title: Juan Carlos Arias Acosta

abstract: Juan Carlos Arias Acosta a.k.a "Machete" is a two-time Olympian cyclist from Pereira, Colombia. Juan Carlos is a Pan American Champion, who has raced in the Tour de France, Giro d'Italia, and the Road World Championship, among many other major racing events. Juan Carlos Arias is the only Colombian athlete to date to represent the country in two different sports in the Olympics. Juan Carlos Arias has been riding since 1982 out of Colombia S.A. and currently resides in Atlanta, Georgia with his family and children. Prior to becoming a professional cyclist, Juan Carlos Arias played soccer for Maracaneiro Football Club in Bogotá, Colombia.

text:
# Juan Carlos Arias Acosta

**Juan Carlos Arias Acosta** (born December 3, 1964) a.k.a "Machete" is a two-time Olympian cyclist from Pereira, Colombia. Juan Carlos is a Pan American Champion, who has raced in the Tour de France, Giro d'Italia, and the Road World Championship, among many other major racing events.

Juan Carlos Arias is the only Colombian athlete to date to represent the country in two different sports in the Olympics. Juan Carlos Arias has been riding since 1982 out of Colombia S.A. and currently resides in Atlanta, Georgia with his family and children. Prior to becoming a professional cyclist, Juan Carlos Arias played soccer for Maracaneiro Football Club in Bogotá, Colombia.

## Teams

| Year | Team |
| --- | --- |
| 1984 | Selección Colombia Ruta (Colombia) |
| 1985 | Laboratorios Gen-far, Selección Colombia Ruta (Colombia) |
| 1986 | Ferreterīa Reina, Selección Colombia Ruta (Colombia) |
| 1987 | Equipo Olimpico Pilas Varta, Selección Colombia Ruta (Colombia) |
| 1988 | Selección Olympica Colombia Ruta (Colombia) |
| 1989 | Café de Colombia \- Mavic (Colombia) |
| 1990 | Café de Colombia (Colombia) |
| 1991 | Pony Malta - Avianca, Selección Colombia (Colombia) |
| 1993 | Rust-Oleum (Colombia) |
| 1994 | Equipo Postobón MTB, Selección Colombia MTB (Colombia) |
| 1995 | Equipo Bike House, Selección Colombia MTB (Colombia) |
| 1996 | Selección Olympica Colombia MTB (Colombia) |
| 1997 | Equipo BikeHouse (Colombia) |
| 2012 | Ford - Lifetime Bikes (Atlanta, Georgia, US) |

## Accolades

* 1984 - Road Champion Colombia
* 1985 - Champion Trinidad & Togabo Classic
* 1987 - Pan-American Games Route Champion
* 1987 - Champion Tour of Guadeloupe, France
* 1987 - Sub-Champion Giro de Veneto, Italy
* 1987 - Vuelta de Malaga, Spain, Sub-Champion (Ganador de Etapa y de la Montaña)
* 1988 - 31st in Olympic Games, Road, Amateurs, Tongillo Road, Seoul
* 1991 - National Championship, Road, Elite, Colombia
* 1996 - Placed 34 in Olympic Games in Atlanta, United States
* 2015 - Champion Georgia State Road Race, United States
* 2017 - Sub Champion Grand Fondo, New York, United States
* 2017 - Champion Georgia State Road Race, United States

## Achievements

* 1984 – Departmental Champion Cundinamarca
* 1985 – Champion Tour Trinidad & Tobago
* 1986 – Colombian National Route Champion
* 1986 – Placed 27 in Colorado Spring Route World Championship
* 1987 – Pan-American Route Champion
* 1987 – Second place in Giro de Venneto – Italy- winner of one stage and of the mountain
* 1987 – Winner of the Regularity, winner of one stage and sub-champion of the Tour of Malaga in Spain
* 1987 – Champion of the Tour of Guadalupe
* 1987 – Champion of the regularity and of the bonus sprint in the Tour of Colombia
* 1987 – Sub-champion of the bonus sprint in classic RCN
* 1987 – Placed 17 in the world championship of the route in Austria
* 1988 – Placed 31 in the Olympic Games in Seoul – Korea
* 1988 – Sub-champion of the Tour de Malaga in Spain
* 1988 – National route Sub-Champion of Colombia
* 1989 – Placed 41 in Tour de Spain
* 1989 – Placed 71 Giro de Italy
* 1989 – Placed 17 and sub-champion of the mountain of the week in Catalana in Spain
* 1989 – champion of the "Clasica Roldanillo" – Colombia
* 1990 – Participation Tour de Spain
* 1990 – Participation Giro de Italy
* 1990 – Placed 16 in the race "Paris NLZA" in France
* 1990 – Champion of the regularity and of the bonus sprint in the Tour of Colombia
* 1990 – Champion of the bonus sprint in "El Classico RCN" and subchampion of the regularity in Colombia
* 1991 – Participation in the Giro de Italy
* 1991 – Sub-champion Profesional of route
* 1991 – Champion of the regularity and winner of two stages in LAS "Clasicas de Boyaca and Cundinmarca"
* 1991 – Placed 21 in the "Tour do Portugal"
* 1992 – Sub-champion of the regularity in the Tour a Colombia and ninth place in the general
* 1993 – Sub-champion of Yardley Gold of mountain biking and winner of 1 Valida
* 1994 – Champion national of mountain biking, winner of 3 Validas of the championship and champion of the Yardley Gold tournament
* 1994 – Placed 41 in the world championship of mountain biking in Colorado (US), best Colombian
* 1995 – Third in the national championship of mountain biking and sub-champion of the Yardley Gold tournament
* 1995 – Placed 71 in the world championship and best Colombian
* 1995 – Placed 10 in the Latin-American championship of mountain biking in Cordoba (Argentina)
* 1995 – Champion of the rally totoritas in Lima (Peru) of mountain biking
* 1996 – National champion of mountain biking in "Producciones Tournament" world championship of mountain biking, winner of 3 stages
* 1996 – Placed 34 in Olympic Games in Atlanta US
* 1996 – Fourth place in "Bolivarianos of Quito" Ecuador
* 1996 – Subchampion of the "Rally Totoritas in Lima" – Peru
* 1997 – Fourth place in the Pan-American Championship in Santiago de Chile
* 1997 – Subchampion Latin American mountain biking
* 1997 – National subchampion of mountain biking cross-country – Colombia
* 1997 – Winner of 3 stages of the national championship and 4 place in championship
* 1997 – Champion of the "Rally de Totoritas in Lima"- Peru
* 1997 – Champion of one "Valida Copa Norva" in U.S.
* 1997 – Second place "Valida Copa Norva" IN U.S.
* 1997 – Placed 30 in "Parada de Copa" of the world U.S.
* 1998 – Subchampion of the super mountain bike in Chile
* 1998 – Subchampion tour of "Volcan Villa Rica" – Chile
* 1998 – Second in championship national cross country of mountain biking for stages – Colombia
* 1998 – 10th place in Pan-American Toluca - Mexico
* 1998 – 3 place in Rally Totoritas - Peru
* 2000 – 5 place in Championship Pan-American in Puerto Rico
* 2000 – 3 place in Championship National per stage cross country - Colombia
* 2015 - Champion Georgia State Road Race, United States
* 2017 - Sub Champion Grand Fondo, New York, United States
* 2017 - Champion Georgia State Road Race, United States

## InfoBox

Juan Carlos Arias Acosta
| Personal information | |
| --- | --- |
| Nickname | Machete |
| Born | (1964-12-03) December 3, 1964<br>Pereira, Risaralda, Colombia |
| Height | 5 ft 10 in (1.78 m) |
| Weight | 176 lb (80 kg) |
| Team information | |
| Current team | Ford - Lifetime Bikes (Atlanta, Georgia, US) |
| Role | Rider |
| Rider type | Road and mountain biking |
| Professional team | |
| 1990–present | Café de Colombia (Colombia), Pony Malta - Avianca (Colombia) |
|  | |


title: Juan Liscano

abstract: Juan Liscano Velutini was a Venezuelan poet, folklorist, writer and critic. He was director of Monte Ávila Editores. Major examples of his poetic work are: Nuevo mundo Orinoco (1959), Cármenes (1966) and Fundaciones (1981). Also wrote: Panorama de la literatura venezolana actual (1973) Espiritualidad y literatura: una relación tormentosa (1976), Los fuegos apagados (1990) and El origen sigue siendo (1991). In 1990, Liscano published a personal Anthology, a route for his poetic trajectory. He won the Venezuelan National Prize for Literature in 1951.

text:
# Juan Liscano

**Juan Liscano Velutini** (7 July 1915 – 17 February 2001) was a Venezuelan poet, folklorist, writer and critic. He was director of Monte Ávila Editores. Major examples of his poetic work are: *Nuevo mundo Orinoco* (1959), *Cármenes* (1966) and *Fundaciones* (1981). Also wrote: *Panorama de la literatura venezolana actual* (1973) *Espiritualidad y literatura: una relación tormentosa* (1976), *Los fuegos apagados* (1990) and *El origen sigue siendo* (1991). In 1990, Liscano published a personal Anthology, a route for his poetic trajectory. He won the Venezuelan National Prize for Literature in 1951.

## InfoBox

| Juan Liscano | |
| --- | --- |
| Juan Liscano in 1994 | |
| Born | Juan Liscano Velutini
(1915-07-07)7 July 1915
Caracas, Venezuela |
| Died | 17 February 2001(2001-02-17) (aged 85)
Caracas, Venezuela |
| Occupation(s) | poet, folklorist, writer, critic |
| Signature | |
|  | |


title: 1940 Cuban general election

text:
# 1940 Cuban general election

General elections were held in Cuba on 14 July 1940. Fulgencio Batista won the presidential election running under the People's Socialist Coalition banner. Although the Partido Auténtico emerged as the largest single party in the House of Representatives, Bastista's electoral alliance, the Democratic Socialist Coalition, won a majority of seats. Voter turnout was 73%.

