title: Oreonebria atrata

abstract: Oreonebria atrata is a species of ground beetle in the Nebriinae subfamily that is endemic to Austria.

text:
# Oreonebria atrata

***Oreonebria atrata*** is a species of ground beetle in the Nebriinae subfamily that is endemic to Austria.

## InfoBox

| *Oreonebria atrata* | |
| --- | --- |
|
| Scientific classification | |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Carabidae |
| Genus: | *Oreonebria* |
| Species: | ***O. atrata*** |
| Binomial name | |
| ***Oreonebria atrata***<br>(Dejean, 1826) | |
|
| Synonyms | |
| * *Nebria atrata* Dejean, 1826 | |


title: Mordella vesconis

abstract: Mordella vesconis is a species of beetle in the genus Mordella of the family Mordellidae, which is part of the superfamily Tenebrionoidea. It was discovered in 1851.

text:
# Mordella vesconis

***Mordella vesconis*** is a species of beetle in the genus *Mordella* of the family Mordellidae, which is part of the superfamily Tenebrionoidea. It was discovered in 1851.

## InfoBox

| *Mordella vesconis* | |
| --- | --- |
|
| Scientific classification | |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Suborder: | Polyphaga |
| Family: | Mordellidae |
| Subfamily: | Mordellinae |
| Tribe: | Mordellini |
| Genus: | *Mordella* |
| Species: | ***M. vesconis*** |
| Binomial name | |
| ***Mordella vesconis***<br>Solier, 1851 | |
|


title: Mircea Bolba

abstract: Mircea Bolba was a Romanian football midfielder and manager.

text:
# Mircea Bolba

**Mircea Bolba** (31 October 1961 – 6 January 2021) was a Romanian football midfielder and manager.

## Career

As a footballer, Bolba played for Olimpia Satu Mare, Steaua București, ASA Târgu Mureș, Politehnica Timișoara and FC Bihor Oradea, among others. After retirement, Bolba started his career as a manager, coaching over years especially teams from Satu Mare County, such as Olimpia Satu Mare (several times), Fink Fester Petrești, Talna Orașu Nou or Turul Micula. Bolba also managed other teams, especially from the region of Transylvania, among them Arieșul Turda, Silvania Șimleu Silvaniei, Unirea Dej or Someșul Dej.

Mircea Bolba died in the morning of 6 January 2021, at the age of 59. At the moment of death, he was the manager of Olimpia MCMXXI Satu Mare, a fan-owned football club and also a phoenix club of Olimpia Satu Mare.

Bolba died from COVID-19 in 2020.

## InfoBox

Mircea Bolba
| Personal information | | | |
| --- | --- | --- | --- |
| Date of birth | (1961-10-30)30 October 1961 | | |
| Place of birth | Craidorolț, Romania | | |
| Date of death | 6 January 2021(2021-01-06) (aged 59) | | |
| Place of death | Satu Mare, Romania | | |
| Position(s) | Midfielder | | |
| Senior career\* | | | |
| Years | **Team** | **Apps** | **(Gls)** |
| 1977–1980 | Olimpia Satu Mare | 20 | (4) |
| 1980–1981 | Steaua București | 8 | (1) |
| 1981–1982 | ASA Târgu Mureș | 19 | (2) |
| 1982–1984 | Olimpia Satu Mare |  | (11) |
| 1984–1987 | Politehnica Timișoara | 74 | (49) |
| 1987–1989 | Olimpia Satu Mare |  | (14) |
| 1989–1990 | Bihor Oradea | 25 | (7) |
| 1990 | Sportul 30 Decembrie |  | (0) |
| 1990–1991 | Evagoras Paphos |  | (12) |
| 1991–1992 | Armătura Zalău |  | (0) |
| 1992–1993 | Inter Sibiu | 3 | (0) |
| 1993 | Armătura Zalău |  | (0) |
| 1995 | Olimpia Satu Mare | 9 | (1) |
| Total |  | **158** | **(101)** |
| International career | | | |
| 1981 | Romania U20 | 3 | (0) |
| Managerial career | | | |
| 2004–2006 | Olimpia Satu Mare | | |
| 2006 | Fink Fester Petrești | | |
| 2007 | Olimpia Satu Mare | | |
| 2007 | Talna Orașu Nou | | |
| 2007–2008 | Arieșul Turda | | |
| 2008 | Silvania Șimleu Silvaniei | | |
| 2008–2009 | Unirea Dej | | |
| 2010 | Talna Orașu Nou | | |
| 2010–2011 | Olimpia II Satu Mare | | |
| 2011 | FCMU Baia Mare | | |
| 2011–2012 | Unirea Dej | | |
| 2011–2016 | Olimpia II Satu Mare | | |
| 2016 | Olimpia Satu Mare | | |
| 2017 | Olimpia Satu Mare (assistant) | | |
| 2018 | Turul Micula | | |
| 2018 | Unirea Dej | | |
| 2018–2019 | Someșul Dej | | |
| 2020 | Someșul Dej | | |
| 2020–2021 | Olimpia Satu Mare | | |
| Medal record      Representing  Romania  FIFA World Youth Championship  FIFA U-20 World Cup 1981 | | | |
| \*Club domestic league appearances and goals | | | |


title: Kasibugga

abstract: Kasibugga is a twin-town in Srikakulam district of the Indian state of Andhra Pradesh. It is a municipality and the part in mandal of Palasa.

text:
# Kasibugga

**Kasibugga** is a twin-town in Srikakulam district of the Indian state of Andhra Pradesh. It is a municipality and the part in mandal of Palasa .

## Geography

Kasibugga is located at 18° 45' 33N 84° 24' 58E. It has an average elevation of 38 meters (127 feet).

## Administration

Kasibugga comes under Palasa (Assembly constituency) and the urban local body is ruled by Palasa-Kasibugga Municipality.

## Transport

Kasibugga is well connected with major cities in the state of Andhra Pradesh like Visakhapatnam and other cities and towns in Telangana and Odisha. National Highway 16(formerly NH5) bypasses through the town.

The nearest railway station is Palasa railway station which is connected to the town.

## InfoBox

| Kasibugga | |
| --- | --- |
| town | |
| KT Road | |
| KasibuggaLocation in Andhra Pradesh, India | |
| Coordinates: 18°45′50″N 84°25′27″E / 18.764006°N 84.424130°E / 18.764006; 84.424130 | |
| Country | India |
| State | Andhra Pradesh |
| District | Srikakulam |
| Government | |
| Type | Municipality |
| Body | Palasa-Kasibugga Municipality, SUDA |
| Languages | |
| Official | Telugu |
| Time zone | UTC+5:30 (IST) |
| PIN | 532222 |
| Telephone code | 08945 |
| Vehicle registration | AP-30 (former)<br>AP–39 (from 30 January 2019) |
| Website | Palasa–Kasibugga Municipality |


title: Frederick Byron (cricketer)

abstract: Hon. Frederick Byron was an English first-class cricketer and barrister. The son of George Byron, 7th Baron Byron, he was born at Cheltenham in February 1822. He was educated at Westminster School, before going up to Balliol College, Oxford. While studying at Oxford, Byron made a single appearance in first-class cricket for Oxford University against the Marylebone Cricket Club at Oxford in 1841. Batting twice in the match, he was dismissed for 6 runs by James Cobbett in the Oxford first-innings, while in their second-innings he was dismissed for 2 runs by the same bowler. He became a fellow at All Souls College in 1843. After graduating from Oxford, he became a member of Lincoln's Inn and was called to the bar in 1848. He was commissioned as a lieutenant in the Sherwood Foresters in April 1850. Byron was appointed as a deputy lieutenant for Essex in September 1853. He was promoted to captain in the Sherwood Foresters in March 1859. Byron married Mary Jane Wescomb in 1851, with the couple having three children. He died suddenly at Westminster in April 1861, predeceasing his father. Byron's son George later became the 9th Baron Byron upon the death of Bryon's elder brother, George Byron, 8th Baron Byron.

text:
# Frederick Byron (cricketer)

**Hon. Frederick Byron** DL (3 February 1822 – 4 April 1861) was an English first-class cricketer and barrister.

The son of George Byron, 7th Baron Byron, he was born at Cheltenham in February 1822. He was educated at Westminster School, before going up to Balliol College, Oxford. While studying at Oxford, Byron made a single appearance in first-class cricket for Oxford University against the Marylebone Cricket Club at Oxford in 1841. Batting twice in the match, he was dismissed for 6 runs by James Cobbett in the Oxford first-innings, while in their second-innings he was dismissed for 2 runs by the same bowler. He became a fellow at All Souls College in 1843.

After graduating from Oxford, he became a member of Lincoln's Inn and was called to the bar in 1848. He was commissioned as a lieutenant in the Sherwood Foresters in April 1850. Byron was appointed as a deputy lieutenant for Essex in September 1853. He was promoted to captain in the Sherwood Foresters in March 1859. Byron married Mary Jane Wescomb in 1851, with the couple having three children. He died suddenly at Westminster in April 1861, predeceasing his father. Byron's son George later became the 9th Baron Byron upon the death of Bryon's elder brother, George Byron, 8th Baron Byron.

## InfoBox

Frederick Byron
| Personal information | |
| --- | --- |
| Full name | Frederick Byron |
| Born | 2 February 1822
Cheltenham, Gloucestershire,
England |
| Died | 4 April 1861(1861-04-04) (aged 39)
Westminster, London, England |
| Batting | Unknown |
| Domestic team information | |
| Years | Team |
| 1841 | Oxford University |
|  | |
| Career statistics | |
| Competition First-class  Matches 1  Runs scored 8  Batting average 4.00  100s/50s –/–  Top score 6  Catches/stumpings 2/– | |
|  | |
| Source: Cricinfo, 4 February 2020 | |


title: Wakehurst F.C.

abstract: Wakehurst Football Club are a Northern Irish, intermediate football club who currently play in the Ballymena & Provincial Football League. The club, founded in 1969, hails from Ballymena, although home matches are played at Moyola Park's ground at Mill Meadow. Wakehurst formerly played at the second pitch at the Ballymena Showgrounds, home of Ballymena United, but for 2009–10 this pitch was deemed not to meet the criteria for the Championship, and home games were played at the ground of Tobermore United in Tobermore, County Londonderry, for that season; Wakehurst moved to Castledawson for 2010–11. It is the club's intention eventually to return to Ballymena. In 2016, the club was relegated from the Northern Ireland Football League and spent a season in the Ballymena & Provincial Football League before announcing their withdrawal from the competition. Club colours are black, and white (home) and blue (away). The club is currently managed by John Clarke. The club returned to the Ballymena & Provincial League for the 2016–17 season and were joined by fellow Championship 2 drop outs, Glebe Rangers and Coagh United. At the end of the season they announced their withdrawal from football although indicated that it would be a one-year hiatus rather than permanent. The club played at junior level in the Ballymena & District League and Northern Amateur League until stepping up to intermediate football in 2003.

text:
# Wakehurst F.C.

**Wakehurst Football Club** are a Northern Irish, intermediate football club who currently play in the Ballymena & Provincial Football League. The club, founded in 1969, hails from Ballymena, although home matches are played at Moyola Park's ground at Mill Meadow. Wakehurst formerly played at the second pitch at the Ballymena Showgrounds, home of Ballymena United, but for 2009–10 this pitch was deemed not to meet the criteria for the Championship, and home games were played at the ground of Tobermore United in Tobermore, County Londonderry, for that season; Wakehurst moved to Castledawson for 2010–11. It is the club's intention eventually to return to Ballymena. In 2016, the club was relegated from the Northern Ireland Football League and spent a season in the Ballymena & Provincial Football League before announcing their withdrawal from the competition.

Club colours are black, and white (home) and blue (away).

The club is currently managed by John Clarke.

The club returned to the Ballymena & Provincial League for the 2016–17 season and were joined by fellow Championship 2 drop outs, Glebe Rangers and Coagh United. At the end of the season they announced their withdrawal from football although indicated that it would be a one-year hiatus rather than permanent.

The club played at junior level in the Ballymena & District League and Northern Amateur League until stepping up to intermediate football in 2003.

