Cooper Undergraduate Library in 1959, and a women's residence hall in 1962.

LBC&W also constructed buildings for other universities in the Columbia area, including Allen College, Benedict College, Columbia College, Lutheran Theological Seminary, and Fort Jackson. At Allen College, LBC&W constructed the library in 1971 on Hampton Street. At Benedict College, the firm constructed the Benjamin F. Payton Learning Resources Center in 1971–73, the Human Resources Center, the library, and Mather Hall. At Columbia College, the firm constructed Asbury Hall in 1965 on Russell Ave and the Women's Dormitory. LBC&W constructed four buildings for the Lutheran Theological Seminary, including the President's Home in 1962, Student Apartments in 1960, the Student Union in 1961, and Yost Administration Building in 1960.

### Government buildings

The firm's practice of modern planning corresponded with the goals of local governments that wanted to improve city environments. LBC&Ws use of “Total Design” in the construction of South Carolina’s State Capitol Complex, for example, highlighted how the firm stressed attention to the total environment of a project and attempted to improve the neighborhood. Similar to the way LBC&W approached Cornell Arms, this was another response to the conversation on the complexities of modern living. The plan for the State Capitol Complex embodied the comprehensive approach of LBC&W’s “Total Design” philosophy as it emphasized architectural cohesion, landscaping, parking and traffic, and necessary functional elements to ensure that the complex suited the state government’s needs.

The Capitol Complex is by far the most recognizable LBC&W government project in Columbia, but other commissions in the city include the Harden Street Fire Station and the U.S. Post Office. The goal of LBC&W's comprehensive planning approach was to introduce order and regularity to the sites. The Capitol Complex specifically was meant to serve as an example for how the rest of the downtown could be formed, with pedestrian pathways and easy parking. Columbia relied on LBC&W to pave the way for the city to enter the 21st century.

## Completed projects (partial)

| Name of Project | Location | Name of Client | Year of Work Completion | Estimated Cost |
| --- | --- | --- | --- | --- |
| Cornell Arms Apartments | Columbia, South Carolina | Cornell G. Fuller | 1949 | $1,500,000 |
| Darlington Apartments | Charleston, South Carolina | Leonard D. Long | 1950 | $1,626,000 |
| Sergeant Jasper Apartments | Charleston, South Carolina | J. C. Long | 1950 | $2,500,000 |
| Clemson House Hotel (Demolished in 2017) | Clemson, South Carolina | Clemson University | 1950 |
| The Darlington | Atlanta, Georgia |  | 1951 | $5,250,000 |
| James F. Byrnes Residence | Columbia, South Carolina | James F. Byrnes | 1955 |  |
| Russell House Student Union | Columbia, South Carolina | University of South Carolina | 1955 |  |
| Columbia Country Club | Columbia, South Carolina |  | 1962 |  |
| Abbeville County Courthouse Renovation | Abbeville, South Carolina | Abbeville County, South Carolina | 1964 |  |
| Ashley House (Charleston, South Carolina) | Charleston, South Carolina | M. B. Kahn Construction Company | 1966 | $2,000,000 |
| Seneca Senior High School | Seneca, South Carolina | Oconee County School District | 1967 | $1,150,000 |
| Richland Memorial Hospital | Columbia, South Carolina | Richland County Hospital | 1967 | $25,000,000 |
| Belk Hall | Due West, SC | Erskine College | 1967 |
| 1601 Assembly Street Post Office | Columbia, South Carolina |  | 1968 |  |
| Carolina Coliseum | Columbia, South Carolina | University of South Carolina | 1969 | $10,000,000 |
| Federal City College | Washington, D.C. | District of Columbia | 1972 | $954,000 |
| General Electric Plant | Mebane, North Carolina | General Electric Company | 1972 | $400,000 |
| Moncrief Army Community Hospital | Fort Jackson (South Carolina) | Savannah District, U.S. Army Corps of Engineers | 1972 | $10,800,000 |
| Pepsi-Cola Bottling Plant | Columbia, South Carolina | Pepsi-Cola Company | 1973 | $2,000,000 |
| Edgar A. Brown Building | Columbia, South Carolina | Government of South Carolina | 1973 | $3,000,000 |
| Gulf Reston International Center | Reston, Virginia | Gulf Reston Inc., Sheraton Hotels and Resorts | 1973 | $10,000,000 |
| Bankers Trust Tower | Columbia, South Carolina |  | 1974 |  |

## Further reading

Primary

* AIA Roster, LBC&W, January 1953, 6–9. http://public.aia.org/sites/hdoaa/wiki/AIA%20scans/Rosters/LylesBissettCarlisleWolff\_roster.pdf
* Anonymous, “William Gordon Lyles,” undated manuscript, LBC&W file, South Carolina State Historic Preservation Office.
* Grantham, Anjuli. “LBC&W and the Making of Modernist Columbia.” LBC&W file, South Carolina State Preservation Office.
* *LBC&W promotional brochure*, January 1, 1965, WFA.
* *LBC&W promotional brochure*, 1950, WFA.
* Mr. & Mrs. Louis M. Wolff Family Archives of the Elsie B. Wolff Family Trust, H. Michael Wolff Trustee (WFA).
* "Profile William G. Lyles of Lyles, Bissettt, Carlisle & Wolff." *Columbia Review of Architecture.* 7, no. 1 (1964): 23-34.
* Wolff, Louis. “Modern Architecture: Its Purposes and Aims.” *South Carolina Magazine* (January 1953): 8–11, 68–70.

Secondary

* Breuer, Marcel. *Marcel Breuer: Sun and Shadow, The Philosophy of an Architect.* Edited by Peter Blake. New York: Dodd, Mead, & Company, 1955.
* Calquhoun, Alan. *Modern Architecture*. Oxford: Oxford University Press, 2002.
* Chandler, Andrew. “Lyles, Bissett, Carlisle & Wolff.” *The South Carolina Encyclopedia* (Columbia: University of South Carolina Press, 2006), 576.
* Hitchcock, Henry-Russell and Philip Johnson. *The International Style: Architecture Since 1922*. New York: The Norton Company, 1932.
* Gordon, Lynn A. “LBC&W: from the Attic to the High-Rise and Beyond,” Sandlapper. *The Magazine of South Carolina*, July 1974.
* McAlester, Virginia Savage. *A Field Guide to American Houses*. New York: Alfred A. Knopf, 2013.
* Kaufman, Terri Wolff. "Mid-Century Modern," September 23, 2013. http://imageous.com/twkwriter/?p=339.
* National Park Service. "Mid-Twentieth Century Modern Architecture Movement in the United States, 1920-1979." National Register of Historic Places Multiple Property Nomination, NR# 64501197.
* “William G. Lyles of Lyles, Bissett, Carlisle & Wolff, Columbia,” *Review of Architecture* 7, no. 1 (1964): 23-34.
* Perry, Walter, Charles Wilson, and Samuel Lapham. *Architectural Practice in South Carolina, 1913-1963.* Columbia, SC: State Printing, 1963.


title: Lyons Switch, Oklahoma

abstract: Lyons Switch is a census-designated place (CDP) in Adair County, Oklahoma, United States. The population was 288 at the 2010 census.

text:
# Lyons Switch, Oklahoma

**Lyons Switch** is a census-designated place (CDP) in Adair County, Oklahoma, United States. The population was 288 at the 2010 census.

## Geography

According to the United States Census Bureau, the CDP has a total area of 8.6 square miles (22.4 km2), of which 8.3 square miles (21.6 km2) is land and 0.35 square miles (0.9 km2), or 3.80%, is water.

## Demographics

Historical population
| Census | Pop. | Note |  |
| --- | --- | --- | --- |
| 2020 | 518 |  |  |
| U.S. Decennial Census | | | |

As of the census of 2000, there were 227 people, 90 households, and 68 families residing in the CDP. The population density was 27.4 people per square mile (10.6 people/km2). There were 101 housing units at an average density of 12.2 per square mile (4.7/km2). The racial makeup of the CDP was 48.02% White, 42.73% Native American, and 9.25% from two or more races. Hispanic or Latino of any race were 0.88% of the population.

There were 90 households, out of which 32.2% had children under the age of 18 living with them, 53.3% were married couples living together, 14.4% had a female householder with no husband present, and 24.4% were non-families. 23.3% of all households were made up of individuals, and 12.2% had someone living alone who was 65 years of age or older. The average household size was 2.52 and the average family size was 2.93.

In the CDP, the population was spread out, with 27.3% under the age of 18, 4.4% from 18 to 24, 23.3% from 25 to 44, 30.4% from 45 to 64, and 14.5% who were 65 years of age or older. The median age was 40 years. For every 100 females, there were 104.5 males. For every 100 females age 18 and over, there were 111.5 males.

The median income for a household in the CDP was $26,458, and the median income for a family was $31,667. Males had a median income of $26,250 versus $16,250 for females. The per capita income for the CDP was $15,148. About 6.7% of families and 11.5% of the population were below the poverty line, including 15.6% of those under the age of eighteen and 14.3% of those 65 or over.

