text:
Governor-General of Finland

The governor-general of Finland (Suomen kenraalikuvernööri; generalguvernör över Finland; генерал-губернатор Финляндии) was the military commander and the highest administrator of Finland sporadically under Swedish rule in the 17th and 18th centuries and continuously in the autonomous Grand Duchy of Finland between 1809 and 1917.

Swedish realm
After the final abolition of the Duchy of Finland and related feudal privileges in the late 16th century, the king of Sweden sporadically granted most or all of Finland under a specially appointed governor-general, who took care of the matters in the eastern part of the country more or less according to his own best judgement. Best known of these officials is count Per Brahe whose reign is still referred to in Finland as the "count's days" (kreivin aikaan), meaning something positive that happens just in time.

List of Swedish governors-general of Finland
Translation in Generalguvernör av Finland

Grand Duchy of Finland
During the time when Finland was ruled by the Russian Empire as a grand duchy, the governor-general's position was permanent. He was viceroy of the emperor, who was not personally present in Helsinki, but resided in St Petersburg, just outside of Finnish borders. The governor-general was constitutionally the chairman of the Senate of Finland, the government in the autonomous grand duchy. The chairmanship he represented, with two votes in the Senate, belonged to the grand duke of Finland, a title held by the emperor of Russia. The governor-general was the highest representative of the emperor and received his instructions directly from the imperial government in Saint Petersburg.

Finnish citizenship was not required of the governor-general, contrary to all other highest positions such as senators and the minister-secretary of state. Most governors-general were Russians, men whom the emperor trusted as counterparts of potential Finnish separatism. Many of them, up to Baron Platon Rokassovsky, however were also made Finnish subjects, by granting them a Finnish nobility rank.

Many of the governors-general were disliked by the Finnish population. The first man on the post, Georg Magnus Sprengtporten, resigned after only a year. Another, Nikolai Bobrikov, was assassinated in 1904 by the Finnish nationalist Eugen Schauman. On the other hand, several governors-general worked in a way that guaranteed the Finnish autonomy in face of the interests of ministers of the imperial court.

The governor-general between 1831 and 1855, Prince Menshikov, sojourned his entire term in St Petersburg, being simultaneously the Russian minister of navy. Gubernatorial duties in Helsinki were cared for by the deputy governor-general. For most of the term, in that position was general Alexander Amatus Thesleff (born 1778).

List of Russian governors-general of Finland
Translation in Генерал-губернатор Финляндии

title: Governor-General of Finland


text:
Talk:Small business

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Raubsjosh.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 09:31, 17 January 2022 (UTC)

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 6 January 2020 and 25 April 2020. Further details are available on the course page. Student editor(s): Egarn005.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 09:31, 17 January 2022 (UTC)

Wiki Education assignment: College Composition II
— Assignment last updated by Lindseybean28 (talk) 21:24, 9 May 2024 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Small business


text:
Juniper, New Brunswick

Juniper (2001 pop.: 450) is a hamlet in Carleton County, New Brunswick, Canada. Juniper is located in Aberdeen Parish. It is situated on Route 107, which runs from Route 105 at Bristol, northeast to Juniper, and then bends southeast towards Napadogan and Deersdale. Geographic coordinates: 46° 33' North, 67° 13' West; elevation 899 ft.

Juniper is named for the low growing juniper shrub which allegedly grows in the boggy spruce forest near Juniper Station.

The local economy is largely forestry-based, which employees roughly half of the population. In November 2006, the village started experiencing trouble keeping its paper mills open due to a decrease in the price of paper.

The economy also benefits from some hunting and fishing-related tourism, as the village is on the South Branch of the Southwest Miramichi River, renowned for its salmon and trout fishing.

The nearby Juniper Barrens String Bog, the largest bog in the area, covers 12 square kilometres, and is home to the White Fringed Orchid (Platanthera blepharglottis), an uncommon type of Butterfly Orchid, and the sedge (grass) Carex eburnea. The peat is two to three metres deep. The bog is one of several unique sites in Maine and the Maritime Provinces of Canada, featured on the Irving Forest Discovery Network.

Juniper's post office dates from 1918.

Religion
The village has three churches, Roman Catholic, United Church of Canada, and a United Pentecostal Church.

Education
The village is in School District 14 and has one public school, Juniper Elementary School, formerly Juniper High School.

Transportation
A line of the Canadian national Railway passes through Juniper.

Notable people
The best known resident of the village was the Right Honourable Hugh John Flemming, Premier of New Brunswick and Canadian Federal Minister of Forestry, who was the son of Sarah and the Right Honourable James Kidd Flemming, a Premier of New Brunswick himself. He went to work at his family's mill, Flemming and Gibson, in Juniper at the age of fifteen, but retired to a home near Woodstock, New Brunswick, after retiring from Parliament in 1972, and also in Fredericton, New Brunswick.

Flemming's wife, Aida Flemming, founded the International Kindness Club for Children, a club to teach children to love and be kind to animals, and was active in a number of charities.

The New Brunswick Kindness Club now has members in many provinces and countries, including every Canadian province, the Yukon Territory, the United States, India, England, France, Norway, the West Indies, Belize, Ireland, Australia, Korea, Japan, and many countries in Africa. Doctor Albert Schweitzer, famous for his medical and humanitarian work, served as an Honorary President of the International Kindness Club, before it was incorporated into the Humane Society of the United States (HSUS), of which Mrs. Flemming became an honorary board member.

title: Juniper, New Brunswick


text:
Orf (disease)

Orf is a farmyard pox, a type of zoonosis. It causes small pustules in the skin of primarily sheep and goats, but can also occur on the hands of humans. A pale halo forms around a red centre. It may persist for several weeks before crusting and then either resolves or leaves a hard lump. There is usually only one lesion, but there may be many, and they are not painful. Sometimes there are swollen lymph glands.

It is caused by a Parapoxvirus. It can occur in humans who handle infected animals or contaminated objects. One third of cases may develop erythema multiforme. Once resolved, a person can still be infected again.

Generally, treatment options are limited. Injecting the lesion with cidofovir or applying imiquimod has been tried. It is sometimes necessary to cut them out. The vaccine used in sheep to prevent orf is live and has been known to cause disease in humans.

The disease is endemic in livestock herds worldwide. A recent outbreak emerged in southwest Ethiopia between October 2019 and May 2020.

Humans
Orf is a zoonotic disease, meaning humans can contract this disorder through direct contact with infected sheep and goats or with fomites carrying the orf virus. It causes a purulent-appearing papule locally and generally no systemic symptoms. Infected locations can include the finger, hand, arm, face and even the penis (caused by infection either from contact with the hand during urination or from bestiality). Consequently, it is important to observe good personal hygiene and to wear gloves when treating infected animals. It may appear similar to cowpox and pseudocowpox.

While orf is usually a benign self-limiting illness which resolves in 3-6 weeks, in the immunocompromised it can be very progressive and even life-threatening. One percent topical cidofovir has been successfully used in a few patients with progressive disease. Serious damage may be inflicted on the eye if it is infected by orf, even among healthy individuals. The virus can survive in the soil for at least six months.

Other animals
Orf is primarily a disease of sheep and goats although it has been reported as a natural disease in humans, steenbok and alpacas, chamois and tahrs, reindeer, musk oxen, dogs, cats, mountain goats, bighorn sheep, dall sheep, and red squirrels.

Sheep and goats
It has been recorded since the late 19th century and has been reported from most sheep-or goat-raising areas, including those in Europe, the Middle East, the United States, Africa, Asia, South America, Canada, New Zealand and Australia. Orf is spread by fomites and direct contact. In some environments, infection is injected by scratches from thistles of both growing and felled plants. Symptoms include papules and pustules on the lips and muzzle, and less commonly in the mouth of young lambs and on the eyelids, feet, and teats of ewes. The lesions progress to thick crusts which may bleed. Orf in the mouths of lambs may prevent suckling and cause weight loss, and can infect the udder of the mother ewe, thus potentially leading to mastitis. Sheep are prone to reinfection. Occasionally the infection can be extensive and persistent if the animal does not produce an immune response.

A live virus vaccine (ATCvet code: ) is made from scab material and usually given to ewes at the age of two months, but only to lambs when there is an outbreak. The vaccine can cause disease in humans.

In sheep and goats, the lesions mostly appear on or near the hairline and elsewhere on the lips and muzzle. In some cases the lesions appear on and in the nostrils, around the eyes, on the thigh, coronet, vulva, udder, and axilla. In rare cases, mostly involving young lambs, lesions are found on the tongue, gums, roof of the mouth and the oesophagus. It has also been reported a number of times to cause lesions in the rumen. In one case it was shown that a severe form of orf virus caused an outbreak involving the gastrointestinal tract, lungs, heart, as well as the buccal cavity, cheeks, tongue and lips. Another severe case was reported pharyngitis, genital lesions and infection of the hooves which led to lameness and, in some cases, sloughing of the hoof.

More typically, sheep will become free of orf within a week or so as the disease runs its course. Sheep custodians can assist by ensuring infected lambs receive sufficient milk and separating out the infected stock to slow down cross-transmission to healthy animals. It is advisable for those handling infected animals to wear disposable gloves to prevent cross infection and self-infection. A veterinarian must be contacted if there is a risk of misdiagnosis with other, more serious conditions.

title: Orf (disease)


text:
User:Roepers/sandbox

Map_wiki

title: User:Roepers/sandbox


text:
Stefan the First-Crowned

Stefan Nemanjić (Стефан Немањић, ), known as Stefan the First-Crowned (Стефан Првовенчани, ; c. 1165 – 24 September 1228), was the Grand Prince of Serbia from 1196 and the King of Serbia from 1217 until his death in 1228. He was the first Serbian king by Nemanjić dynasty; due to his transformation of the Serbian Grand Principality into the Kingdom of Serbia and the assistance he provided his brother Saint Sava in establishing the Serbian Orthodox Church.

Early life
Stefan Nemanjić was the second-eldest son of Grand Prince Stefan Nemanja and Anastasija. His older brother and heir apparent, Vukan, ruled over Zeta and the neighbouring provinces (the highest appanage) while his younger brother Rastko (later known as Saint Sava) ruled over Hum.

The Byzantines attacked Serbia in 1191, raiding the banks of the South Morava. Nemanja had a tactical advantage, and began to raid the Byzantine armies. Isaac II Angelos summoned a peace treaty, and the marriage of Nemanja's son Stefan to Eudokia Angelina, the niece of Isaac II, was confirmed. Stefan Nemanjić received the title of sebastokrator.

Conflict over succession
Throughout the 12th century, Serbs were at the center of war events between Byzantium and Hungary for dominance. In such circumstances, Serbs had no chance of gaining independence. Their only chance was to look for an ally on third side.