## Players

### Current First Team Squad

As of

Note: Flags indicate national team as defined under FIFA eligibility rules. Players may hold more than one non-FIFA nationality.

| No. Pos. Nation Player  GK  NIR Greg Shannon  GK  NIR Andy Findlay  GK  NIR Dean Adams  DF  NIR Kyle Crawford  DF  NIR Kurtis McCartney  DF  NIR Peter McClure  DF  NIR Andrew Millar  DF  NIR Corey Price  DF  NIR Anthony Shaw  DF  NIR Niall Swann | No. Pos. Nation Player  DF  NIR Conor Ross  MF  NIR Ryan Bamber  MF  NIR Andrew Laughlin  MF  NIR Nicky Black  MF  NIR David McLaughlin  MF  NIR Steven Mellon  MF  NIR David Johnston  MF  NIR Aaran Weir |
| --- | --- |

## Honours

### Junior honours

* **County Antrim Junior Shield: 1**
    + 1989–90

## InfoBox

Wakehurst
| Full name | Wakehurst Football Club |
| --- | --- |
| Nickname(s) | The 'Hurst |
| Founded | 1969 |
| Ground | Mill Meadow |
| Manager | John Clarke |
| League | Ballymena & Provincial Football League |
| 2018–19 | Ballymena & Provincial Football League, 11th |
|  | |
|  | |
|  | |


title: Heart of the Dragon (British TV series)

abstract: Heart of the Dragon is a 1984 British documentary television series directed by David Kennard. It covered life in China, with 12 one hour episodes, each on a different aspect of Chinese life. It was first aired in England on Channel 4, and in the United States by PBS. The 12-episode series won several international awards, including an Emmy.

text:
# Heart of the Dragon (British TV series)

***Heart of the Dragon*** is a 1984 British documentary television series directed by David Kennard. It covered life in China, with 12 one hour episodes, each on a different aspect of Chinese life. It was first aired in England on Channel 4, and in the United States by PBS. The 12-episode series won several international awards, including an Emmy.

## Awards

| Year | Award | Category | Result |
| --- | --- | --- | --- |
| 1984 | 12th International Emmy Awards | Best Documentary | Won |
| 1985 | Primetime Emmy Award | Outstanding Informational Series | Nominated |
| 1985 | BAFTA Awards | Best Factual Series | Nominated |
| 1985 | BAFTA Awards | Best Editing | Nominated |
|

## InfoBox

| *Heart of the Dragon* | |
| --- | --- |
| Directed by | David Kennard |
| Starring | Anthony Quayle |
| Country of origin | England |
| Original language | English |
| No. of seasons | 1 |
| No. of episodes | 12 |
| Production | |
| Executive producers | Alasdair Clayre
Peter Montagnon
Nigel Houghton |
| Running time | 57 minutes |
| Production company | Channel 4 Television Corporation |
| Original release | |
| Network | Channel 4 |


title: Hamworthy United F.C.

abstract: Hamworthy United Football Club is a football club based in Hamworthy, a suburb of Poole, England. Formed in 1970 as a merger of Hamworthy and Trinidad Old Boys, they are currently members of the Wessex League Division One and play at the County Ground. The club are affiliated to the Dorset FA.

text:
# Hamworthy United F.C.

**Hamworthy United Football Club** is a football club based in Hamworthy, a suburb of Poole, England. Formed in 1970 as a merger of Hamworthy and Trinidad Old Boys, they are currently members of the Wessex League Division One and play at the County Ground. The club are affiliated to the Dorset FA.

## History

### Pre-merger

Hamworthy Football Club was established in 1926, and were founder members of the Dorset Combination in 1957. Trinidad Old Boys joined the Dorset Combination in 1965.

### Post-merger

The two clubs merged in 1970 to form Hamworthy United, continuing in the Dorset Combination and playing at Hamworthy's County Ground. They were Dorset Combination champions in 1976–77 and won the League Cup in 1989–90. In 2002 the league was renamed the Dorset Premier League, with Hamworthy going on to win the league in its first season under the new name. They retained the title the following season, also winning the league's Charity Shield, and were promoted to Division One of the Wessex League.

In their first season in the Wessex League, Hamworthy won the League Cup, defeating Thatcham Town in the final. They went on to win the Dorset Senior Cup the following season with a 2–1 win over Poole Town in the final. In 2006 Division One of the Wessex League was renamed the Premier Division. They reached the final of the League Cup in 2008–09 and the Dorset Senior Cup in 2013–14, but lost in both matches.

Hamworthy won the Wessex League Cup in 2020–21, beating United Services Portsmouth 3–1 in the final. The 2021–22 season saw the club win the Premier Division, earning promotion to Division One South of the Southern League. At the start of the 2022–23 season they won the inaugural Wessex League Charity Shield, defeating Shaftesbury 2–0. The club went on to finish third in Division One South, qualifying for the promotion play-offs. After beating Evesham United 3–0 in the semi-finals, they lost the final 2–0 to Sholing. In October 2023 the club withdrew from the Southern League, stating that they would focus on their reserve team in the Dorset Premier League.

## Ground

Hamworthy moved to the County Ground in 1950. A new grandstand was built in 1956 and opened by Stanley Rous. The ground became home to the new club after the 1970 merger. In 2023 the grandstand was condemned after failing safety checks.

## Honours

* **Wessex League**
    + Premier Division champions 2021–22
    + League Cup winners 2004–05, 2020–21
    + Charity Shield winners 2022–23
* **Dorset Premier League**
    + Champions 1976–77, 2002–03, 2003–04
    + League Cup winners 1989–90
    + Charity Shield winners 2003–04
* **Dorset Senior Cup**
    + Winners 2005–06

## Records

50°42′54″N 2°00′05″W / 50.71500°N 2.00139°W / 50.71500; -2.00139

## InfoBox

Hamworthy United
|  | |
| --- | --- |
| Full name | Hamworthy United Football Club |
| Nickname(s) | The Hammers |
| Founded | 1970 |
| Ground | The County Ground, Hamworthy |
| Capacity | 2,000 |
| Manager | Dan Cann |
| League | Wessex League Division One |
| 2023–24 | Southern League Division One South (withdrew) |
| Website | Club website |
|  | |
|  | |
|  | |


title: Haploparmena

abstract:
Haploparmena is a genus of longhorn beetles of the subfamily Lamiinae, containing the following species:
  - Haploparmena angolana Aurivillius, 1913
  - Haploparmena marmorata Breuning, 1940

text:
# Haploparmena

***Haploparmena*** is a genus of longhorn beetles of the subfamily Lamiinae, containing the following species:

## InfoBox

| *Haploparmena* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Cerambycidae |
| Tribe: | Morimopsini |
| Genus: | *Haploparmena* |
|


title: Industrial Extraction

abstract: Industrial Extraction is the process by which harmful air contaminants are removed from the work place for the protection of employees and the environment. In the UK, the Health and Safety Executive has implemented COSHH regulations to ensure all industrial workplaces protect the health of their employees via effective Local Exhaust Ventilation (LEV). This policy is now being mirrored in other parts of the world including China and North America. Harmful air contaminants can be particles, gases or vapours and/or combinations or all three. ‘Particles’ include dusts, fumes, mists and fibres.

text:
# Industrial Extraction

**Industrial Extraction** is the process by which harmful air contaminants are removed from the work place for the protection of employees and the environment.

In the UK, the Health and Safety Executive has implemented COSHH regulations to ensure all industrial workplaces protect the health of their employees via effective Local Exhaust Ventilation (LEV). This policy is now being mirrored in other parts of the world including China and North America.

Harmful air contaminants can be particles, gases or vapours and/or combinations or all three. ‘Particles’ include dusts, fumes, mists and fibres.

## Extraction systems

Extraction systems to remove airborne particles from industrial workplaces have been in use for a number of years.

### Centrifugal systems

Centrifugal systems are used in a wide range of manufacturing applications in industries including aerospace, automotive, medical, defence and food production. These systems use a perforated drum with specially designed vanes which rotate at very high speeds. Oil mist is drawn into the unit and impacts on the vanes at high velocity and specially designed synthetic pads assist the collection process and filter out stray solid particles.

The centrifugal force then pushes the oil to the unit’s outer case where it drains back to the machine for re-use or collection and clean air is returned to the workshop through the top of the unit. The dangerous particles have been removed and employees are protected from the potential health hazards associated with breathing in polluted air.

1. "COSHH and engineering workers – key messages – COSHH".
2. "Local exhaust ventilation – workplace fume and dust extraction".
3. Controlling airborne contaminants at work: A guide to local exhaust ventilation LEV, HSE 2011, Page 11.


title: Morrisby Profile

text:
# Morrisby Profile

The Morrisby Profile is a matched series of timed cognitive aptitude tests. The current version is screen-based and was first published in 2014. In this version, five different aptitudes are assessed: verbal, numerical, abstract, spatial and mechanical. The assessments each present a series of items and the candidate selects their answer from the options provided. The first three tests have two parts each. Each section is preceded by some untimed practice items. The results are normed against a standardisation sample. Norms are available to a lower limit of 14 years of age. See Norm-referenced test. The results are presented as a bar chart, forming a profile of the individual's results on the five measures.

## Questionnaires

The five aptitude assessments are presented alongside an untimed careers interest questionnaire. This is a Likert scale based questionnaire of up to 103 questions. The results are ipsative and indicate relative strength of interest in 10 career interest categories, 5 workstyle and 4 workplace dimensions. An optional, untimed Personality Test is also available. This follows a similar structure to the Myers Briggs Type Indicator but breaks with Personality type theory in that it permits indistinct results on each of the four bi-polar scales giving 81 potential categorisations.

The total administration time for the five aptitude assessments and both questionnaires is typically a little under 1 hour 40 minutes.

## Context

The Morrisby Profile is only available within the Morrisby Careers platform. The results are used to generate career, subject and study suggestions. The system links to the Gatsby career benchmarks and the SkillsBuilder essential skills framework. It carries the Career Development Institute's Career Assured award and the matrix accreditation.

## History

The Morrisby Profile is derived from the Differential Test Battery developed by John Morrisby in the UK and first published in 1955. This was heavily revised, although following a similar format to its precursor, and renamed Morrisby Profile in 1991. A further revision occurred in 2005 which was finally discontinued in 2020. All these versions were paper and pencil based and comprised six aptitude tests coupled with 4 personality metrics and a pair of optional dexterity tests. The current online version has been available since 2014.


title: Root of unity

abstract: In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform. Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly n nth roots of unity, except when n is a multiple of the (positive) characteristic of the field.

text:
# Root of unity

In mathematics, a **root of unity**, occasionally called a **de Moivre number**, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform.

Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly n nth roots of unity, except when n is a multiple of the (positive) characteristic of the field.

## General definition

An *nth root of unity*, where n is a positive integer, is a number z satisfying the equation $z^{n}=1.$ Unless otherwise specified, the roots of unity may be taken to be complex numbers (including the number 1, and the number −1 if n is even, which are complex with a zero imaginary part), and in this case, the nth roots of unity are $\exp \left({\frac {2k\pi i}{n}\right)=\cos {\frac {2k\pi }{n}+i\sin {\frac {2k\pi }{n},\qquad k=0,1,\dots ,n-1.}}}$

However, the defining equation of roots of unity is meaningful over any field (and even over any ring) *F*, and this allows considering roots of unity in *F*. Whichever is the field *F*, the roots of unity in *F* are either complex numbers, if the characteristic of *F* is 0, or, otherwise, belong to a finite field. Conversely, every nonzero element in a finite field is a root of unity in that field. See Root of unity modulo *n* and Finite field for further details.

An nth root of unity is said to be **primitive** if it is not an mth root of unity for some smaller m, that is if

$$z^{n}=1\quad {\text{and}\quad z^{m}\neq 1{\text{ for }m=1,2,3,\ldots ,n-1.}}$$

If *n* is a prime number, then all *n*th roots of unity, except 1, are primitive.

In the above formula in terms of exponential and trigonometric functions, the primitive nth roots of unity are those for which k and n are coprime integers.