## InfoBox

| Lyons Switch, Oklahoma | |
| --- | --- |
| Census-designated place | |
| Location within Adair County and the state of Oklahoma | |
| Coordinates: 35°46′28″N 94°42′19″W / 35.77444°N 94.70528°W / 35.77444; -94.70528 | |
| Country | United States |
| State | Oklahoma |
| County | Adair |
| Area | |
| Total | 13.06 sq mi (33.82 km2) |
| Land | 12.70 sq mi (32.90 km2) |
| Water | 0.35 sq mi (0.92 km2) |
| Elevation | 988 ft (301 m) |
| Population (2020) | |
| Total | 518 |
| Density | 40.77/sq mi (15.74/km2) |
| Time zone | UTC-6 (Central (CST)) |
| Summer (DST) | UTC-5 (CDT) |
| FIPS code | 40-44775 |
| GNIS feature ID | 2408155 |


title: Tusmore, South Australia

abstract: Tusmore is a suburb in the inner east of Adelaide, South Australia.

text:
# Tusmore, South Australia

**Tusmore** is a suburb in the inner east of Adelaide, South Australia.

## History

In 1839, a pastoralist William Rogers, settled in the area and named his land *Tusmore* after his birthplace in Oxfordshire, England.

In 1911 the area roughly corresponding to modern-day Tusmore, known as Section 291, was owned by the Colonial Board of Advice of the South Australian Company. In that year the Board subdivided the land, and several streets in Tusmore are named after board members from that time: Bakewell, Barr-Smith, Brandreth, Fisher, Kennaway and Stirling.

The Tusmore Post Office was in the Council offices for many years, until a new building erected on the corner plot located diagonally opposite the Portrush Road /Greenhill Road junction in 1951 retained the name, despite being located in Glenside, until 1967.

## Facilities

A recreational park, **Tusmore Park**, straddles the suburbs of Tusmore and Heathpool. It has a public children's paddling pool, large grassed areas which may be used for ball games, five tennis courts, a children's playground, seating areas and electric barbecues. First Creek, dry in summer, runs through the park, and a Scout hall is situated adjacent on the western side.

The building complex housing the Burnside Civic Centre, Council Chambers, Burnside Community Centre, Ballroom and Library, is on the corner of Portrush Road and Greenhill Road.

The Burnside City Uniting Church faces Portrush Road.

## InfoBox

| Tusmore
Adelaide, South Australia | |
| --- | --- |
| Tusmore | |
| Coordinates | 34°56′S 138°38′E / 34.933°S 138.633°E / -34.933; 138.633 |
| Population | 1,503 (SAL 2021) |
| Established | 1839 |
| Postcode(s) | 5065 |
| Location | 6 km (4 mi) from Adelaide |
| LGA(s) | City of Burnside |
| State electorate(s) | Bragg |
| Federal division(s) | Sturt |
| **Suburbs around Tusmore:**  Toorak Gardens Heathpool
Leabrook Erindale  Toorak Gardens Tusmore Hazelwood Park
Burnside  Glenside Linden Park Linden Park | |


title: M-84 (Michigan highway)

abstract: M-84 is a north–south state trunkline highway in the Lower Peninsula of the US state of Michigan. The highway starts on the west side of Saginaw at an intersection with M-58 and runs north through residential and commercial areas. There are two colleges or universities near the trunkline as it connects Saginaw with Bay City, providing an alternative to the freeway that carries Interstate 75/US Highway 23 (I-75/US 23). The northern terminus is at a pair of intersections with M-25 on the east side of the Saginaw River in Bay City. There have been two other highways to bear the M-84 moniker. The first was one in the Upper Peninsula and the second was in The Thumb area. The current highway was originally part of M-47 until that road was relocated onto what was formerly US 10 in the Tri-Cities area. Since the 1960s reuse of the number, M-84 has been extended in the 1970s to replace part of Business Loop I-75 in Bay City. Other projects have reconstructed and widened the roadway through the Bay City area in the early 21st century.

text:
# M-84 (Michigan highway)

**M-84** is a north–south state trunkline highway in the Lower Peninsula of the US state of Michigan. The highway starts on the west side of Saginaw at an intersection with M-58 and runs north through residential and commercial areas. There are two colleges or universities near the trunkline as it connects Saginaw with Bay City, providing an alternative to the freeway that carries Interstate 75/US Highway 23 (I-75/US 23). The northern terminus is at a pair of intersections with M-25 on the east side of the Saginaw River in Bay City.

There have been two other highways to bear the M-84 moniker. The first was one in the Upper Peninsula and the second was in The Thumb area. The current highway was originally part of M-47 until that road was relocated onto what was formerly US 10 in the Tri-Cities area. Since the 1960s reuse of the number, M-84 has been extended in the 1970s to replace part of Business Loop I-75 (BL I-75, now Business Spur I-75, BS I-75) in Bay City. Other projects have reconstructed and widened the roadway through the Bay City area in the early 21st century.

## Route description

M-84 begins at M-58 in a residential area on the west side of Saginaw heading due north on Bay Street. At this point, it is five lanes, with two lanes in each direction and a center turn lane. The highway enters Saginaw Township as Bay Road and serves as a major artery in the area, passing the Fashion Square Mall and several other shopping centers and major retail stores near Tittabawassee Road. The main entrance to Saginaw Valley State University is located on M-84 at Pierce Road just south of the SaginawBay county line.

North of the line, the highway follows West Side Saginaw Road through fields in a less urbanized area. East of University Center and the campus of Delta College, M-84 crosses over I-75/US 23 at exit 160 and proceeds through several curves into Bay City. At the intersection with Euclid Avenue on the city line, M-13 merges in from the north and the two highways run concurrently along Salzburg Avenue. Since this segment of highway is both northbound M-84 and southbound M-13 along eastbound Salzburg Avenue, the two trunklines form a wrong-way concurrency.

M-13/M-84 crosses the west channel of the Saginaw River near the Ted Putz Nature Area to Middle Ground island. The highway continues over the east channel on the Lafayette Avenue Bridge, a drawbridge, to Lafayette Avenue on the eastern bank of the river. At the intersection with Broadway Street, M-13 turns southward, and M-84 continues eastward two more blocks. Turning north on Garfield Street, the highway runs parallel to the river through a residential area. North of the 14th Street intersection, Garfield Street curves northeasterly into Washington Avenue, passing to the east of an industrial complex on the river. At the intersection with McKinley Street, a one-way street, M-84 meets the eastbound direction of M-25 and BS I-75. One block north, M-84 terminates at the intersection with 7th Street, which carries westbound M-25 and BS I-75; both intersections also mark BS I-75's terminus immediately east of the Veterans Memorial Bridge.

The Michigan Department of Transportation (MDOT) maintains M-84 like other state highways in Michigan. As a part of these maintenance responsibilities, the department tracks the volume of traffic that uses the roadways under its jurisdiction. These volumes are expressed using a metric called annual average daily traffic, which is a statistical calculation of the average daily number of vehicles on a segment of roadway. MDOT's surveys in 2010 showed that the highest traffic level along M-84 was 26,408 vehicles daily in Saginaw; the lowest count was 8,405 vehicles per day on Washington Street in Bay City. Two sections of M-84 have been listed on the National Highway System; the section from the southern terminus north to Tittabawassee Road in the Saginaw area, and from the I-75/US 23 interchange north to M-25 in the Bay City area. The system is a network of roads important to the country's economy, defense, and mobility.

## History

The first M-84 in Michigan was in the Upper Peninsula starting in 1919; the highway ran from Garnet to McLeods Corner, southeast of Newberry, following the current Borgstrom Road in Mackinac County and County Road 393 in Luce County. The highway was replaced by an extension of M-48 in 1926. The M-84 designation was then immediately reused for a section of the former M-31 in The Thumb; it ran from M-81 near Reese running through Fairgrove and Akron to M-29 at Unionville. This iteration was replaced by M-83 in 1930.

The I-75/US 10/US 23 freeway was completed between Saginaw and Bay City in late 1960 or early 1961; M-47 was relocated to the former US 10 between Saginaw and Midland, and M-84 was redesignated along the former M-47 between M-81 at Saginaw and the freeway in Bay City. A new BL I-75 was created at the same time along the former M-47 in Bay City. This business loop would be split in half in 1971 resulting in a new business spur; M-84 was extended over the southern section between M-25 and I-75/US 10/US 23.

A reconstruction project in 2004–05 resulted in the roadway being widened to four lanes between Pierce Road in Kochville Township of Saginaw County and Delta Road in Frankenlust Township in Bay County. The 2009 reconstruction resulted in new bridges over I-75 and widening of the road from Delta Road to 2 Mile Road. Additional construction scheduled for 2011 resulted in the widening of the road from 2 Mile to Euclid.