In 1190, the German Emperor Friedrich Barbarossa drowned in the river Calycadnus. At the same time, Emperor Isaac II Angelos launched a punitive expedition against the Serbs, and Nemanja was defeated in the battle of South Morava. In fact, Constantinople did not want to subdue the Serbs, but to regain Niš and the main road to Belgrade, as well as to make allies of the rebellious Serbs. The peace treaty provided for Stefan Nemanjić, the middle son of the grand zoupan Stefan Nemanja, to marry a Byzantine princess, i.e. niece of the Byzantine emperor.

The concluded peace envisages that the grand zoupan Nemanja will be succeeded by his middle son Stefan, who received the Byzantine title of sebastokrator and the Byzantine princess Eudokia for a wife, and not the firstborn Vukan.

In 1196, at the state assembly near Church of Saints Peter and Paul, Stefan Nemanja abdicated the throne in favor of his middle son Stefan, who became the grand zoupan of Serbia. He left his eldest son Vukan in charge of Zeta, Travunija, Hvosno and Toplica. Nemanja became a monk in his old age and was given the name Simeon. Shortly afterwards, he went to Byzantium, to Mount Athos, where his youngest son Sava had been a monk for some time. They received permission from the Byzantine emperor to rebuild the abandoned Hilandar monastery. The new Pope Innocent III, who in a letter in 1198 called on the entire West to liberate the Holy Land, was not satisfied with the fact that the Serbs were subordinated to the Patriarch of Constantinople, but wanted to return them to Rome through Vukan. In 1198, the Hungarian dux Andrew conquered Hum (Hercegovina) of grand zoupan Stefan and rebelled against brother king Emeric but did not gain legitimacy from Rome. In any case, the Hungarians became dominant on the eastern Adriatic coast. But Venice, because of its business interests, did not like the eastern coast of the Adriatic to be controlled by the mighty Byzantium or Hungary. Vukan and the Hungarian king Emeric (1196–1204) make an alliance against Stefan, after which a civil war breaks out in Serbia. The action against Stefan was preceded by his letter to the Pope in which he asked for the crown. Around 1200, Stefan expelled his wife Eudokia, a daughter of Alexios III Angelos, who found refuge with Vukan in Zeta. Emeric saw Stefan's move as an open attack on his crown, because in Hungary it was traditionally believed that only it in the region could have primacy with the Roman pope. Stefan lost the conflicts and had to flee the country in 1202 to the ruler of Bulgaria Kaloyan.

In the meantime, control of the newly formed crusade army was taken over by the powerful Venetian doge Enrico Dandolo, who, to the surprise of all, including the pope himself, in the Fourth Crusade first sent an attack on Hungarian Zara in 1202, and then on Byzantium, whose capital Constantinople crusaders conquered in April 1204. Stefan uses this situation and in the counter-offensive, with the help of Prince Kaloyan, he returns to the throne in Ras in 1204, while Vukan retreats to Zeta. The fighting between the brothers was stopped in 1205 and relations were established as they were before the outbreak of the conflict. Meanwhile, in November 1204, the Hungarian king Emeric died and the Kaloyan of Bulgaria was crowned for king by the Pope.

Numerous states were created on the ruins of Byzantium, which were almost equal in strength. The Crusaders founded the Kingdom of Thessalonica, the principality of Achaia, the duchy of Athens and Thebes, the duchy of Archipelago or Naxos. They were all under rule of Latin emperor of Constantinople. The remaining Byzantine factions also formed their own successor states on the fringes of the empire, at Niceae and Trebizond in Asia Minor, and at Epiros in west Balkan. Of the newly created Greek states, two gained some stability and survived through this period: Niceae under the Laskaris dynasty, which soon became an empire (1208), and Epiros, which took considerably to rise to same status (1224–27). The two rivals sought to present themselves as lawful successor of Empire of the Romans and to get the upper hand in the struggle for its restoration. Bulgaria was located to the north, and Serbia to the northwest. Serbia's neighbors at the time were Epirus to the south, Bulgaria to the east, and the Hungary to the north and west.

Later rule
After the death of Kaloyan, there was a succession war in Bulgaria. Tsar Boril, the most ambitious of the nobles, took the throne and exiled Alexius Slav, Ivan Asen II and Strez (of the Asen family). Strez, the first cousin or brother of Boril, took refuge in Serbia, and was warmly welcomed at the court of Stefan II. Even though Boril requested the extradition of Strez to Bulgaria with gifts and bribes, Stefan II refused. Kaloyan had conquered Belgrade, Braničevo, Niš and Prizren, all of which were claimed by Serbia. At the same time, Boril was unable to take military action against Strez and his Serbian patron, as he had suffered a major defeat at the hands of the Latins at Plovdiv. Stefan went as far as to become a blood brother with Strez, in order to assure him of his continued favor.

Andrija Mirosavljević was entitled to the governance of Hum, as the heir of Miroslav of Hum, the uncle of Stefan II, but the Hum nobles chose his brother Petar as Prince of Hum. Petar exiled Andrija and Miroslav's widow (the sister of Ban Kulin of Bosnia), and Andrija fled to Serbia, to the court of Stefan II. In the meantime, Petar fought successfully with neighbouring Bosnia and Croatia. Stefan sided with Andrija and went to war and secured Hum and Popovo field for Andrija sometime after his accession. Petar was defeated and crossed the Neretva, continuing to rule the west and north of the Neretva, which had in 1203 been briefly occupied by Andrew II of Hungary. Stefan gave the titular and supreme rule of Hum to his son Radoslav, while Andrija held the district of Popovo with the coastal lands of Hum, including Ston. By agreement, when Radoslav died, the lands were bound to Andrija.

Đorđe of Zeta, in order to secure his lands from Stefan, accepted Venetian suzerainty, possibly in 1208. Đorđe may have done this due to tensions between the two, although this must not be the case. Venice, after the Fourth Crusade, tried to exert control of the Dalmatian ports, and managed in 1205 to submit Ragusa – Đorđe submitted to prevent that Venice claimed his ports of southern Dalmatia.

Đorđe promised Venice military aid in case of a revolt by another theoretical Venetian vassal, Dhimitër Progoni, the Prince of Albania and Lord of Kruja. This was likely related to the Serbia-Zeta conflict. Stefan II married off his daughter, Komnena, to prince Dhimitër Progoni in 1208. The marriage resulted in close ties and an alliance between Stefan and Dimitri amidst these conflicts. Kruja is conquered by Epirote Despot Michael I Komnenos Doukas, and Dimitri is not heard of in any surviving sources. After Dhimitër's death, the lands are left to Komnena, who soon married Greek-Albanian Gregorios Kamonas, who took power of Kruja, strengthening relations with Serbia, which had after a Serbian assault on Scutari been weakened. Đorđe disappears from sources, and Stefan II controls Zeta by 1216, probably through military action. Stefan either put Zeta under his personal rule, or assigned it to his son Stefan Radoslav. Zeta would from now on have no special status, and would be given to the heir apparent.

Despot Michael I of Epirus conquered Skadar, and tried to press beyond, but was stopped by the Serbs and his murder by one of his servants in 1214 or 1215. He was succeeded by his half-brother Theodore Komnenos Doukas. Theodore took on a policy of aggressive expansion, and allied himself with Stefan II. Stefan Radoslav married Anna Angelina Komnene Doukaina, the daughter of Theodore.

Coronation and autocephaly
Having long wanted to call himself king, Stefan set about procuring a royal crown from the papacy. It is not clear what Stefan promised in regard to the status of the Catholic Church, which had numerous adherents in the western and coastal parts of his realm, but a papal legate finally arrived in 1217 and crowned Stefan. In 1217 Stefan Nemanjić declared his independence from Byzantium and was crowned as king, adopting the title: "Crowned King and Autocrat of all Serbian and coastal lands". The influence of the Catholic Church in Serbia did not last long but angered Serbian clergy. Many opposed Stefan's coronation, with Sava protesting by leaving Serbia and returning to Mount Athos. Later Serbian churchmen were also bothered by Stefan's relations with the papacy; while Stefan and Sava's contemporary Domentian wrote that the coronation was performed by a papal legate, a century later Theodosius the Hilandarian claimed that Stefan was crowned by Sava. The contradiction led some Serbian historians to conclude that Stefan underwent two coronations, first by the legate and in 1219 by Sava, but modern scholars tend to agree that only the former took place.

The disagreements surrounding Stefan's coronation were definitively resolved in 2018 by finding evidences that the papal legate never came to Serbia and that Stefan was actually crowned by his brother Sava in 1219.

Marriage, monastic vows, and death
Stefan was married, around 1186, to Eudokia Angelina, the youngest daughter of Alexius Angelus and Euphrosyne Doukaina Kamaterina. Eudokia was the niece of the current Byzantine Emperor Isaac II Angelus. Isaac II arranged the marriage. According to the Greek historian Nicetas Choniates, Stefan and Eudocia quarreled and separated, accusing one another of adultery, after June 1198. They had three sons and two daughters:

 * King Stefan Radoslav, ruled 1228–1233
 * King Stefan Vladislav I, ruled 1233–1243
 * Archbishop Sava II (born Predislav, proclaimed Saint)
 * Princess Komnena Nemanjić, Grand Duchess of Kruja

Stefan remarried in 1207/1208, his second wife was Anna Dandolo, granddaughter of Venetian doge Enrico Dandolo. They had one son and one daughter:

He built many fortresses including Maglič. At the end of his life, Stefan took the monastic vow under the name Symeon and died soon after. He was canonized as his father was.
 * King Stefan Uroš I, ruled 1243–1276

Legacy
Local tradition, related to the Reževići Monastery claims that it was king Stefan who built (in 1223 or 1226) the Church of the Dormition of the Mother of God (Црква Успења Пресвете Богородице).

In fiction

 * The 2017 television series Nemanjići – rađanje kraljevine (Nemanjić Dynasty – Birth of a Kingdom) features him as the main protagonist.

title: Stefan the First-Crowned


text:
User:Poor-brother

Dear Wikipedians,

I heard about Wiki on NPR last week and, I have to say, am wholly impressed and excited! I'll update this page off and on, but for now here is a little information you can use to get to know me better:

http://profiles.yahoo.com/herveus

http://www.celtic-catholic-church.org

title: User:Poor-brother


text:
Talk:Reiter's syndrome

Redirect categorization
This redirect was categorized based on scheme outlined at WP:DERM:CAT. ---kilbad (talk) 01:28, 10 February 2010 (UTC)

title: Talk:Reiter's syndrome


text:
Rassa

Rassa may refer to:

 * Rässa, a village in Saare County, Estonia
 * Rassa, Piedmont, town in Italy
 * Refugee Advocacy Service of South Australia
 * Rassa or ryasa or rason, the word for a cassock in the Eastern Orthodox church
 * Rassa, alternative spelling for the village of Rassau in Wales
 * Rassa, variante spelling for the region of Raška in Latin sources

title: Rassa


text:
Principality of Serbia (early medieval)

The Principality of Serbia (Кнежевина Србија) was one of the early medieval states of the Serbs, located in the western regions of Southeastern Europe. It existed from the 8th century up to c. 969–971 and was ruled by the Vlastimirović dynasty. Its first ruler known by name was Višeslav who started ruling around 780. While by that time, starting from the year 680–681, the Bulgarian state had taken the lands to the east. Vlastimir resisted and defeated the Bulgarian army in a three-year-war (839–842), and the two powers lived in peace for some decades. Vlastimir's three sons succeeded in ruling Serbia together, although not for long; Serbia became a key part in the power struggle between the Byzantines and Bulgarians, predominantly allied with the Byzantines, which also resulted in major dynastic wars for a period of three decades. The principality was annexed in 924 by Simeon I and subjected to Bulgarian rule until 933 when Serbian prince Časlav was established as ruler of the Serbian land, becoming the most powerful ruler of the Vlastimirović dynasty.