Subsequent sections of this article will comply with complex roots of unity. For the case of roots of unity in fields of nonzero characteristic, see Finite field § Roots of unity. For the case of roots of unity in rings of modular integers, see Root of unity modulo *n*.

## Elementary properties

Every *n*th root of unity *z* is a primitive *a*th root of unity for some *a**n*, which is the smallest positive integer such that *z**a* = 1.

Any integer power of an *n*th root of unity is also an *n*th root of unity, as

$$(z^{k})^{n}=z^{kn}=(z^{n})^{k}=1^{k}=1.$$

This is also true for negative exponents. In particular, the reciprocal of an *n*th root of unity is its complex conjugate, and is also an *n*th root of unity:

$$\frac {1}{z}=z^{-1}=z^{n-1}={\bar {z}.}$$

If *z* is an *n*th root of unity and *a*  *b* (mod *n*) then *z**a* = *z**b*. Indeed, by the definition of congruence modulo *n*, *a* = *b* \+ *kn* for some integer *k*, and hence

$$z^{a}=z^{b+kn}=z^{b}z^{kn}=z^{b}(z^{n})^{k}=z^{b}1^{k}=z^{b}.$$

Therefore, given a power *z**a* of *z*, one has *z**a* = *z**r*, where 0 ≤ *r* \< *n* is the remainder of the Euclidean division of a by n.

Let *z* be a primitive *n*th root of unity. Then the powers *z*, *z*2, ..., *z**n*−1, *z**n* = *z*0 = 1 are *n*th roots of unity and are all distinct. (If *z**a* = *z**b* where 1 ≤ *a* \< *b**n*, then *z**b**a* = 1, which would imply that *z* would not be primitive.) This implies that *z*, *z*2, ..., *z**n*−1, *z**n* = *z*0 = 1 are all of the *n*th roots of unity, since an *n*th-degree polynomial equation over a field (in this case the field of complex numbers) has at most *n* solutions.

From the preceding, it follows that, if *z* is a primitive *n*th root of unity, then $z^{a}=z^{b}$ if and only if $a\equiv b{\pmod {n}.}$ If *z* is not primitive then $a\equiv b{\pmod {n}}$ implies $z^{a}=z^{b},$ but the converse may be false, as shown by the following example. If *n* = 4, a non-primitive *n*th root of unity is *z* = –1, and one has $z^{2}=z^{4}=1$, although $2\not \equiv 4{\pmod {4}.}$

Let *z* be a primitive *n*th root of unity. A power *w* = *z**k* of z is a primitive *a*th root of unity for

$$a={\frac {n}{\gcd(k,n)},}$$

where $\gcd(k,n)$ is the greatest common divisor of n and k. This results from the fact that *ka* is the smallest multiple of k that is also a multiple of n. In other words, *ka* is the least common multiple of k and n. Thus

$$a={\frac {\operatorname {lcm} (k,n)}{k}={\frac {kn}{k\gcd(k,n)}={\frac {n}{\gcd(k,n)}.}}}$$

Thus, if *k* and *n* are coprime, *zk* is also a primitive *n*th root of unity, and therefore there are *φ*(*n*) distinct primitive *n*th roots of unity (where *φ* is Euler's totient function). This implies that if *n* is a prime number, all the roots except +1 are primitive.

In other words, if R(*n*) is the set of all *n*th roots of unity and P(*n*) is the set of primitive ones, R(*n*) is a disjoint union of the P(*n*):

$$\operatorname {R} (n)=\bigcup \_{d\\,|\\,n}\operatorname {P} (d),$$

where the notation means that *d* goes through all the positive divisors of *n*, including 1 and *n*.

Since the cardinality of R(*n*) is *n*, and that of P(*n*) is *φ*(*n*), this demonstrates the classical formula

$$\sum \_{d\\,|\\,n}\varphi (d)=n.$$

## Group properties

### Group of all roots of unity

The product and the multiplicative inverse of two roots of unity are also roots of unity. In fact, if *xm* = 1 and *yn* = 1, then (*x*−1)*m* = 1, and (*xy*)*k* = 1, where *k* is the least common multiple of *m* and *n*.

Therefore, the roots of unity form an abelian group under multiplication. This group is the torsion subgroup of the circle group.

### Group of *n*th roots of unity

For an integer *n*, the product and the multiplicative inverse of two *n*th roots of unity are also *n*th roots of unity. Therefore, the *n*th roots of unity form an abelian group under multiplication.

Given a primitive *n*th root of unity *ω*, the other *n*th roots are powers of *ω*. This means that the group of the *n*th roots of unity is a cyclic group. It is worth remarking that the term of *cyclic group* originated from the fact that this group is a subgroup of the circle group.

### Galois group of the primitive *n*th roots of unity

Let $\mathbb {Q} (\omega )$ be the field extension of the rational numbers generated over $\mathbb {Q} $ by a primitive *n*th root of unity *ω*. As every *n*th root of unity is a power of *ω*, the field $\mathbb {Q} (\omega )$ contains all *n*th roots of unity, and $\mathbb {Q} (\omega )$ is a Galois extension of $\mathbb {Q} .$

If *k* is an integer, *ωk* is a primitive *n*th root of unity if and only if *k* and *n* are coprime. In this case, the map

$$\omega \mapsto \omega ^{k}$$

induces an automorphism of $\mathbb {Q} (\omega )$, which maps every *n*th root of unity to its *k*th power. Every automorphism of $\mathbb {Q} (\omega )$ is obtained in this way, and these automorphisms form the Galois group of $\mathbb {Q} (\omega )$ over the field of the rationals.

The rules of exponentiation imply that the composition of two such automorphisms is obtained by multiplying the exponents. It follows that the map

$$k\mapsto \left(\omega \mapsto \omega ^{k}\right)$$

defines a group isomorphism between the units of the ring of integers modulo *n* and the Galois group of $\mathbb {Q} (\omega ).$

This shows that this Galois group is abelian, and implies thus that the primitive roots of unity may be expressed in terms of radicals.

### Galois group of the real part of the primitive roots of unity

The real part of the primitive roots of unity are related to one another as roots of the minimal polynomial of $2\cos(2\pi /n).$ The roots of the minimal polynomial are just twice the real part; these roots form a cyclic Galois group.

## Trigonometric expression

De Moivre's formula, which is valid for all real x and integers n, is

$$\left(\cos x+i\sin x\right)^{n}=\cos nx+i\sin nx.$$

Setting *x* = /*n* gives a primitive nth root of unity – one gets

$$\left(\cos {\frac {2\pi }{n}+i\sin {\frac {2\pi }{n}\right)^{n}=\cos 2\pi +i\sin 2\pi =1,}}$$

but

$$\left(\cos {\frac {2\pi }{n}+i\sin {\frac {2\pi }{n}\right)^{k}=\cos {\frac {2k\pi }{n}+i\sin {\frac {2k\pi }{n}\neq 1}}}}$$

for *k* = 1, 2, …, *n* − 1. In other words,

$$\cos {\frac {2\pi }{n}+i\sin {\frac {2\pi }{n}}}$$

is a primitive nth root of unity.

This formula shows that in the complex plane the nth roots of unity are at the vertices of a regular n-sided polygon inscribed in the unit circle, with one vertex at 1 (see the plots for *n* = 3 and *n* = 5 on the right). This geometric fact accounts for the term "cyclotomic" in such phrases as cyclotomic field and cyclotomic polynomial; it is from the Greek roots "cyclo" (circle) plus "tomos" (cut, divide).

Euler's formula

$$e^{ix}=\cos x+i\sin x,$$

which is valid for all real x, can be used to put the formula for the nth roots of unity into the form

$$e^{2\pi i{\frac {k}{n},\quad 0\leq k\<n.}}$$

It follows from the discussion in the previous section that this is a primitive nth-root if and only if the fraction *k*/*n* is in lowest terms; that is, that k and n are coprime. An irrational number that can be expressed as the real part of the root of unity; that is, as $\cos(2\pi k/n)$, is called a trigonometric number.

## Algebraic expression

The *n*th roots of unity are, by definition, the roots of the polynomial *xn* − 1, and are thus algebraic numbers. As this polynomial is not irreducible (except for *n* = 1), the primitive *n*th roots of unity are roots of an irreducible polynomial (over the integers) of lower degree, called the *n*th cyclotomic polynomial, and often denoted Φ*n*. The degree of Φ*n* is given by Euler's totient function, which counts (among other things) the number of primitive *n*th roots of unity. The roots of Φ*n* are exactly the primitive *n*th roots of unity.

Galois theory can be used to show that the cyclotomic polynomials may be conveniently solved in terms of radicals. (The trivial form $\sqrt\[{n}\]{1}$ is not convenient, because it contains non-primitive roots, such as 1, which are not roots of the cyclotomic polynomial, and because it does not give the real and imaginary parts separately.) This means that, for each positive integer n, there exists an expression built from integers by root extractions, additions, subtractions, multiplications, and divisions (and nothing else), such that the primitive nth roots of unity are exactly the set of values that can be obtained by choosing values for the root extractions (k possible values for a kth root). (For more details see § Cyclotomic fields, below.)

Gauss proved that a primitive nth root of unity can be expressed using only square roots, addition, subtraction, multiplication and division if and only if it is possible to construct with compass and straightedge the regular n-gon. This is the case if and only if *n* is either a power of two or the product of a power of two and Fermat primes that are all different.

If z is a primitive nth root of unity, the same is true for 1/*z*, and $r=z+{\frac {1}{z}}$ is twice the real part of z. In other words, Φ*n* is a reciprocal polynomial, the polynomial $R\_{n}$ that has r as a root may be deduced from Φ*n* by the standard manipulation on reciprocal polynomials, and the primitive nth roots of unity may be deduced from the roots of $R\_{n}$ by solving the quadratic equation $z^{2}-rz+1=0.$ That is, the real part of the primitive root is $\frac {r}{2},$ and its imaginary part is $\pm i{\sqrt {1-\left({\frac {r}{2}\right)^{2}.}}}$

The polynomial $R\_{n}$ is an irreducible polynomial whose roots are all real. Its degree is a power of two, if and only if n is a product of a power of two by a product (possibly empty) of distinct Fermat primes, and the regular n-gon is constructible with compass and straightedge. Otherwise, it is solvable in radicals, but one are in the casus irreducibilis, that is, every expression of the roots in terms of radicals involves *nonreal radicals*.

### Explicit expressions in low degrees

* For *n* = 1, the cyclotomic polynomial is Φ1(*x*) = *x* − 1 Therefore, the only primitive first root of unity is 1, which is a non-primitive *n*th root of unity for every *n* \> 1.
* As Φ2(*x*) = *x* \+ 1, the only primitive second (square) root of unity is −1, which is also a non-primitive *n*th root of unity for every even *n* \> 2. With the preceding case, this completes the list of real roots of unity.
* As Φ3(*x*) = *x*2 \+ *x* \+ 1, the primitive third (cube) roots of unity, which are the roots of this quadratic polynomial, are $\frac {-1+i{\sqrt {3}{2},\ {\frac {-1-i{\sqrt {3}{2}.}}}}}$
* As Φ4(*x*) = *x*2 \+ 1, the two primitive fourth roots of unity are *i* and *i*.
* As Φ5(*x*) = *x*4 \+ *x*3 \+ *x*2 \+ *x* \+ 1, the four primitive fifth roots of unity are the roots of this quartic polynomial, which may be explicitly solved in terms of radicals, giving the roots $\frac {\varepsilon {\sqrt {5}-1}{4}\pm i{\frac {\sqrt {10+2\varepsilon {\sqrt {5}{4},}}}}}$ where $\varepsilon $ may take the two values 1 and −1 (the same value in the two occurrences).
* As Φ6(*x*) = *x*2*x* \+ 1, there are two primitive sixth roots of unity, which are the negatives (and also the square roots) of the two primitive cube roots: $\frac {1+i{\sqrt {3}{2},\ {\frac {1-i{\sqrt {3}{2}.}}}}}$
* As 7 is not a Fermat prime, the seventh roots of unity are the first that require cube roots. There are 6 primitive seventh roots of unity, which are pairwise complex conjugate. The sum of a root and its conjugate is twice its real part. These three sums are the three real roots of the cubic polynomial $r^{3}+r^{2}-2r-1,$ and the primitive seventh roots of unity are $\frac {r}{2}\pm i{\sqrt {1-{\frac {r^{2}{4},}}}}$ where r runs over the roots of the above polynomial. As for every cubic polynomial, these roots may be expressed in terms of square and cube roots. However, as these three roots are all real, this is casus irreducibilis, and any such expression involves non-real cube roots.
* As Φ8(*x*) = *x*4 \+ 1, the four primitive eighth roots of unity are the square roots of the primitive fourth roots, ±*i*. They are thus $\pm {\frac {\sqrt {2}{2}\pm i{\frac {\sqrt {2}{2}.}}}}$
* See Heptadecagon for the real part of a 17th root of unity.