## Major intersections

| County | Location | mi | km | Destinations | Notes |
| --- | --- | --- | --- | --- | --- |
| Saginaw | Saginaw | 0.000 | 0.000 | M-58
Bay Street | Bay Street continues from beyond southern terminus; M-58 follows a one-way pairing on State Street and Davenport Avenue |
| Bay | Frankenlust Township | 9.547–
9.636 | 15.364–
15.508 | I-75 / US 23 Mackinac Bridge, Saginaw | Exit 160 on I-75/US 23 |
| | Bay CityMonitor Township city line | 11.963 | 19.253 |
M-13 north Standish | Western end of M-13 concurrency |
| | Bay City | 13.081 | 21.052 |
M-13 south Saginaw | Eastern end of M-13 concurrency |
| | 14.641–
14.710 | 23.562–
23.673 |
BS I-75 west / M-25 / LHCT (McKinley Street, 7th Street) |  |
| 1.000 mi = 1.609 km; 1.000 km = 0.621 mi
 | | | | | |

Template:Attached KML/M-84 (Michigan highway)KML is from Wikidata * M-84 at Michigan Highways

## InfoBox

| M-84 | |
| --- | --- |
| M-84 highlighted in red | |
| Route information | |
| Maintained by MDOT | |
| Length | 14.710 mi (23.673 km) |
| Existed | 1960–present |
| Major junctions | |
| South end | M-58 in Saginaw |
| Major intersections | I-75 / US 23 near Bay City |
| North end | M-25 in Bay City |
|  | |
| Location | |
| Country | United States |
| State | Michigan |
| Counties | Saginaw, Bay |
|  | |
| Highway system | |
|  | |
| M-83   M-85 | |


title: M-86 (Michigan highway)

abstract: M-86 is an east–west state trunkline highway in the US state of Michigan in the southern portion of the Lower Peninsula. The highway starts at Business US Highway 131 and M-60 in Three Rivers and ends at US Highway 12 (US 12) near Coldwater. In between, it crosses farm country and runs along a section of the Prairie River. Following a highway originally numbered M-7, the roadway was renumbered M-86 in 1940. It has been a part of the state highway system at least since 1927. Two other roadways carried the M-86 designation in the 1920s. Two bridges along the road are eligible for inclusion on the National Register of Historic Places (NRHP).

text:
# M-86 (Michigan highway)

**M-86** is an east–west state trunkline highway in the US state of Michigan in the southern portion of the Lower Peninsula. The highway starts at Business US Highway 131 (Bus. US 131) and M-60 in Three Rivers and ends at US Highway 12 (US 12) near Coldwater. In between, it crosses farm country and runs along a section of the Prairie River. Following a highway originally numbered **M-7**, the roadway was renumbered M-86 in 1940. It has been a part of the state highway system at least since 1927. Two other roadways carried the M-86 designation in the 1920s. Two bridges along the road are eligible for inclusion on the National Register of Historic Places (NRHP).

## Route description

M-86 begins in Three Rivers at a junction with Bus. US 131 and M-60. From there the road travels south out of town on Main Street and across the St. Joseph River. After crossing the river, the highway runs through a residential area of town and turns eastward into rural farm lands. M-86 crosses the Prairie River and follows Burr Oak Street into the community of Centreville. The highway switches to follow Main Street through downtown Centreville; east of downtown, Main Street curves along a bend in the river, and it runs parallel to the river out of town. As part of its support of the state highway system, the Michigan Department of Transportation (MDOT) tracks the traffic levels along the roads it maintains. These traffic counts are expressed in terms of average annual daily traffic (AADT), a calculation of the vehicles using a segment of roadway on a typical day of the year. In 2009, MDOT measured 7,642 vehicles including 138 trucks along M-86 in Centreville, the highest traffic levels along the whole highway. As the highway leaves town, it passes by the north side of Lake Templene, and Sand Lake near Nottawa before meeting M-66.

From the junction, M-86 and M-66 run concurrently to the north for about 1.5 miles (2.4 km), at which point M-86 branches off to the east while M-66 continues on a northerly route. M-86 continues east through agricultural land into the village of Colon. The highway follows South Street and turns north on Blackstone Avenue between Sturgeon and Palmer lakes. Turning to follow State Street, the trunkline heads out of the village to the southeast. It continues eastward along Colon Road, passing north of Matteson Lake near Matteson and through Batavia Center. In Coldwater Township, M-86 experienced its lowest traffic level in 2009 at 1,872 vehicles and 129 trucks AADT. The highway terminates at US 12 west of Coldwater near the Branch County Memorial Airport and Messenger Lake. No segment of M-86 has been listed on the National Highway System, a system of roads important to the nation's economy, defense, and mobility.

## History

### Previous designations

Upon its inception in 1921, a very different M-86 was routed along a portion of present-day M-66 from M-46 at Six Lakes northward to Remus, ending at M-24 (modern M-20). A few years later in 1924–25, M-66 was extended north to Remus, supplanting the contemporary M-86. At the same time, the M-86 designation was relocated to Ionia County to run from M-44 in Orleans to M-43 (present day M-66) just east of there. In late 1929, M-44 was extended east from Orleans to junction with M-43, once again, causing M-86 to be supplanted and removed from the highway system.

### Current designation

| M-7 | |
| --- | --- |
|  | |
| Location | Three Rivers Coldwater |
| Length | 34.059 mi (54.813 km) |
| Existed | 1927–1940 |

By the end of 1927, the Michigan State Highway Department (MSHD) had designated a highway numbered M-7 between Three Rivers and Centreville. This highway was extended east by the middle of 1936. The route connected US 131 in downtown Three Rivers to US 112 outside Coldwater. At the time of the extension, all of M-7 was a gravel road. Later that year, the original segment between Three Rivers and Colon was paved, and the state extended the hard-surface route as far as Nottawa in 1937.

In 1940, at the same time all single-digit highway numbers were renumbered in the state, the M-86 designation replaced M-7. This incarnation of M-86 followed its present-day routing. Near Nottawa, M-86 ran concurrently with the contemporary M-78 north and east to Colon. In late 1948 or early 1949, the last section of highway was paved in Branch County, hard-surfacing all of M-86 for the first time. A change related to M-66 and M-78 altered M-86 in 1965. South of Battle Creek, M-66 replaced M-78. Rather than follow M-78 between Colon and Athens, M-66 used a different series of roads. The net result was that along M-86, the M-78 concurrency was replaced by a shorter M-66 concurrency. The routing has remain unchanged since.

### Historic bridges

M-86 currently uses one bridge eligible for listing on the NRHP. The span over the St. Joseph River in Three Rivers was built in 1903. It is a five-span concrete arch bridge constructed to look as though created from stacked masonry blocks. The current railings were added in 1952 by the MSHD during a repair project.

The second historic structure was the bridge over the Prairie River in Centreville. This camelback pony truss span was moved to that location in 1938–39, although it was originally built on an unknown location in 1923. In the move, two sidewalks, one on either side of the trusses, were eliminated from the structure. This project was part of Public Works Administration relief work in the area. The structure was moved to Crystal Springs Road in Cass County's Pokagon Township in 2016.

## Major intersections

| County | Location | mi | km | Destinations | Notes |
| --- | --- | --- | --- | --- | --- |
| St. Joseph | Three Rivers | 0.000 | 0.000 |
Bus. US 131 / M-60 Niles, Kalamazoo, Jackson |  |
| | NottawaColon township line | 12.684 | 20.413 |
M-66 south Sturgis | Southern end of M-66 concurrency |
| | 14.425–
14.546 | 23.215–
23.410 |
M-66 north Battle Creek | Northern end of M-66 concurrency |
| Branch | Coldwater Township | 34.059 | 54.813 | US 12 Sturgis, Coldwater |  |
| 1.000 mi = 1.609 km; 1.000 km = 0.621 mi
 | | | | | |

Template:Attached KML/M-86 (Michigan highway)KML is from Wikidata * M-86 at Michigan Highways

## InfoBox

| M-86 | |
| --- | --- |
| M-86 highlighted in red | |
| Route information | |
| Maintained by MDOT | |
| Length | 34.059 mi (54.813 km) |
| Existed | 1940–present |
| Major junctions | |
| West end |
Bus. US 131 / M-60 in Three Rivers |
| Major intersections | M-66 near Nottawa |
| East end | US 12 near Coldwater |
|  | |
| Location | |
| Country | United States |
| State | Michigan |
| Counties | St. Joseph, Branch |
|  | |
| Highway system | |
|  | |
| M-85   M-87 | |
| M-6 **M-7**  US 8 | |


title: Turán graph

abstract:
The Turán graph, denoted by T, is a complete multipartite graph; it is formed by partitioning a set of n vertices into r subsets, with sizes as equal as possible, and then connecting two vertices by an edge if and only if they belong to different subsets. Where q and s are the quotient and remainder of dividing n by r, the graph is of the form K q + 1, q + 1, …, q, q, and the number of edges is
  - n 2 − s 2 2 +. For r ≤ 7, this edge count can be more succinctly stated as ⌊ n 2 2 ⌋. The graph has s subsets of size q + 1, and r − s subsets of size q ; each vertex has degree n − q − 1 or n − q. It is a regular graph if n is divisible by r.

text:
# Turán graph

The **Turán graph**, denoted by $T(n,r)$, is a complete multipartite graph; it is formed by partitioning a set of $n$ vertices into $r$ subsets, with sizes as equal as possible, and then connecting two vertices by an edge if and only if they belong to different subsets. Where $q$ and $s$ are the quotient and remainder of dividing $n$ by $r$ (so $n=qr+s$), the graph is of the form $K\_{q+1,q+1,\ldots ,q,q}$, and the number of edges is

$\left(1-{\frac {1}{r}\right){\frac {n^{2}-s^{2}{2}+{s \choose 2}}}}$.