An important process during this period was the Christianization of the Serbs, completed by the establishment of Christianity as state-religion in the second half of the 9th century. The principality was annexed by the Byzantines in c. 969–971 and ruled as the Catepanate of Ras. The main information of the history of the principality and Vlastimirović dynasty are recorded in the contemporary historical work De Administrando Imperio (written c. 948–949).

Background
Slavs (Sklavenoi) settled throughout the Balkans during the 6th and the 7th centuries, thus marking the end of the early Byzantine rule in those regions. The history of the early medieval Serbian principality and the Vlastimirović dynasty is recorded in the work De Administrando Imperio (On the Governance of the Empire, abbr. "DAI"), compiled by the Byzantine Emperor Constantine VII Porphyrogenitus (r. 913–959). The work mentions the first Serbian ruler, without a name (known conventionally as "Unknown Archon"), that led the White Serbs to southeastern Europe and received the protection of Emperor Heraclius (r. 610–641), prior to the Bulgar invasion (680). The Serbian ruler was titled "Prince (archon) of the Serbia" (αρχων Σερβλίας). The DAI mentions that this ruler was succeeded by a son, followed by a grandson, and historians generally accept the accounts of DAI on succession of princes from the same family, but their names are unknown until the coming of Višeslav (c. 780-800).

Višeslav, Radoslav and Prosigoj (circa 780–830)

The time and circumstances of the first three Serbian rulers are almost unknown. The first of the dynasty known by name was Višeslav who began his rule around 780, being a contemporary of Charlemagne (fl. 768–814). The Serbs at that time were organized into župe (sing. župa), a confederation of village communities (roughly the equivalent of a county), headed by a local župan (a magistrate or governor); the governorship was hereditary, and the župan reported to the Serbian prince, whom they were obliged to aid in war. According to DAI, "baptized Serbia" (known erroneously in historiography as Raška), included the inhabited cities (καστρα/kastra) of Destinikon (Δεστινίκον), Tzernabouskeï (Τζερναβουσκέη), Megyretous (Μεγυρέτους), Dresneïk (Δρεσνεήκ), Lesnik (Λεσνήκ), and Salines (Σαληνές), while the "small land" (χοριον/chorion) of Bosnia (Βοσωνα), part of Serbia, had the cities of Katara (Κατερα) and Desnik (Δέσνηκ). The other Serb-inhabited lands (or principalities) that were mentioned included the "countries" of Paganija, Zahumlje and Travunija, while the "land" of Duklja was held by the Byzantines (it was presumably settled with Serbs as well). Given the large territory, the Serbs most likely arrived as a small military elite which managed to organize and assimilate other already settled and more numerous Slavs. These polities bordered "Serbia" to the north. The exact borders of the early Serbian state are unclear.

Although Višeslav is only mentioned by name, the DAI mentions that the Serbs served the Byzantine Emperor and that they were at this time at peace with the Bulgars, whose neighbors they were and with whom they shared a common frontier. The First Bulgarian Empire, under Telerig, planned to colonize some of their lands with more Slavs from the neighbouring Berziti, as the earlier Bulgar expansion had caused massive Slav migrations and depopulation of Bulgaria — in 762, more than 200,000 people fled to Byzantine territory and were relocated to Asia Minor. The Bulgars were defeated in 774, after Constantine V learned of their planned raid. In 783, a large Slavic uprising took place in the Byzantine Empire, stretching from Macedonia to the Peloponnese, which was subsequently quelled by Byzantine patrikios Staurakios.

Višeslav was succeeded by his son Radoslav, then grandson Prosigoj, and one of these two most likely ruled during the revolt of Ljudevit Posavski against the Franks (819–822); according to Einhard's Royal Frankish Annals, written in 822, Ljudevit went from his seat at Sisak to the Serbs, with Einhard mentioning that for the Serbs "is said to be holding a great part of Dalmatia" (ad Sorabos, quae natio magnam Dalmatiae partem obtinere dicitur). According to Živković, the usage of the term Dalmatia in the Royal Frankish Annals to refer both to the land where Serbs ruled as well as to the lands under the rule of Croat duke, was likely a reflection of the Franks' territorial aspirations towards the entire area of the former Roman Province of Dalmatia.Though the described borders mark a large area, it is mostly a mountainous and inaccessible terrain, rugged with the high ranges of the Dinarides. Within this region, the Serbs settled only a small, isolated and mutually distant river valleys, karst fields and fertile basins. Those patches of the territory had fertile land, suitable for the agriculture, while the barely accessible, some mountain regions remained uninhabited. Višeslav's great-grandson Vlastimir began his rule during 830s, and he is the oldest Serbian ruler on which there is more substantial data.

Countering Bulgarian expansion (805–829)
In the east, the Bulgarian Empire grew strong. In 805 Krum conquered the Braničevci, Timočani and Obotrites, to the east of Serbia, and banished their tribal chiefs and replaced them with administrators appointed by the central government. In 815, the Bulgarians and Byzantines signed a 30-year peace treaty, but in 818, during the rule of Omurtag (814–836), the Braničevci and Timočani together with other tribes of the frontiers, revolted and seceded from Bulgaria because of an administrative reform that had deprived them much of their local authority. The Timočani left the society (association, alliance ) of the Bulgarian Empire, and sought, together with the Danubian Obotrites and Guduscani, protection from Holy Roman Emperor Louis the Pious (r. 813–840), and met him at his court at Herstal. The Timočani migrated into Frankish territory, somewhere in Lower Pannonia, and were last mentioned in 819, when they were persuaded by Ljudevit to join him in fighting the Franks. The Danubian Obotrites stayed in Banat, and resisted the Bulgars until 824 when nothing more is heard of them. Krum sent envoys to the Franks and requested that the precise boundary be demarcated between them, and negotiations lasted until 826, when the Franks neglected him. The Bulgars answered by subjugating the Slavs that lived in Pannonia. Then the Bulgars sent ships up the Drava river, and, in 828, devastated Upper Pannonia north of the Drava. There was more fighting in 829 as well, and, by this time, the Bulgars had conquered all of their former Slavic allies.

The Bulgarian Empire had a general policy of expansion in which they would first impose the payment of tribute on a neighboring people and the obligation of supplying military assistance in the form of an alliance (society), leaving them internal self-government and local rulers, and when the need for this kind of relationship expired, they would terminate the self-government of the said people and impose their direct and absolute power, integrating them fully into the Bulgarian political and cultural system.

Vlastimir, Mutimir and Prvoslav (830–892)
Vlastimir succeeded his father, Prosigoj, in c. 830. He united the Serbian tribes in the vicinity. The Serbs were alarmed, and most likely consolidated due to the spreading of the Bulgarian Empire towards their borders by the Bulgarian conquest of neighbouring Slavs, and possibly sought to cut off the Bulgar expansion to the south (Macedonia). Emperor Theophilos (r. 829–842) was recognized as the nominal suzerain (overlord) of the Serbs, and most likely encouraged them to thwart the Bulgars. The thirty-year-peace treaty between the Byzantines and Bulgars, signed in 815, was still in effect.

According to Constantine VII, the Serbs and Bulgars had lived peacefully as neighbours until the Bulgar invasion in 839 (in the last years of Theophilos). It is not known what exactly prompted the war, as Porphyrogenitus gives no clear answer; whether it was a result of Serbian-Bulgarian relations, i.e., the Bulgar conquest to the southeast, or a result of the Byzantine-Bulgarian rivalry, in which Serbia was allied with the Byzantines. According to Porphyrogenitus, the Bulgars wanted to continue their conquest of Slav lands and subjugate the Serbs. Presian I (r. 836–852) launched an invasion into Serbian territory in 839, which led to a war that lasted for three years, in which the victorious army of Vlastimir expelled Presian from Serbia; Presian lost a large number of his men, and made no territorial gains. The Serbs had an advantage in the forests and gorges. The defeat of the Bulgars, who had become one of the greater powers in the 9th century, shows that Serbia was an organized state, fully capable of defending its borders, and possessed a very high military and administrative organization. It is not known whether Serbia at the time of Vlastimir had a fortification system and developed military structures with clearly defined roles of the župan. After the victory over the Bulgars, Vlastimir's status rose, and according to Fine he went on to expand to the west, taking Bosnia, and Herzegovina (known as Hum). In the meantime; Braničevo, Morava, Timok, Vardar and Podrimlje were occupied by the Bulgars. Vlastimir married off his daughter to Krajina, the son of a local župan of Trebinje, Beloje, in ca. 847/848. With this marriage, Vlastimir elevated the title of Krajina to archon. The Belojević family was thus entitled to rule Travunia.

After Vlastimir's death, the rule was divided among his three sons: Mutimir, Strojimir and Gojnik. The brothers defeated the Bulgars once again c. 853-854, capturing Bulgarian prince Vladimir, son of Boris of Bulgaria. After that, Serbs and the Bulgarians concluded peace. During the following period, the Christianization of the Serbs was completed. Mutimir maintained the communion with the Eastern Church (Constantinople) when Pope John VIII invited him to recognize the jurisdiction of the bishopric of Sirmium.

The Serbs and Bulgarians adopted the Old Slavonic liturgy instead of the Greek. Sometime after defeating the Bulgarians, Mutimir ousted his brothers, who fled to Bulgaria. He kept Gopnik's son Petar Gojniković in his court, but he managed to escape to Croatia. Mutimir ruled until 890, being succeeded by his son Prvoslav. However, Prvoslav was overthrown by Petar who had returned from his exile in Croatia in c. 892.

Peter, Pavle and Zaharija (892–927)
The name Peter suggests that Christianity had started to permeate into Serbia, undoubtedly through Serbia's contacts with the Bulgarians and Byzantines. Peter secured himself on the throne (after fending off a challenge from Klonimir, son of Stojmir) and was recognized by Tsar Symeon I of Bulgaria. An alliance was signed between the two states. Already having Travunia's loyalty, Peter began to expand his state north and west. He annexed the Bosna River valley, and then moved west securing allegiance from the Narentines, a fiercely independent, pirateering Slavic tribe. However, Peter's expansion into Dalmatia brought him into conflict with Prince Michael of Zahumlje, who has also grown powerful, ruling the coastal Principality of Zachlumia.