## Periodicity

If z is a primitive nth root of unity, then the sequence of powers

… , *z*−1, *z*0, *z*1, …

is n-periodic (because *z* *j* \+ *n* = *z* *j**z* *n* = *z* *j* for all values of j), and the n sequences of powers

*sk*: … , *z* *k*⋅(−1), *z* *k*⋅0, *z* *k*⋅1, …

for *k* = 1, … , *n* are all n-periodic (because *z* *k*⋅(*j* \+ *n*) = *z* *k**j*). Furthermore, the set {*s*1, … , *sn*} of these sequences is a basis of the linear space of all n-periodic sequences. This means that *any* n-periodic sequence of complex numbers

… , *x*−1 , *x*0 , *x*1, …

can be expressed as a linear combination of powers of a primitive nth root of unity:

$$x\_{j}=\sum \_{k}X\_{k}\cdot z^{k\cdot j}=X\_{1}z^{1\cdot j}+\cdots +X\_{n}\cdot z^{n\cdot j}$$

for some complex numbers *X*1, … , *X**n* and every integer j.

This is a form of Fourier analysis. If j is a (discrete) time variable, then k is a frequency and *X**k* is a complex amplitude.

Choosing for the primitive nth root of unity

$$z=e^{\frac {2\pi i}{n}=\cos {\frac {2\pi }{n}+i\sin {\frac {2\pi }{n}}}}$$

allows *x**j* to be expressed as a linear combination of cos and sin:

$$x\_{j}=\sum \_{k}A\_{k}\cos {\frac {2\pi jk}{n}+\sum \_{k}B\_{k}\sin {\frac {2\pi jk}{n}.}}$$

This is a discrete Fourier transform.

## Summation

Let SR(*n*) be the sum of all the nth roots of unity, primitive or not. Then

$$\operatorname {SR} (n)={\begin{cases}1,&n=1\\0,&n\>1.\end{cases}}$$

This is an immediate consequence of Vieta's formulas. In fact, the nth roots of unity being the roots of the polynomial *X**n* – 1, their sum is the coefficient of degree *n* – 1, which is either 1 or 0 according whether *n* = 1 or *n* \> 1.

Alternatively, for *n* = 1 there is nothing to prove, and for *n* \> 1 there exists a root *z* ≠ 1 – since the set *S* of all the nth roots of unity is a group, *zS* = *S*, so the sum satisfies *z* SR(*n*) = SR(*n*), whence SR(*n*) = 0.

Let SP(*n*) be the sum of all the primitive nth roots of unity. Then

$$\operatorname {SP} (n)=\mu (n),$$

where *μ*(*n*) is the Möbius function.

In the section Elementary properties, it was shown that if R(*n*) is the set of all nth roots of unity and P(*n*) is the set of primitive ones, R(*n*) is a disjoint union of the P(*n*):

$$\operatorname {R} (n)=\bigcup \_{d\\,|\\,n}\operatorname {P} (d),$$

This implies

$$\operatorname {SR} (n)=\sum \_{d\\,|\\,n}\operatorname {SP} (d).$$

Applying the Möbius inversion formula gives

$$\operatorname {SP} (n)=\sum \_{d\\,|\\,n}\mu (d)\operatorname {SR} \left({\frac {n}{d}\right).}$$

In this formula, if *d* \< *n*, then SR(*n*/*d*) = 0, and for *d* = *n*: SR(*n*/*d*) = 1. Therefore, SP(*n*) = *μ*(*n*).

This is the special case *c**n*(1) of Ramanujan's sum *c**n*(*s*), defined as the sum of the sth powers of the primitive nth roots of unity:

$$c\_{n}(s)=\sum \_{a=1 \atop \gcd(a,n)=1}^{n}e^{2\pi i{\frac {a}{n}s}.}$$

## Orthogonality

From the summation formula follows an orthogonality relationship: for *j* =1, … , *n* and *j′* =1, … , *n*

$$\sum \_{k=1}^{n}{\overline {z^{j\cdot k}\cdot z^{j'\cdot k}=n\cdot \delta \_{j,j'}}}$$

where δ is the Kronecker delta and z is any primitive nth root of unity.

The *n*×*n* matrix U whose (*j*, *k*)th entry is

$$U\_{j,k}=n^{-{\frac {1}{2}\cdot z^{j\cdot k}}}$$

defines a discrete Fourier transform. Computing the inverse transformation using Gaussian elimination requires (*n*3) operations. However, it follows from the orthogonality that U is unitary. That is,

$$\sum \_{k=1}^{n}{\overline {U\_{j,k}\cdot U\_{k,j'}=\delta \_{j,j'},}}$$

and thus the inverse of U is simply the complex conjugate. (This fact was first noted by Gauss when solving the problem of trigonometric interpolation.) The straightforward application of U or its inverse to a given vector requires *O*(*n*2) operations. The fast Fourier transform algorithms reduces the number of operations further to *O*(*n* log *n*).

## Cyclotomic polynomials

The zeros of the polynomial

$$p(z)=z^{n}-1$$

are precisely the nth roots of unity, each with multiplicity 1. The nth *cyclotomic polynomial* is defined by the fact that its zeros are precisely the *primitive* nth roots of unity, each with multiplicity 1.

$$\Phi \_{n}(z)=\prod \_{k=1}^{\varphi (n)}(z-z\_{k})$$

where *z*1, *z*2, *z*3, …, *z*φ(*n*) are the primitive nth roots of unity, and φ(*n*) is Euler's totient function. The polynomial Φ*n*(*z*) has integer coefficients and is an irreducible polynomial over the rational numbers (that is, it cannot be written as the product of two positive-degree polynomials with rational coefficients). The case of prime n, which is easier than the general assertion, follows by applying Eisenstein's criterion to the polynomial

$$\frac {(z+1)^{n}-1}{(z+1)-1},$$

and expanding via the binomial theorem.

Every nth root of unity is a primitive dth root of unity for exactly one positive divisor d of n. This implies that

$$z^{n}-1=\prod \_{d\\,|\\,n}\Phi \_{d}(z).$$

This formula represents the factorization of the polynomial *z**n* − 1 into irreducible factors:

$$\begin{aligned}z^{1}-1&=z-1\\z^{2}-1&=(z-1)(z+1)\\z^{3}-1&=(z-1)(z^{2}+z+1)\\z^{4}-1&=(z-1)(z+1)(z^{2}+1)\\z^{5}-1&=(z-1)(z^{4}+z^{3}+z^{2}+z+1)\\z^{6}-1&=(z-1)(z+1)(z^{2}+z+1)(z^{2}-z+1)\\z^{7}-1&=(z-1)(z^{6}+z^{5}+z^{4}+z^{3}+z^{2}+z+1)\\z^{8}-1&=(z-1)(z+1)(z^{2}+1)(z^{4}+1)\\\end{aligned}$$

Applying Möbius inversion to the formula gives

$$\Phi \_{n}(z)=\prod \_{d\\,|\\,n}\left(z^{\frac {n}{d}-1\right)^{\mu (d)}=\prod \_{d\\,|\\,n}\left(z^{d}-1\right)^{\mu \left({\frac {n}{d}\right)},}}$$

where *μ* is the Möbius function. So the first few cyclotomic polynomials are

Φ1(*z*) = *z* − 1 Φ2(*z*) = (*z*2 − 1)⋅(*z* − 1)−1 = *z* \+ 1 Φ3(*z*) = (*z*3 − 1)⋅(*z* − 1)−1 = *z*2 \+ *z* \+ 1 Φ4(*z*) = (*z*4 − 1)⋅(*z*2 − 1)−1 = *z*2 \+ 1 Φ5(*z*) = (*z*5 − 1)⋅(*z* − 1)−1 = *z*4 \+ *z*3 \+ *z*2 \+ *z* \+ 1 Φ6(*z*) = (*z*6 − 1)⋅(*z*3 − 1)−1⋅(*z*2 − 1)−1⋅(*z* − 1) = *z*2*z* \+ 1 Φ7(*z*) = (*z*7 − 1)⋅(*z* − 1)−1 = *z*6 \+ *z*5 \+ *z*4 \+ *z*3 \+ *z*2 +*z* \+ 1 Φ8(*z*) = (*z*8 − 1)⋅(*z*4 − 1)−1 = *z*4 \+ 1

If p is a prime number, then all the pth roots of unity except 1 are primitive pth roots. Therefore, $\Phi \_{p}(z)={\frac {z^{p}-1}{z-1}=\sum \_{k=0}^{p-1}z^{k}.}$ Substituting any positive integer ≥2 for z, this sum becomes a base z repunit. Thus a necessary (but not sufficient) condition for a repunit to be prime is that its length be prime.

Note that, contrary to first appearances, *not* all coefficients of all cyclotomic polynomials are 0, 1, or −1. The first exception is Φ105. It is not a surprise it takes this long to get an example, because the behavior of the coefficients depends not so much on n as on how many odd prime factors appear in n. More precisely, it can be shown that if n has 1 or 2 odd prime factors (for example, *n* =150) then the nth cyclotomic polynomial only has coefficients 0, 1 or −1. Thus the first conceivable n for which there could be a coefficient besides 0, 1, or −1 is a product of the three smallest odd primes, and that is 357 = 105. This by itself doesn't prove the 105th polynomial has another coefficient, but does show it is the first one which even has a chance of working (and then a computation of the coefficients shows it does). A theorem of Schur says that there are cyclotomic polynomials with coefficients arbitrarily large in absolute value. In particular, if $n=p\_{1}p\_{2}\cdots p\_{t},$ where $p\_{1}\<p\_{2}\<\cdots \
p\_{t},$ and *t* is odd, then 1 − *t* occurs as a coefficient in the nth cyclotomic polynomial.

Many restrictions are known about the values that cyclotomic polynomials can assume at integer values. For example, if p is prime, then *d*Φ*p*(*d*) if and only if *d* ≡ 1 (mod *p*).

Cyclotomic polynomials are solvable in radicals, as roots of unity are themselves radicals. Moreover, there exist more informative radical expressions for nth roots of unity with the additional property that every value of the expression obtained by choosing values of the radicals (for example, signs of square roots) is a primitive nth root of unity. This was already shown by Gauss in 1797. Efficient algorithms exist for calculating such expressions.

## Cyclic groups

The nth roots of unity form under multiplication a cyclic group of order n, and in fact these groups comprise all of the finite subgroups of the multiplicative group of the complex number field. A generator for this cyclic group is a primitive nth root of unity.

The nth roots of unity form an irreducible representation of any cyclic group of order n. The orthogonality relationship also follows from group-theoretic principles as described in Character group.

The roots of unity appear as entries of the eigenvectors of any circulant matrix; that is, matrices that are invariant under cyclic shifts, a fact that also follows from group representation theory as a variant of Bloch's theorem. In particular, if a circulant Hermitian matrix is considered (for example, a discretized one-dimensional Laplacian with periodic boundaries), the orthogonality property immediately follows from the usual orthogonality of eigenvectors of Hermitian matrices.