For $r\leq 7$, this edge count can be more succinctly stated as $\left\lfloor \left(1-{\frac {1}{r}\right){\frac {n^{2}{2}\right\rfloor }}}$. The graph has $s$ subsets of size $q+1$, and $r-s$ subsets of size $q$; each vertex has degree $n-q-1$ or $n-q$. It is a regular graph if $n$ is divisible by $r$ (i.e. when $s=0$).

## Turán's theorem

Turán graphs are named after Pál Turán, who used them to prove Turán's theorem, an important result in extremal graph theory.

By the pigeonhole principle, every set of *r* + 1 vertices in the Turán graph includes two vertices in the same partition subset; therefore, the Turán graph does not contain a clique of size *r* + 1. According to Turán's theorem, the Turán graph has the maximum possible number of edges among all (*r* + 1)-clique-free graphs with *n* vertices. Keevash & Sudakov (2003) show that the Turán graph is also the only (*r* + 1)-clique-free graph of order *n* in which every subset of α*n* vertices spans at least $\frac {r\\,{-}\\,1}{3r}(2\alpha -1)n^{2}$ edges, if α is sufficiently close to 1. The Erdős–Stone theorem extends Turán's theorem by bounding the number of edges in a graph that does not have a fixed Turán graph as a subgraph. Via this theorem, similar bounds in extremal graph theory can be proven for any excluded subgraph, depending on the chromatic number of the subgraph.

## Special cases

Several choices of the parameter *r* in a Turán graph lead to notable graphs that have been independently studied.

The Turán graph *T*(2*n*,*n*) can be formed by removing a perfect matching from a complete graph *K*2*n*. As Roberts (1969) showed, this graph has boxicity exactly *n*; it is sometimes known as the *Roberts graph*. This graph is also the 1-skeleton of an *n*-dimensional cross-polytope; for instance, the graph *T*(6,3) = *K*2,2,2 is the octahedral graph, the graph of the regular octahedron. If *n* couples go to a party, and each person shakes hands with every person except his or her partner, then this graph describes the set of handshakes that take place; for this reason, it is also called the **cocktail party graph**.

The Turán graph *T*(*n*,2) is a complete bipartite graph and, when *n* is even, a Moore graph. When *r* is a divisor of *n*, the Turán graph is symmetric and strongly regular, although some authors consider Turán graphs to be a trivial case of strong regularity and therefore exclude them from the definition of a strongly regular graph.

The class of Turán graphs can have exponentially many maximal cliques, meaning this class does not have few cliques. For example, the Turán graph $T(n,\lceil n/3\rceil )$ has 3*a*2*b* maximal cliques, where 3*a* + 2*b* = *n* and *b*  2; each maximal clique is formed by choosing one vertex from each partition subset. This is the largest number of maximal cliques possible among all *n*-vertex graphs regardless of the number of edges in the graph; these graphs are sometimes called **Moon–Moser graphs**.

## Other properties

Every Turán graph is a cograph; that is, it can be formed from individual vertices by a sequence of disjoint union and complement operations. Specifically, such a sequence can begin by forming each of the independent sets of the Turán graph as a disjoint union of isolated vertices. Then, the overall graph is the complement of the disjoint union of the complements of these independent sets.

Chao & Novacky (1982) show that the Turán graphs are *chromatically unique*: no other graphs have the same chromatic polynomials. Nikiforov (2005) uses Turán graphs to supply a lower bound for the sum of the *k*th eigenvalues of a graph and its complement.

Falls, Powell & Snoeyink (2003) develop an efficient algorithm for finding clusters of orthologous groups of genes in genome data, by representing the data as a graph and searching for large Turán subgraphs.

Turán graphs also have some interesting properties related to geometric graph theory. Pór & Wood (2005) give a lower bound of Ω((*rn*)3/4) on the volume of any three-dimensional grid embedding of the Turán graph. Witsenhausen (1974) conjectures that the maximum sum of squared distances, among *n* points with unit diameter in **R***d*, is attained for a configuration formed by embedding a Turán graph onto the vertices of a regular simplex.

An *n*-vertex graph *G* is a subgraph of a Turán graph *T*(*n*,*r*) if and only if *G* admits an equitable coloring with *r* colors. The partition of the Turán graph into independent sets corresponds to the partition of *G* into color classes. In particular, the Turán graph is the unique maximal *n*-vertex graph with an *r*-color equitable coloring.

* Chao, C. Y.; Novacky, G. A. (1982). "On maximally saturated graphs". *Discrete Mathematics*. **41** (2): 139–143. doi:10.1016/0012-365X(82)90200-X.
* Falls, Craig; Powell, Bradford; Snoeyink, Jack (2003). "Computing high-stringency COGs using Turán type graphs" (PDF).
* Keevash, Peter; Sudakov, Benny (2003). "Local density in graphs with forbidden subgraphs" (PDF). *Combinatorics, Probability and Computing*. **12** (2): 139–153. doi:10.1017/S0963548302005539. S2CID 17854032.
* Moon, J. W.; Moser, L. (1965). "On cliques in graphs". *Israel Journal of Mathematics*. **3**: 23–28. doi:10.1007/BF02760024. S2CID 9855414.
* Nikiforov, Vladimir (2007). "Eigenvalue problems of Nordhaus-Gaddum type". *Discrete Mathematics*. **307** (6): 774–780. arXiv:math.CO/0506260. doi:10.1016/j.disc.2006.07.035.
* Pór, Attila; Wood, David R. (2005). "No-three-in-line-in-3D". *Proc. Int. Symp. Graph Drawing (GD 2004)*. Lecture Notes in Computer Science no. 3383, Springer-Verlag. pp. 395–402. doi:10.1007/b105810. hdl:11693/27422.
* Roberts, F. S. (1969). Tutte, W.T. (ed.). "On the boxicity and cubicity of a graph". *Recent Progress in Combinatorics*: 301–310.
* Turán, P. (1941). "Egy gráfelméleti szélsőértékfeladatról (On an extremal problem in graph theory)". *Matematikai és Fizikai Lapok*. **48**: 436–452.
* Witsenhausen, H. S. (1974). "On the maximum of the sum of squared distances under a diameter constraint". *American Mathematical Monthly*. **81** (10): 1100–1101. doi:10.2307/2319046. JSTOR 2319046.

## InfoBox

| Turán graph | |
| --- | --- |
| The Turán graph T(13,4) | |
| Named after | Pál Turán |
| Vertices | $n$ |
| Edges | ~ $\left(1-{\frac {1}{r}\right){\frac {n^{2}{2}}}}$ |
| Radius | $\left\\{{\begin{array}{ll}\infty &r=1\\2&r\leq n/2\\1&{\text{otherwise}\end{array}\right.}}}$ |
| Diameter | $\left\\{{\begin{array}{ll}\infty &r=1\\1&r=n\\2&{\text{otherwise}\end{array}\right.}}}$ |
| Girth | $\left\\{{\begin{array}{ll}\infty &r=1\vee (n\leq 3\wedge r\leq 2)\\4&r=2\\3&{\text{otherwise}\end{array}\right.}}}$ |
| Chromatic number | $r$ |
| Notation | $T(n,r)$ |
| Table of graphs and parameters | |


title: Turán sieve

abstract: In number theory, the Turán sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Pál Turán in 1934.

text:
# Turán sieve

In number theory, the **Turán sieve** is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Pál Turán in 1934.

## Description

In terms of sieve theory the Turán sieve is of *combinatorial type*: deriving from a rudimentary form of the inclusion–exclusion principle. The result gives an *upper bound* for the size of the sifted set.