## Results

### President

| Candidate | | Party | Votes | % |
| --- | --- | --- | --- | --- |
|  | Fulgencio Batista | Democratic Socialist Coalition | 805,125 |  |
|  | Ramón Grau | Opposition Front | 573,576 |  |
|  | Reynaldo Márquez | National Agrarian Party |  | |
| Total | | |  | |
|  | | | | |
| Total votes | | | 1,421,563 |  |
| Registered voters/turnout | | | 1,936,212 | 73.42 |
| Source: Nohlen | | | | |

### Senate

| Party or alliance | | | | Seats |
| --- | --- | --- | --- | --- |
|  | Democratic Socialist Coalition |  | Republican Democratic Party | 10 |
| | |  | Liberal Party of Cuba | 5 |
| | |  | Nationalist Union | 5 |
| | |  | Democratic National Association | 2 |
| | |  | Cuban Popular Party | 0 |
| | |  | Communist Revolutionary Union | 0 |
|  | Opposition Front |  | Partido Auténtico | 8 |
| | |  | ABC | 3 |
| | |  | Republican Action | 3 |
| Total | | | | 36 |
|  | | | | |
| Source: Nohlen | | | | |

### House of Representatives

| Party or alliance | | | | Seats |
| --- | --- | --- | --- | --- |
|  | Democratic Socialist Coalition |  | Liberal Party of Cuba | 23 |
| | |  | Republican Democratic Party | 22 |
| | |  | Nationalist Union | 21 |
| | |  | Democratic National Association | 18 |
| | |  | Communist Revolutionary Union | 10 |
|  | Opposition Front |  | Partido Auténtico | 34 |
| | |  | Republican Action | 16 |
| | |  | ABC | 12 |
| Total | | | | 156 |
|  | | | | |
| Source: Nohlen | | | | |

1. Dieter Nohlen (2005) *Elections in the Americas: A data handbook, Volume I*, p203 ISBN 978-0-19-928357-6
2. Nohlen, p204

## InfoBox

1940 Cuban general election
| --- | |
| --- | --- |
|  | |
|  | |
| Presidential election | |
| Nominee **Fulgencio Batista** Ramón Grau   Party Independent Auténtico  Alliance CSD Opposition Front  Popular vote **805,125** 573,576 | |
| ---  **President before election**
Federico Laredo Brú
Republican Action **Elected President**
Fulgencio Batista
Independent | |
|  | |


title: Reevesby Island

abstract: Reevesby Island is a small, uninhabited island in the Sir Joseph Banks group of islands in southern Spencer Gulf, South Australia. The island is one of the largest in the Sir Joseph Banks Conservation Park and is home to many unique species including greater stick-nest rats, hooded plovers, little penguins and Cape Barren geese. Since 2018, a group of volunteers now known as the Friends of Reevesby Island have been restoring the old homestead on the island, which was inhabited until it became a conservation park in 1974. Author and local historian Eric Kotz is a member. The homestead is encircled by a low fence which was built to keep the island's resident Tiger snakes and Death adders away from the island's human inhabitants.

text:
# Reevesby Island

Reevesby Islandclass=notpageimage|Location of Reevesby Island (South Australia)

**Reevesby Island** is a small, uninhabited island in the Sir Joseph Banks group of islands in southern Spencer Gulf, South Australia. The island is one of the largest in the Sir Joseph Banks Conservation Park and is home to many unique species including greater stick-nest rats, hooded plovers, little penguins and Cape Barren geese. Since 2018, a group of volunteers now known as the Friends of Reevesby Island have been restoring the old homestead on the island, which was inhabited until it became a conservation park in 1974. Author and local historian Eric Kotz is a member. The homestead is encircled by a low fence which was built to keep the island's resident Tiger snakes and Death adders away from the island's human inhabitants.

34°31′34″S 136°16′49″E / 34.52611°S 136.28028°E / -34.52611; 136.28028


title: Sherwood, Tennessee

abstract: Sherwood is an unincorporated community in Franklin County, Tennessee, United States. It is located along Tennessee State Route 56 13.1 miles (21.1 km) southeast of Winchester, and just north of the Alabama state line. Sherwood has a post office with ZIP code 37376.

text:
# Sherwood, Tennessee

**Sherwood** is an unincorporated community in Franklin County, Tennessee, United States. It is located along Tennessee State Route 56 13.1 miles (21.1 km) southeast of Winchester, and just north of the Alabama state line. Sherwood has a post office with ZIP code 37376.

## Demographics

Historical population
| Census | Pop. | Note |  |
| --- | --- | --- | --- |
| 2020 | 122 |  |  |
| U.S. Decennial Census | | | |

## Geography and Location

The Crow Creek Valley, in which Sherwood is situated, is a relatively narrow valley surrounded on three sides (north, east, and west) by the Cumberland Plateau (including Lost Cove), with the southern end of the valley opening toward Alabama. Crow Creek, which flows from Lost Cove Cave, drains the valley and flows through the western part of Sherwood, emptying into the Tennessee River at Guntersville Lake near Stevenson, Alabama, several miles to the south. Sherwood lies at an elevation of 669 feet (204 m).

State Route 56, the only major highway that passes through Sherwood, traverses the valley from north-to-south. To the north, the road ascends more than 1,000 feet (300 m) to Sewanee atop the Cumberland Plateau. To the south, the road continues into Alabama as State Route 117, eventually reaching Stevenson. Railroad tracks run alongside the highway for much of its stretch in the valley.

## History

Human habitation in the Sherwood area is very ancient as evidenced by the many thousands of Native American projectile points in the nearby fields. The town location is at the intersection of many old Native American routes which the modern trails and roads often follow. It is located on an old Stagecoach route approximately midway between Sewanee and Anderson, Alabama and is representative of the hamlets and villages that were once commonplace in the area coves and valleys.

A small community called Kitchen's Station or Catchings Station had existed as a Stagecoach stop earlier at the location. Named for station master Meridith Catchings, the small community began appearing on railroad maps after the Civil War. The town of Sherwood was named for Charles D. Sherwood, lieutenant governor of Minnesota during the Civil War. The Tennessee State Legislature approved his charter for the *Tennessee Immigration and Land Company* on April 15, 1878. That same day, Sherwood purchased the 1,410 acres of land for his northern colony from John F. Anderson. On June 19, 1878, a local paper announced that the name of Kitchen's \[Catching's\] Station would be changed to Sherwood. A number of sources have erroneously reported that Charles Sherwood was lieutenant governor of Wisconsin and that the town was established in 1875. This information probably came from the *Goodspeed History Tennessee: Giles, Franklin, Lincoln, and Moore Counties.* In 1989 the Sherwood Elementary School was closed and approximately 25-28 children from Sherwood, a teacher, and several aides became part of the Sewanee Public School community.

### The Railroad

With the construction of the strategically important Cowan Tunnel 5 miles (8.0 km) to the north in 1852, train stops were created through the Crow Creek Valley, including at Catchings Station (Sherwood). Notably, at this station there were and continue to be pusher engines which are required to assist with train ascents up the steep mountain grade to the tunnel. Correspondingly, on the other side of the tunnel in Cowan, Tennessee, there are also pusher engines.

In 1915, a passenger train and a freight train collided in Sherwood, killing fifteen and injuring twenty-two.

### Gager Lime Company

The Gager Lime Manufacturing Company was established by Byron Gager in 1892 and operated a limestone quarry and lime kilns in the community. The lime production facilities operated until 1949.

As of the 1930 census, Sherwood had 1,700 residents, but the community's population declined to 900 in the 1950s as its economy stalled after the closing of the limestone plant.

The castle-like ruins of the lime production facilities and silos, which are unusual for their Egyptian Revival and Gothic Revival styling, remain in the community. The Tennessee Preservation Trust included them on its Ten in Tennessee Endangered Properties List for 2002–2003, citing their architectural distinctiveness and expressing concern that a "continued lack of maintenance" threatened their survival.

### Epiphany Mission

In 1899, the Epiphany Episcopal Mission was established in Sherwood after the Episcopal church began to provide schooling for local children. The church structure was built in 1902, replaced in 1928, burned in 1960, and then rebuilt in 1967. The 1928 structure is maintained as a partial ruin on the grounds of the modern structure. During the Great Depression, the Episcopal priest Father George Jones began a publishing a series of pamphlets to raise funds and awareness of the impoverished community; these pamphlets were later republished in 1954 as book entitled *Candles in the Dark Boreen*.

In 1956, the mission helped train a group of women and opened a shirt factory in Sherwood in an attempt to create local jobs.

## Threatened snail species

The painted snake-coiled forest snail is only found in the Sherwood area. The snail was first found in the area in 1906 and was designated as a threatened species in 1978. Anguispira picta has the common names of painted snake-coiled forest snail and painted tigersnail and is a rare species of air-breathing land snail, a terrestrial pulmonate gastropod mollusk in the family Discidae, the disc snails.

## InfoBox

| Sherwood, Tennessee | |
| --- | --- |
| Unincorporated community | |
| Post office and houses | |
| SherwoodSherwood | |
| Coordinates: 35°04′34″N 85°55′24″W / 35.07611°N 85.92333°W / 35.07611; -85.92333 | |
| Country | United States |
| State | Tennessee |
| County | Franklin |
| Area | |
| Total | 0.91 sq mi (2.35 km2) |
| Land | 0.91 sq mi (2.35 km2) |
| Water | 0.00 sq mi (0.00 km2) |
| Elevation | 669 ft (204 m) |
| Population (2020) | |
| Total | 122 |
| Density | 134.51/sq mi (51.95/km2) |
| Time zone | UTC-6 (Central (CST)) |
| Summer (DST) | UTC-5 (CDT) |
| ZIP code | 37376 |
| Area code | 931 |
| GNIS feature ID | 1303571 |


# Discovery and development of non-nucleoside reverse-transcriptase inhibitors

Non-nucleoside reverse-transcriptase inhibitors (NNRTIs) are antiretroviral drugs used in the treatment of human immunodeficiency virus (HIV). NNRTIs inhibit reverse transcriptase (RT), an enzyme that controls the replication of the genetic material of HIV. RT is one of the most popular targets in the field of antiretroviral drug development.

Discovery and development of NNRTIs began in the late 1980s and in the end of 2009 four NNRTI had been approved by regulatory authorities and several others were undergoing clinical development. Drug resistance develops quickly if NNRTIs are administered as monotherapy and therefore NNRTIs are always given as part of combination therapy, the highly active antiretroviral therapy (HAART).

## History

Acquired immunodeficiency syndrome (AIDS) is a leading cause of death in the world. It was identified as a disease in 1981. Two years later the etiology agent for AIDS, the HIV was described. HIV is a retrovirus and has two major serotypes, HIV-1 and HIV-2. The pandemic mostly involves HIV-1 while HIV-2 has lower morbidity rate and is mainly restricted to western Africa.

In the year 2009 over 40 million people were infected worldwide with HIV and the number keeps on growing. The vast majority of infected individuals live in the developing countries.

HIV drugs do not cure HIV infection, but the treatment aims at improving the quality of patients´ lives and decreased mortality.

25 antiretroviral drugs were available in 2009 for the treatment of HIV infection. The drugs belong to six different classes that act at different targets. The most popular target in the field of antiretroviral drug development is the HIV-1 reverse transcriptase (RT) enzyme. There are two classes of drugs that target the HIV-1 RT enzyme, nucleoside/nucleotide reverse-transcriptase inhibitors (NRTIs/NtRTIs) and non-nucleoside reverse-transcriptase inhibitors (NNRTIs). Drugs in these classes are important components of the HIV combination therapy called highly active antiretroviral therapy, better known as HAART.

In 1987, the first drug for the treatment of HIV infection was approved by the U.S. Food and Drug Administration (FDA). This was the NRTI called zidovudine. In the late 1980s, during further development of NRTIs, the field of NNRTIs discovery began. The development of NNRTIs improved quickly into the 1990s and they soon became the third class of antiretroviral drugs, following the protease inhibitors.