Although allied to Simeon I of Bulgaria, Peter became increasingly disgruntled by the fact that he was essentially subordinate to him. Peter's expansion toward the coast facilitated contacts with the Byzantines, by way of the strategies of Dyrrhachium. Searching for allies against Bulgaria, the Byzantines showered Peter with gold and promises of greater independence if he would join their alliance - a convincing strategy. Peter might have been planning an attack on Bulgaria with the Magyars, showing that his realm had stretched north to the Sava river. However, Michael of Zahumlje forewarned Symeon of this plan, since Michael was an enemy of Peter, and a loyal vassal of Symeon. What followed was multiple Bulgarian interventions and a succession of Serb rulers.

Symeon attacked Serbia (in 917) and deposed Peter, placing Pavle Branović (a grandson of Mutimir) as Prince of Serbia, subordinate to Symeon (although some scholars suggest that Symeon took control over Serbia directly at this time). Unhappy with this, the Byzantines then sent Zaharija Prvoslavljević in 920 to oust Pavle, but he failed and was sent to Bulgaria as prisoner. The Byzantines then succeeded in turning Prince Pavle to their side. In turn, Zaharija invaded Serbia with a Bulgarian force, and ousted his cousin Pavle in 922. However, he too turned to Byzantium. A punitive force sent by the Bulgarians was defeated. Thus we see a continuous cycle of dynastic strife amongst Vlastimir's successors, stirred on by the Byzantine and Bulgarians, who were effectively using the Serbs as pawns. Whilst Bulgarian help was more effective, Byzantine help seemed preferable. Simeon made peace with the Byzantines to settle affairs with Serbia once and for all. In 924, he sent a large army accompanied by Časlav, son of Klonimir. The army forced Zaharija to flee to Croatia. The Serbian župans were then summoned to recognize Časlav as the new Prince. When they came, however, they were all imprisoned and taken to Bulgaria, as too was Časlav. Much of Serbia was ravaged, and many people fled to Croatia, Bulgaria and Constantinople. Simeon made Serbia into a Bulgarian province so that Bulgaria now bordered Croatia and Zahumlje. He then resolved to attack Croatia, because it was a Byzantine ally and had sheltered the Serbian Prince.

Časlav (933–943/960)
The Bulgarian rule over Serbia lasted only three years. After Symeon died, Časlav Klonimirović (933- c. 943/960) led Serb refugees back to Serbia. He secured the allegiance of the Dalmatian duchies and ended Bulgarian rule in central Serbia. After Tomislav's death, Croatia was in near-anarchy as his sons vied for sole rule, so Časlav was able to extend his domain north to the Vrbas river (gaining the allegiance of the chiefs of the various Bosnian župas).

During this apogee of Serbian power, Christianity and culture penetrated Serbia, as the Serb prince lived in peaceful and cordial relations with the Byzantines. However, strong as it had grown to be, Serbia's power (as in other early Slavic states) was only as strong as its ruler. There was no centralized rule, but instead a confederacy of Slavic principalities. The existence of the unified Grand Principality was dependent on the allegiance of the lesser princes to Časlav. When he died defending Bosnia against Magyar incursions sometime between 950 and 960, the coalition disintegrated.

After this, there is a gap in the history of hinterland Serbia (in later western sources: Rascia), as it was annexed by the Byzantine Empire (c. 970). The dynasty continued to rule the maritime regions, and in the 990s, Jovan Vladimir rose as the most powerful Serbian prince, ruling over present-day Montenegro, eastern Herzegovina, and northern Albania. This state became known as Duklja, after the ancient Roman town of Doclea. However, by 997, it was made subject to tsar Samuel of Bulgaria.

When the Byzantines finally defeated the Bulgarians, they regained control over most of the Balkans for the first time in four centuries. Serbian lands were governed by a strategos presiding over the Theme of Sirmium. However, local Serbian princes continued to reign as vassals to the Byzantine Emperor, maintaining local autonomy over their lands, while only nominally being Byzantine subjects. Forts were maintained in Belgrade, Sirmium, Niš and Braničevo. These were, for the most part, in the hands of local nobility, which often revolted against Byzantine rule.

Fall and aftermath
After Časlav died c. 943/960, the hinterland of Serbia was annexed by the Byzantines and reorganized as the Catepanate of Ras, (971–976). Serbia lost its centralized rule and the provinces once again came under the Empire. Jovan Vladimir emerged later as a ruler of Duklja, a small territory centered in Bar on the Adriatic coast, as a Byzantine vassal. His realm was called Serbia, Dalmatia, Sklavonia, etc., and eventually included much of the maritime provinces, including Travunia and Zachlumia. His realm probably stretched into the hinterland to include some parts of Zagorje (inland Serbia and Bosnia) as well. Vladimir's pre-eminent position over other Slavic nobles in the area explains why Emperor Basil approached him for an anti-Bulgarian alliance. With his hands tied by war in Anatolia, Emperor Basil required allies for his war against Tsar Samuel, who ruled a Bulgarian empire stretching over Macedonia. In retaliation, Samuel invaded Duklja in 997, and pushed through Dalmatia up to the city of Zadar, incorporating Bosnia and Serbia into his realm. After defeating Vladimir, Samuel reinstated him as a vassal prince. We do not know what Vladimir's connection was to the previous princes of Serbia, or to the rulers of Croatia—much of what is written in the Chronicle of the Priest of Duklja about the genealogy of the Doclean rulers is mythological. Vladimir was murdered by Vladislav, Samuel's nephew and successor of his son, circa 1016 AD. The last prominent member of his family, his uncle Dragimir, was killed by some local citizens in Kotor in 1018. That same year, the Byzantines defeated the Bulgarians, and in one masterful stroke re-took virtually all of southeastern Europe.

Government
The Serbian ruler was titled "Prince (archon) of the Serbs" (αρχων Σερβλίας). In Serbian historiography, the Slavic title of knez (кнез) is used instead of the Greek arhont (архонт). The DAI mentions that the Serbian throne is inherited by the son, i.e. the first-born; his descendants succeeded him, though their names are unknown until the coming of Višeslav. The Serbs at that time were organized into župe ( župa), a confederation of village communities (roughly the equivalent of a county), headed by a local župan (a magistrate or governor); the governorship was hereditary, and the župan reported to the Serbian prince, whom they were obliged to aid in war.

Historian B. Radojković (1958) proposed that Serbia was a "divided principality". According to him, Višeslav could have been a chief military leader (veliki vojvoda) who with his company seized the entire power in his hands and turned himself into a hereditary ruler, as Veliki župan; in this way, the first Serbian state was thus established after 150 years of permanent living in the new homeland and existence of military democracy. However, B. Radojković's work was discredited by Sima Ćirković in 1960.

Cities
According to DAI, baptized Serbia included the following cities (καστρα/kastra), with spellings used in Moravcsik's transcript (1967):

Religion
By the beginning of the 7th century, Byzantine provincial and ecclesiastical order in the region was destroyed by invading Sclaveni and Pannonian Avars. The church life was renewed in the same century in the province of Illyricum and Dalmatia after a more pronounced Christianization of the Serbs and other Slavs by the Roman Church. In the 7th and mid-8th century the area wasn't under jurisdiction of the Patriarchate of Constantinople. Early medieval Serbs are accounted as Christian by 870s, but it was a process that ended in the late 9th century during the time of Basil I, and medieval necropolises until the 13th century in the territory of modern Serbia show an "incomplete process of Christianization" as local Christianity depended on the social structure (urban and rural). Basil I probably sent at least one embassy to Mutimir of Serbia, who decided to maintain the communion of Church in Serbia with the Patriarchate of Constantinople when Pope John VIII invited him to get back to the jurisdiction of the bishopric of Sirmium (see also Archbishopric of Moravia) in a letter dated to May 873. It is considered that Destinikon was an ecclesiastical centre and capital of early medieval Serbia.

The seal of Strojimir (d. between 880 and 896), the brother of Mutimir, was bought by the Serbian state in an auction in Germany. The seal has a Patriarchal cross in the center and Greek inscriptions that say: "God, help Strojimir (CTPOHMIP)".

Petar Gojniković (r. 892–917) was evidently a Christian prince. Christianity presumably was spreading in his time. Also, since Serbia bordered Bulgaria, Christian influence—and perhaps missionaries—came from there. This would increase during the twenty-year peace. The previous generation (Mutimir, Strojimir and Gojnik) had Slav names, but the following (Petar, Stefan, Pavle, Zaharija) had Christian names, an indication of strong Byzantine missions to Serbia, as well as to the Slavs of the Adriatic coast, in the 870s.

The imperial charter of Basil II from 1020 to the Archbishopric of Ohrid, in which the rights and jurisdictions were established, mentions that the Episcopy of Ras belonged to the Bulgarian autocephal church during the time of Peter I (927–969) and Samuel of Bulgaria (977–1014). It is considered that it was possibly founded by the Bulgarian emperor, or it is the latest date when could have been integrated to the Bulgarian Church. If previously existed, it probably was part of the Bulgarian metropolis of Morava, but certainly not of Durrës. If it was on the Serbian territory, seems that the Church in Serbia or part of the territory of Serbia became linked and influenced by the Bulgarian Church between 870 and 924. Anyway, the church would have been protected by Bulgarian controlled forts. By then, at the latest, Serbia must have received the Cyrillic alphabet and Slavic religious text, already familiar but perhaps not yet preferred to Greek.

Notable early church buildings include the Monastery of Holy Archangel Michael on Prevlaka, built in the beginning of the 9th century, on the location of older churches of three-nave structure with three apses to the East, dating from the 3rd and 6th centuries, Bogorodica Hvostanska (6th century) and Church of Saints Peter and Paul.

Archaeology

 * Church of Saint Apostles Peter and Paul in Ras
 * Sočanica basilica
 * Gradina, Sebečevska reka, in Raška
 * Gradina Martinića, Zeta
 * Gradina, Brsenica, near Sjenica
 * Gradina on Jelica, near Čačak
 * Gradina on Postenj, near Petar's Church

title: Principality of Serbia (early medieval)


text:
Beefcake

Beefcake is a performance or a form of glamour photography depicting a large and muscular male body. Beefcake is also a publication genre. A role a person plays in a performance may be called beefcake. The term was believed to be first used by Hollywood columnist Sidney Skolsky.