## Cyclotomic fields

By adjoining a primitive nth root of unity to $\mathbb {Q} ,$ one obtains the nth cyclotomic field $\mathbb {Q} (\exp(2\pi i/n)).$This field contains all nth roots of unity and is the splitting field of the nth cyclotomic polynomial over $\mathbb {Q} .$ The field extension $\mathbb {Q} (\exp(2\pi i/n))/\mathbb {Q} $ has degree φ(*n*) and its Galois group is naturally isomorphic to the multiplicative group of units of the ring $\mathbb {Z} /n\mathbb {Z} .$

As the Galois group of $\mathbb {Q} (\exp(2\pi i/n))/\mathbb {Q} $ is abelian, this is an abelian extension. Every subfield of a cyclotomic field is an abelian extension of the rationals. It follows that every *n*th root of unity may be expressed in term of *k*-roots, with various *k* not exceeding φ(*n*). In these cases Galois theory can be written out explicitly in terms of Gaussian periods: this theory from the *Disquisitiones Arithmeticae* of Gauss was published many years before Galois.

Conversely, *every* abelian extension of the rationals is such a subfield of a cyclotomic field – this is the content of a theorem of Kronecker, usually called the *Kronecker–Weber theorem* on the grounds that Weber completed the proof.

## Relation to quadratic integers

For *n* = 1, 2, both roots of unity  and −1 are integers.

For three values of n, the roots of unity are quadratic integers:

For four other values of n, the primitive roots of unity are not quadratic integers, but the sum of any root of unity with its complex conjugate (also an nth root of unity) is a quadratic integer.

For *n* = 5, 10, none of the non-real roots of unity (which satisfy a quartic equation) is a quadratic integer, but the sum *z* \+ *z* = 2 Re *z* of each root with its complex conjugate (also a 5th root of unity) is an element of the ring **Z**\[1+5/2\] (*D* = 5). For two pairs of non-real 5th roots of unity these sums are inverse golden ratio and minus golden ratio.

For *n* = 8, for any root of unity *z* \+ *z* equals to either 0, ±2, or ± (*D* = 2).

For *n* = 12, for any root of unity, *z* \+ *z* equals to either 0, ±1, ±2 or ± (*D* = 3).


title: Mircea Bedivan

abstract: Mircea Bedivan is a former Romanian handball player who competed in the 1984 Summer Olympics. He was a member of the Romanian handball team which won the bronze medal. He played all six matches and scored two goals. After retiring from active play with Dinamo Bucharest, he became a coach, managing CSM Călărași, CSM Ploieşti and Energia Lignitul Pandurii Târgu Jiu.

text:
# Mircea Bedivan

**Mircea Bedivan** (born 8 October 1957 in Constanţa) is a former Romanian handball player who competed in the 1984 Summer Olympics.

He was a member of the Romanian handball team which won the bronze medal. He played all six matches and scored two goals.

After retiring from active play with Dinamo Bucharest, he became a coach, managing CSM Călărași, CSM Ploieşti and Energia Lignitul Pandurii Târgu Jiu.

## InfoBox

Mircea Bedivan
| Medal record | | |
| --- | --- | --- |
| Men's Handball | | |
| Representing  Romania | | |
| Olympic Games | | |
|  | 1984 Los Angeles | Team |


title: Katari Bohnar

abstract: Dadikha is a village in Dadikha Gram panchayat, Bilhaur Tehsil, Kanpur Nagar district, Uttar Pradesh, India. It is located 67 km away from Kanpur City. According to 2011 Census of India the total population of the village is 1,120, out of 612 are males and 508 are females.

text:
# Katari Bohnar

**Dadikha** is a village in Dadikha Gram panchayat, Bilhaur Tehsil, Kanpur Nagar district, Uttar Pradesh, India. It is located 67 km away from Kanpur City. According to 2011 Census of India the total population of the village is 1,120, out of 612 are males and 508 are females.

## InfoBox

| Katari Bohnar | |
| --- | --- |
| Village | |
| Katari BohnarLocation in Kanpur, Uttar Pradesh, IndiaKatari BohnarKatari Bohnar (India) | |
| Coordinates: 26°53′N 80°05′E / 26.88°N 80.09°E / 26.88; 80.09 | |
| Country | India |
| State | Uttar Pradesh |
| District | Kanpur Nagar |
| Population (2011 Census of India) | |
| Total | 1,120 |
| Languages | |
| Official | Hindi |
| Time zone | UTC+5:30 (IST) |
| PIN | 209202 |
| Vehicle registration | UP-78 |


title: Thunderbox Gold Mine

abstract: The Thunderbox Gold Mine is a gold mine 41 km south-east of Leinster, Western Australia. It was formerly owned by Norilsk Nickel, which placed it in care and maintenance in 2007, but is now owned by Northern Star Resources.

text:
# Thunderbox Gold Mine

The **Thunderbox Gold Mine** is a gold mine 41 km south-east of Leinster, Western Australia. It was formerly owned by Norilsk Nickel, which placed it in care and maintenance in 2007, but is now owned by Northern Star Resources.

## Ethemology

The mine is named after the colloquial Australian term for a toilet, thunderbox, which was given to the site in its early exploration days because the only available toilet on site was a 44 gallon drum on top of an old drill hole.

## History

The Thunderbox gold deposit is a relatively recent discovery by Western Australian gold mining standards, having been located through drilling in mid-1999. The deposit was jointly owned by Lionore (60%) and Dalrymple Resources (40%).

The owners conducted a feasibility study in 2001 and predicted a mine life of five years and a gold resource of 850,000 ounces, to be mined in an open-pit operation. The company moved the processing plant from Mount Todd to the mine, and first gold production was achieved at the end of 2002.

In mid-2003, Lionore and Dalrymple announced a merger of the two companies, with the new entity continuing to be called Lionore.

After good results in the mine's first two years of operation, Thunderbox suffered a difficult 2005, with lower-than-expected production in the second half of the year. Water shortages and equipment reliability issues were two of the main reasons for the decline in production, but write-downs because of its short remaining mine life led to large financial losses for the Thunderbox operation. Lionore at this stage was contemplating selling the mine.

In April 2007, it was once more reported that the mine was for sale.

Norilsk acquired the mine in June 2007, when it took over Lionore Mining.

Lionore Mining was taken over by Russian company Norilsk in June 2007, after a bidding war between Norilsk and Xstrata saw the former succeeding with the higher offer. Xstrata had originally offered C$18.50 for every Lionore share, countered by a Norilsk offer of C$21.50 per share. Xstrata raised their offer to C$25, which forced Norilsk to present a final offer of C$27.50.

Shortly after the takeover, Norilsk announced that it would not continue mining at Thunderbox, instead preferring to concentrate on the company's nickel projects. The mine eventually closed in November 2007.

After the closure of the mine, Norilsk used the camp at Thunderbox for accommodation for its workers at the nearby Waterloo Nickel Mine, until the latter was also placed into care and maintenance.

In January 2014, Saracen Mineral Holdings purchased the mine alongside the Bannockburn Gold Mine and the Waterloo Nickel Mine, for an immediate A$20 million cash payment, a production- and gold price related deferred A$3 million cash payment and up to A$17 million in royalties.

The board of Saracen Mineral Holdings approved a project to develop the Thunderbox deposit in quarter three of the 2015 financial year, with prestrip mining commencing in 2015. First gold was poured in February 2016.

In October 2020, a merger between Northern Star Resources and Saracen Metal Holdings was proposed. The merger was completed in February 2021 when Saracen was de-listed from the Australian Securities Exchange, the Northern Star Resources mine thereby passing into Northern Star's ownership.

As of 2022, mining occurs in both open pit and underground operations.

## Production

Production figures of the mine:

| Year | Production | Grade | Cost per ounce |
| --- | --- | --- | --- |
| 2002 | 17,790 ounces | 2.38 g/t | US$95 |
| 2003 | 212,459 ounces |  | US$138 |
| 2004 | 156,916 ounces |  | US$265 |
| 2005 | 145,413 ounces |  | US$339 |
| 2006 | 155,203 ounces |  | US$352 |
| 2007 <sup>\[2\]</sup> | 39,345 ounces |  | US$518 |
| 2007–2016 | *Care and maintenance* | | |
| 2016–17 |  |  |  |
| 2017–18 |  |  |  |
| 2018–19 |  |  |  |
| 2019–20 | 184,538 ounces |  | A$731 |
| 2020–21 | 143,990 ounces |  | A$924 |
| 2021–22 | 132,502 ounces | 1.5 g/t | A$1,817 |
| 2022–23 | 159,782 ounces | 1.4 g/t | A$2,116 |

* **^\[1\]** The Thunderbox Gold Mine is part of the Yandal Production Centre but production figures were reported separately for 2020–21 as it was a new acquisition.
* **^\[2\]** Results for January to March 2007 quarter only.

### Bibliography

* Louthean, Ross (ed.). *The Australian Mines Handbook: 2003-2004 Edition*. Louthean Media Pty Ltd.

## InfoBox

Thunderbox
| Location | |
| --- | --- |
| Thunderbox Gold MineLocation in Western Australia | |
| Location | Leinster |
| State | Western Australia |
| Country | Australia |
| Coordinates | 28°10′52″S 121°00′00″E / 28.18111°S 121.00000°E / -28.18111; 121.00000 |
| Production | |
| Products | Gold |
| Production | 159,782 ounces |
| Financial year | 2022–23 |
| History | |
| Opened | 2002 |
| Active | 2002–20072016–present |
| Owner | |
| Company | Northern Star Resources |
| Website | www.nsrltd.com |
| Year of acquisition | 2021 |
|  | |


title: Wakako

abstract: Wakako is a feminine Japanese given name.

text:
# Wakako

**Wakako** (わかこ, ワカコ) is a feminine Japanese given name.

## Possible writings

* わかこ (in hiragana)
* ワカコ (in katakana)
* 和佳子 "Japanese/peace, excellent, child"
* 和歌子 "traditional Japanese poetry, child"
* 若子 "young child"
* 和加子 "child who adds peace"

## People with the given name

## InfoBox

Wakako
| Gender | Female |
| --- | --- |
| Origin | |
| Word/name | Japanese |
| Meaning | It can have many different meanings depending on the kanji used. |
| Other names | |
| Related names | Waka |


title: Heart of the Golden West

abstract: Heart of the Golden West is a 1942 American Western film starring Roy Rogers.

text:
# Heart of the Golden West

***Heart of the Golden West***  is a 1942 American Western film starring Roy Rogers.

## Plot

Roy helps the ranchers of Cherokee City when Ross Lambert (McDonald) doubles the rates to ship their cattle to market. Roy contacts the owner of a steamboat, Colonel Silas Popen (Catlett) to see about shipping cattle by boat. Roy and the Sons of the Pioneers plan a warm western welcome for Popen and his daughter, Mary Lou (Terry). James Barabee (Paul Harvey), head of the Cattleman's Association, sends Roy a telegram saying that Popen hates everything western, but Lambert intercepts the telegram, so Roy makes a bad first impression. Lambert also stages a saloon brawl to terrify Popen; the noise scares the horses of Popen's wagon and causes a runaway. Roy saves Popen and Mary Lou, but Popen still refuses to ship cattle.

Mary Lou takes matters into her own hands and tells the ranchers to round up the cattle and bring them to Barabee's ranch. Lambert has some of his men set fire to the steamboat. While the ranch hands are out fighting the fire he rustles all the cattle. Popen has fallen into a well on the ranch and overhears Lambert discussing the crime with his men. When Popen is rescued he reveals that the cattle have been taken under a waterfall to a swamp. The ranchers retrieve the cattle and arrest Lambert and his men. Roy rescues Mary Lou, who has been kidnapped by Lambert. Popen signs a contract agreeing to transport the cattle.