Let *A* be a set of positive integers  *x* and let *P* be a set of primes. For each *p* in *P*, let *A**p* denote the set of elements of *A* divisible by *p* and extend this to let *A**d* be the intersection of the *A**p* for *p* dividing *d*, when *d* is a product of distinct primes from *P*. Further let *A*1 denote *A* itself. Let *z* be a positive real number and *P*(*z*) denote the product of the primes in *P* which are  *z*. The object of the sieve is to estimate

$$S(A,P,z)=\left\vert A\setminus \bigcup \_{p\mid P(z)}A\_{p}\right\vert .$$

We assume that |*A**d*| may be estimated, when *d* is a prime *p* by

$$\left\vert A\_{p}\right\vert ={\frac {1}{f(p)}X+R\_{p}}$$

and when *d* is a product of two distinct primes *d* = *p* *q* by

$$\left\vert A\_{pq}\right\vert ={\frac {1}{f(p)f(q)}X+R\_{p,q}}$$

where *X*   =   |*A*| and *f* is a function with the property that 0  *f*(*d*)  1. Put

$$U(z)=\sum \_{p\mid P(z)}f(p).$$

Then

$$S(A,P,z)\leq {\frac {X}{U(z)}+{\frac {2}{U(z)}\sum \_{p\mid P(z)}\left\vert R\_{p}\right\vert +{\frac {1}{U(z)^{2}\sum \_{p,q\mid P(z)}\left\vert R\_{p,q}\right\vert .}}}}$$

## Applications

* Alina Carmen Cojocaru; M. Ram Murty. *An introduction to sieve methods and their applications*. London Mathematical Society Student Texts. Vol. 66. Cambridge University Press. pp. 47–62. ISBN 0-521-61275-6.
* Greaves, George (2001). *Sieves in number theory*. Springer-Verlag. ISBN 3-540-41647-1.
* Halberstam, Heini; Richert, H.-E. (1974). *Sieve Methods*. London Mathematical Society Monographs. Vol. 4. Academic Press. ISBN 0-12-318250-6. MR 0424730. Zbl 0298.10026.
* Christopher Hooley (1976). *Applications of sieve methods to the theory of numbers*. Cambridge University Press. p. 21. ISBN 0-521-20915-3.


title: Luther Kirk

abstract: Luther Kirk is an American football safety who is a free agent. He played college football at Illinois State and was signed by the Dallas Cowboys as an undrafted free agent in 2020.

text:
# Luther Kirk

**Luther Kirk** (born November 7, 1996) is an American football safety who is a free agent. He played college football at Illinois State and was signed by the Dallas Cowboys as an undrafted free agent in 2020.

## Early years

Kirk was born on November 7, 1996, in Garland, Texas. He attended Garland High School, and played quarterback and safety for their football team.

As a senior, he completed 87-of-165 passing attempts, throwing for 1,160 yards and 12 touchdowns, while also posting 93 carries for 798 rushing yards and five touchdowns.

## College career

Kirk accepted a football scholarship from Illinois State University. As a freshman in 2015, he appeared in 10 games as a backup safety, making a total of 18 tackles and 4 passes defensed.

As a sophomore in 2016, he played in all 12 games, finishing the year with 15 defensive tackles and leading the team with 9 special teams tackles.

Kirk stayed in school, but left the football team in 2017, returning for Spring 2018 workouts. He was named team captain that year, and started all 11 games at the safety position. His five interceptions tied for first in the Missouri Valley Football Conference (MVFC). He also placed second on the team with 61 tackles, and was named first-team all-conference at the end of the year.

As a senior in 2019, he started all 15 games at strong safety, leading the team with 89 tackles, while also making 6 passes defensed, 3 sacks and one forced fumble. He was named an AFCA FCS Coaches' and HERO Sports FCS All-America first-team selection and earned STATS FCS All-America second-team honors.

## Professional career

### Dallas Cowboys

Kirk was signed as an undrafted free agent by the Dallas Cowboys after the 2020 NFL draft on April 26. He was waived at the final roster cuts on September 5, but re-signed to the practice squad a day later. He was released from the practice squad on September 15.

### Minnesota Vikings

On September 28, Kirk was signed by the Minnesota Vikings to their practice squad. He was promoted to the active roster prior to their game against the Green Bay Packers, and reverted afterwards. Kirk was waived/injured after the final roster cuts in August 2021.

### Atlanta Falcons

On October 25, 2021, Kirk was signed by the Atlanta Falcons to the practice squad. He was elevated to the active roster for their game against the Buffalo Bills, and made his NFL debut in the 15–29 loss.

On May 16, 2022, Kirk was waived by the Falcons.

### Cleveland Browns

On May 17, 2022, Kirk was claimed off waivers by the Cleveland Browns. He was waived on August 22, 2022.

## InfoBox

Luther Kirk
| Personal information | |
| --- | --- |
| Born: | (1996-11-07) November 7, 1996<br>Garland, Texas, U.S. |
| Height: | 6 ft 2 in (1.88 m) |
| Weight: | 195 lb (88 kg) |
| Career information | |
| High school: | Garland (TX) |
| College: | Illinois State |
| Position: | Safety |
| Undrafted: | 2020 |
| Career history | |
|  | |
| * Offseason and/or practice squad member only | |
|  | |
| Career highlights and awards | |
| * All-MVFC (2018) | |
|  | |
| Career NFL statistics | |
| Games played: 1 | |
|  | |
| Player stats at **PFR** | |
|  | |


title: Twin Cities 400

abstract: The 400 was a named passenger train operated by the Chicago and North Western Railway between Chicago and Saint Paul, with a final stop in Minneapolis. The train took its name from the schedule of 400 miles between the cities in 400 minutes, and was also a nod to "The Four Hundred Club", a term coined by Ward McAllister to refer to the social elite of New York City in the late 19th century. It was an express train with limited stops between Chicago and the Twin Cities. The "400" ran from 1935 to 1963 on the Chicago to Twin Cities route. The C&NW later named their other passenger trains using the number "400".

text:
# Twin Cities 400

The ***400*** (later named the ***Twin Cities 400***) was a named passenger train operated by the Chicago and North Western Railway between Chicago and Saint Paul, with a final stop in Minneapolis. The train took its name from the schedule of 400 miles between the cities in 400 minutes, and was also a nod to "The Four Hundred Club", a term coined by Ward McAllister to refer to the social elite of New York City in the late 19th century. It was an express train with limited stops between Chicago and the Twin Cities. The "400" ran from 1935 to 1963 on the Chicago to Twin Cities route. The C&NW later named their other passenger trains using the number *"400"*.

## Background

A lightweight streamlined train, the Pioneer Zephyr, was introduced in 1934 the United States by the Chicago, Burlington and Quincy Railroad. The CB&Q was a competitor to the Chicago and North Western Railway on Chicago to Minneapolis-St.Paul rail service. The C&NW had not invested in the new diesel powered passenger train technology, but decided to upgrade track and motive power for higher speeds with heavyweight, steam-powered trains.

### Adams cutoff

The main route between Chicago and the Twin Cities for the C&NW went through Madison, Wisconsin and met the Chicago, St. Paul, Minneapolis and Omaha Railway in Elroy, Wisconsin. The C&NW Chicago to St. Paul *Viking* train used this route through Madison, taking about 12 hours. In 1910, the Milwaukee, Sparta, and Northwestern Railroad, a subsidiary of the C&NW, began the "Air Line" or "Adams Cutoff" from Adams, Wisconsin towards Sparta, Wisconsin. It began operation in 1911. This railroad met the Omaha Railway in Wyeville, Wisconsin as part of the new route between Milwaukee and St. Paul, but not going through Madison. It became the route for the overnight North Western Limited, which used heavyweight Pullman cars between Chicago and the Twin Cities. The North Western Limited took 12 hours on this route.

### Higher speed to Milwaukee

C&NW made their first upgrades in 1934 along the 85-mile (137 km) line between Chicago and Milwaukee, Wisconsin, introducing the 90-minute *Pacemaker* service to compete with the Chicago, Milwaukee, St. Paul & Pacific Railroad (Milwaukee Road) which introduced a similar train.

### Competition to the Twin Cities

Attention then turned to faster trains to Saint Paul: The CB&Q ran a *Zephyr* demonstration train between Chicago and the Twin Cities that summer with the intent to run regular service the next year, and the Milwaukee Road introduced similar plans. The C&NW focused on the Adams cutoff route running west from Milwaukee. The railroad also upgraded its locomotives and passenger cars. Four C&NW Class E-2 4-6-2 Pacific locomotives built by American-Schenectady in 1923 were converted to run on oil rather than coal and had other upgrades to help them run at high speed, becoming Class E-2-a engines. The passenger cars got air conditioning and improved suspension parts for a smoother ride.

## Service history

A test run was made on December 30, 1934, but the regular train started on January 2, 1935. *Time* dubbed the *400*, "the fastest train scheduled on the American Continent, fastest in all the world on a stretch over 200 mi." While the *400* implied "400 miles in 400 minutes", Chicago to St. Paul was 408.6 miles (657.6 km) in 420 minutes (7 hours), with the station stop at St. Paul and the last leg to Minneapolis taking another 30 minutes. The *400s* had priority over all other trains; the employee timetable specified that "Freight trains, transfer trains, and switch engines must clear the schedules of Nos. 400 and 401 \[by\] fifteen (15) minutes." Other *400* trains would receive similar instructions in later years, and the rule remained in effect for most of the *Twin Cities 400'*s existence.

On the first day the train reached 91 miles per hour (146 km/h). On April 28 the schedule was shortened by 30 minutes to reach the mile-a-minute pace the line promised, and matching the 6½-hour pace of the newly introduced Milwaukee Road *Hiawatha* and the Burlington's *Twin Cities Zephyr*. This included a 75-minute schedule between Chicago and Milwaukee, averaging 68 mph (109 km/h) there and 63 mph (101 km/h) overall. One day in late 1935 the *400* needed to make up time and reached 108 mph (174 km/h). Later, streamlined diesel trains were said to reach 112 mph (180 km/h).