Actors typecast as beefcake
Beefcake poses by male actors were used far less frequently than cheesecake (pin-up) layouts of actresses. Nevertheless, as early as the 1920s, photographs were taken of such stars as Rudolph Valentino and Ramon Novarro to highlight their physical appeal. Male physique shots of famous stars were even less frequent during the early talking picture era, outside of stars of jungle films such as Johnny Weissmuller (Tarzan) and Buster Crabbe. The 1940s saw a rise in shirtless shots of such stars as Tyrone Power, Guy Madison, Sterling Hayden and Victor Mature; and in the 1950s movie magazines began running swimsuit shots of actors such as Tony Curtis, Rock Hudson, Tab Hunter, Jeff Chandler, Robert Conrad and Robert Wagner almost as frequently as they did with actresses. This period also included the rise of bodybuilding magazines, which continue to be popular to the present day, as well as musclemen movie stars such as Steve Reeves who were often barely dressed in their action/adventure films. In the 1980s, heavily muscular actors Arnold Schwarzenegger, Lou Ferrigno, and Sylvester Stallone continued to star in beefcake-type action/adventure movies (such as Conan the Barbarian or Hercules ).

1970 to present
The 1970s proved a golden age for beefcake with the debut of Playgirl magazine and its completely nude pictorials of men, Cosmopolitan magazine's famous semi-nude centerfolds of actors including Burt Reynolds, and the rise of pornography directed at both female and gay male audiences in both magazines and films.

Today, it is common to see beefcake shots of male sex symbols on the cover of general interest magazines. For many actors and models, shirtless poses are their most revealing, in line with their conservative images.

In advertisement, beefcake male models have become a popular ingredient for "spicy" (and often humorous) commercial spots; for example, British pop star Nick Kamen remains most famous for his 1985 beefcake performance in Levi's "Launderette" TV commercial. In the ad, he strips down in order to stone-wash his blue jeans in a 1950s style public laundromat while he waits clad only in boxer shorts; it was selected for "The 100 Greatest TV Ads" in 2000 and followed by many others, often bare-chested.

Many professional male bodybuilders advertise their services, offering advice concerning nutrition and training, sometimes marketing their videos in which training programmes are demonstrated.

A 1999 film of the same name, Beefcake, details the history of the Athletic Model Guild, an early company known for their photos of men in various publications.

title: Beefcake


text:
Martin Gore

Martin Lee Gore (born 23 July 1961) is an English musician and songwriter. He is one of the founding members of the electronic rock band Depeche Mode and is the band's main songwriter. He is the band's guitarist and keyboardist, and occasionally provides lead vocals. Gore possesses a tenor singing voice which contrasts with lead vocalist Dave Gahan's dramatic baritone. He is also known for his flamboyant and (sometimes) androgynous stage persona. Gore has also released several solo albums and collaborated with former Depeche Mode member Vince Clarke as part of VCMG.

Gore's songs include themes such as sex, religion and politics. He has said he feels lyrical themes that tackle issues related to solitude and loneliness are a better representation of reality, whereas he finds "happy songs" fake and unrealistic. At the same time, he asserts that the band's music contains "an element of hope".

In 1999, he received the Ivor Novello Award from the British Academy of Songwriters, Composers and Authors for "International Achievement". He was given the Moog Innovation Award "for his many contributions to the exploration of sound in popular music" in 2019, and became a Rock and Roll Hall of Fame member in late 2020 with fellow active Depeche Mode members Dave Gahan and Andy Fletcher, as well as past members Clarke and Alan Wilder. Following the death of Fletcher in May 2022, Gore became the longest-serving member of the band.

Early life
Martin Lee Gore was born in London, England. His biological father was an African-American G.I. stationed in Britain. Gore was raised by his stepfather David Gore and biological mother Pamela, who both worked at the Ford of Britain motor plant in Dagenham. He believed his stepfather was his biological father until the age of 30, when he learned of his biological father. Gore later met his biological father in the American South. Gore has described his upbringing as "normal" and "stable" and has said that although he was a well-behaved child, he was an introvert who preferred to spend time reading alone rather than with school peers. However, he also stated that he enjoyed his time at school and took part in foreign exchange trips. His family briefly lived in Hornchurch during his upbringing before moving to Basildon, where he attended the Nicholas Comprehensive School. During school he was the guitarist in a local band called Norman and the Worms.

Gore taught himself to play keyboard from the 1970s, never receiving formal training. He learned to perform chart hits, figuring out their structures via the magazine Disco 45. He shared a class with Andy "Fletch" Fletcher, Alison Moyet and Perry Bamonte. Gore left Nicholas Comprehensive after completing his A-levels in 1979 and took a job as a bank cashier. During evenings, weekends and any other spare time, he remained involved with Norman and the Worms. He became interested in electronic music upon hearing acts such as Kraftwerk, the Human League and Orchestral Manoeuvres in the Dark (OMD). He borrowed a Korg 700S from a friend, before purchasing a Yamaha CS5, his first synthesizer.

Gore has two younger half-sisters, Karen, born in 1967, and Jacqueline, born in 1968.

Depeche Mode
In 1980, Gore reunited with classmate Andy Fletcher at the Van Gogh club. Fletcher recruited him into his band Composition of Sound, along with Vince Clarke. Soon the band drafted Dave Gahan to be the band's lead singer after hearing him sing "Heroes" by David Bowie. Gore is the band's keyboardist, contributes backing vocals, and occasionally provides lead vocals.

When explaining the band's choice for their name, 'Depeche Mode' (which was taken from French fashion magazine Dépêche Mode), Gore said, "It means 'hurried fashion' or 'fashion dispatch'. I like the sound of that." However, the magazine's name (and hence the band's) correctly translates to something like "Fashion News" or "Fashion Update".

Gore wrote two tracks on Depeche Mode's debut album, Speak & Spell: "Tora! Tora! Tora!" and the instrumental "Big Muff". "Any Second Now (Voices)" features Gore's first lead vocals for the band. When Clarke announced his departure from Depeche Mode in 1981, Gore became the principal songwriter for the band. Songs Gore wrote for Depeche Mode's second album, A Broken Frame (1982), differed musically and lyrically from Clarke's. Gore's writing became gradually darker and more political on subsequent Depeche Mode albums. He sings lead vocals on several of the band's songs, notably ballads – his tenor voice provides a contrast to Gahan's dramatic baritone.

Gore sometimes plays guitar (typically his Gretsch White Falcon or Gretsch Double Anniversary) on Depeche Mode songs. The first time guitar was used as the main instrument was on "Personal Jesus", although he used small guitar parts on previous songs, such as "Behind the Wheel" and "Love, in Itself". Gore's guitar playing developed even more on Songs of Faith and Devotion. In live performances, he switches his keyboards for his guitar on some older Depeche Mode songs, such as "Never Let Me Down Again" and "A Question of Time". In mid-1990, Gore said, "I think in a way we've been at the forefront of new music; sort of chipping away at the standard rock format stations."

Other work
Gore has released the following solo albums: Counterfeit EP (1989), Counterfeit² (2003), MG (2015) and The Third Chimpanzee (2021). He covered the song "Coming Back to You" for the Leonard Cohen tribute album Tower of Song (1995).

VCMG
Former Depeche Mode colleague Vince Clarke collaborated with Gore for the first time since 1981 as techno duo VCMG on an instrumental minimalist electronic dance album called Ssss, released on 12 March 2012. The first single, Spock, was originally released worldwide exclusively on Beatport on 30 November 2011. The second, Single Blip, was also released exclusively on Beatport on 20 February 2012, and the third one, Aftermaths, was released on 20 August 2012.

MG
In late February 2015, several teaser images were displayed on Gore's official Facebook page, citing a hashtag "MGxMG", which was later revealed to be a promotional tool for his new solo studio album, titled MG (named similarly to his previous collaborative album, VCMG, with Vince Clarke from 2012). In a news post on his official website and various social media on 2 March, this confirmation of his new studio album announced its release would be on 27 or 28 April and previewed a track, Europa Hymn, from the new album.

Electric Ladyboy studio
Gore has a personal studio in Santa Monica with a sizeable collection of Euroracks, Moog and Erica synthesizers (among others), where he has recorded solo work and written music for Depeche Mode.

Awards
On 27 May 1999, Gore was presented with an award by Daniel Miller for "International Achievement" by the British Academy of Songwriters, Composers and Authors at the 44th Ivor Novello Awards.

In 2019, Gore received the Moog Innovation Award "for his many contributions to the exploration of sound in popular music". "Musical pioneer Martin Gore's masterful electronic meditations on the human condition have illuminated the connection between transformative sound and pure emotion for decades. A founding member of the band Depeche Mode, Gore's sensual electronic compositions and introspective lyrics have resonated with faithful audiences around the world and impacted the direction of countless visionary artists from Trent Reznor to Johnny Cash. Gore's enduring ability to connect the rawest aspects of the human experience to the dance floor defined an era and perpetually reminds us what it means to be human through the emotional power of electronic sound."

Personal life
Gore lives in Santa Barbara, California. He started dating lingerie designer and model Suzanne Boisvert after meeting in Paris in 1989. They married in August 1994, had three children and divorced in 2006. In June 2014, he married Kerrilee Kaski, with whom he has two daughters.

Gore became a vegetarian for health and moral reasons (along with bandmate Alan Wilder) in 1983.

He had stress-induced seizures during the band's 1993 Devotional Tour and publicly acknowledged his past alcoholism. During a break on the Devotional Tour in Denver, Colorado, he was arrested by local police and fined $50 for holding a loud party in his hotel room.

In a 2017 interview, Dave Gahan described both himself and Gore as autistic.

He is a supporter of Arsenal Football Club.

with VCMG

 * Ssss (Mute, 2012)

Remixes

 * 1994 Spirit Feel – "Rejoice" (Mystic Span mix)
 * 1995 Garbage – "Queer" (The Most Beautiful Woman in Town mix)
 * 1999 ON – "Soluble Words" (Sublingual remix)
 * 2003 Señor Coconut and His Orchestra – "Smooth Operator" (In-Disguise remix)
 * 2013 Diamond Version – "Get Yours" (Martin L. Gore remix)
 * 2022 Jean-Michel Jarre – "Brutalism Take 2"

title: Martin Gore


text:
Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space.

The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space. In general relativity, which involves the pseudo-Riemannian setting, this is reflected by the presence of the Ricci tensor in the Raychaudhuri equation. Partly for this reason, the Einstein field equations propose that spacetime can be described by a pseudo-Riemannian metric, with a strikingly simple relationship between the Ricci tensor and the matter content of the universe.

Like the metric tensor, the Ricci tensor assigns to each tangent space of the manifold a symmetric bilinear form. Broadly, one could analogize the role of the Ricci curvature in Riemannian geometry to that of the Laplacian in the analysis of functions; in this analogy, the Riemann curvature tensor, of which the Ricci curvature is a natural by-product, would correspond to the full matrix of second derivatives of a function. However, there are other ways to draw the same analogy.

In three-dimensional topology, the Ricci tensor contains all of the information which in higher dimensions is encoded by the more complicated Riemann curvature tensor. In part, this simplicity allows for the application of many geometric and analytic tools, which led to the solution of the Poincaré conjecture through the work of Richard S. Hamilton and Grigori Perelman.