The NNRTIs are HIV-1 specific and have no activity against HIV-2 and other retroviruses. The first NNRTI, nevirapine was discovered by researchers at Boehringer Ingelheim and approved by the FDA in 1996. In the next two years two other NNRTIs were approved by the FDA, delavirdine in 1997 and efavirenz in 1998. These three drugs are so-called first generation NNRTIs. The need for NNRTIs with better resistance profile led to the development of the next generation of NNRTIs. Researchers at Janssens Foundation and Tibotec discovered the first drug in this class, etravirine, which was approved by the FDA in 2008. The second drug in this class, rilpivirine, was also discovered by Tibotec and was approved by the FDA in 2011. In addition to these four NNRTIs several other are in clinical development.

## The HIV-1 reverse transcriptase enzyme

### Function

Reverse transcriptase (RT) is an enzyme that controls the replication of the genetic material of HIV and other retroviruses. The enzyme has two enzymatic functions. Firstly it acts as a polymerase where it transcribes the single-stranded RNA genome into single-stranded DNA and subsequently builds a complementary strand of DNA. This provides a DNA double helix which can be integrated in the host cell's chromosome. Secondly it has ribonuclease H (Rnase H) activity as it degrades the RNA strand of RNA-DNA intermediate that forms during viral DNA synthesis.

### Structure

The HIV-1 RT is an asymmetric 1000-amino acid heterodimer composed of p66 (560 amino acids) and p51 subunits (440 amino acids). The p66 subunit has two domains, a polymerase and ribonuclease H. The polymerase domain contains four subdomains, which have been termed “fingers”, “palm”, “thumb” and “connection” and it is often compared to a right hand. The role of the p66 subunit is to carry out the activity of RT whereas it contains the active sites of the enzyme. The p51 is believed to play mainly a structural role.

## Binding and pharmacophore

Despite the chemical diversity of NNRTIs they all bind at the same site in the RT. The binding occurs allosterically in a hydrophobic pocket located approximately 10  from the catalytic site in the palm domain of the p66 subunit site of the enzyme. The NNRTI binding pocket (NNIBP) contains five aromatic (Tyr-181, Tyr-188, Phe-227 and Trp-229), six hydrophobic (Pro-59, Leu-100, Val-106, Val-179, Leu-234 and Pro-236) and five hydrophilic (Lys-101, Lys-103, Ser-105, Asp-132 and Glu-224) amino acids that belong to the p66 subunit and additional two amino acids (Ile-135 and Glu-138) belonging to the p51 subunit. Each NNRTI interacts with different amino acid residues in the NNIBP.

An important factor in the binding of the first generation NNRTIs, such as nevirapine, is the butterfly-like shape. Despite their chemical diversity they assume very similar butterfly-like shape. Two aromatic rings of NNRTIs conform within the enzyme to resemble the wings of a butterfly (figure 2). The butterfly structure has a hydrophilic centre as a ‘body’ and two hydrophobic moieties representing the wings. Wing I is usually a heteroaromatic ring and wing II is a phenyl or allyl substituent. Wing I has a functional group at one side of the ring which is capable of accepting and/or donating hydrogen bonds with the main chain of the amino acids Lys-101 and Lys-103. Wing II interacts through π-π interactions with a hydrophobic pocket, formed in most part by the side chains of aromatic amino acids. On the butterfly body a hydrophobic part fills a small pocket which is mainly formed by the side chains of Lys-103, Val-106 and Val-179. However many other NNRTIs have been found to bind to RT in different modes. Second generation NNRTIs such as diarylpyrimidins (DAPYs), have a horseshoe-like shape with two lateral hydrophobic wings and a pyrimidine ring which is the central polar part.

The NNIBP is elastic and the conformation depends on the size, specific chemical composition and binding mode of the NNRTI. The total structure of RT has segmental flexibility that depends on the nature of the bound NNRTI. It's important for the inhibitor to have flexibility to be able to bind in the modified pockets of a mutant target. Inhibitor flexibility may not affect the inhibitor-target interactions.

## Mechanism of action

The NNRTIs act by binding non-competitively to the RT enzyme (figure 3). The binding causes conformational change in the three-dimensional structure of the enzyme and creates the NNIBP. Binding of NNRTI to HIV-1 RT makes the p66 thumb domain hyper extended because it induces rotamer conformation changes in amino acid residues Tyr-181 and Tyr-188. This affects the catalytic activity of the enzyme and blocks the HIV-1 replication by inhibiting the polymerase active site of the RT's p66 subunit. The global conformational change additionally destabilizes the enzyme on its nucleic acid template and reduces its ability to bind nucleotides. The transcription of the viral RNA is inhibited and therefore the replication rate of the virus reduces. Although the exact molecular mechanism is still hypothetical this has been demonstrated by multiple studies to be the primary mechanism of action.

In addition to this proposed primary mechanism of action it has been shown that the NNRTIs have other mechanisms of action and interfere with various steps in the reverse transcriptase reaction. It has been suggested that the inhibition of reverse transcription by the NNRTIs may be due to effects on the RT Rnase H activity and/or template/primer binding. Some NNRTIs interfere with HIV-1 Gag-Pol polyprotein processing by inhibiting the late stage of HIV-1 replication.

It is important to gain profound understanding of the various mechanism of action of the NNRTIs in order to develop next-generation NNRTIs and for understanding the mechanism of drug resistance.

## Drug discovery and design

The development of effective anti-HIV drugs is difficult due to wide variations in nucleotide and amino acid sequences. The perfect anti-HIV drug chemical should be effective against drug resistance mutation. Understanding the target RT enzyme and its structure, mechanism of drug action and the consequence of drug resistance mutations provide useful information which can be helpful to design more effective NNRTIs. The RT enzyme can undergo change due to mutations that can disturb NNRTI binding.

### Discovery

The first two classes of compounds that were identified as NNRTIs were the 1-(2-2-hydroxyethoxymethyl)-6-(phenylthio)thymine (HEPT) and tetrahydroimidazo\[4,5,1-jkj\] \[1,4\]benzodiazepin-2(1H)-one and -thione (TIBO) compounds. The discovery of the TIBO compounds led to the definition of the NNRTI class in the late 1980s when they were unexpectedly found to inhibit RT. This finding initiated researches on mechanism of action for these compounds. The HEPT compounds were described before the TIBO compounds and were originally believed to be NRTIs. Later it was discovered that they shared common mechanism of action with the TIBO compounds. Both the HEPT and TIBO compounds were first to be identified as highly specific and potent HIV-1 RT inhibitors, not active against other RTs. These compounds do not interrupt the cellular or mitochondrial DNA synthesis. The specificity of the NNRTIs for HIV-1 is considered the hallmark of the NNRTI drug class.

### Development

#### First generation NNRTIs

After the discovery of HEPT and TIBO, compounds screening methods were used to develop BI-RG-587, the first NNRTI commonly known as nevirapine. Like HEPT and TIBO, nevirapine blocked viral RT activity by non-competitive inhibition (with respect to dNTP binding). This reinforced the idea that the new class of anti-HIV inhibitors was inhibiting the activity of RT but not at the active site. Several molecular families of NNRTIs have emerged following screening and evolution of many molecules.

Three NNRTI compounds of the first generation have been approved by the FDA for treating HIV-1 infection. Nevirapine was approved in 1996, delavirdine in 1997 and efavirenz in 1998 (table 1). Two of these drugs, nevirapine and efavirenz, are cornerstones of first line HAART while delavirdine is hardly used nowadays. The structure of these three drugs show the wide array of rings, substituents, and bonds that allow activity against HIV-1 RT. This diversity demonstrates why so many non-nucleosides have been synthesised but doesn't explain why only three drugs have reached the market. The main problem has been the potency of these compounds to develop resistance.

**Table 1** First generation NNRTIs approved by the FDA
|  |  |  |
| --- | --- | --- |
| Nevirapine | Delavirdine | Efavirenz |

##### Development from α-APA to ITU

Crystal structure analysis showed that the first generation NNRTIs (for example TIBO, nevirapine and α-APA) bind HIV-1 RT in a “butterfly-like” conformation. These first generation NNRTIs were vulnerable against the common drug-resistance mutations like Tyr-181C and Tyr-188L/H. This triggered the need for finding new and more effective NNRTIs. ITU (imidoylthiourea), a promising series of NNRTIs emerged from α-APA analogs (figure 4). The ITU compounds were obtained by extending the linker that binds the aryl side groups of the α-APA. A potent ITU compound, R100943, was obtained by an arrangement of the chemical composition of the side groups based on structure-activity relationships (SAR). A crystal structure of the HIV-1/R100943 complex demonstrated that ITU compounds are more flexible than α-APA compound. The ITU compounds showed distinct mode of binding where they bound with "horseshoe" or "U" mode. The 2,6-dichlorophenyl part of R100943 which corresponds chemically to the wing II 2,6-dibromophenyl part of the α-APA occupied the wing I part in the NNIBP whereas the 4-cyanoanilino part of R100943 occupies the wing II position in the NNIBP.

R100943 inhibited HIV-1 and was considerably effective against a number of key NNRTI-resistant mutants like G190A mutation, which caused high-level resistance to loviride (α-APA) and nevirapine. G190A mutation was thought to cause resistance by occupying a part of the binding pocket that would otherwise be filled by the linker part of the butterfly shaped NNRTIs. R100943, in the horseshoe mode of binding, is located at a distance of approximately 6.0 Å from G190. When compared with nevirapine and loviride which bind in the butterfly shape the ITU derivatives revealed improved activity against Tyr-181C and Tyr-188L mutants. A structural study suggested that a potent TIBO compound could partly supplement for the effects of the Tyr-181C mutation by moving itself in the non-nucleoside inhibitor binding pocket (NNIBP) of the mutant RT. In this context, R100943 has torsional freedom that enables the conformational alternations of the NNRTI. This torsional freedom could be used by the ITU derivate to bind to a mutated NNIBP and thus compensating for the effects of a resistance mutation. Nevertheless, the potency of R100943 against HIV-1 resistant mutants was not adequate for it to be considered as an effective drug candidate. Additionally, the chemical stability of the imidoylthiourea part of the ITU derivative was not favorable for an oral drug.

##### Development from ITU to DATA

Changes in the imidoylthiourea complexes led to the synthesis of a new class of compounds, diaryltriazine (DATA). In these compounds, the thiourea part of the ITU compounds was replaced by a triazine ring. The DATA compounds were more potent than the ITU compounds against common NNRTI resistant mutant strains. R106168, a prototype DATA compound, was rather easy to synthesize. Multiple substitutions were made at different positions on all of the three rings and on the linkers connecting the rings. In the pocket, most of the DATA derivatives conformed a horseshoe conformation. The two wings in R106168 (2,6-dichlorobenzyl and 4-cyanoanilino) occupied positions in the pocket similar to that of the two wings of the derivatives of ITU. The central part of the DATA compounds, in which the triazine ring replaced the thiourea group of ITU derivatives, is positioned between the side chains of L100 and V179. This removed a number of torsional degrees of freedom in the central part while keeping the flexibility between the triazine ring and the wings.