## Cast

## InfoBox

| Heart of the Golden West | |
| --- | --- |
| Directed by | Joseph Kane |
| Written by | Earl Felton |
| Starring | Roy Rogers<br>Ruth Terry |
| Music by | Sons of the Pioneers |
| Distributed by | Republic Pictures |
| Release date | * 1942 (1942) |
| Running time | 65 minutes |
| Country | United States |
| Language | English |


title: Handsome spurfowl

abstract: The handsome spurfowl is a species of bird in the pheasant family Phasianidae. It is a large, up to 35 cm long, terrestrial forest bird with a dark reddish brown plumage, grey head, red bill and legs, brown iris, bare red orbital skin and rufous grey below. Both sexes are similar. The female is slightly smaller than male. The young has duller plumage. The handsome spurfowl is distributed in mountain forests of eastern Democratic Republic of the Congo, southwest Uganda and borders between Burundi and Rwanda. It is a shy and elusive bird, more often heard than seen. The diet consists mainly of seeds.

text:
# Handsome spurfowl

The **handsome spurfowl** (***Pternistis nobilis***) is a species of bird in the pheasant family Phasianidae. It is a large, up to 35 cm long, terrestrial forest bird with a dark reddish brown plumage, grey head, red bill and legs, brown iris, bare red orbital skin and rufous grey below. Both sexes are similar. The female is slightly smaller than male. The young has duller plumage.

The handsome spurfowl is distributed in mountain forests of eastern Democratic Republic of the Congo, southwest Uganda and borders between Burundi and Rwanda. It is a shy and elusive bird, more often heard than seen. The diet consists mainly of seeds.

## Taxonomy

The handsome spurfowl was described in 1908 by the German ornithologist Anton Reichenow from a specimen collected on Mount Sabyinyo in the Virunga Mountains. Mount Sabyinyo is in Rwanda, on the border with the Uganda and the Democratic Republic of the Congo. Reichenow coined the binomial name *Francolinus nobilis*. The species is now placed in the genus *Pternistis* that was introduced by the German naturalist Johann Georg Wagler in 1832. The specific epithet *nobilis* is Latin for "noble", "famous" or "renowned". The handsome spurfowl is monotypic: no subspecies are recognised.

## Status and Conservation

Although locally common across much of its range, and evaluated as Least Concern on the IUCN Red List of Threatened Species. Recent surveys for the species in prime habitat in southwestern Uganda detected its presence at only 1 in 10 survey points. The research concluded that a reanalysis of the status of the handsome francolin could be justified in the light of its apparent strong preference for montane bamboo forest, which is a rare and patchy habitat.

## InfoBox

| Handsome francolin | |
| --- | --- |
|  | |
| Conservation status | |
|
Least Concern  (IUCN 3.1) | |
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Chordata |
| Class: | Aves |
| Order: | Galliformes |
| Family: | Phasianidae |
| Genus: | *Pternistis* |
| Species: | ***P. nobilis*** |
| Binomial name | |
| ***Pternistis nobilis***
(Reichenow, 1908) | |
|
|  | |
| geographic distribution | |
| Synonyms | |
| *Francolinus nobilis* | |


title: Haploparmena angolana

abstract: Haploparmena angolana is a species of beetle in the family Cerambycidae. It was described by Per Olof Christopher Aurivillius in 1913 and is known from Angola.

text:
# Haploparmena angolana

***Haploparmena angolana*** is a species of beetle in the family Cerambycidae. It was described by Per Olof Christopher Aurivillius in 1913 and is known from Angola.

## InfoBox

| *Haploparmena angolana* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Cerambycidae |
| Genus: | *Haploparmena* |
| Species: | ***H. angolana*** |
| Binomial name | |
| ***Haploparmena angolana***<br>Aurivillius, 1913 | |
|


title: Vaccinium hirsutum

abstract: Vaccinium hirsutum is a species of flowering plant in the heath family known by the common name hairy blueberry. This species is endemic to a small area in the southern Appalachian Mountains, where it is only known from a few counties in eastern Tennessee, northern Georgia, and the Carolinas. Vaccinium hirsutum is native to dry oak-pine ridges, where it can be locally abundant. It is a shrub up to 75 cm tall, forming large colonies. Leaves are rather thick, elliptical, densely hairy, up to 62 mm long. Vaccinium hirsutum produces white, cylindrical flowers in late spring, followed by hairy, black berries in the summer.

text:
# Vaccinium hirsutum

***Vaccinium hirsutum*** is a species of flowering plant in the heath family known by the common name **hairy blueberry**. This species is endemic to a small area in the southern Appalachian Mountains, where it is only known from a few counties in eastern Tennessee, northern Georgia, and the Carolinas.

*Vaccinium hirsutum* is native to dry oak-pine ridges, where it can be locally abundant. It is a shrub up to 75 cm (28 inches) tall, forming large colonies. Leaves are rather thick, elliptical, densely hairy, up to 62 mm (2 1/2 inches) long.

*Vaccinium hirsutum* produces white, cylindrical flowers in late spring, followed by hairy, black berries in the summer.

## InfoBox

| *Vaccinium hirsutum* | |
| --- | --- |
|  | |
| Conservation status | |
|
Vulnerable  (NatureServe) | |
| Scientific classification | |
| Kingdom: | Plantae |
| *Clade*: | Tracheophytes |
| *Clade*: | Angiosperms |
| *Clade*: | Eudicots |
| *Clade*: | Asterids |
| Order: | Ericales |
| Family: | Ericaceae |
| Genus: | *Vaccinium* |
| Species: | ***V. hirsutum*** |
| Binomial name | |
| ***Vaccinium hirsutum***
Buckley 1843 | |
|
| Synonyms | |
| *Cyanococcus hirsutus* (Buckley) Small | |


title: Root pressure

abstract: Root pressure is the transverse osmotic pressure within the cells of a root system that causes sap to rise through a plant stem to the leaves. Root pressure occurs in the xylem of some vascular plants when the soil moisture level is high either at night or when transpiration is low during the daytime. When transpiration is high, xylem sap is usually under tension, rather than under pressure, due to transpirational pull. At night in some plants, root pressure causes guttation or exudation of drops of xylem sap from the tips or edges of leaves. Root pressure is studied by removing the shoot of a plant near the soil level. Xylem sap will exude from the cut stem for hours or days due to root pressure. If a pressure gauge is attached to the cut stem, the root pressure can be measured. Root pressure is caused by active distribution of mineral nutrient ions into the root xylem. Without transpiration to carry the ions up the stem, they accumulate in the root xylem and lower the water potential. Water then diffuses from the soil into the root xylem due to osmosis. Root pressure is caused by this accumulation of water in the xylem pushing on the rigid cells. Root pressure provides a force, which pushes water up the stem, but it is not enough to account for the movement of water to leaves at the top of the tallest trees. The maximum root pressure measured in some plants can raise water only to 6.87 meters, and the tallest trees are over 100 meters tall.

text:
# Root pressure

**Root pressure** is the transverse osmotic pressure within the cells of a root system that causes sap to rise through a plant stem to the leaves.

Root pressure occurs in the xylem of some vascular plants when the soil moisture level is high either at night or when transpiration is low during the daytime. When transpiration is high, xylem sap is usually under tension, rather than under pressure, due to transpirational pull. At night in some plants, root pressure causes guttation or exudation of drops of xylem sap from the tips or edges of leaves. Root pressure is studied by removing the shoot of a plant near the soil level. Xylem sap will exude from the cut stem for hours or days due to root pressure. If a pressure gauge is attached to the cut stem, the root pressure can be measured.

Root pressure is caused by active distribution of mineral nutrient ions into the root xylem. Without transpiration to carry the ions up the stem, they accumulate in the root xylem and lower the water potential. Water then diffuses from the soil into the root xylem due to osmosis. Root pressure is caused by this accumulation of water in the xylem pushing on the rigid cells. Root pressure provides a force, which pushes water up the stem, but it is not enough to account for the movement of water to leaves at the top of the tallest trees. The maximum root pressure measured in some plants can raise water only to 6.87 meters, and the tallest trees are over 100 meters tall.

## Role of endodermis

The endodermis in the root is important in the development of root pressure. The endodermis is a single layer of cells between the cortex and the pericycle. These cells allow water movement until it reaches the Casparian strip, made of suberin, a waterproof substance. The Casparian strip prevents mineral nutrient ions from moving passively through the endodermal cell walls. Water and ions move in these cell walls via the apoplast pathway. Ions outside the endodermis must be actively transported across an endodermal cell membrane to enter or exit the endodermis. Once inside the endodermis, the ions are in the symplast pathway. They cannot diffuse back out again but can move from cell to cell via plasmodesmata or be actively transported into the xylem. Once in the xylem vessels or tracheids, ions are again in the apoplast pathway. Xylem vessels and tracheids transport water up the plant but lack cell membranes. The Casparian strip substitutes for their lack of cell membranes and prevents accumulated ions from diffusing passively in apoplast pathway out of the endodermis. The ions accumulating interior to the endodermis in the xylem create a water potential gradient and by osmosis, water diffuses from the moist soil, across the cortex, through the endodermis and into the xylem.

Root pressure can transport water and dissolved mineral nutrients from roots through the xylem to the tops of relatively short plants when transpiration is low or zero. The maximum root pressure measured is about 0.6 megapascals but some species never generate any root pressure. The main contributor to the movement of water and mineral nutrients upward in vascular plants is considered to be the transpirational pull. However, sunflower plants grown in 100% relative humidity grew normally and accumulated the same amount of mineral nutrients as plants in normal humidity, which had a transpiration rate 10 to 15 times the plants in 100% humidity. Thus, transpiration may not be as important in upward mineral nutrient transport in relatively short plants as often assumed.

Xylem vessels sometimes empty over winter. Root pressure may be important in refilling the xylem vessels. However, in some species vessels refill without root pressure.

Root pressure is often high in some deciduous trees before they leaf out. Transpiration is minimal without leaves, and organic solutes are being mobilized so decrease the xylem water potential. Sugar maple accumulates high concentrations of sugars in its xylem early in the spring, which is the source of maple sugar. Some trees "bleed" xylem sap profusely when their stems are pruned in late winter or early spring, e.g. maple and elm. Such bleeding is similar to root pressure only sugars, rather than ions, may lower the xylem water potential. In the unique case of maple trees, sap bleeding is caused by changes in stem pressure and not root pressure.

It is very likely that all grasses produce root pressure. In bamboos, root pressure is correlated with maximum height of a clone.


title: USS Anderton

abstract: USS Anderton (SP-530), originally to have been USS Raymond J. Anderton (SP-530), was a patrol vessel and minesweeper that served in the United States Navy from 1917 to 1919.

text:
# USS Anderton

**USS *Anderton* (SP-530)**, originally to have been **USS *Raymond J. Anderton* (SP-530)**, was a patrol vessel and minesweeper that served in the United States Navy from 1917 to 1919.

## Acquisition and commissioning

*Anderton* was built in 1911 by Robert Palmer and Son, Noank, Groton, Connecticut, as the steam fishing trawler *Raymond J. Anderton*. She was purchased from her owner, T. B. Hayes, for service in World War I and delivered to the U.S. Navy on 18 June 1917. Originally she was to have been named USS *Raymond J. Anderton*, but she was renamed USS *Anderton* on 28 July 1917 prior to commissioning as required by a United States Department of the Navy general order mandating that the names of all section patrol craft be shortened to surnames only; during her Navy career, she referred to by both names as well as by the name *R. J. Anderton*. She was converted for naval service and commissioned at the Boston Navy Yard at Boston, Massachusetts, on 18 August 1917 as USS *Anderton* (SP-530).

## World War I

Originally assigned to the 2nd Naval District in southern New England, *Anderton* was reassigned during conversion to Squadron 4, Patrol Force, and ordered prepared for "distant service", and soon after commissioning got underway for France via the Azores as a unit of the 3rd Patrol Division. Arriving in France in September 1917, her division reinforced the 1st and 2nd Patrol Divisions, which had arrived earlier. Later shifted to the 12th Patrol Division, she operated off the French coast, initially assigned to coastal convoy escort duties. She and similar trawlers assigned to these duties were soon found to be unsuited to them, and after USS *Rehoboth* (SP-384) foundered off Ushant, France, on 4 October 1917, they were reassigned to minesweeping duties.

*Anderton* was one of the first four ships in her patrol division to have minesweeping gear installed. She departed Brest, France, on 3 December 1917 in company with three similar trawlers, and 6 December 1917 began minesweeping exercises in Quiberon Bay. On 13 February 1918, she became the first of the ships to catch a mine in her sweep gear, and on 21 February 1918 she and USS *McNeal* (SP-333) cut two mines apiece.