In differential geometry, lower bounds on the Ricci tensor on a Riemannian manifold allow one to extract global geometric and topological information by comparison (cf. comparison theorem) with the geometry of a constant curvature space form. This is since lower bounds on the Ricci tensor can be successfully used in studying the length functional in Riemannian geometry, as first shown in 1941 via Myers's theorem.

One common source of the Ricci tensor is that it arises whenever one commutes the covariant derivative with the tensor Laplacian. This, for instance, explains its presence in the Bochner formula, which is used ubiquitously in Riemannian geometry. For example, this formula explains why the gradient estimates due to Shing-Tung Yau (and their developments such as the Cheng-Yau and Li-Yau inequalities) nearly always depend on a lower bound for the Ricci curvature.

In 2007, John Lott, Karl-Theodor Sturm, and Cedric Villani demonstrated decisively that lower bounds on Ricci curvature can be understood entirely in terms of the metric space structure of a Riemannian manifold, together with its volume form. This established a deep link between Ricci curvature and Wasserstein geometry and optimal transport, which is presently the subject of much research.

Definition
Suppose that $$\left( M, g \right)$$ is an $$n$$-dimensional Riemannian or pseudo-Riemannian manifold, equipped with its Levi-Civita connection $$\nabla$$. The Riemann curvature of $$M$$ is a map which takes smooth vector fields $$X$$, $$Y$$, and $$Z$$, and returns the vector field$$R(X,Y)Z := \nabla_X\nabla_Y Z - \nabla_Y\nabla_XZ - \nabla_{[X,Y]}Z$$on vector fields $$X, Y, Z$$. Since $$R$$ is a tensor field, for each point $$p \in M$$, it gives rise to a (multilinear) map:$$\operatorname{R}_p:T_pM\times T_pM\times T_pM\to T_pM.$$Define for each point $$p \in M$$ the map $$\operatorname{Ric}_p:T_pM\times T_pM\to\mathbb{R}$$ by

$$\operatorname{Ric}_p(Y,Z) := \operatorname{tr}\big(X\mapsto \operatorname{R}_p(X,Y)Z\big).$$

That is, having fixed $$Y$$ and $$Z$$, then for any orthonormal basis $$v_1, \ldots, v_n$$ of the vector space $$T_p M$$, one has

$$\operatorname{Ric}_p(Y,Z) = \sum_{i=1} \langle\operatorname{R}_p(v_i, Y) Z, v_i \rangle.$$

It is a standard exercise of (multi)linear algebra to verify that this definition does not depend on the choice of the basis $$v_1, \ldots, v_n$$.

In abstract index notation,

$$\mathrm{Ric}_{ab} = \mathrm{R}^{c}{}_{bca} = \mathrm{R}^{c}{}_{acb}. $$

Sign conventions. Note that some sources define $$R(X,Y)Z$$ to be what would here be called $$-R(X,Y)Z;$$ they would then define $$\operatorname{Ric}_p$$ as $$-\operatorname{tr}(X\mapsto \operatorname{R}_p(X,Y)Z).$$ Although sign conventions differ about the Riemann tensor, they do not differ about the Ricci tensor.

Definition via local coordinates on a smooth manifold
Let $$\left( M, g \right)$$ be a smooth Riemannian or pseudo-Riemannian $$n$$-manifold. Given a smooth chart $$\left( U, \varphi \right)$$ one then has functions $$g_{ij}: \varphi(U) \rightarrow \mathbb{R}$$ and $$g^{ij}: \varphi(U) \rightarrow \mathbb{R}$$ for each $$i, j = 1, \ldots, n$$ which satisfy

$$ \sum_{k=1}^n g^{ik}(x)g_{kj}(x) = \delta^{i}_j = \begin{cases} 1 & i=j \\ 0 & i \neq j \end{cases} $$

for all $$x \in \varphi(U)$$. The latter shows that, expressed as matrices, $$g^{ij}(x) = (g^{-1})_{ij}(x)$$. The functions $$g_{ij}$$ are defined by evaluating $$g$$ on coordinate vector fields, while the functions $$g^{ij}$$ are defined so that, as a matrix-valued function, they provide an inverse to the matrix-valued function $$x \mapsto g_{ij}(x)$$.

Now define, for each $$a$$, $$b$$, $$c$$, $$i$$, and $$j$$ between 1 and $$n$$, the functions

$$\begin{align} \Gamma_{ab}^c &:= \frac{1}{2} \sum_{d=1}^n \left(\frac{\partial g_{bd}}{\partial x^a} + \frac{\partial g_{ad}}{\partial x^b} - \frac{\partial g_{ab}}{\partial x^d}\right)g^{cd}\\ R_{ij} &:= \sum_{a=1}^n\frac{\partial\Gamma_{ij}^a}{\partial x^a} - \sum_{a=1}^n\frac{\partial\Gamma_{ai}^a}{\partial x^j} + \sum_{a=1}^n\sum_{b=1}^n\left(\Gamma_{ab}^a\Gamma_{ij}^b - \Gamma_{ib}^a\Gamma_{aj}^b\right) \end{align}$$

as maps $$\varphi: U \rightarrow \mathbb{R}$$.

Now let $$\left( U, \varphi \right)$$ and $$\left( V, \psi \right)$$ be two smooth charts with $$U \cap V \neq \emptyset$$. Let $$R_{ij}: \varphi(U) \rightarrow \mathbb{R}$$ be the functions computed as above via the chart $$\left( U, \varphi \right)$$ and let $$r_{ij}: \psi(V) \rightarrow \mathbb{R}$$ be the functions computed as above via the chart $$\left( V, \psi \right)$$. Then one can check by a calculation with the chain rule and the product rule that

$$ R_{ij}(x) = \sum_{k,l=1}^n r_{kl}\left(\psi\circ\varphi^{-1}(x)\right)D_i\Big|_x \left(\psi\circ\varphi^{-1}\right)^kD_j\Big|_x \left(\psi\circ\varphi^{-1}\right)^l. $$

where $$D_{i}$$ is the first derivative along $$i$$th direction of $$\mathbb{R}^n$$. This shows that the following definition does not depend on the choice of $$\left( U, \varphi \right)$$. For any $$p \in U$$, define a bilinear map $$\operatorname{Ric}_p : T_p M \times T_p M \rightarrow \mathbb{R}$$ by

$$ (X, Y) \in T_p M \times T_p M \mapsto \operatorname{Ric}_p(X,Y) = \sum_{i,j=1}^n R_{ij}(\varphi(x))X^i(p)Y^j(p), $$

where $$X^1, \ldots, X^n$$ and $$Y^1, \ldots, Y^n$$ are the components of the tangent vectors at $$p$$ in $$X$$ and $$Y$$ relative to the coordinate vector fields of $$\left( U, \varphi \right)$$.

It is common to abbreviate the above formal presentation in the following style:

The final line includes the demonstration that the bilinear map Ric is well-defined, which is much easier to write out with the informal notation.

Comparison of the definitions
The two above definitions are identical. The formulas defining $$\Gamma_{ij}^k$$ and $$R_{ij}$$ in the coordinate approach have an exact parallel in the formulas defining the Levi-Civita connection, and the Riemann curvature via the Levi-Civita connection. Arguably, the definitions directly using local coordinates are preferable, since the "crucial property" of the Riemann tensor mentioned above requires $$M$$ to be Hausdorff in order to hold. By contrast, the local coordinate approach only requires a smooth atlas. It is also somewhat easier to connect the "invariance" philosophy underlying the local approach with the methods of constructing more exotic geometric objects, such as spinor fields.

The complicated formula defining $$R_{ij}$$ in the introductory section is the same as that in the following section. The only difference is that terms have been grouped so that it is easy to see that $$R_{ij}=R_{ji}.$$

Properties
As can be seen from the symmetries of the Riemann curvature tensor, the Ricci tensor of a Riemannian manifold is symmetric, in the sense that

$$\operatorname{Ric}(X ,Y) = \operatorname{Ric}(Y,X)$$

for all $$X,Y\in T_pM.$$

It thus follows linear-algebraically that the Ricci tensor is completely determined by knowing the quantity $$\operatorname{Ric}(X, X)$$ for all vectors $$X$$ of unit length. This function on the set of unit tangent vectors is often also called the Ricci curvature, since knowing it is equivalent to knowing the Ricci curvature tensor.

The Ricci curvature is determined by the sectional curvatures of a Riemannian manifold, but generally contains less information. Indeed, if $$\xi$$ is a vector of unit length on a Riemannian $$n$$-manifold, then $$\operatorname{Ric}(\xi, \xi)$$ is precisely $$(n - 1)$$ times the average value of the sectional curvature, taken over all the 2-planes containing $$\xi$$. There is an $$(n - 2)$$-dimensional family of such 2-planes, and so only in dimensions 2 and 3 does the Ricci tensor determine the full curvature tensor. A notable exception is when the manifold is given a priori as a hypersurface of Euclidean space. The second fundamental form, which determines the full curvature via the Gauss–Codazzi equation, is itself determined by the Ricci tensor and the principal directions of the hypersurface are also the eigendirections of the Ricci tensor. The tensor was introduced by Ricci for this reason.

As can be seen from the second Bianchi identity, one has

$$\operatorname{div}\operatorname{Ric} = \frac{1}{2}dR,$$

where $$R$$ is the scalar curvature, defined in local coordinates as $$g^{ij}R_{ij}.$$ This is often called the contracted second Bianchi identity.

Direct geometric meaning
Near any point $$p$$ in a Riemannian manifold $$\left( M, g \right)$$, one can define preferred local coordinates, called geodesic normal coordinates. These are adapted to the metric so that geodesics through $$p$$ correspond to straight lines through the origin, in such a manner that the geodesic distance from $$p$$ corresponds to the Euclidean distance from the origin. In these coordinates, the metric tensor is well-approximated by the Euclidean metric, in the precise sense that

$$g_{ij} = \delta_{ij} + O \left(|x|^2\right) .$$

In fact, by taking the Taylor expansion of the metric applied to a Jacobi field along a radial geodesic in the normal coordinate system, one has $$g_{ij} = \delta_{ij} - \frac{1}{3} R_{ikjl}x^kx^l + O\left(|x|^3\right) .$$

In these coordinates, the metric volume element then has the following expansion at $g$:

$$d\mu_g = \left[ 1 - \frac{1}{6} R_{jk}x^j x^k+ O\left(|x|^3\right) \right] d\mu_\text{Euclidean} ,$$

which follows by expanding the square root of the determinant of the metric.

Thus, if the Ricci curvature $$\operatorname{Ric}(\xi, \xi)$$ is positive in the direction of a vector $$\xi$$, the conical region in $$M$$ swept out by a tightly focused family of geodesic segments of length $$\varepsilon$$ emanating from $$p$$, with initial velocity inside a small cone about $$\xi$$, will have smaller volume than the corresponding conical region in Euclidean space, at least provided that $$\varepsilon$$ is sufficiently small. Similarly, if the Ricci curvature is negative in the direction of a given vector $$\xi$$, such a conical region in the manifold will instead have larger volume than it would in Euclidean space.