Chemical substitution or modification in the three-aromatic-ring backbone of the DATA compounds had substantial effect on the activity. R120393, a DATA analog, was designed with a chloroindole part in wing I to expand interactions with the side chain of conserved W229 of the polymerase primer grip loop. R120393 had similar effect as R106168 against most of the NNRTI-resistant mutants. The cloroindole part interacted with the hydrophobic core of the pocket and influenced the binding mode of the R120393 so it went deeper into the pocket compared to the wing I position of other DATA analogs. Crystal structures showed that the DATA compounds could bind the NNIBP in different conformations. The capability to bind in multiple modes made the NNRTIs stronger against drug-resistance mutations. Variability between the inhibitors could be seen when the chemical composition, size of wing I and the two linker groups connecting the rings were altered. The potency of the NNRTIs changed when the triazine nitrogen atoms were substituted with carbons.

#### Next generation NNRTIs

Researchers used multi-disciplinary approach to design NNRTIs with better resistance profile and an increased genetic barrier to the development of resistance. A new class of compounds, diarylpyrimide (DAPY), were discovered with the replacement of the central triazine ring from the DATA compounds, with a pyrimidine. This new class was more effective against drug resistant HIV-1 strains than the corresponding DATA analogs. The replacement enabled substitutions to the CH-group at the 5-position of the central aromatic ring. One of the first DAPY compounds, dapivirine (with R1= 2,4,6-trimethylanilino, R2 = R3 = H and Y = NH) was found to be effective against drug-resistant HIV-1 strains. Systematic chemical substitutions were made at the R1, R2, R3 and Y positions to find new DAPY derivatives. This led to the discovery of etravirine which has a bromine substitution at the 5-position (R3) of the pyrimidine ring (with R1 = 2,6-dimethyl-4-cyanoanilino, R2 = NH2 and Y = O) (figure 5). Etravirine was discovered by researchers at the Jansen Research Foundation and Tibotec and approved in 2008 by the FDA. It is used in treatment-experienced adult patients with HIV infection that is multidrug resistant in combination with other antiretroviral drugs.

## Resistance

When treating infection, whether bacterial or viral, there is always a risk of the infectious agent to develop drug resistance. The treatment of HIV infection is especially susceptible to drug resistance which is a serious clinical concern in the chemotherapeutic treatment of the infection. Drug resistant HIV-strains emerge if the virus is able to replicate in the presence of the antiretroviral drugs.

NNRTI-resistant HIV-strains have the occurring mutations mainly in and around the NNIBP affecting the NNRTI binding directly by altering the size, shape and polarity on different areas of the pocket or by affecting, indirectly, the access to the pocket. Those mutations are primarily noted in domains which span amino acids 98-108, 178-190 or 225-238 of the p66 subunit. The most frequent mutations observed in viruses isolated from patients who have been on a failing NNRTI containing chemotherapy are Lys-103N and Tyr-181C. NNRTI resistance has been linked to over 40 amino acid substitutions in vitro and in vivo.

Antiretroviral drugs are never used in monotherapy due to rapid resistance development. The highly active antiretroviral therapy (HAART) was introduced in 1996. The treatment regimen combines three drugs from at least two different classes of antiretroviral drugs.

The advance of etravirine over other NNRTIs is that multiple mutations are required for the development of drug resistance. The drug has also shown activity against viruses with common NNRTI resistance associated mutations and cross-resistance mutations.

## Current status

Five drugs in the class of NNRTIs have been approved by regulatory authorities. These are the first generation NNRTIs nevirapine, delavirdine and efavirenz and the next generation NNRTIs etravirine, and rilpivirine. Several other NNRTIs underwent clinical development but were discontinued due to unfavourable pharmacokinetic, efficacy and/or safety factors. Currently there are four other NNRTIs undergoing clinical development, IDX899, RDEA-428 and lersivirine (table 2).

### Rilpivirine

Rilpivirine is a DAPY compound like etravirine and was discovered when further optimization within this family of NNRTIs was conducted. The resistance profile and the genetic barrier to the development of resistance is comparable to etravirine *in vitro*. The advantage of rilpivirine over etravirine is a better bioavailability and it is easier to formulate than etravirine. Etravirine has required extensive chemical formulation work due to poor solubility and bioavailability. Rilpivirine was approved by the FDA for HIV therapy in May 2011 under the brand name Edurant. Edurant is approved for treatment-naive patients with a viral load of 100,000 copies/mL or less at therapy initiation. Its recommended dosage is 25 mg orally once daily with a meal, in combination with other antiretrovirals. It is contraindicated for use with proton pump inhibitors due to the increased gastric pH causing decreased rilpivirine plasma concentrations, potentially resulting in loss of virologic response and possible resistance. A fixed-dose drug combining rilpivirine with emtricitabine and tenofovir disoproxil (TDF), was approved by the U.S. Food and Drug Administration in August 2011 under the brand name Complera. A newer fixed-dose drug also combining rilpivirine with emtricitabine and tenofovir alafenamide (TAF) was approved in March 2016 under the brand name Odefsey.

### RDEA806

In 2007 a new family of triazole NNRTIs was presented by researchers from the pharmaceutical company Ardea Biosciences. The selected candidate from the screening executed was RDEA806 belonging to the family of triazoles. It has similar resistance profile against selected NNRTI resistant HIV-1 strains to other next generation NNRTIs. The candidate entered phase IIb clinical trials in the end of 2009, but no further trial have been initiated. Ardea was sold to AstraZeneca in 2012.

### Fosdevirine (IDX899)

Fosdevirine (also known as IDX899 and GSK-2248761) is another next generation NNRTI developed by Idenix Pharmaceuticals and ViiV Healthcare. It belongs to the family of 3-phosphoindoles. *In vitro* studies have shown comparable resistance profile to that of the other next generation NNRTIs. In November 2009 the candidate entered phase II clinical trials, but the trial and all further development was halted when 5 of 35 subjects receiving fosdevirine experienced delayed-onset seizures.

### Lersivirine (UK-453061)

Lersivirine belongs to the pyrazole family and is another next generation NNRTI in clinical trials developed by the pharmaceutical company ViiV Healthcare. The resistance profile is similar to that of other next generation NNRTIs. In the end of 2009 lersivirine was in phase IIb. In February 2013, ViiV Healthcare announced a stop of the development program investigating lersivirine.

**Table 2** Represents the drug candidates that have been in clinical development
| Drug candidate | RDEA806 | Fosdevirine (IDX899) | Lersivirine (UK-453061) |
| --- | --- | --- | --- |
| Chemical structure |  |  |  |
| Phase of development | IIb | II | IIb |


abstract: Chena Hot Springs are a system of thermal mineral springs located within the Yukon-Tanana Plateau near the town of Chena Hot Springs, approximately 50 miles northeast of Fairbanks, Alaska. The springs consist of several hot soaking pools and a rock-lined warm lake only accessible to those over age 18. There is also a glassed-in indoor 90 °F swimming pool located at an onsite lodge that is powered by a geothermal power plant nearby. There is now a small 8 person Jacuzzi outdoors heated to the same temperature as the indoor pool. In the winter there is a covered path to the lake. A rare form of quartz-encrusted zeolite, yugawaralite, was found near Chena Hot Springs. It has also been found near hot springs in Japan and Iceland. Canadian First Nations peoples and Native Alaskans traditionally used hot springs for healing and bathing. In the early years of the 20th Century, Chena hot springs were used by homesteaders and surveyors.

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# Chena Hot Springs (thermal mineral springs)

**Chena Hot Springs** are a system of thermal mineral springs located within the Yukon-Tanana Plateau near the town of Chena Hot Springs, approximately 50 miles northeast of Fairbanks, Alaska.

The springs consist of several hot soaking pools and a rock-lined warm lake only accessible to those over age 18. There is also a glassed-in indoor 90 °F swimming pool located at an onsite lodge that is powered by a geothermal power plant nearby.

There is now a small 8 person Jacuzzi outdoors heated to the same temperature as the indoor pool. In the winter there is a covered path to the lake.

A rare form of quartz-encrusted zeolite, yugawaralite, was found near Chena Hot Springs. It has also been found near hot springs in Japan and Iceland.

Canadian First Nations peoples and Native Alaskans traditionally used hot springs for healing and bathing. In the early years of the 20th Century, Chena hot springs were used by homesteaders and surveyors.

## Water profile

The hot mineral water emerges from the ground at 153 °F / 67 °C. The mineral content of the water includes silica, sodium, iron, potassium, aluminum, carbonate, calcium, magnesium, chloride, bicarbonate, sulfate, fluoride, nitrate, lithium, boric acid and ammonia.

## InfoBox

| Chena Hot Springs | |
| --- | --- |
|  | |
|  | |
| Location | Yukon-Tanana Plateau |
| Coordinates | 65°03′11″N 146°03′20″W / 65.05306°N 146.05556°W / 65.05306; -146.05556 |
| Elevation | 1,200 feet |
| Type | Geothermal |
| Discharge | 165 °F / 74 °C |
| Temperature | 153°F / 67°C |


title: Black Eye Productions

abstract: Black Eye Books is a small but influential Canadian comic book publishing company founded by Michel Vrana. Under the auspices of Vrana, Black Eye was known as a publisher of artfully designed alternative comics and graphic novels, most of whose cartoonists have gone on to successful careers with fellow Canadian publisher Drawn & Quarterly. For several years, Vrana acted as Drawn & Quarterly's exclusive outside design consultant. In 2019 the company was relaunched as a micro-press with a focus on using crowdfunding to bring projects to fruition.

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# Black Eye Productions

**Black Eye Books** (formerly called **Black Eye Productions**) is a small but influential Canadian comic book publishing company founded by Michel Vrana. Under the auspices of Vrana, Black Eye was known as a publisher of artfully designed alternative comics and graphic novels, most of whose cartoonists have gone on to successful careers with fellow Canadian publisher Drawn & Quarterly. For several years, Vrana acted as Drawn & Quarterly's exclusive outside design consultant. In 2019 the company was relaunched as a micro-press with a focus on using crowdfunding to bring projects to fruition.

## History

Vrana's first worked with publisher **Tragedy Strikes Press**, which operated out of Guelph, Ontario, from 1991–1993. Comics published by Tragedy Strikes Press included Nick Craine's *The Cheeseheads*, the anthology series *Reactor Girl*, Jay Stephens' *Sin*, Carol Swain's *Way Out Strips*, and the first issue of Dylan Horrocks' *Pickle*. *Sin* and *Pickle* were picked up by Black Eye Books; *Way Out Strips* was picked up by Fantagraphics.