On 12 January 1918, USS *P. K. Bauman* (SP-377), while operating in a fog near Concarneau, struck a rock and began taking on water. *Anderton* arrived to render assistance and took *Bauman* under tow, but *Bauman* sank before the ships could arrive at Lorient.

For the remainder World War I, *Anderton* operated out of Lorient. Besides minesweeping duty and covering the convoy routes from Penmarch to Bouy de Boeufs, *Anderton* reinforced coastal convoy escorts as required, cleared the Teignouse Channel and other important passages of mines for the passage of troopships in the vicinity of Belle Île, and operated at night off Penmarch, using her primitive listening gear ("sea tubes") to detect German submarines. On 5 September 1918, when a German submarine torpedoed the transport USS *Mount Vernon* (ID-4508), USS *Barnegat* (SP-1232) and *Anderton* assisted *Mount Vernon* into Brest for repairs.

## Postwar

In the weeks following the end of World War I on 11 November 1918, *Anderton* continued minesweeping operations to make sure that shipping could travel safely in areas mined during the war. When that work was completed in the spring of 1919, *Anderton* departed Brest on the morning of 27 April 1919 bound for the United States in company with other U.S. Navy trawlers, but rough weather soon forced them to return to port. As *Anderton* did so, she towed the disabled USS *Courtney* (SP-375), but *Courtney* sank that evening about 25 minutes before the returning convoy sighted Ar Men light. A northwesterly gale made the sea very rough, and the remaining ships had to fight heavy seas, snow, and hail squalls before they reached Brest on the afternoon of 28 April 1919. *Anderton* remained at Brest through the summer of 1919.

## Disposal

*Anderton* was decommissioned at Brest on 8 September 1919 and put up for sale abroad. However, her prewar owners reacquired her, and she operated commercially under her original name, *Raymond J. Anderton*, until 1922.

## InfoBox

| USS *Anderton* (SP-530) Photographed probably at the Boston Navy Yard in Boston, Massachusetts, circa August 1917 while preparing for deployment overseas. Two battleships are in the background, with that in the center being either USS *Delaware* (Battleship # 28) or USS *North Dakota* (Battleship # 29). | |
| --- | --- |
| History | |
| United States | |
| Name | * USS *Raymond J. Anderton* (1917) * USS *Anderton* (1917-1919) |
| Namesake |  |
| Builder | Robert Palmer and Son, Noank, Groton, Connecticut |
| Completed | 1911 |
| Acquired | 18 June 1917 |
| Commissioned | 18 August 1917 |
| Decommissioned | 8 September 1919 |
| Fate | Returned to owner 1919 |
| Notes | In service as commercial fishing trawler *Raymond J. Anderton* 1911-1917 and 1919-1922 |
| General characteristics | |
| Type | Patrol vessel and Minesweeper |
| Tonnage | 290 gross register tons |
| Length | 139 ft 6 in (42.52 m) |
| Beam | 23 ft 0 in (7.01 m) |
| Draft | 12 ft 0 in (3.66 m) mean |
| Speed | 11 knots |
| Armament |  |


title: Rafael Escalona

abstract: Rafael Calixto Escalona Martinez was a Colombian composer and troubadour. He was known for being one of the most prominent vallenato music composers and troubadours of the genre and for being the co-founder of the Vallenato Legend Festival, along with Consuelo Araújo and Alfonso López Michelsen. He was also a long-time friend of Gabriel García Márquez, who included him in his stories and once told him that his own masterpiece novel, One Hundred Years of Solitude, was just a 350-page Vallenato. Escalona's songs compile the history and stories of the Magdalena Department of the past 20th century. Escalona was an atypical music composer: he does not play any instruments or sing so his songs can in some ways be difficult to analyze. His songs constitute a legacy of a past generation of Colombians in his memory, a pictorial collage, full of grace, that narrates stories, customs and gossips from his region. He also left a legacy of his loves and pains, humour and poetry. In 1991, Caracol TV produced a television series named Escalona, after him.

text:
# Rafael Escalona

**Rafael Calixto Escalona Martinez** (May 26, 1926 – May 13, 2009) was a Colombian composer and troubadour. He was known for being one of the most prominent vallenato music composers and troubadours of the genre and for being the co-founder of the Vallenato Legend Festival, along with Consuelo Araújo and Alfonso López Michelsen.

He was also a long-time friend of Gabriel García Márquez, who included him in his stories and once told him that his own masterpiece novel, *One Hundred Years of Solitude*, was just a 350-page Vallenato. Escalona's songs compile the history and stories of the Magdalena Department of the past 20th century. Escalona was an atypical music composer: he does not play any instruments or sing so his songs can in some ways be difficult to analyze. His songs constitute a legacy of a past generation of Colombians in his memory, a pictorial collage, full of grace, that narrates stories, customs and gossips from his region. He also left a legacy of his loves and pains, humour and poetry. In 1991, Caracol TV produced a television series named *Escalona*, after him.

## Early life

He was born on May 26, 1926, to Colonel Clemente Escalona Labarces, veteran of Thousand Days War and Margarita Martinez Celedon in Patillal. Because Patillal was a village in a rural area surrounded by farms, it was relatively small and there wasn't that much to do after school, other than play with other kids and make up games; build miniature farms or build kites and fly them all day. He had a very happy childhood, and dreamed of becoming a painter or cartoonist, usually drawing funny depictions of classmates and teachers. But his all time friend and classmate, Jaime Molina was better at drawing than him, something that drove him instead, to read poetry and songs. He grew up listening to peasants and troubadours of the region that often passed by the village bringing news from Valledupar and other regions, since there was no post office or other source of news that arrived at this isolated place.

## Youth, the High School Dropout

He moved to Valledupar to attend high school at The Loperena National High School where he composed his first song at the age of fifteen in 1943 called "El profe Castañeda". He wrote the song in honor and sadness of his favourite teacher being transferred to a school in Riohacha, his natural reaction was to dedicate a song to "el viejo Pedro" as he called him, since he grew up listening to local troubadours. His classmates, who were also saddened over the teacher's departure, embraced his song. From then on, he saw himself doing something that he was good at, and started writing songs whenever a situation merged; started composing about his love experiences, about the people that interacted with him or were known in the region and these people's stories of happenings, basically compilations of his everyday experiences and thoughts. In 1945, feeling bored and short of motivation for school, Escalona was transferred to a school in Barranquilla for a short period and then to the Celedon Lyceum High School in Santa Marta, where he composed "El Hambre del Liceo" (the lyceum Hunger), complaining about the poor food quality that the school offered. Tired of school he dropped out and went back to Valledupar.

## The Farmer

In Valledupar he devoted his time to working at his parents’ farm and learning about agriculture. He started planting rice. Apparently he also tried to break into the illegal coffee trade by bringing contraband from Aruba with a friend named "Pipe" Socarras. He became a partygoing "parrandero" and a heavy drinker of whiskey and rum. He also started courting many women at once. On April 14, 1951, he finally married Marina Arzuaga Mejía, also known as "La Maye", who would give him six of his presently suspected thirty-six children. (After many years, he would divorce her).

## An approach to Politicians

By the 1950s he had become a renowned composer and usually befriended with local political leaders in "parrandas". He always departed with people from Patillal including Hernando Molina, husband of Consuelo Araújo. By the 1960s, when former President of Colombia Alfonso López Michelsen became governor of the newly created Department of Cesar, Lopez was invited to live in Hernando Molina's house. In this "vallenato parrandas" or parties, Escalona, Consuelo Araújo and Lopez decided to create a Vallenato Festival. López also invited them in many occasions to Bogotá, where he organized vallenato parrandas and introduced them to Colombia's political leaders. In 1968 the first Vallenato Legend Festival took place.

## Death

He died on the afternoon May 13, 2009, in Bogotá, Colombia due to heart failure. He had been interned for almost two weeks in the Santa Fe Clinic in Bogotá and had been on a medical ventilator and unconscious earlier that day. Before he died Escalona received a visit from the Colombian Ex-President Ernesto Samper Pizano.

## Songs

* "El Hambre del Liceo"
* "La casa en el aire"
* "Elegía a Jaime Molina"
* "La vieja sara"
* "El Almirante Padilla"
* "La patillalera"
* "La custodia de Badillo"
* "El villanuevero"
* "El general Dangond"
* "La historia"
* "Honda herida"
* "La brasilera"
* "El arco iris"
* "El perro de Pavajeau"
* "EL jerre jerre"
* "La Privincia"
* "El testamento"
* "El Bachiller"
* "Maria Tere"

## InfoBox

| Rafael Escalona | |
| --- | --- |
| Rafael Escalona | |
| Background information | |
| Birth name | Rafael Calixto Escalona Martinez |
| Also known as | "El Maestro" (The Master) |
| Born | (1926-05-26)May 26, 1926
Patillal, Cesar, Colombia |
| Died | May 13, 2009(2009-05-13) (aged 82)
Bogotá, DC, Colombia |
| Genres | Vallenato |
| Occupation(s) | Composer, diplomat |
| Years active | 1941–2009 |


title: Maxwell Wintrobe

abstract: Maxwell Myer Wintrobe was an Austrian-born American physician who was a 20th-century authority in the medical field of hematology and one of the pioneers of chemotherapy. His 1942 textbook on hematology, Clinical Hematology, was the first dedicated work in the field and he contributed to the diagnostic approach of anemia and copper metabolism, amongst many other achievements.

text:
# Maxwell Wintrobe

**Maxwell Myer Wintrobe** (October 27, 1901 – December 9, 1986) was an Austrian-born American physician who was a 20th-century authority in the medical field of hematology and one of the pioneers of chemotherapy. His 1942 textbook on hematology, *Clinical Hematology*, was the first dedicated work in the field and he contributed to the diagnostic approach of anemia and copper metabolism, amongst many other achievements.

## Biography

Wintrobe was born in Austria (Fred 2007), contrary to previous historical records. His family name reflects the Jewish origin of his parents, Herman and Ethel, who emigrated from Austria with their son Max in 1906. Canadian census records show that the family arrived in Halifax, Nova Scotia in 1906, where Ethel's four brothers were living at the time. The family moved to Manitoba in 1912. Wintrobe attended the University of Manitoba from the early age of 15, where he graduated in 1921 and obtained his M.D. in 1926. He married Becky Zamphir, and moved to the United States, where he obtained a PhD at Tulane University in New Orleans, Louisiana in 1929; his thesis was titled "The Erythrocyte in Man".

Initially working in Johns Hopkins Hospital, where he served on the faculty, he was appointed as professor of internal medicine at the College of Medicine of the University of Utah in 1943; he also served as the first Chairman of the Department of Medicine and physician-in-chief for the Salt Lake County General Hospital.

In Salt Lake City he led research in hereditary and metabolic disorders (1945–1973) and cardiovascular research (1969–1973). He retired officially in 1965, but remained in function until 1973 (Valentine 1990). In that year he was elected to the National Academy of Sciences.

## Works

In New Orleans, Wintrobe pioneered new ways of measuring the hematocrit, including what are now known as Wintrobe indices: mean cell volume, mean cell hemoglobin, and mean cell hemoglobin concentration, all quantitative measures of the red blood cell population (Wintrobe 1932). Much of this work continued in Hopkins and Utah, where he also worked on pernicious anemia, copper metabolism and Wilson's disease, sickle-cell disease and other anemias.

Wintrobe was the principal editor of *Clinical Hematology*, which first appeared in 1942 and is in its eleventh edition (Greer *et al.* as of 2003), still bearing his name. He was part of the team that pioneered the use of chemotherapy in cancer (Goodman *et al.* 1946). He was one of the editors of the first edition (1950) of *Harrison's Principles of Internal Medicine*.

In 1980, he published *Blood, pure and eloquent*, and in 1985 he published *Hematology, the Blossoming of a Science*. Both works are historical overviews of his field.