The Ricci curvature is essentially an average of curvatures in the planes including $$\xi$$. Thus if a cone emitted with an initially circular (or spherical) cross-section becomes distorted into an ellipse (ellipsoid), it is possible for the volume distortion to vanish if the distortions along the principal axes counteract one another. The Ricci curvature would then vanish along $$\xi$$. In physical applications, the presence of a nonvanishing sectional curvature does not necessarily indicate the presence of any mass locally; if an initially circular cross-section of a cone of worldlines later becomes elliptical, without changing its volume, then this is due to tidal effects from a mass at some other location.

Applications
Ricci curvature plays an important role in general relativity, where it is the key term in the Einstein field equations.

Ricci curvature also appears in  the Ricci flow equation, first introduced by Richard S. Hamilton in 1982, where certain one-parameter families of Riemannian metrics are singled out as solutions of a geometrically-defined partial differential equation. In harmonic local coordinates the Ricci tensor can be expressed as. $$R_{ij} = -\frac{1}{2}\Delta \left(g_{ij}\right) + \text{lower-order terms},$$ where $$g_{ij}$$ are the components of the metric tensor and $$\Delta$$ is the Laplace–Beltrami operator. This fact motivates the introduction of the Ricci flow equation as a natural extension of the heat equation for the metric. Since heat tends to spread through a solid until the body reaches an equilibrium state of constant temperature, if one is given a manifold, the Ricci flow may be hoped to produce an 'equilibrium' Riemannian metric which is Einstein or of constant curvature. However, such a clean "convergence" picture cannot be achieved since many manifolds cannot support such metrics. A detailed study of the nature of solutions of the Ricci flow, due principally to Hamilton and Grigori Perelman, shows that the types of "singularities" that occur along a Ricci flow, corresponding to the failure of convergence, encodes deep information about 3-dimensional topology. The culmination of this work was a proof of the geometrization conjecture first proposed by William Thurston in the 1970s, which can be thought of as a classification of compact 3-manifolds.

On a Kähler manifold, the Ricci curvature determines the first Chern class of the manifold (mod torsion). However, the Ricci curvature has no analogous topological interpretation on a generic Riemannian manifold.

Global geometry and topology
Here is a short list of global results concerning manifolds with positive Ricci curvature; see also classical theorems of Riemannian geometry. Briefly, positive Ricci curvature of a Riemannian manifold has strong topological consequences, while (for dimension at least 3), negative Ricci curvature has no topological implications. (The Ricci curvature is said to be positive if the Ricci curvature function $$\operatorname{Ric}(\xi, \xi)$$ is positive on the set of non-zero tangent vectors $$\xi$$.) Some results are also known for pseudo-Riemannian manifolds.

These results, particularly Myers' and Hamilton's, show that positive Ricci curvature has strong topological consequences. By contrast, excluding the case of surfaces, negative Ricci curvature is now known to have no topological implications; has shown that any manifold of dimension greater than two admits a complete Riemannian metric of negative Ricci curvature. In the case of two-dimensional manifolds, negativity of the Ricci curvature is synonymous with negativity of the Gaussian curvature, which has very clear topological implications. There are very few two-dimensional manifolds which fail to admit Riemannian metrics of negative Gaussian curvature.
 * 1) Myers' theorem (1941) states that if the Ricci curvature is bounded from below on a complete Riemannian n-manifold by $$(n - 1)k > 0$$, then the manifold has diameter $$\leq \pi / \sqrt{k}$$. By a covering-space argument, it follows that any compact manifold of positive Ricci curvature must have finite fundamental group. Cheng (1975) showed that, in this setting, equality in the diameter inequality occurs if only if the manifold is isometric to a sphere of a constant curvature $$k$$.
 * 2) The Bishop–Gromov inequality states that if a complete $$n$$-dimensional Riemannian manifold has non-negative Ricci curvature, then the volume of a geodesic ball is less than or equal to the volume of a geodesic ball of the same radius in Euclidean $$n$$-space. Moreover, if $$v_p(R)$$ denotes the volume of the ball with center $$p$$ and radius $$R$$ in the manifold and $$V(R) = c_n R^n$$ denotes the volume of the ball of radius $$R$$ in Euclidean $$n$$-space then the function $$v_p(R) / V(R)$$ is nonincreasing. This can be generalized to any lower bound on the Ricci curvature (not just nonnegativity), and is the key point in the proof of Gromov's compactness theorem.)
 * 3) The Cheeger–Gromoll splitting theorem states that if a complete Riemannian manifold $$\left( M, g \right)$$ with $$\operatorname{Ric} \geq 0$$ contains a line, meaning a geodesic $$\gamma : \mathbb{R} \to M$$ such that $$d(\gamma(u), \gamma(v)) = \left| u - v \right|$$ for all $$u, v \in \mathbb{R}$$, then it is isometric to a product space $$\mathbb{R} \times L$$. Consequently, a complete manifold of positive Ricci curvature can have at most one topological end.  The theorem is also true  under some additional hypotheses for complete Lorentzian manifolds (of metric  signature $$\left( + - - \ldots \right)$$) with non-negative Ricci tensor.
 * 4) Hamilton's first convergence theorem for Ricci flow has, as a corollary, that the only compact 3-manifolds which have Riemannian metrics of positive Ricci curvature are the quotients of the 3-sphere by discrete subgroups  of SO(4) which act properly discontinuously. He later extended this to allow for  nonnegative Ricci curvature. In particular, the only simply-connected possibility  is the 3-sphere itself.

Behavior under conformal rescaling
If the metric $$g$$ is changed by multiplying it by a conformal factor $$e^{2f}$$, the Ricci tensor of the new, conformally-related metric $$\tilde{g} = e^{2f} g$$ is given  by

$$\widetilde{\operatorname{Ric}}=\operatorname{Ric}+(2-n)\left[ \nabla df-df\otimes df\right]+\left[\Delta f -(n-2)\|df\|^2\right]g ,$$

where $$\Delta = *d*d$$ is the (positive spectrum) Hodge Laplacian, i.e., the opposite of the usual trace of the Hessian.

In particular, given a point $$p$$ in a Riemannian manifold, it is always possible to find metrics conformal to the given metric $$g$$ for which the Ricci tensor vanishes at $$p$$. Note, however, that this is only pointwise assertion; it is usually impossible to make the Ricci curvature vanish identically on the entire manifold by a conformal rescaling.

For two dimensional manifolds, the above formula shows that if $$f$$ is a harmonic function, then the conformal scaling $$g \mapsto e^{2f}g$$ does not change the Ricci tensor (although it still changes its trace with respect to the metric unless $$f = 0$$.

Trace-free Ricci tensor
In Riemannian geometry and pseudo-Riemannian geometry, the trace-free Ricci tensor (also called traceless Ricci tensor) of a Riemannian or pseudo-Riemannian $$n$$-manifold $$\left( M, g \right)$$ is the tensor defined by

$$Z = \operatorname{Ric} - \frac{1}{n}Rg ,$$

where $$\operatorname{Ric}$$ and $$R$$ denote the Ricci curvature and scalar curvature of $$g$$. The name of this object reflects the fact that its trace automatically vanishes: $$\operatorname{tr}_gZ\equiv g^{ab}Z_{ab} = 0.$$ However, it is quite an important tensor since it reflects an "orthogonal decomposition" of the Ricci tensor.

The orthogonal decomposition of the Ricci tensor
The following, not so trivial, property is

$$\operatorname{Ric} = Z + \frac{1}{n}Rg.$$

It is less immediately obvious that the two terms on the right hand side are orthogonal to each other:

$$\left\langle Z, \frac{1}{n}Rg\right\rangle_g \equiv g^{ab}\left(R_{ab} - \frac{1}{n}Rg_{ab}\right) = 0.$$

An identity which is intimately connected with this (but which could be proved directly) is that

$$\left|\operatorname{Ric}\right|_g^2 = |Z|_g^2 + \frac{1}{n}R^2.$$

The trace-free Ricci tensor and Einstein metrics
By taking a divergence, and using the contracted Bianchi identity, one sees that $$Z = 0$$ implies $\frac{1}{2}dR - \frac{1}{n}dR = 0$. So, provided that $n ≥ 3$ and $$M$$ is connected, the vanishing of $$Z$$ implies that the scalar curvature is constant. One can then see that the following are equivalent:

 * $$Z = 0$$
 * $$\operatorname{Ric} = \lambda g$$ for some number $$\lambda$$
 * $$\operatorname{Ric} = \frac{1}{n}Rg$$

In the Riemannian setting, the above orthogonal decomposition shows that $$R^2 = n|\operatorname{Ric}|^2$$ is also equivalent to these conditions. In the pseudo-Riemmannian setting, by contrast, the condition $$|Z|_g^2 = 0$$ does not necessarily imply $$Z = 0,$$ so the most that one can say is that these conditions imply $$R^2 = n \left|\operatorname{Ric}\right|_g^2.$$

In particular, the vanishing of trace-free Ricci tensor characterizes Einstein manifolds, as defined by the condition $$\operatorname{Ric} = \lambda g$$ for a number $$\lambda.$$ In general relativity, this equation states that $$\left( M, g \right)$$ is a solution of Einstein's vacuum field equations with cosmological constant.

Kähler manifolds
On a Kähler manifold $$X$$, the Ricci curvature determines the curvature form of the canonical line bundle . The canonical line bundle is the top exterior power of the bundle of holomorphic Kähler differentials:

$$ \kappa = {\textstyle\bigwedge}^n ~ \Omega_X. $$

The Levi-Civita connection corresponding to the metric on $$X$$ gives rise to a connection on $$\kappa$$. The curvature of this connection is the 2-form defined by

$$\rho(X,Y) \;\stackrel{\text{def}}{=}\; \operatorname{Ric}(JX,Y)$$

where $$J$$ is the complex structure map on the tangent bundle determined by the structure of the Kähler manifold. The Ricci form is a closed 2-form. Its cohomology class is, up to a real constant factor, the first Chern class of the canonical bundle, and is therefore a topological invariant of $$X$$ (for compact $$X$$) in the sense that it depends only on the topology of $$X$$ and the homotopy class of the complex structure.