Black Eye acted as a comic book publisher from 1992 to 1998, when Vrana transitioned the business to graphic design studio. In 2019, Vrana relaunched Black Eye Books to publish the previously cancelled 11th issue of *Pickle*, by Dylan Horrocks. This was followed by the publication of *Dejects*, by Jay Stephens, the first full-colour publication from Black Eye. From 2010-2024, Black Eye Books published Jay Stephens’ horror series *Dwellings*. Other publications since 2019 include the collected *Dishman* by John MacLeod, *That Distant Fire* by JR Hughto and Curt Merlo, *Assorted Baggage* by Matthew Daley, and a box set of James Kochalka books: *Elf Cat is Famous*, *Moon Book Prototype*, and *Duck Fighter*.

## Publications

### Ongoing titles and limited series

* *Atomic City Tales* vol. 1 (Jay Stephens, 1994–1995)
* *Berlin* (Jason Lutes, 1996–1998)
* *Dear Julia* (Brian Biggs, 4 issues, 1996-1997)
* *The Land of Nod* vol. 1 (Jay Stephens, 1996–1997)
* *Pickle* (Dylan Horrocks, 1992-1997, 2019)
* *The Sands* (Tom Hart, 1996–1997)
* *Sin Comics* (Jay Stephens, 1993–1994)
* *Sputnik* (anthology, 1993–1994)
* *Dwellings* (Jay Stephens, 2010–2024)

### Graphic novels/trade paperbacks

* *Atomic City Tales* (Jay Stephens, 1994)
* *Black Candy* (Matt Madden, 1998) ISBN 978-0-9698874-6-1
* *A Complete Lowlife* (Ed Brubaker, 1997)
* *Dance Me Outside: The Illustrated Screenplay* (Nick Craine, 1994) ISBN 978-0-9698874-0-9
* *Dejects* (Jay Stephens, 2019) ISBN 978-1-9991635-0-1
* *Hicksville* (Dylan Horrocks, 1998)
* *Human Remains* (Darren Raye & Sean Scoffield, 1994)
* *Jar of Fools* (Jason Lutes, 1995)
* *The Land of Nod Treasury* (Jay Stephens, 1994)
* *The Sands: a Picture Story* (Tom Hart, 1998) ISBN 978-0-9698874-8-5

## Cartoonists associated with Black Eye

## InfoBox

Black Eye Books
|
|  |
| Industry | Comics |
| Predecessor | Black Eye Productions |
| Founded | 1992 |
| Founder | Michel Vrana |
| Headquarters | Toronto, Ontario, Canada |
| Website | www.blackeye.ca |


title: China National Highway 228

abstract: China National Highway 228 (228国道) is a planned highway of the National Highway System of the People's Republic of China to run from Dandong, Liaoning on the China–North Korea border to Dongxing, Guangxi on the China–Vietnam border. This route follows the coastline of Mainland China closely and has a planned length of 7,800 km (4,800 mi).

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# China National Highway 228

**China National Highway 228** (228国道) is a planned highway of the National Highway System of the People's Republic of China to run from Dandong, Liaoning on the China–North Korea border to Dongxing, Guangxi on the China–Vietnam border.

This route follows the coastline of Mainland China closely and has a planned length of 7,800 km (4,800 mi).

## Route

The route will run from Dandong, Liaoning on the China–North Korea border to Dongxing, Guangxi on the China–Vietnam border. En route, it will pass through Dalian and Yingkou in Liaoning; Binhai New Area in Tianjin; Huanghua in Hebei; Dongying, Yantai, Weihai, Qinghai, and Rizhao in Shandong; Lianyungang and Nantong in Jiangsu; Shanghai; Jiaxing, Ningbo, Taizhou, Wenzhou, and Ningde in Zhejiang; Fuzhou, Quanzhou, and Xiamen in Fujian; Shantou, Shenzhen, Zhuhai, Zhanjiang in Guangdong; and Beihai and Fangchenggang in Guangxi.

## Shanghai segment

The segment of G228 in Shanghai is planned to follow the basic route of the G40 Shanghai–Xi'an Expressway, and will pass through Chongming District, Pudong District, Fengxian District, and Jinshan District.

## Zhejiang segment

G228 will be the first national highway serving Yuhuan County.

In late 2015 and early 2016, the government put out requests for tenders relating to various segments of G228 in Wenzhou, including for a bridge to be built on the Ao River for the Pingyang County to Cangnan County segment of the highway, and for work on the Longsha Township (龙沙乡) to Dailing She Ethnic Township segment.

## InfoBox

| National Highway 228 | |
| --- | --- |
| 228国道 | |
|  | |
| Major junctions | |
| From | Dandong, Liaoning |
| To | Dongxing, Guangxi |
|  | |
| Location | |
| Country | China |
|  | |
| Highway system | |
|  | |
| G227   G229 | |


title: Dynatron oscillator

abstract: In electronics, the dynatron oscillator, invented in 1918 by Albert Hull at General Electric, is an obsolete vacuum tube electronic oscillator circuit which uses a negative resistance characteristic in early tetrode vacuum tubes, caused by a process called secondary emission. It was the first negative resistance vacuum tube oscillator. The dynatron oscillator circuit was used to a limited extent as beat frequency oscillators (BFOs), and local oscillators in vacuum tube radio receivers as well as in scientific and test equipment from the 1920s to the 1940s but became obsolete around World War 2 due to the variability of secondary emission in tubes. Negative transconductance oscillators, such as the transitron oscillator invented by Cleto Brunetti in 1939, are similar negative resistance vacuum tube oscillator circuits which are based on negative transconductance in a pentode or other multigrid vacuum tube. These replaced the dynatron circuit and were employed in vacuum tube electronic equipment through the 1970s.

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# Dynatron oscillator

Dynatron vacuum tube signal generator, 1931. It covered the range 1.8 to 15 MHz. The circuit was used in signal generators due to its frequency stability, which was compared to crystal oscillatorsThe dynatron oscillator circuit was also used as the local oscillator in early vacuum tube superheterodyne radio receivers, such as this 1931 Crosley model 122 seven tube radio.

In electronics, the **dynatron oscillator**, invented in 1918 by Albert Hull at General Electric, is an obsolete vacuum tube electronic oscillator circuit which uses a negative resistance characteristic in early tetrode vacuum tubes, caused by a process called secondary emission. It was the first negative resistance vacuum tube oscillator. The dynatron oscillator circuit was used to a limited extent as beat frequency oscillators (BFOs), and local oscillators in vacuum tube radio receivers as well as in scientific and test equipment from the 1920s to the 1940s but became obsolete around World War 2 due to the variability of secondary emission in tubes.

Negative transconductance oscillators, such as the **transitron oscillator** invented by Cleto Brunetti in 1939, are similar negative resistance vacuum tube oscillator circuits which are based on negative transconductance (a fall in current through one grid electrode caused by an increase in voltage on a second grid) in a pentode or other multigrid vacuum tube. These replaced the dynatron circuit and were employed in vacuum tube electronic equipment through the 1970s.

## How they work

The dynatron and transitron oscillators differ from many oscillator circuits in that they do not use feedback to generate oscillations, but negative resistance. A tuned circuit (resonant circuit), consisting of an inductor and capacitor connected together, is "almost" an oscillator: it can store electric energy in the form of oscillating currents, "ringing" analogously to a tuning fork. If a tuned circuit could have zero electrical resistance, once oscillations were started it would function as an oscillator, producing a continuous sine wave. But because of the inevitable resistance inherent in actual circuits, without an external source of power the energy in the oscillating current is dissipated as heat in the resistance, and any oscillations decay to zero.

In the dynatron and transitron circuits, a vacuum tube is biased so that one of its electrodes has negative differential resistance. This means that when the voltage on the electrode with respect to the cathode is increased, the current through it decreases. A tuned circuit is connected between the electrode and the cathode. The negative resistance of the tube cancels the positive resistance of the tuned circuit, creating in effect a tuned circuit with zero AC resistance. A spontaneous continuous sinusoidal oscillating voltage at the resonant frequency of the tuned circuit is generated, started by electrical noise in the circuit when it is turned on.

An advantage of these oscillators was that the negative resistance effect was largely independent of frequency, so by using suitable values of inductance and capacitance in the tuned circuit they could operate over a wide frequency range, from a few hertz to around 20 MHz. Another advantage was that they used a simple single LC tuned circuit without the taps or "tickler" coils required by oscillators such as the Hartley or Armstrong circuits.

## Dynatron oscillator

In the dynatron a tetrode tube is used. In some tetrodes the plate (anode) has negative differential resistance, due to electrons knocked out of the plate when electrons from the cathode hit it, called *secondary emission*. This causes a downward "kink" in the plate current vs. plate voltage curve *(graph below, grey region)* when the screen grid is biased at a higher voltage than the plate, as described below. This negative resistance was mostly a feature of older tubes, of 1940s or earlier vintage. In most modern tetrodes, to prevent parasitic oscillations the plate is given a coating which drastically reduces the unwanted secondary emission, so these tubes have virtually no negative resistance "kink" in their plate current characteristic, and cannot be used in dynatron oscillators.

The tetrode wasn't the only tube which could generate dynatron oscillations. Early triodes also had secondary emission and thus negative resistance, and before the tetrode was invented they were used in dynatron oscillators by biasing the control grid more positive than the plate. Hull's first dynatron oscillator in 1918 used a special "dynatron" vacuum tube of his own design *(shown above)*, a triode in which the grid was a heavy plate perforated with holes which was robust enough to carry high currents. This tube saw little use as standard triode and tetrodes could function adequately as dynatrons. The term "dynatron" came to be applied to all negative resistance oscillations in vacuum tubes; for example the split-anode magnetron was said to work by "dynatron oscillation".

An advantage of the dynatron circuit was that it could oscillate over a very wide frequency range; from a few hertz to 20 MHz. It also had very good frequency stability compared to other LC oscillators of that time, and was even compared to crystal oscillators. The circuit became popular after the advent of cheap tetrode tubes such as the UY222 and UY224 around 1928. It was used in beat frequency oscillators (BFOs) for code reception and local oscillators in superheterodyne receivers as well as in laboratory signal generators and scientific research. RCA's 1931 prototype television used two UY224 tubes as dynatron oscillators to generate the vertical deflection (28 Hz) and horizontal deflection (2880 Hz) signals for the CRT's deflection coils.

However the dynatron had some drawbacks. It was found that the amount of secondary emission current from the plate varied unpredictably from tube to tube, and also within a single tube over its operating life; eventually it would stop oscillating. When replacing the tube, several might have to be tried to find one that would oscillate in a circuit. In addition, since dynatron oscillations were a source of instability in amplifiers, the tetrode's main application, tube manufacturers began applying a graphite coating to the plate which virtually eliminated secondary emission. By 1945 the use of the dynatron circuit was declining.

### Secondary emission

Plate current (*I*b) vs plate voltage curves for tetrodes:An early tetrode, the RCA 24-A from 1929, showing on the lefthand side the negative resistance "kink" in the curves due to secondary emission. At a screen voltage *V*C2 of 90 V it has negative resistance between about *V*p = 10 to 60 V.A modern tetrode, the 6P25. Due to a coating on the plate, there is very little secondary emission, so there is virtually no negative resistance region ("kink") in the curves, making this tube unusable for dynatron operation.