C&NW renamed the first *400* to *Twin Cities 400* in late 1941 as the C&NW prepared to rename almost all of its passenger trains as part of the *400* fleet, including the *Flambeau 400*, *Minnesota 400*, *Peninsula 400*, *Shoreland 400*, *Valley 400* and the later *Kate Shelley 400*.

From 1950 to 1955 the train ran its shortest schedule, 6¼ hours between St. Paul and Chicago, an average of over 65 mph (105 km/h). In 1952 the railroad installed automatic train stop along the eastern half of the route from Chicago to Wyeville due to regulations from the Interstate Commerce Commission. This allowed the train to run at 95 to 100 mph (153 to 161 km/h) there, although the western part of the line did not get upgrades and was limited to 79 mph (127 km/h). The pace reverted to a 6½-hour schedule in 1955 and in 1960 to the 7-hour pace established in 1935. C&NW ceased running the *Twin Cities 400* in 1963 and all intercity passenger service on C&NW ended with the formation of Amtrak in 1971. Today, the Twin Cities to Chicago route is served by the Amtrak *Borealis*, which takes about seven hours. The route is also covered by the Seattle/Portland-to-Chicago *Empire Builder*. Both trains run on the former Milwaukee Road, now Canadian Pacific.

### July 1959 derailment

On July 30, 1959, the Twin Cities 400 left the rails between Knapp and Menomonie in Dunn County, Wisconsin. Fifty people were taken to area hospitals with injuries out of the 115 passengers.

## Equipment

The *400* was notable for fast trains of its day in that it originally ran with rebuilt or upgraded, rather than new equipment. This stood in stark comparison to the Milwaukee Road's *Hiawatha* and the Burlington *Zephyrs*, each of which first ran with brand new locomotives and cars. Each *400* train required two steam locomotives, which were swapped partway through the trip, primarily because some grease fittings on the train could not withstand the entire journey at high speed.

The steam locomotives were upgraded to feature a 45° lamp on top of the boiler just ahead of the smokestack. These lights were intended to announce the approach of the train and could be seen for a great distance in rural areas. In 1937, one locomotive was equipped with a prototype Mars light, the first ever put into use. The three-million-candela lamp had a gyrating reflector which traced a figure-8 pattern ahead of the engine.

C&NW updated the train in 1939 with two pairs of EMD E3A locomotives and lightweight streamlined passenger cars. Two engines were required because the diesels didn't have as much power as the older steam locomotives. However, they were extremely reliable, with only one major breakdown in the first two years of service. These were followed by E6 locomotives in 1941, and E7s in 1947. E8s saw some service in the 1950s, though they were initially purchased for other routes.

## Route

The train originated at the Chicago and North Western Terminal (now the Ogilvie Transportation Center) on Madison Street in Chicago. It ran to Milwaukee on the lakefront commuter line and stopped at the Lake Front Depot on Wisconsin Avenue. It ran to Wyeville, Wisconsin where it followed the Omaha Road route to St. Paul. It stopped at the Saint Paul Union Depot, and then made the short run to the Minneapolis Great Northern Depot over the Stone Arch Bridge.

*The North Western Limited* train was an overnight train that also used the *Twin Cities 400* route, but taking 9 hours and only stopping at Altoona and Adams between St. Paul and Milwaukee.

*The Viking* was another named C&NW passenger train that followed a different route, through Elroy, Wisconsin and Madison, Wisconsin, and made limited stops between Chicago and St. Paul. It took roughly 12 hours as a daylight train. *The Victory* was the overnight train on this route.

## Name

Along the routes of the *Twin Cities 400* and its sister trains, there were a number of bars titled "400 Club", paying homage to the train and the social status.

## Bibliography

## InfoBox

| *400*
*Twin Cities 400* | |
| --- | --- |
| The 400 of 1936 | |
| Overview | |
| Service type | Express train |
| Status | Discontinued |
| Locale | Minnesota, Wisconsin, Illinois |
| First service | January 2, 1935 |
| Last service | July 23, 1963 |
| Former operator(s) |  |
| Route | |
| Termini | Great Northern Depot,
Minneapolis, Minnesota
North Western Terminal,
Chicago, Illinois |
| Stops | 10 |
| Train number(s) | 400, 401 |
| Technical | |
| Track gauge | 4 ft 8+12 in (1,435 mm) standard gauge |
| Operating speed | 63 mph (101 km/h) average (1950–1955) |
| Route map | |


title: Twin Cities Air Service

abstract: Twin Cities Air Service was an American fixed-base operator and charter airline based at Auburn, Maine and operated from Auburn/Lewiston Municipal Airport and the Portland International Jetport. The airline was a certified Part 135 operator, provided on demand and commuter service, while the FBO provided standard aircraft services and maintenance, specializing in overhauls of the Cessna 400 series aircraft. Beginning in March 2010, Twin Cities Air Service began a scheduled commuter route between Portland, Maine, and Yarmouth, Nova Scotia. At the time of the initiation of this route, Twin Cities was the only scheduled carrier into the Yarmouth Airport, and was the only scheduled international service into the Portland International Jetport.

text:
# Twin Cities Air Service

**Twin Cities Air Service** was an American fixed-base operator and charter airline based at Auburn, Maine and operated from Auburn/Lewiston Municipal Airport and the Portland International Jetport. The airline was a certified Part 135 operator, provided on demand and commuter service, while the FBO provided standard aircraft services and maintenance, specializing in overhauls of the Cessna 400 series aircraft. Beginning in March 2010, Twin Cities Air Service began a scheduled commuter route between Portland, Maine, and Yarmouth, Nova Scotia. At the time of the initiation of this route, Twin Cities was the only scheduled carrier into the Yarmouth Airport, and was the only scheduled international service into the Portland International Jetport.

## History

Twin Cities Air Service was founded in 1992 as a fixed-base operator at the Auburn airport. The company has since expanded to include on demand air charter services, airframe maintenance and support, and scheduled international air service. Ch-aviation stated "Out of Business", the last change on the Website was 2012, it seems the company has ceased.

## Fleet

Twin Cities Air Service currently operated a fleet of five aircraft. The majority of these aircraft are available for on-demand charter operations throughout the Northeastern United States, although the aircraft are certified to operate in Canada, Bermuda, and parts of The Caribbean and Central America. A single Cessna aircraft is devoted to the scheduled service between Portland, Maine and Yarmouth, Nova Scotia.

As of March 2010 the Twin Cities fleet includes:

## InfoBox

Twin Cities Air Service
| IATA ICAO Call sign  TCY TWIN CITY | |
| --- | --- |
| Founded | 1992 |
| Ceased operations | unknown (after 2012) |
| Hubs | Auburn/Lewiston Municipal Airport |
| Focus cities | Portland International Jetport |
| Fleet size | 5 |
| Destinations | 2 |
| Headquarters | Auburn, Maine |
| Website | http://www.twincitiesairservice.com |


title: Tuva silver vole

abstract:
The Tuva silver vole is a species of rodent in the family Cricetidae.
It is found in Mongolia and Russian Federation.

text:
# Tuva silver vole

The **Tuva silver vole** (*Alticola tuvinicus*) is a species of rodent in the family Cricetidae. It is found in Mongolia and Russian Federation.

* Musser, G. G.; Carleton, M. D. (2005), "Superfamily Muroidea", in Wilson, D. E.; Reeder, D. M. (eds.), *Mammal Species of the World a Taxonomic and Geographic Reference* (3rd ed.), Baltimore: Johns Hopkins University Press, pp. 894–1531, ISBN 0-8018-8221-4

## InfoBox

| Tuva silver vole | |
| --- | --- |
| Conservation status | |
|
Least Concern  (IUCN 3.1) | |
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Chordata |
| Class: | Mammalia |
| Order: | Rodentia |
| Family: | Cricetidae |
| Subfamily: | Arvicolinae |
| Genus: | *Alticola* |
| Species: | ***A. tuvinicus*** |
| Binomial name | |
| ***Alticola tuvinicus***
Ognev, 1950 | |
|
| Synonyms | |
| *Alticola khubsugulensis
Alticola kosogol* | |


title: Lytta funerea

abstract: Lytta funerea is a species of blister beetle in the family Meloidae. It is found in North America.

text:
# Lytta funerea

***Lytta funerea*** is a species of blister beetle in the family Meloidae. It is found in North America.

## Further reading

## InfoBox

| *Lytta funerea* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Meloidae |
| Genus: | *Lytta* |
| Species: | ***L. funerea*** |
| Binomial name | |
| ***Lytta funerea***<br>(Fall, 1901) | |
|


title: M. M. Abdul Khader

abstract: Manadath Mohammed Pillay Abdul Khader was an Indian lawyer, jurist, and politician who served as the Advocate General of Kerala from 1969 to 1979.

text:
# M. M. Abdul Khader

**Manadath Mohammed Pillay Abdul Khader** (27 February 1925 – 10 August 1993) was an Indian lawyer, jurist, and politician who served as the Advocate General of Kerala from 1969 to 1979.