Conversely, the Ricci form determines the Ricci tensor by

$$\operatorname{Ric}(X, Y) = \rho(X, JY).$$

In local holomorphic coordinates $$z^\alpha$$, the Ricci form is given by

$$\rho = -i\partial\overline{\partial}\log\det\left(g_{\alpha\overline{\beta}}\right)$$

where $∂$ is the Dolbeault operator and

$$g_{\alpha\overline{\beta}} = g\left(\frac{\partial}{\partial z^\alpha}, \frac{\partial}{\partial\overline{z}^\beta}\right).$$

If the Ricci tensor vanishes, then the canonical bundle is flat, so the structure group can be locally reduced to a subgroup of the special linear group $$SL(n; \mathbb{C})$$. However, Kähler manifolds already possess holonomy in $$U(n)$$, and so the (restricted) holonomy of a Ricci-flat Kähler manifold is contained in $$SU(n)$$. Conversely, if the (restricted) holonomy of a 2$$n$$-dimensional Riemannian manifold is contained in $$SU(n)$$, then the manifold is a Ricci-flat Kähler manifold.

Generalization to affine connections
The Ricci tensor can also be generalized to arbitrary affine connections, where it is an invariant that plays an especially important role in the study of projective geometry (geometry associated to unparameterized geodesics). If $$\nabla$$ denotes an affine connection, then the curvature tensor $$R$$ is the (1,3)-tensor defined by

$$R(X,Y)Z = \nabla_X\nabla_Y Z - \nabla_Y\nabla_XZ - \nabla_{[X,Y]}Z$$

for any vector fields $$X, Y, Z$$. The Ricci tensor is defined to be the trace:

$$\operatorname{ric}(X,Y) = \operatorname{tr}\big(Z\mapsto R(Z,X)Y\big).$$

In this more general situation, the Ricci tensor is symmetric if and only if there exists locally a parallel volume form for the connection.

Discrete Ricci curvature
Notions of Ricci curvature on discrete manifolds have been defined on graphs and networks, where they quantify local divergence properties of edges. Ollivier's Ricci curvature is defined using optimal transport theory. A different (and earlier) notion, Forman's Ricci curvature, is based on topological arguments.

title: Ricci curvature


text:
Talk:Killing field

Untitled
Is it named after Wilhelm Killing? Should mention him in the article. wshun 19:11 24 Jul 2003 (UTC) Killing Fields Involved With The Holocaust:

This may be bunk.
I think we need some citations on this term being used in modern warfare. Machine gunners do not use the term "killing field" rather they use beaten zone for where the rounds impact. So in light of this, I'm redirecting the redirect to the disambig page. 24.45.14.255 01:42, 3 August 2007 (UTC)

Reason to not use killing field term..
The term 'beaten zone' and 'danger space' are more appropriate in modern warfare. Also, there needs to be some citations for the use of the term, both in modern warfare and ancient warfare. Rhetth 01:50, 3 August 2007 (UTC)

title: Talk:Killing field


text:
Xerox art

Xerox art (sometimes, more generically, called copy art, electrostatic art, scanography or xerography) is an art form that began in the 1960s. Prints are created by putting objects on the glass, or platen, of a copying machine and by pressing "start" to produce an image. If the object is not flat, or the cover does not totally cover the object, or the object is moved, the resulting image is distorted in some way. The curvature of the object, the amount of light that reaches the image surface, and the distance of the cover from the glass, all affect the final image. Often, with proper manipulation, rather ghostly images can be made. Basic techniques include: Direct Imaging, the copying of items placed on the platen (normal copy); Still Life Collage, a variation of direct imaging with items placed on the platen in a collage format focused on what is in the foreground/background; Overprinting, the technique of constructing layers of information, one over the previous, by printing onto the same sheet of paper more than once; Copy Overlay, a technique of working with or interfering in the color separation mechanism of a color copier; Colorizing, vary color density and hue by adjusting the exposure and color balance controls; Degeneration is a copy of a copy degrading the image as successive copies are made; Copy Motion, the creation of effects by moving an item or image on the platen during the scanning process. Each machine also creates different effects.

Accessible art
Xerox art appeared shortly after the first Xerox copying machines were made. It is often used in collage, mail art and book art. Publishing collaborative mail art in small editions of Xerox art and mailable book art was the purpose of International Society of Copier Artists (I.S.C.A.) founded by Louise Odes Neaderland.

Throughout the history of copy art San Francisco and Rochester are mentioned frequently. Rochester was known as the Imaging Capital of the World with Eastman Kodak and Xerox, while many artists with innovative ideas created cutting edge works in San Francisco. Alongside the computer boom a copy art explosion was taking place. Copy shops were springing up all over San Francisco, and access to copiers made it possible to create inexpensive art of unique imagery. Multiple prints of assemblage and collage meant artists could share work more freely. Print on demand meant making books and magazines at the corner copy shop without censorship and with only a small outlay of funds. Comic book artists could quickly use parts of their work over and over.

Early history 1960s–1970s
The first artists recognized to make copy art are Charles Arnold, Jr., and Wallace Berman. Charles Arnold, Jr., an instructor at Rochester Institute of Technology, made the first photocopies with artistic intent in 1961 using a large Xerox camera on an experimental basis. Berman, called the "father" of assemblage art, would use a Verifax photocopy machine (Kodak) to make copies of the images, which he would often juxtapose in a grid format. Berman was influenced by his San Francisco Beat circle and by Surrealism, Dada, and the Kabbalah. Sonia Landy Sheridan began teaching the first course in the use of copiers at the Art Institute of Chicago in 1970.

In the 1960s and 1970s, Esta Nesbitt was one of the earliest artists experimenting with xerox art. She invented three xerography techniques, named transcapsa, photo-transcapsa, and chromacapsa. Nesbitt worked closely with Anibal Ambert and Merle English at Xerox Corporation, and the company sponsored her art research from 1970 until 1972.

Seth Siegelaub and Jack Wendler made Untitled (Xerox Book) with artists Carl Andre, Robert Barry, Douglas Huebler, Joseph Kosuth, Sol LeWitt, Robert Morris, and Lawrence Weiner in 1968.

Copy artists' dependence upon the same machines does not mean that they share a common style or aesthetic. Artists as various as Ian Burn (a conceptual/process artist who made another Xerox Book in 1968), Laurie-Rae Chamberlain (a punk-inspired colour Xeroxer exhibiting in the mid 1970s) and Helen Chadwick (a feminist artist using her own body as subject matter in the 1980s) have employed photocopiers for very different purposes.

Other artists who have made significant use of the machines include: Carol Key, Sarah Willis, Joseph D. Harris, Tyler Moore, the Copyart Collective of Camden, as well as:

in continental Europe
 * Guy Bleus
 * Alighiero Boetti (Nove Xerox AnneMarie, 1969)
 * Bruno Munari (Xerografie series, begun in 1963)
 * M. Vänçi Stirnemann
 * Vittore Baroni
 * Piermario Ciani

in the UK
 * Graham Harwood
 * Tim Head
 * David Hockney
 * Alison Marchant
 * Russell Mills

in Brazil
 * Paulo Bruscky
 * León Ferrari
 * Hudinilson Jr.
 * Eduardo Kac
 * Letícia Parente
 * Mário Ramiro

in Canada
 * Evergon

in the US
 * Pati Hill
 * Ginny Lloyd
 * Tom Norton
 * Sonia Landy Sheridan

In the mid-1970s Pati Hill did art experiments with an IBM copier. Hill's resulting xerox artwork was exhibited at Centre Pompidou, Paris, the Musée d’Art Moderne de la Ville de Paris, and the Stedelijk Museum, Amsterdam, among other venues in Europe and the US.

Recognition of the art form
San Francisco had an active Xerox arts scene that started in 1976 at the LaMamelle gallery with the All Xerox exhibit and in 1980 the International Copy Art Exhibition, curated and organized by Ginny Lloyd, was also held at LaMamelle gallery. The exhibition traveled to San Jose, California, and Japan. Lloyd also made the first copy art billboard (the first of three) with a grant from Eyes and Ears Foundation.

A gallery named Studio 718 moved into the Beat poet area of San Francisco's North Beach neighborhood. It shared space in part with Postcard Palace, where several copy artists sold postcard editions; the space also housed a Xerox 6500. At around the same time color copy calendars produced in multiple editions made by Barbara Cushman sold at her store and gallery, A Fine Hand.

In the 1980, Marilyn McCray curated the Electroworks Exhibit held at the Cooper-Hewitt Museum in New York and International Museum of Photography at George Eastman House. On view at the Cooper Hewitt were more than 250 examples of prints, limited-edition books, graphics, animation, textiles, and 3-D pieces produced by artists and designers.

Galeria Motivation of Montreal, Canada, held an exhibit of copy art in 1981. PostMachina, an exhibit in Bologna, Italy, held in 1984, featured copy art works.

In May 1987, artist and curator George Muhleck wrote in Stuttgart about the international exhibition "Medium: Photocopie" that it inquired into "new artistic ways of handling photocopy." The book which accompanied the exhibition was sponsored mainly by the Goethe Institut of Montreal, with additional support from the Ministere des Affaires Culturelles du Quebec.

The complete collection I.S.C.A. Quarterlies is housed at the Jaffe Book Arts Collection of the Special Collections of the Wimberly Library at Florida Atlantic University in Boca Raton, Florida. The collection began in 1989 with several volumes donated by the Bienes Museum of the Modern Book, in Fort Lauderdale, FL. The Jaffe hosted an exhibition in 2010 of copy art by Ginny Lloyd, showcasing her works and copy art collection. She lectures and teaches workshops at the Jaffe on copy art history and techniques. She previously taught the workshop in 1981 at Academie Aki, Other Books and So Archive, and Jan Van Eyck Academie in The Netherlands; Image Resource Center in Cleveland and University of California - Berkeley.

In 2017–2018, the Whitney Museum of American Art in New York presented Experiments in Electrostatics: Photocopy Art from the Whitney’s Collection, 1966–1986, organized by curatorial fellow Michelle Donnelly.

Current artwork
Copiers add to the arts, as can be seen by surrealist Jan Hathaway's combining color xerography with other media, Carol Heifetz Neiman's layering prismacolor pencil through successive runs of a color photocopy process (1988-1990), or R.L. Gibson's use of large scale xerography such as in Psychomachia (2010).

In 1991, independent filmmaker Chel White completed a 4-minute animated film titled "Choreography for Copy Machine (Photocopy Cha Cha)". All of the film's images were created solely by using the unique photographic capabilities of a Sharp mono-colour photocopier to generate sequential pictures of hands, faces, and other body parts. Layered colors were created by shooting the animation through photographic gels. The film achieves a dream-like aesthetic with elements of the sensual and the absurd. The Berlin International Film Festival describes it as "a swinging essay about physiognomy in the age of photo-mechanical reproduction. The Austin Film Society dubs it, "Doubtlessly the best copy machine art with delightfully rhythmic sequences of images, all to a cha-cha-cha beat." The film screened in a special program at the 2001 Sundance Film Festival, and was awarded Best Animated Short Film at the 1992 Ann Arbor Film Festival.

Manufacturers of the machines are an obvious source of funding for artistic experimentation with copiers and such companies as Rank, Xerox, Canon and Selex have been willing to lend machines, sponsor shows and pay for artists-in-residence programs.

title: Xerox art