In an electron tube, when electrons emitted by the cathode strike the plate, they can knock other electrons out of the surface of the metal, an effect called *secondary emission*. In a normal tetrode amplifier this is an unwanted effect, and the screen grid next to the plate is biased at a lower potential than the plate, so these *secondary electrons* are repelled and return to the plate due to its positive charge.

However, if the screen grid is operated at a higher potential than the plate, the secondary electrons will be attracted to it, and return to ground through the screen grid supply. This represents a current of electrons *I*G2 *away* from the plate, which reduces the net plate current *I*P below the cathode current *I*C

$$I\_{P}=I\_{C}-I\_{G2}\\,$$

Higher plate voltage causes the primary electrons to hit the plate with more energy, releasing more secondary electrons. Therefore, starting at the voltage at which the primary electrons have enough energy to cause secondary emission, around *V*P = 10V, there is an operating region *(grey)* in which an increase in plate voltage causes more electrons to leave the plate than the additional electrons arriving at the plate, and therefore a net reduction in plate current.

### Negative resistance

Since in this region an increase in plate voltage causes a decrease in plate current, the AC plate resistance, that is the differential output resistance of the tube, is negative:

$$r\_{P}={\Delta V\_{P} \over \Delta I\_{P}\<0\\,}$$

As with other negative differential resistance devices like the tunnel diode, this negative resistance can be used to create an oscillator. A parallel tuned circuit is connected in the plate circuit of the tetrode. The circuit will oscillate if the magnitude of the negative plate resistance is less than the parallel resistance ***R*** of the tuned circuit, including any load connected to the oscillator.

$$|r\_{P}|\<R\\,$$

The frequency of oscillation is close to the resonant frequency of the tuned circuit.

$$f={1 \over 2\pi }{\sqrt {1 \over LC}\\,}$$

### Design

As can be seen from the graphs, for dynatron operation the screen grid had to be biased at a considerably higher voltage than the plate; at least twice the plate voltage. The plate voltage swing is limited to the negative resistance region of the curve, the downward "kink", so to achieve the largest output voltage swing, the tube should be biased in the center of the negative resistance region.

The negative resistance of older tetrode tubes was around 10kΩ - 20kΩ, and can be controlled by varying the control grid bias. If the magnitude of the negative resistance |***r*P**| is just small enough to start oscillation, just a little smaller than the positive resistance ***R*** of the tuned circuit, the oscillation frequency will be very stable, and the output waveform will be almost sinusoidal. If the negative resistance is made significantly smaller than the positive resistance, the voltage swing will extend into the nonlinear part of the curve, and the peaks of the sine wave output will be flattened ("clipped").

## Transitron oscillator

The transitron oscillator, invented by Cledo Brunetti in 1939, (although a similar effect was observed in tetrodes by Balthasar van der Pol in 1926, and Edward Herold described a similar oscillator in 1935) is a negative resistance oscillator circuit using a pentode vacuum tube, in which, instead of the plate, the screen grid has negative resistance due to being coupled to the suppressor grid. See the circuit at right. In the transitron, the screen grid is biased at a positive voltage *(battery B1)* above the plate voltage while the suppressor grid is biased negatively *(battery B2)*, at or below the cathode voltage. Therefore, all the electrons will be reflected by the negative suppressor grid and none will get through to the plate. The reflected electrons will instead be attracted to the screen grid, so the screen current will be high while the plate current will be zero. However, if the suppressor grid voltage is increased, as it approaches zero (the cathode voltage) electrons will begin to pass through it and reach the plate, so the number diverted to the screen grid, and thus the screen current, will decrease. Since the other grids don't take significant current the cathode current $\scriptstyle I\_{\text{C}}$ is split between the plate $\scriptstyle I\_{\text{P}}$ and the screen grid $\scriptstyle I\_{\text{G2}}$:

$$I\_{\text{G2}=I\_{\text{C}-I\_{\text{P}\\,}}}$$

The division of current between the screen grid and plate is controlled by the suppressor voltage. This inverse relationship is indicated by saying the transconductance between the screen and suppressor grid (the change in screen current Δ*I*G2 divided by the change in suppressor voltage Δ*V*G3) is negative.

Since the suppressor grid voltage and not the screen grid voltage controls the screen current, if the suppressor and screen grid are coupled together with a capacitor (*C2*) so there is a constant potential difference between them, increasing the screen grid voltage will increase the suppressor voltage, resulting in a decrease in screen current. This means the screen grid has negative differential resistance with respect to the cathode, and can be used to create oscillations.

In the transitron circuit, the screen and suppressor grids are coupled with a bypass capacitor (*C2*) which has a low impedance at the oscillation frequency, so they have a constant potential difference. The parallel tuned circuit (*C1-L*) is connected between the screen grid and the cathode (through battery *B1*). The negative resistance of the screen grid cancels the positive resistance of the tuned circuit, causing oscillations. As in the dynatron oscillator the control grid can be used to adjust the negative resistance.

Since the transitron oscillator didn't depend on secondary emission it was far more reliable than the dynatron. However, because the screen grid is not designed to handle high power, the oscillator's output power is limited. Other tubes with multiple grids beside the pentode, such as the hexode and pentagrid converter tube, have been be used to make similar negative transconductance oscillators. Pentode tubes used in this circuit have a negative transconductance of only around −250 microsiemens, giving a negative resistance of −4000Ω. Tubes with more grids, such as the pentagrid converter, can be used to make transitron oscillators with higher transconductance, resulting in smaller negative resistance.


title: Siege of Martyropolis (531)

abstract: A siege of Martyropolis occurred in the Autumn of 531 during the Iberian War between the Sasanian Empire under Kavadh I and the Byzantine Empire under Justinian I. A Roman raid from Martyropolis triggered the Sasanians to launch a siege on the newly fortified frontier city. Initially, the Sasanians had the upper hand, but a series of political events and logistical issues led them to withdraw. It was the last conflict of the Iberian War.

text:
# Siege of Martyropolis (531)

A **siege of Martyropolis** occurred in the Autumn of 531 during the Iberian War between the Sasanian Empire under Kavadh I and the Byzantine Empire under Justinian I.

A Roman raid from Martyropolis triggered the Sasanians to launch a siege on the newly fortified frontier city. Initially, the Sasanians had the upper hand, but a series of political events and logistical issues led them to withdraw. It was the last conflict of the Iberian War.

## Background

Earlier, the Sasanian king Kavadh I had ordered a campaign which resulted in a battle at Callinicum. Although the Persians were victorious, the victory was narrow, and no fortress was captured, thus making the campaign inconclusive. Both Belisarius and Azarethes, the Byzantine and Sasanian generals at Callinicum, respectively, were dismissed due to the high casualties of this battle. Emperor Justinian I then appointed Sittas as strategos in charge of the east.

At this time, Justinian's policy was to bolster the Roman position and at the same time try to make a truce with the Persians.

In Mesopotamia, Bessas had recently been appointed as *dux Mesopotamiae* with the frontier city of Martyropolis as his base, which was recently fortified by emperor Justinian I. From there, he performed a successful raid into the Sasanian border land of Arzanene, killing hundreds.

## Siege

This led the Sasanians to lay siege on Martyropolis with a capable force under three veteran generals, Adergoudounbades ("Chanaranges"), Bawi ("Aspebedes"), and Mihr-Mihroe. Roman garrison force was commanded by Bessas and Bouzes. Sittas and his Ghassanid ally Al-Harith ibn Jabalah were stationed near the city, but avoided engagement since the Persians had the upper hand in the conflict.

However, a series of political events, including the death of Kavadh I and the perceived threat of Huns, as well as the arrival of winter and the presence of Roman reinforcements at Amida all led the Sasanian field commanders to abandon the siege and agree on an armistice.

## Aftermath

Justinian I and the new Sasanian king Khosrow I signed a peace treaty dubbed Perpetual Peace a year later, ending the Iberian War.

* Greatrex, Geoffrey; Lieu, Samuel N. C. (2002). The Roman Eastern Frontier and the Persian Wars (Part II, 363–630 AD). London: Routledge. ISBN 0-415-14687-9, p. 95

## InfoBox

| Siege of Martyropolis (531) | |
| --- | --- |
| Part of the Iberian War | |
| Date Autumn 531 AD  Location Martyropolis, Byzantine Empire
(modern-day Silvan, Şanlıurfa, Turkey)38°8′31.99″N 41°0′5.00″E / 38.1422194°N 41.0013889°E / 38.1422194; 41.0013889  Result * Tactical Sasanian failure * End of the Iberian War | |
| Belligerents | |
| Sasanian Empire
Huns | Byzantine Empire
Ghassanids |
| Commanders and leaders | |
| Chanaranges
Bawi
Mihr-Mihroe | ***Garrison force:***
Bouzes
*Dux* Bessas
Bishop Nonnus

***Field army** (not engaged):*
*Strategos* Sittas
Hermogenes
Al-Harith ibn Jabalah |
| Strength | |
| Large army | |
| class=notpageimage|Location within Turkey | |


title: Spruce Grove-Stony Plain

abstract: Spruce Grove-Stony Plain is a provincial electoral district in Alberta, Canada. The district is one of 87 districts mandated to return a single member (MLA) to the Legislative Assembly of Alberta using the first past the post method of voting. It was contested for the first time in the 2019 Alberta election.

text:
# Spruce Grove-Stony Plain

**Spruce Grove-Stony Plain** is a provincial electoral district in Alberta, Canada. The district is one of 87 districts mandated to return a single member (MLA) to the Legislative Assembly of Alberta using the first past the post method of voting. It was contested for the first time in the 2019 Alberta election.

## Geography

The district is located west of Edmonton, containing the City of Spruce Grove and the Town of Stony Plain. The district boundaries match the municipal boundaries of the two communities. It is bisected by Highway 16A and bordered by the Yellowhead Highway to the North.

## History

| Members for Spruce Grove-Stony Plain | | | | |
| --- | --- | --- | --- | --- |
| Assembly | Years | Member | | Party |
| *See Spruce Grove-St. Albert 2012-2019
and Stony Plain 1905-2019* | | | | |
| 30th | 2019–2023 |  | Searle Turton | United Conservative |
| 31st | 2023 | | | |

The district was created in 2017 when the Electoral Boundaries Commission recommended abolishing Spruce Grove-St. Albert and Stony Plain, creating a district that is well above the provincial average in population. The Commission reasoned this was preferable to placing part of either community in a neighbouring district.