* Fred, H. L. (2007). "Maxwell Myer Wintrobe: New history and a new appreciation". *Texas Heart Institute Journal*. **34** (3): 328–335. PMC 1995040. PMID 17948084.
* Goodman, L. S.; Wintrobe, M. M.; Dameshek, W.; Goodman, M. J.; Gilman, A.; McLennan, M. T. (1984). "Landmark article Sept. 21, 1946: Nitrogen mustard therapy. Use of methyl-bis(beta-chloroethyl)amine hydrochloride and tris(beta-chloroethyl)amine hydrochloride for Hodgkin's disease, lymphosarcoma, leukemia and certain allied and miscellaneous disorders. By Louis S. Goodman, Maxwell M. Wintrobe, William Dameshek, Morton J. Goodman, Alfred Gilman and Margaret T. McLennan". *JAMA: The Journal of the American Medical Association*. **251** (17): 2255–2261. doi:10.1001/jama.251.17.2255. PMID 6368885.
* Greer JP, Foerster J, Lukens JN. *Wintrobe's Clinical Hematology*, 11th edition. Lippincott Williams & Wilkins, 2003. ISBN 0-7817-3650-1.
* Valentine WN. *Maxwell Myer Wintrobe*. In "Biographical Memoirs". National Academy of Sciences 1990;59:446-472. ISBN 0-309-04198-8. Fulltext.
* Wintrobe, M. M. (1990). "The size and hemoglobin content of the erythrocyte. Methods of determination and clinical application. 1932". *The Journal of Laboratory and Clinical Medicine*. **115** (3): 374–387. PMID 2179436.
* Wintrobe MM. *Blood, pure and eloquent; a story of discovery, of people and ideas.* New York: McGraw-Hill, 1980. ISBN 0-07-071135-6.
* Wintrobe MM. *Hematology, the Blossoming of a Science: A Story of Inspiration and Effort*. Lippincott Williams & Wilkins, 1985. ISBN 0-8121-0961-9.

## InfoBox

| Maxwell Wintrobe | |
| --- | --- |
| Born | (1901-10-27)27 October 1901<br>Austria, Austria-Hungary |
| Died | 9 December 1986(1986-12-09) (aged 85) |
| Occupation | Physician |
| Known for | Wintrobe hematocrit method, introduced in 1929 |


title: Wakai Station

abstract: Wakai Station Wakai Station is a junction passenger railway station located in the town of Shimanto, Takaoka District, Kōchi Prefecture, Japan. It is operated the third-sector Tosa Kuroshio Railway, for which it is station number "TK27" and is also used by the Shikoku Railway Company, for which it has the station number "G27".

text:
# Wakai Station

**Wakai Station** (若井駅, *Wakai-eki*) is a junction passenger railway station located in the town of Shimanto, Takaoka District, Kōchi Prefecture, Japan. It is operated the third-sector Tosa Kuroshio Railway, for which it is station number "TK27" and is also used by the Shikoku Railway Company (JR Shikoku), for which it has the station number "G27".

## Lines

Wakai Station is the nominal terminus of the 77.8 kilometer JR Shikoku Yodo Line to Uwajima Station, although most trains continue past Wakai to terminate at Kubokawa Station. It is also served by the Tosa Kuroshio Railway Nakamura Line and is 4.4 kilometers from the terminus of that line at Kubokawa Station.

## Layout

The station has one side platform serving one track, located on an embankment. At an unmanned station, there is a waiting area on the platform, but no station building. As mentioned above, it is a jointly used station under the jurisdiction of Tosa Kuroshio Railway, and the station name sign is Tosa Kuroshio Railway specification.

## Adjacent stations

| « | | Service | » | |
| --- | --- | --- | --- | --- |
| Tosa Kuroshio Railway | | | | |
| Nakamura Line | | | | |
| Kubokawa |  | Local |  | Kaina |

## Kawaoku S.B.

**Kawaoku S.B.** *Kawaoku Shingōjō* (川奥信号場) is a junction of Tosa Kuroshio Railway Nakamura Line and Shikoku Railway Company Yodo Line in Kawaoku, Kuroshio, Hata District, Kōchi .

The Yodo Line track divides from Nakamura Line at this junction. The track between this junction and Wakai Station is shared by two lines. The shared track and the junction are possessed by Tosa Kuroshio Railway.

### Structure

This S.B. is about 3.6 km far from Wakai Station. This S.B. is on the way of spiral of Nakamura Line between Wakai and Kaina.

Trains of both lines can pass.

One track is straightened so that the trains of Nakamura Line including limited express Nanpū can pass the S.B. without slowing down.

### History

* 1 March 1974 Yodo Line and this S.B. opened.
* 1 April 1987 Both line and the S.B. were inherited by Shikoku Railway Company.
* 1 April 1988 Nakamura Line and the S.B. were inherited by Tosa Kuroshio Railway.

## Surrounding area

## InfoBox

| G27
Wakai Station
若井駅 | |
| --- | --- |
| A view of the platform of Wakai station in September 2007 | |
| General information | |
| Location | Wakai, Shimanto Town, Takaoka District
Kōchi Prefecture 786-0068
Japan |
| Coordinates | 33°11′17″N 133°06′21″E / 33.18807°N 133.105861°E / 33.18807; 133.105861 |
| Operated by |  |
| Line(s) |  |
| Distance | 4.4 km (2.7 mi) from Kubokawa |
| Platforms | 1 side platform |
| Tracks | 1 |
| Construction | |
| Accessible | No - steps lead up to platform |
| Other information | |
| Status | Unstaffed |
| Station code | TK27, G27 |
| History | |
| Opened | 18 December 1963 (1963-12-18) |
| Passengers | |
|  | |
| FY2018 | 17 |
|  | |
|  | |
| Services | |
| Preceding station  JR Shikoku Following station  IejigawaG28towards Uwajima  Yodo Line  KubokawaTerminus | |
|  | |
|  | |
|  | |
| Location  Wakai StationLocation within Kochi PrefectureWakai StationWakai Station (Japan) | |


title: Pierre Parisot

abstract: Pierre Parisot (1697–1769) was a French priest of the Order of Friars Minor Capuchins and a missionary. He was called also Père Norbert, Curé Parisot, Norbert de Bar-le-Duc, Norbert de Lorraine, or Abbé Platel. He opposed Jesuits and wrote against them in his Memoirs of the East Indian Missions in 1744, exposing the methods by which they were obtaining conversions.

text:
# Pierre Parisot

**Pierre Parisot** (16971769) was a French priest of the Order of Friars Minor Capuchins and a missionary. He was called also *Père Norbert*, *Curé Parisot*, *Norbert de Bar-le-Duc*, *Norbert de Lorraine*, or *Abbé Platel*.

He opposed Jesuits and wrote against them in his *Memoirs of the East Indian Missions* in 1744, exposing the methods by which they were obtaining conversions.

## Early life

He was born in Bar-le-Duc in 1697.

## Career

He went by several names, including Père Norbert, Curé Parisot, Norbert de Bar-le-Duc, Norbert de Lorraine, or Abbé Platel. He opposed Jesuits and wrote against them in his *Memoirs of the East Indian Missions* in 1744, exposing the methods by which they obtained conversions. He entered the holy orders and was dispatched on a mission to India as a Capuchin Friar. He became a Capuchin friar in 1716 was ordained to priesthood in 1729. In December 1736, he was appointed as the Procurator of the French mission and was sent to Malabar and later to Pondicherry. He stayed in India for four years, including three years in Pondicherry where he came in contact with Jesuits that led to a conflict.

## Conflict with Jesuits

During his stay in Pondicherry, he came in contact with Jesuits leading to a conflict on the issue of the struggle of the Malabaric rites*.* Claude de Visdelou, a French Jesuit missionary in China had issues in regulating and prohibiting the use of Chinese Rites. Visdelou had arrived in Pondicherry from China on June 25, 1709, long before Parisot. Visdelou remained in Pondicherry until his death as he was not allowed to return to France. As both Visdelou in exile and Pierre Parisot were living in the same House of the Capuchins in the same town, they had issues regarding Malabari rites and thus launched the conflict.

Upon his return to France, Parisot published *Historical Memoirs of the Missions in the Indies* \- a vindictive work with regards to the Society of Jesus. However, his own Order of Friars Minor Capuchin did not support him, and instead opposed him so strongly as to force him to move to England.

He supported himself in England by establishing a tapestry and Turkish carpet manufactory in Paddington, under the patronage of the Duke of Cumberland. He moved it in 1753 to Fulham High Street (possibly on the site now home to building numbers 49-55) with the idea of a 'youth training scheme', where the Gobelins Manufactory had already been established. He eventually returned to France, under the name Abbé Platel, visiting Germany and Portugal while undergoing persecution.

After returning to France, he again wrote and published his principal work *History of the Society of Jesus, from its first foundation by Ignatius Loyola* in six volumes.

## Works


title: Weissella thailandensis

abstract: Weissella thailandensis is a species of Gram-positive bacteria. It is a homofermentative, sphere-shaped lactic acid bacteria. Its type strain is FS61-1T. Its genome has been sequenced.

text:
# Weissella thailandensis

***Weissella thailandensis*** is a species of Gram-positive bacteria. It is a homofermentative, sphere-shaped lactic acid bacteria. Its type strain is FS61-1T (= PCU 210T = NRIC 0298T = HSCC 1412T = JCM 10695T = TISTR 1384T). Its genome has been sequenced.

1. Tanasupawat, S.; Shida, O.; Okada, S.; Komagata, K. (2000). "Lactobacillus acidipiscis sp. nov. and Weissella thailandensis sp. nov., isolated from fermented fish in Thailand". *International Journal of Systematic and Evolutionary Microbiology*. **50** (4): 1479–1485. doi:10.1099/00207713-50-4-1479. ISSN 1466-5026. PMID 10939653.
2. Benomar, N.; Abriouel, H.; Lee, H.; Cho, G.-S.; Huch, M.; Pulido, R. P.; Holzapfel, W. H.; Galvez, A.; Franz, C. M. A. P. (2011). "Genome Sequence of Weissella thailandensis fsh4-2". *Journal of Bacteriology*. **193** (20): 5868. doi:10.1128/JB.05883-11. ISSN 0021-9193. PMC 3187202. PMID 21952542.

## Further reading

## InfoBox

| *Weissella thailandensis* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Bacteria |
| Phylum: | Bacillota |
| Class: | Bacilli |
| Order: | Lactobacillales |
| Family: | Lactobacillaceae |
| Genus: | *Weissella* |
| Species: | ***W. thailandensis***
Tanasupawat *et al*. 2000 |
|
| Synonyms | |
| * *Weissella jogaejeotgali* Lee *et al*. 2015 | |


title: Haploparmena marmorata

abstract: Haploparmena marmorata is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1940.

text:
# Haploparmena marmorata

***Haploparmena marmorata*** is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1940.

## InfoBox

| *Haploparmena marmorata* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Cerambycidae |
| Genus: | *Haploparmena* |
| Species: | ***H. marmorata*** |
| Binomial name | |
| ***Haploparmena marmorata***<br>Breuning, 1940 | |
|


title: Ingalls Kimball

abstract: Ingalls Kimball was an American printer and entrepreneur.

text:
# Ingalls Kimball

**Ingalls Kimball** (born Hannibal Ingalls Kimball; April 2, 1874  October 16, 1933) was an American printer and entrepreneur.

## Early years

Kimball was born in West Newton, Massachusetts to American entrepreneur Hannibal Ingalls Kimball and Mary (Cook) Kimball. He attended Harvard College from 1890 to 1894.

## Career

After graduation, he started the publishing and printing business Stone & Kimball with Herbert S. Stone.

In 1897, Kimball established the Cheltenham Press in New York City. A year later, Kimball commissioned American architect and type designer Bertram Grosvenor Goodhue to design the namesake Cheltenham typeface, considered at one point to be the most widely known typeface in the United States.

In 1916, Kimball established the “National Thrift Bond Corporation.”

## InfoBox

| Ingalls Kimball | |
| --- | --- |
| Born | Hannibal Ingalls Kimball<br>West Newton, Massachusetts |
| Died | October 16, 1933(1933-10-16) (aged 59) |
| Nationality | American |
| Occupation | Entrepreneur |