## Early life and career

Abdul Khader was born on 27 February 1925 in Aluva to M. K. Mohammed Pillay, the younger brother of prominent industrialist and philanthropist, M. K. Mackar Pillay.

In 1952, Khader was elected to the Legislative Assembly of the newly formed state of Travancore-Cochin from the Aluva constituency, defeating future Kerala Pradesh Congress Committee president T. O. Bava. Khader lost re-election in 1954 to the same opponent.

Khader's brother, M. M. Pareed Pillay went on to become the Chief Justice of Kerala and the first chairman of the Kerala State Human Rights Commission.

## Electoral history

### 1952 Travancore-Cochin Legislative Assembly election

1952 Travancore-Cochin Legislative Assembly election: Alwaye
| Party | | Candidate | Votes | % | ±% |
| --- | --- | --- | --- | --- | --- |
|  | **Independent** | **M. M. Abdul Khader** | **15,631** | **52.10** | **{{{change}}}** |
|  | INC | T. O. Bava | 12,717 | 42.39 |  |
|  | Socialist | Ibrahim Kutty | 1,653 | 5.51 |  |
| Margin of victory | | | 2914 | 7.43 |  |
| Turnout | | | 30,001 | 76.48 |  |
|  | Independent **win** (new seat) | | | | |

### 1954 Travancore-Cochin Legislative Assembly election

1954 Travancore-Cochin Legislative Assembly election: Alwaye
| Party | | Candidate | Votes | % | ±% |
| --- | --- | --- | --- | --- | --- |
|  | **INC** | **T. O. Bava** | **16,891** | **54.38** | **+11.99** |
|  | Independent | M. M. Abdul Khader | 14,170 | 45.62 | 6.48 |
| Margin of victory | | | 2721 | 8.76 | +1.33 |
| Turnout | | | 31,061 | 78.77 | +2.29 |
|  | INC **gain** from Independent | | Swing | +11.99 |  |

## InfoBox

| M. M. Abdul Khader | |
| --- | --- |
|  | |
|  | |
| Advocate General of Kerala | |
| **In office**
1969–1979 | |
| Appointed by | V. Viswanathan |
| Member of the Legislative Assembly
of Travancore-Cochin | |
| **In office**
1952–1954 | |
| Preceded by | Position established |
| Succeeded by | T. O. Bava |
| Constituency | Alwaye |
|  | |
| Personal details | |
| Born | (1925-02-27)27 February 1925
Alwaye, Madras Presidency, British India |
| Died | 10 August 1993(1993-08-10) (aged 68)
Aluva, Kerala, India |
| Relatives | M. M. Pareed Pillay (brother)
M. K. Mackar Pillay (uncle) |
| Occupation | lawyer |
|  | |


title: Lærke Buhl-Hansen

abstract: Lærke Buhl-Hansen is a Danish sailor. She placed 15th in the women's RS:X event at the 2016 Summer Olympics.

text:
# Lærke Buhl-Hansen

**Lærke Buhl-Hansen** (born 30 March 1992) is a Danish sailor. She placed 15th in the women's RS:X event at the 2016 Summer Olympics.

## InfoBox

Lærke Buhl-Hansen
| Personal information | |
| --- | --- |
| Nationality | Danish |
| Born | 30 March 1992 (1992-03-30) (age 32)<br>Aarhus, Denmark |
| Height | 167 cm (5 ft 6 in) |
| Weight | 56 kg (123 lb) |
|  | |
| Sailing career | |
| Class(es) | RS:X, IQFOiL |
| Club | Århus Sejlklub |
|  | |


title: Turno, Šentjur

abstract: Turno is a settlement in the Municipality of Šentjur in eastern Slovenia. It lies south of Gorica pri Slivnici, just off the regional road leading to Kozje. The settlement, and the entire municipality, are included in the Savinja Statistical Region, which is in the Slovenian portion of the historical Duchy of Styria.

text:
# Turno, Šentjur

**Turno** (pronounced \[ˈtuːɾnɔ\]) is a settlement in the Municipality of Šentjur in eastern Slovenia. It lies south of Gorica pri Slivnici, just off the regional road leading to Kozje. The settlement, and the entire municipality, are included in the Savinja Statistical Region, which is in the Slovenian portion of the historical Duchy of Styria.

## InfoBox

| Turno | |
| --- | --- |
|  | |
| TurnoLocation in Slovenia | |
| Coordinates: 46°10′54.76″N 15°26′30.61″E / 46.1818778°N 15.4418361°E / 46.1818778; 15.4418361 | |
| Country | Slovenia |
| Traditional region | Styria |
| Statistical region | Savinja |
| Municipality | Šentjur |
| Area | |
| Total | 1.47 km2 (0.57 sq mi) |
| Elevation | 439.4 m (1,441.6 ft) |
| Population (2020) | |
| Total | 104 |
| Density | 71/km2 (180/sq mi) |
|  | |


title: MAFD1

abstract: Major affective disorder 1 is a protein that in humans is encoded by the MAFD1 gene.

text:
# MAFD1

**Major affective disorder 1** is a protein that in humans is encoded by the MAFD1 gene.

## Further reading

## InfoBox

| MAFD1 | | | |
| --- | --- | --- | --- |
|  | | | |
| Identifiers | | | |
| Aliases | MAFD1, BPAD, MD1, major affective disorder 1 | | |
| External IDs | GeneCards: MAFD1; OMA:MAFD1 - orthologs | | |
| Orthologs  Species **Human** **Mouse**  Entrez   Ensembl   UniProt   RefSeq (mRNA)     n/a   n/a   RefSeq (protein)     n/a   n/a   Location (UCSC) n/a n/a  PubMed search  n/a | | | |
| Wikidata | | | |
| View/Edit Human | | | |


title: M27 (Johannesburg)

abstract: M27 is a major road in the City of Johannesburg, South Africa. A large part of the route is named Jan Smuts Avenue which is roughly 12 km long. It begins in the southern suburb of Booysens and heads northwards through the Johannesburg CBD and the northern suburbs of Randburg.

text:
# M27 (Johannesburg)

**M27** is a major road in the City of Johannesburg, South Africa. A large part of the route is named Jan Smuts Avenue which is roughly 12 km long. It begins in the southern suburb of Booysens and heads northwards through the Johannesburg CBD and the northern suburbs of Randburg.

## Route

The M27 begins at the M1 Booysens Street Interchange as a number of off-ramps and heads northwards as Booysens Street through Booysens, Ophirton and into Selby. In Selby, the M27 crosses under the M2 motorway at the Village Road/Selby Interchange into the Johannesburg CBD. Here the route becomes one-way as Pixley Seme Street heading north through the city with Newtown to the west. The M27 as a southbound one-way road through the CBD is called Simmonds Street, starting at the Queen Elizabeth Bridge and runs through under the M2 where it joins Booysens Street. Leaving the CBD the road resumes being dual carriageway as it crosses the railway lines via the Queen Elizabeth Bridge as Queen Elizabeth Drive and into Braamfontein. Turning right, its joined by traffic crossing the Nelson Mandela Bridge and its heads north through to the top of Braamfontein ridge as Bertha Street.

The M27, now called Jan Smuts Avenue begins on Braamfontein's ridge as an extension northwards of Bertha Street at the intersection with Stiemens Street. It passes the East campus of the University of Witwatersrand on its left and Helpmekaar Kollege on the right before descending into the leafy suburb of Parktown where it crosses over a major intersection with the M71 Empire Road. After crossing Empire Road, passes over the M1 De Villiers Graaff motorway again with several entrances and exits at this intersection. Leaving Parktown, the road begins to drop as it descends Parktown Ridge through the hilly and leafy suburbs of Westcliff and Forest Town. As it enters Parkview, it passes through the Herman Eckstein Park, with the Johannesburg Zoo to the right and Zoo Lake to the left.

Narrowing to single lanes in Saxonwold, Jan Smuts Avenue splits northwards at the Cotswold Drive (R25) winding its way out of Saxonwold and into Parkwood. It resumes as a dual carriageway as it climbs into the retail suburb of Rosebank and leafy Parktown North before dropping down into Dunkeld West as a single carriageway. A short while later it resumes as a dual carriageway and passes through Hyde Park where at a major intersection close to the Hyde Park Corner shopping centre, the road splits north-west when it intersects the start of the M81 Winnie Mandela Drive. It passes through Craighall and Craighall Park, crossing the Braamfontein Spruit. It then enters the old Randburg suburbs of Blairgowrie and Bordeaux intersecting Bram Fischer Drive in Ferndale where the M27 Jan Smuts Avenue ends.