## Electoral results

### 2023

| 2023 Alberta general election | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Party | Candidate | Votes | % | ±% |
|  | United Conservative | Searle Turton | 14,365 | 56.99 | -2.36 |
|  | New Democratic | Chantal Saramaga-McKenzie | 10,197 | 40.45 | +11.10 |
|  | Green | Daniel Birrell | 422 | 1.67 |  |
|  | Solidarity Movement | Darlene Clarke | 223 | 0.88 |  |
| Total | | | 25,207 | 99.57 |  |
| Rejected and declined | | | 108 | 0.43 |
| Turnout | | | 25,315 | 61.52 |
| Eligible voters | | | 41,150 |
|  | United Conservative **hold** | | Swing | | -6.73 |
| Source(s) Source: Elections Alberta | | | | | | |

### 2019

| 2019 Alberta general election | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Party | Candidate | Votes | % | ±% |
|  | United Conservative | Searle Turton | 15,843 | 59.35% | 11.15% |
|  | New Democratic | Erin Babcock | 7,836 | 29.36% | 12.38% |
|  | Alberta Party | Ivan G. Boles | 2,597 | 9.73% | 4.58% |
|  | Alberta Independence | Jody Crocker | 417 | 1.56% |  |
| Total | | | 26,693 |  |  |
| Rejected, spoiled and declined | | | 47 | 77 | 16 |
| Eligible electors / turnout | | | 37,296 | 71.74% |  |
|  | United Conservative **pickup** new district. | | | | | | |
| Source(s) Source: "82 - Spruce Grove-Stony Plain, 2019 Alberta general election". *officialresults.elections.ab.ca*. Elections Alberta. Retrieved May 21, 2020.
Alberta. Chief Electoral Officer (2019). 2019 General Election. A Report of the Chief Electoral Officer. Volume II (PDF) (Report). Vol. 2. Edmonton, Alta.: Elections Alberta. pp. 399–403. ISBN 978-1-988620-12-1. Retrieved April 7, 2021. | | | | | | |

### 2015

| Redistributed results, 2015 Alberta election | | | | |
| --- | --- | --- | --- | --- |
| Party | | Votes | % |
|  | New Democratic | 7,738 | 41.74 |
|  | Progressive Conservative | 4,699 | 25.35 |
|  | Wildrose | 4,236 | 22.85 |
|  | Alberta Party | 955 | 5.15 |
|  | Liberal | 683 | 3.68 |
|  | Green | 228 | 1.23 |

## InfoBox

Spruce Grove-Stony Plain
| Alberta electoral district | |
| --- | --- |
| Spruce Grove-Stony Plain within the Edmonton Metropolitan Region (2017 boundaries). | |
| Provincial electoral district | |
| Legislature | Legislative Assembly of Alberta |
| MLA |
     Searle Turton
United Conservative |
| District created | 2017 |
| First contested | 2019 |
| Last contested | 2023 |
| Demographics | |
| Population (2016) | 51,267 |
| Area (km²) | 68.5 |
| Pop. density (per km²) | 748.4 |
| Census division(s) | 11 |
| Census subdivision(s) | Spruce Grove, Stony Plain |


title: Richard Devereux (died 1547)

abstract: Sir Richard Devereux was a rising political figure during the reign of Henry VIII and Edward VI when his career was cut short by his sudden death during the life of his father. His son would complete the family's ascendency when he was created Earl of Essex.

text:
# Richard Devereux (died 1547)

**Sir Richard Devereux** was a rising political figure during the reign of Henry VIII and Edward VI when his career was cut short by his sudden death during the life of his father. His son would complete the family's ascendency when he was created Earl of Essex.

## Family

He was born by 1513, the son of Walter Devereux, 1st Viscount Hereford and Mary Grey (1491-22 February 1538).

His paternal grandparents were John Devereux, 9th Baron Ferrers of Chartley and Cecily Bourchier. His maternal grandparents were Thomas Grey, 1st Marquess of Dorset and his second wife Cecily Bonville, Baroness Harington and Bonville.

## Career

Richard Devereux lived in Carmarthen, Wales where he was Bailiff from 1534 to 1535, and Mayor in 1536 to 1537. He was Commissioner for the tenths of spiritualities for St. David's diocese in 1535. He later came out strongly for the canons in their dispute with Bishop Barlow of St. David's. In 1542 he was a candidate for election to Parliament, and noted for enlivening the town of Carmarthen by his encouragement of unruly behaviour and resort to force, which prompted his adversary to lodge a complaint. Later in 1546 Devereux would be examined by the Privy Council for comments on religious practices he thought were superstitious.

He was Deputy steward of the lordships of Arwystli and Cyfeiliog in Montgomeryshire in 1537. He supported his father in his dispute with the 2nd Earl of Worcester, and the borough of New Carmarthen.

In 1543 he served under Sir John Wallop when he led a small force to help the Emperor Charles V in his invasion of France. He was mentioned in a dispatch on this campaign.

Devereux was Deputy justice and chamberlain of South Wales during the reign of Henry VIII. He was justice of peace for Cardiff and Pembrokeshire in 1543, and Gloucester and Monmouthshire in 1547. He was Custos Rotulorum of Carmarthenshire from 1543 until his death in 1547.

Richard Devereux was created a Knight of the Bath on 20 February 1547 at the coronation of Edward VI of England. Later that year he was made a member of the council in the marches of Wales.

## Parliament

He was elected to Parliament for Carmarthenshire in 1545, and again just prior to his death in 1547.

## Marriage and Children

He married Dorothea Hastings on 1 July 1536, a daughter of George Hastings, 1st Earl of Huntingdon and Anne Stafford.

They had children:

## Death

He died on 13 October 1547. He was buried in the parish church of St. Olave Hart Street, London under the inscription 'Richarde Deuereux, sonne and Heyre to the lord Ferrers of Chartley'. His inquisition post-mortem in July 1548 showed possession of Lamphey which was to be held by his wife in her widowhood, and then to his son, George, for life with remainder to his other son, Walter. He also was possessed of the ancestral Devereux manor of Bodenham, Herefordshire.

## General Biographical References

* Brydges, Egerton. *Collins's Peerage of England, Genealogical, Biographical, and Historical in 9 Volumes*. (London: Rivington, 1812). Volume 1, Page 6 & 7
* Cokayne, G.C. *Complete Baronetage.* (New York; St. Martin's Press, 1984). Volume V, page 326 to 333, Ferrers
* Devereux, Walter Bourchier. “Lives and Letters of the Devereux, Earls of Essex.” (London:J Murray, 1853)
* Edwards, P.S. *Devereux, Richard (by 1513–47), of Carmarthen, Carm. And Lamphey, Pemb. The History of Parliament, British Political, Social & Local History*. . Retrieved 21 July 2014.
* Doyle, James E. "The Official Baronage of England." (London: Longmans, Green, and Co, 1886). Volume 1, page 167.
* Mosely, Charles (editor). *Burke’s Peerage & Baronetage, 106th Edition*. (Switzerland: Burke’s Peerage Genealogical Books, 1999). Volume 1, page 1378

## InfoBox

| Richard Devereux | |
| --- | --- |
| Born | c. 1513 |
| Died | 1547 |
| Spouse(s) | Dorothea Hastings |
| Issue | Walter Devereux, 1st Earl of Essex
Elizabeth Devereux
Sir George Devereux
Ann Devereux |
| Father | Walter Devereux, 1st Viscount Hereford |
| Mother | Mary Grey |


title: Valea Blaznei mine

abstract: The Valea Blaznei mine is a large mine in the north of Romania in Rodna, Bistrița-Năsăud County, 50 km southwest of Bistrița and 699 km north-west of the capital, Bucharest. Valea Blaznei represents one of the largest lead and zinc reserve in Romania having estimated reserves of 10.5 million tonnes of ore grading 0.76% lead and 2.48% zinc thus resulting in 0.08 million tonnes of lead and 0.26 million tonnes of zinc.

text:
# Valea Blaznei mine

The **Valea Blaznei mine** is a large mine in the north of Romania in Rodna, Bistrița-Năsăud County, 50 km southwest of Bistrița and 699 km north-west of the capital, Bucharest. Valea Blaznei represents one of the largest lead and zinc reserve in Romania having estimated reserves of 10.5 million tonnes of ore grading 0.76% lead and 2.48% zinc thus resulting in 0.08 million tonnes of lead and 0.26 million tonnes of zinc.

## InfoBox

Valea Blaznei mine
| Location | |
| --- | --- |
| Location | Rodna |
| Commune | Bistrița-Năsăud County |
| Country | Romania |
| Production | |
| Products | Lead, Zinc, Copper, Sulfur |
| Production | 195 tonnes of lead, 236 tonnes of copper, 5,888 tonnes of sulfur and 635 tonnes of zinc |
| Financial year | 2008 |
| History | |
| Opened | 1774 |


title: Center manifold

abstract: In the mathematics of evolving systems, the concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling. Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the center manifold and in multiscale mathematics because the long time dynamics of the micro-scale often are attracted to a relatively simple center manifold involving the coarse scale variables.

text:
# Center manifold

In the mathematics of evolving systems, the concept of a **center manifold** was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling.

Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the center manifold and in multiscale mathematics because the long time dynamics of the micro-scale often are attracted to a relatively simple center manifold involving the coarse scale variables.

## Informal description

Saturn's rings capture much center-manifold geometry. Dust particles in the rings are subject to tidal forces, which act characteristically to "compress and stretch". The forces compress particle orbits into the rings, stretch particles along the rings, and ignore small shifts in ring radius. The compressing direction defines the stable manifold, the stretching direction defining the unstable manifold, and the neutral direction is the center manifold.

While geometrically accurate, one major difference distinguishes Saturn's rings from a physical center manifold. Like most dynamical systems, particles in the rings are governed by second-order laws. Understanding trajectories requires modeling position and a velocity/momentum variable, to give a tangent manifold structure called phase space. Physically speaking, the stable, unstable and neutral manifolds of Saturn's ring system do not divide up the coordinate space for a particle's position; they analogously divide up phase space instead.

The center manifold typically behaves as an extended collection of saddle points. Some position-velocity pairs are driven towards the center manifold, while others are flung away from it. Small perturbations that generally push them about randomly, and often push them out of the center manifold. There are, however, dramatic counterexamples to instability at the center manifold, called Lagrangian coherent structures. The entire unforced rigid body dynamics of a ball is a center manifold.

A much more sophisticated example is the Anosov flow on tangent bundles of Riemann surfaces. In that case, the tangent space splits very explicitly and precisely into three parts: the unstable and stable bundles, with the neutral manifold wedged between.

## Definition

The **center manifold** of a dynamical system is based upon an equilibrium point of that system. A *center manifold* of the equilibrium then consists of those nearby orbits that neither decay nor grow exponentially quickly.

Mathematically, the first step when studying equilibrium points of dynamical systems is to linearize the system, and then compute its eigenvalues and eigenvectors. The eigenvectors (and generalized eigenvectors if they occur) corresponding to eigenvalues with negative real part form a basis for the stable eigenspace. The (generalized) eigenvectors corresponding to eigenvalues with positive real part form the unstable eigenspace.

Algebraically, let $\frac {d\mathbf {x} }{dt}=\mathbf {f} (\mathbf {x} )\approx ({\mathcal {D}\mathbf {f} )(\mathbf {x} ^{\*})\mathbf {x} }$be a dynamical system, linearized about equilibrium point **x***. The Jacobian matrix (D**f**)(**x***) defines three main subspaces:

* the center subspace, spanned by generalized eigenvectors whose eigenvalues $\lambda $ satisfy $\operatorname {Re} \lambda =0$ (more generally, $|\operatorname {Re} \lambda |\leq \alpha $);
* the stable subspace, spanned by generalized eigenvectors whose eigenvalues $\lambda $ satisfy $\operatorname {Re} \lambda \<0$ (more generally, $\operatorname {Re} \lambda \leq -\beta \<-r\alpha $);
* the unstable subspace, spanned by the generalized eigenvectors whose eigenvalues $\lambda $ satisfy $\operatorname {Re} \lambda \>0$ (more generally, $\operatorname {Re} \lambda \geq \beta \>r\alpha $).

Depending upon the application, other invariant subspaces of the linearized equation may be of interest, including center-stable, center-unstable, sub-center, slow, and fast subspaces.

If the equilibrium point is hyperbolic (that is, all eigenvalues of the linearization have nonzero real part), then the Hartman-Grobman theorem guarantees that these eigenvalues and eigenvectors completely characterise the system's dynamics near the equilibrium. However, if the equilibrium has eigenvalues whose real part is zero, then the corresponding (generalized) eigenvectors form the *center eigenspace*. Going beyond the linearization, when we account for perturbations by nonlinearity or forcing in the dynamical system, the center eigenspace deforms to the nearby center manifold.

If the eigenvalues are precisely zero (as they are for the ball), rather than just real-part being zero, then the corresponding eigenspace more specifically gives rise to a slow manifold. The behavior on the center (slow) manifold is generally not determined by the linearization and thus may be difficult to construct.

Analogously, nonlinearity or forcing in the system perturbs the stable and unstable eigenspaces to a nearby stable manifold and nearby unstable manifold. These three types of manifolds are three cases of an invariant manifold.

Corresponding to the linearized system, the nonlinear system has invariant manifolds, each consisting of sets of orbits of the nonlinear system.

* An invariant manifold tangent to the stable subspace and with the same dimension is the stable manifold.
* The unstable manifold is of the same dimension and tangent to the unstable subspace.
* A center manifold is of the same dimension and tangent to the center subspace. If, as is common, the eigenvalues of the center subspace are all precisely zero, rather than just real part zero, then a center manifold is often called a slow manifold.

## Center manifold theorems

The center manifold existence theorem states that if the right-hand side function $\textbf {f}({\textbf {x})}$ is $C^{r}$ ( $r$ times continuously differentiable), then at every equilibrium point there exists a neighborhood of some finite size in which there is at least one of

In example applications, a nonlinear coordinate transform to a normal form can clearly separate these three manifolds.

In the case when the unstable manifold does not exist, center manifolds are often relevant to modelling. The center manifold emergence theorem then says that the neighborhood may be chosen so that all solutions of the system staying in the neighborhood tend exponentially quickly to some solution $\textbf {y}(t)$ on the center manifold; in formulas, $\mathbf {x} (t)=\mathbf {y} (t)+{\mathcal {O}(e^{-\beta t})\quad {\text{ as }\quad t\to \infty }}$for some rate β. This theorem asserts that for a wide variety of initial conditions the solutions of the full system decay exponentially quickly to a solution on the relatively low dimensional center manifold.

A third theorem, the approximation theorem, asserts that if an approximate expression for such invariant manifolds, say $\textbf {x}={\textbf {X}({\textbf {s})}}$, satisfies the differential equation for the system to residuals $\mathcal {O}(|{\textbf {s}|^{p})}$ as $\textbf {s}\to {\textbf {0}}$, then the invariant manifold is approximated by $\textbf {x}={\textbf {X}({\textbf {s})}}$ to an error of the same order, namely $\mathcal {O}(|{\textbf {s}|^{p})}$.

### Center manifolds of infinite-dimensional or non-autonomous systems

However, some applications, such as to dispersion in tubes or channels, require an infinite-dimensional center manifold. The most general and powerful theory was developed by Aulbach and Wanner. They addressed non-autonomous dynamical systems $\frac {d{\textbf {x}{dt}={\textbf {f}({\textbf {x},t)}}}}$ in infinite dimensions, with potentially infinite dimensional stable, unstable and center manifolds. Further, they usefully generalised the definition of the manifolds so that the center manifold is associated with eigenvalues such that $|\operatorname {Re} \lambda |\leq \alpha $, the stable manifold with eigenvalues $\operatorname {Re} \lambda \leq -\beta \<-r\alpha $, and unstable manifold with eigenvalues $\operatorname {Re} \lambda \geq \beta \>r\alpha $. They proved existence of these manifolds, and the emergence of a center manifold, via nonlinear coordinate transforms.

Potzsche and Rasmussen established a corresponding approximation theorem for such infinite dimensional, non-autonomous systems.

### Alternative backwards theory

All the extant theory mentioned above seeks to establish invariant manifold properties of a specific given problem. In particular, one constructs a manifold that approximates an invariant manifold of the given system. An alternative approach is to construct exact invariant manifolds for a system that approximates the given system---called a backwards theory. The aim is to usefully apply theory to a wider range of systems, and to estimate errors and sizes of domain of validity.

This approach is cognate to the well-established backward error analysis in numerical modeling.

## Center manifold and the analysis of nonlinear systems

As the stability of the equilibrium correlates with the "stability" of its manifolds, the existence of a center manifold brings up the question about the dynamics on the center manifold. This is analyzed by the center manifold reduction, which, in combination with some system parameter μ, leads to the concepts of bifurcations.

## Examples

The Wikipedia entry on slow manifolds gives more examples.

### A simple example

Consider the system

$$\dot {x}=x^{2},\quad {\dot {y}=y.}$$

The unstable manifold at the origin is the *y* axis, and the stable manifold is the trivial set {(0, 0)}. Any orbit not on the stable manifold satisfies an equation of the form $y=Ae^{-1/x}$ for some real constant *A*. It follows that for any real *A*, we can create a center manifold by piecing together the curve $y=Ae^{-1/x}$ for *x* \> 0 with the negative *x* axis (including the origin). Moreover, all center manifolds have this potential non-uniqueness, although often the non-uniqueness only occurs in unphysical complex values of the variables.

### Delay differential equations often have Hopf bifurcations

Another example shows how a center manifold models the Hopf bifurcation that occurs for parameter $a\approx 4$ in the delay differential equation $dx}/{dt}=-ax(t-1)-2x^{2}-x^{3$. Strictly, the delay makes this DE infinite-dimensional.

Fortunately, we may approximate such delays by the following trick that keeps the dimensionality finite. Define $u\_{1}(t)=x(t)$ and approximate the time-delayed variable, $x(t-1)\approx u\_{3}(t)$, by using the intermediaries $du\_{2}/{dt}=2(u\_{1}-u\_{2})$ and $du\_{3}/{dt}=2(u\_{2}-u\_{3})$.

For parameter near critical, $a=4+\alpha $, the delay differential equation is then approximated by the system

$$\frac {d{\textbf {u}{dt}=\left\[{\begin{array}{ccc}0&0&-4\\2&-2&0\\0&2&-2\end{array}\right\]{\textbf {u}+\left\[{\begin{array}{c}-\alpha u\_{3}-2u\_{1}^{2}-u\_{1}^{3}\\0\\0\end{array}\right\].}}}}}$$

In terms of a complex amplitude $s(t)$ and its complex conjugate $\bar {s}(t)$, the center manifold is

$$\textbf {u}=\left\[{\begin{array}{c}e^{i2t}s+e^{-i2t}{\bar {s}\\\{\frac {1-i}{2}e^{i2t}s+{\frac {1+i}{2}e^{-i2t}{\bar {s}\\\-{\frac {i}{2}e^{i2t}s+{\frac {i}{2}e^{-i2t}{\bar {s}\end{array}\right\]+{O}(\alpha +|s|^{2})}}}}}}}}$$

and the evolution on the center manifold is

$$\frac {ds}{dt}=\left\[{\frac {1+2i}{10}\alpha s-{\frac {3+16i}{15}|s|^{2}s\right\]+{O}(\alpha ^{2}+|s|^{4})}}$$

This evolution shows the origin is linearly unstable for $\alpha \>0\ (a\>4)$, but the cubic nonlinearity then stabilises nearby limit cycles as in classic Hopf bifurcation.

1. Roberts, A.J. (1993). "The invariant manifold of beam deformations. Part 1: the simple circular rod". *J. Elast*. **30**: 1–54. doi:10.1007/BF00041769. S2CID 123743932.
2. Aulbach, B.; Wanner, T. (2000). "The Hartman–Grobman theorem for Caratheodory-type differential equations in Banach spaces". *Nonlinear Analysis*. **40** (1–8): 91–104. doi:10.1016/S0362-546X(00)85006-3.
3. Carr, Jack (1981). *Applications of centre manifold theory*. Applied Mathematical Sciences. Vol. 35. Springer-Verlag. doi:10.1007/978-1-4612-5929-9. ISBN 978-0-387-90577-8.
4. Kelley, A. (1967). "The stable, center-stable, center, center-unstable and unstable manifolds". *J. Differential Equations*. **3** (4): 546–570. Bibcode:1967JDE.....3..546K. doi:10.1016/0022-0396(67)90016-2.
5. Guckenheimer & Holmes (1997), Section 3.2
6. Guckenheimer & Holmes (1997), Theorem 3.2.1
7. Murdock, James (2003). *Normal forms and unfoldings for local dynamical systems*. Springer-Verlag.
8. Iooss, G.; Adelmeyer, M. (1992). *Topics in Bifurcation Theory*. p. 7.
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10. Aulbach, B.; Wanner, T. (1996). "Integral manifolds for Caratheodory type differential equations in Banach spaces". In Aulbach, B.; Colonius, F. (eds.). *Six Lectures on Dynamical Systems*. Singapore: World Scientific. pp. 45–119. ISBN 9789810225483.
11. Aulbach, B.; Wanner, T. (1999). "Invariant foliations for Caratheodory type differential equations in Banach spaces". In Lakshmikantham, V.; Martynyuk, A. A. (eds.). *Advances of Stability Theory at the End of XX Century*. Gordon & Breach.
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13. Potzsche, C.; Rasmussen, M. (2006). "Taylor approximation of integral manifolds". *Journal of Dynamics and Differential Equations*. **18** (2): 427–460. Bibcode:2006JDDE...18..427P. doi:10.1007/s10884-006-9011-8. S2CID 59366945.
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15. Hochs, Peter; Roberts, A.J. (2019). "Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions". *J. Differential Equations*. **267** (12): 7263–7312. arXiv:1906.04420. Bibcode:2019JDE...267.7263H. doi:10.1016/j.jde.2019.07.021. S2CID 184487247.
16. Chicone 2010, p. 344.

### Further reading