## InfoBox

| Metropolitan route M27 | |
| --- | --- |
| Route information | |
| Maintained by Johannesburg Roads Agency and Gauteng Department of Roads and Transport | |
| Length | 18.3 km (11.4 mi) |
| Existed | 1890s–present |
| Major junctions | |
| South end | M1 Booysens Road Interchange, Booysens |
| Major intersections | M7 Kliprivier Drive, Booysens
M2 Village Road/Selby Interchange
R29 Anderson St/Marshal St, Marshalltown
R24 Albertina Sisulu Rd/Commissioner Str, Johannesburg CBD
M10 Smit Street, Braamfontein
M18 De Korte St/Jorissen St, Braamfontein
M1 Junction 14 Jan Smuts Ave/M27, Parktown
M16 Upper Park Drive, Forrest Town
Westcliff Drive, Westcliff
R25 Cotswold Drive, Saxonwold
M20 Chester Road, Parkwood
Bolton Road, Parkwood
M30 7th Avenue, Parktown North
Jellico Avenue, Rosebank
M81 Winnie Mandela Drive, Hyde Park
M13 Republic Road, Randburg |
| North end | M71 Bram Fischer Drive, Randburg |
|  | |
| Location | |
| Country | South Africa |
|  | |
| Highway system | |
|  | |
| M22   M30 | |


title: M27 link

abstract: The M27 link, formally Link, Cartridge, Metallic Belt, 5.56mm, M27 is a metallic disintegrating link issued by the United States armed forces and among NATO and designed for use in belt-fed firearms. It holds 5.56×45mm NATO ammunition.

text:
# M27 link

The **M27 link**, formally **Link, Cartridge, Metallic Belt, 5.56mm, M27** is a metallic disintegrating link issued by the United States armed forces and among NATO and designed for use in belt-fed firearms. It holds 5.56×45mm NATO ammunition.

## History

The first scaled-down version of the mid-20th century M13 link was developed in the early 1960s for the Stoner 63 belt-fed light machine gun/squad automatic weapon and designated as the "S-63 BRW" link. In the early 1970s this scaling-down concept was further developed. The resulting modified link had a slightly different angle of pitch and was adapted as the M27 link for use with the FN Minimi/M249 SAW. The M27 link is used on the FN Minimi/M249, HK23, MG4, CETME Ameli, K3, Mini-SS and Negev, among others.

## Design details

Each M27 link consists of a single piece of metal curved into two partial cylinders, into which adjacent rounds slide. Like the M13 link, the M27 link is a push-through design. Rounds are extracted by pushing forward out of the link. With the round freed, the link disintegrates (detaches from the belt) and is ejected. This is in contrast with older belt systems which were typically made of fabric and were fed straight through the weapon without disintegrating. MIL-L-63532C stipulates that the force to strip a NATO approved round from the M27 link should be between 5.5 and 16 lbf (24.5 and 71.2 ) and the belt should have a minimal tensile strength of 33 lbf (146.8 ). A single M27 link weighs approximately 2  (30.9 gr).

The links often have an extra anti-corrosion surface treatment, generally (oil impregnated) black phosphate, and can be collected and reassembled by hand with fresh ammunition, but in practice this is not commonly done as it is labor-intensive, and the inexpensive links are considered disposable.


title: Tyler Medeiros

abstract: Tyler Medeiros is a Canadian singer, songwriter, and dancer.

text:
# Tyler Medeiros

**Tyler Medeiros** (born July 11, 1995) is a Canadian singer, songwriter, and dancer.

## Personal life

Medeiros was born and raised in Toronto, Ontario, to a Portuguese father and an Italian mother. He attended St. Anthony's Catholic Elementary School in Toronto from Junior Kindergarten until he graduated grade 8 in 2009. Medeiros is also known as the cousin of singers Shawn Desman and Danny Fernandes. In 2012, he was signed by Flo Rida and embarked on a Canadian tour alongside Victoria Duffield, Cody Simpson, and Big Time Rush.

Medeiros began taking dancing lessons at the age of ten and signed with CP Records in 2010. Currently, he occasionally resides in Los Angeles to further his career.

## Musical career

Medeiros' first single was "Girlfriend" featuring labelmate and cousin Danny Fernandes. The video premiered on Family Channel and also MuchMusic. It was followed up with his second single "Say I Love You (Please Don't Go)" that features rapper Lil Twist sampling on a KC and the Sunshine Band song. Both videos were directed by Marc André Debruyne. Medeiros also appeared on the cover of July–August 2011 issue of the Canadian teen magazine *Vervegirl*. Tyler was chosen my Family Channel to sing and perform the theme song to their 2011 Bullying Awareness Week Stand Up! campaign. The song, called "What's Up, Stand Up," was written by RyanDan members Ryan Kowarsky and Dan Kowarsky as well as Maks Gabriel. The video premiered on the Family Channel on November 15, 2011.

In 2012 Medeiros signed with Flo Rida's IMG Label in a joint project with CP Records. Shortly after the signing, he joined Flo Rida and Pitbull for the Planet Pit Tour across Canada. On June 1, 2012, it was announced that Medeiros would be a main performer at the *Big Ticket Summer Concert* put on by Family Channel on August 26 along with Bridgit Mendler, R5, Veronica and Allstar Weekend. In June 2012 it was also announced that Tyler would join Big Time Rush and Cody Simpson on a cross Canada tour in September. September 4, the tour kick off in Montreal coincided with Medeiros release of *TM* – his debut EP.

The first song off *TM* was "#QTEEs" and the second was "Radio" ft. Flo Rida.

## Discography

### Extended play

* 2012: *TM*

### Singles

| Year | Title | Peak | Album |
| --- | --- | --- | --- |
| | | CAN
 | |
| 2010 | "Girlfriend"
(feat. Danny Fernandes) | 90 | *TM* |
| 2011 | "Say I Love You (Please Don't Go)"
(feat. Lil Twist) | 88 | |
| | "What's Up Stand Up" |  | |
| 2012 | "#QTEEs" |  | |
| | "Radio"
(feat. Flo Rida) |  | |

## Videography

* 2010: "Girlfriend" (feat. Danny Fernandes)
* 2011: "Say I Love You (Please Don't Go)" (feat. Lil Twist)

## InfoBox

| Tyler Medeiros | |
| --- | --- |
| Born | (1995-07-11) July 11, 1995
Toronto, Ontario, Canada |
| Genres | Pop |
| Instrument | Vocals |
| Years active | 2010–present |
| Labels | CP Records, International Music Group |


title: Tygerberg Nature Reserve

abstract: Tygerberg Nature Reserve is a 300-hectare (740-acre) nature reserve in the Tierberg range of hills in the northern suburbs of Cape Town, South Africa. In 1657 the 7 km long range of hills became known as Luipaerts Berghen, named for the characteristic spots, or “heuweltjies”, which dot its slopes and are visible from afar. These are believed to be fossilized termitaria, and occur widely in Shale Renosterveld. Since 1661 the range was known as the Tijgerberghen, "tijger" being the Cape Dutch word for a leopard. The southernmost section of the Tierberg range is currently protected in Tygerberg Nature Reserve. The nature reserve represents one of the few surviving pockets of the highly threatened Swartland Shale Renosterveld vegetation type. The 300 ha reserve has an exceptional number of species. There are nearly five hundred different plant species here, twelve of which are threatened with extinction and eight of which exist only in Cape Town. Three of the plant species of Tygerberg exist only within the boundaries of the reserve itself. In addition, there are over a hundred bird species and a variety of wild mammals, reptiles and amphibians. The Plattekloof Dam is located just west of the hills, and is being restored to a natural wetland. The park hosts the Kristo Pienaar Environmental Education Centre with its library and resource centre. This is a popular venue for school excursions and education programmes.

text:
# Tygerberg Nature Reserve

**Tygerberg Nature Reserve** is a 300-hectare (740-acre) nature reserve in the Tierberg range of hills in the northern suburbs of Cape Town, South Africa.

In 1657 the 7 km long range of hills became known as Luipaerts Berghen (‘Leopard’s Mountain’), named for the characteristic spots, or “heuweltjies”, which dot its slopes and are visible from afar. These are believed to be fossilized termitaria, and occur widely in Shale Renosterveld. Since 1661 the range was known as the Tijgerberghen (‘Tiger Mountain’), "tijger" being the Cape Dutch word for a leopard. The southernmost section of the Tierberg range is currently protected in Tygerberg Nature Reserve.

The nature reserve represents one of the few surviving pockets of the highly threatened **Swartland Shale Renosterveld** vegetation type. The 300 ha reserve has an exceptional number of species. There are nearly five hundred different plant species here, twelve of which are threatened with extinction and eight of which exist only in Cape Town. Three of the plant species of Tygerberg exist only within the boundaries of the reserve itself. In addition, there are over a hundred bird species and a variety of wild mammals, reptiles and amphibians.

The Plattekloof Dam is located just west of the hills, and is being restored to a natural wetland. The park hosts the **Kristo Pienaar Environmental Education Centre** with its library and resource centre. This is a popular venue for school excursions and education programmes.

## InfoBox

| Tygerberg Nature Reserve | |
| --- | --- |
| Walking trail in Tygerberg Nature Reserve | |
| Map of the City of Cape Town | |
| Location | Bellville, South Africa |
| Coordinates | 33°52′42″S 18°35′50″E / 33.8783°S 18.5972°E / -33.8783; 18.5972 |
| Area | 300 ha (740 acres) |
| Established | 1973 |
| City of Cape Town Nature Reserves | |