Early life.

Zhuge Liang was born in 181 in Yangdu County, Langya Commandery (present-day Yishui, Shandong Province). As his father Zhuge Gui died when he was still young, he was raised by Zhuge Xuan (a cousin of Zhuge Gui) in Yuzhang Commandery. When Zhuge Xuan was driven out of Yuzhang Commandery in 195, Zhuge Liang followed Zhuge Xuan to live with his friend, Liu Biao, the governor of Jing Province.  Zhuge Liang grew to be a tall man (≈189 cm). He enjoyed reciting "Liangfu Yin" (), a folk song popular in Shandong, his birthplace. He had a habit of comparing himself to the sage minister Guan Zhong and military leader Yue Yi. Although few people took him seriously, Zhuge Liang developed close friendships with influential members of the local literati such as Xu Shu, Cui Zhouping, Meng Jian and Shi Tao. Zhuge Liang also maintained close relations with other well-known intellectuals such as Sima Hui, Pang Degong and Huang Chengyan. Huang Chengyan once told Zhuge Liang, "I heard that you're seeking a spouse. I've an ugly daughter with yellow skin and dark complexion, but her talent matches yours." Zhuge Liang agreed and married Huang Chengyan's daughter. Sima Hui compared Zhuge Liang to a sleeping dragon.

Service under Liu Bei.

When Liu Bei was residing at Xinye County and taking shelter under Jing Province's governor, Liu Biao, he visited Sima Hui, who told him, "Confucian academics and common scholars, how much do they know about current affairs? Those who analyse current affairs well are elites. Crouching Dragon and Young Phoenix are the only ones in this region." Xu Shu later recommended Zhuge Liang to Liu Bei again, and Liu wanted to ask Xu to invite Zhuge to meet him. However, Xu Shu replied, "You must visit this man in person. He cannot be invited to meet you." Liu Bei succeeded in recruiting Zhuge Liang in 207 after paying three personal visits. This is contradicted in the later "Annotations" by Pei Songzhi which claim Zhuge Liang visited him first. Zhuge Liang presented the Longzhong Plan to Liu Bei and left his residence to follow Liu. Afterwards, Liu Bei became very close to Zhuge Liang and often had discussions with him. Guan Yu and Zhang Fei were displeased with their relationship and complained about it. Liu Bei explained, "Now that I have Kongming, I am like a fish that has found water. I hope you'll stop making unpleasant remarks." Guan Yu and Zhang Fei then stopped complaining.

As a diplomat.

In 208, Liu Biao died and was succeeded by his younger son, Liu Cong, who surrendered Jing Province to Cao Cao. When Liu Bei heard of Liu Cong's surrender, he led his followers (both troops and civilians) on an exodus southward to Xiakou, engaging Cao Cao's forces in a brief skirmish at the Battle of Changban along the way. While in Xiakou, Liu Bei sent Zhuge Liang to follow Lu Su to Jiangdong to discuss the formation of an alliance between him and Sun Quan.  Zhuge Liang met Sun Quan in Chaisang and proposed two solutions to him, "If you can use the forces of Wuyue to resist the central government, why not break ties (with Cao Cao) in advance? If you cannot oppose, why not demobilise the troops, discard your armour and surrender to the north?" After Sun Quan's viceroy, Zhou Yu, analysed the situation and pointed out weaknesses in Cao Cao's army, Sun finally agreed to ally with Liu Bei in resisting Cao Cao. Zhuge Liang returned to Liu Bei's camp with Sun Quan's envoy, Lu Su, to make preparation for the upcoming war.

As a logistics officer.

In late 208, the allied armies of Liu Bei and Sun Quan scored a decisive victory over Cao Cao's forces at the Battle of Red Cliffs. Cao Cao retreated to Ye city, while Liu Bei proceeded to conquer territories in Jiangnan, covering most of southern Jing Province. Zhuge Liang was appointed Military Advisor General of the Household (). He was put in charge of governing Lingling (present day Yongzhou, Hunan), Guiyang and Changsha commanderies and collecting taxes to fund the military.  In 211, Liu Zhang, governor of Yi Province (covering present-day Sichuan and Chongqing), requested aid from Liu Bei in attacking Zhang Lu in Hanzhong Commandery. Liu Bei left Zhuge Liang, Guan Yu, Zhang Fei and others in charge of Jing Province while he led an army into Yi Province. Liu Bei promptly agreed to Liu Zhang's proposal, but secretly planned to take over Liu Zhang's land. The following year, Liu Zhang discovered Liu Bei's intention, and the two turned hostile and waged war on each other. Zhuge Liang, Zhang Fei and Zhao Yun led separate forces to reinforce Liu Bei in the attack on Yi Province's capital, Chengdu, while Guan Yu stayed behind to guard Jing Province. In 214, Liu Zhang surrendered and Liu Bei took control of Yi Province.  Liu Bei appointed Zhuge Liang as Military Advisor General () and let him administer affairs of his personal office (office of the General of the Left ()). Whenever Liu Bei embarked on military campaigns, Zhuge Liang remained to defend Chengdu and ensured a steady flow of supply of troops and provisions. In 221, in response to Cao Pi's usurping of Emperor Xian's throne, Liu Bei's subordinates advised him to declare himself emperor. After initially refusing, Liu Bei was eventually persuaded by Zhuge Liang to do so and became ruler of Shu Han. Liu Bei named Zhuge Liang his chancellor and put him in charge of the imperial agency where Zhuge assumed the functions of the head of the imperial secretariat. Zhuge Liang was appointed Colonel-Director of Retainers () after Zhang Fei's death.

Service under Liu Shan.

In the spring of 223, Liu Bei retreated to Yong'an (present-day Fengjie County, Chongqing) after his defeat at the Battle of Xiaoting and became seriously ill. He summoned Zhuge Liang from Chengdu and said to him, "You're ten times more talented than Cao Pi, and capable of both securing the country and accomplishing our great mission. If my son can be assisted, then assist him. If he proves incompetent, then you may take over the throne." Zhuge Liang replied tearfully, "I'll do my utmost and serve with unwavering loyalty until death." Liu Bei then ordered his son, Liu Shan, to administer state affairs together with Zhuge Liang and regard Zhuge as his father.

As a regent.

After Liu Bei's death, Liu Shan ascended to the throne of Shu Han. He granted Zhuge Liang the title "Marquis of Wu District" () and created an office for him. Not long later, Zhuge Liang was appointed governor of Yi Province and put in charge of all state affairs. At the same time, the commanderies in Nanzhong rebelled against Shu, but Zhuge Liang did not send troops to suppress the revolt as Liu Bei's death was still recent. Liu Bei was finally persuaded after his defeat to Lu Xun, that an alliance with Wu as a must. Zhuge sent Deng Zhi and Chen Zhen to make peace with Eastern Wu and reentered an alliance with Wu. Zhuge Liang would consistently send envoys to Wu to improve diplomatic relations between the two states.

Southern Campaign.

During his reign as regent, Zhuge Liang set Shu's objective as the restoration of the Han dynasty, which, from Shu's point of view, had been usurped by the state of Cao Wei. He felt that in order to attack Wei, a complete unification of Shu was first needed. Zhuge Liang was worried that the local clans would work with the Nanman tribes in Nanzhong to stage a revolt. Fearing the possibility that the peasants might rebel and press into areas surrounding the capital Chengdu while he was attacking Wei in the north, Zhuge Liang decided to pacify the southern tribes first.  In the spring of 225, regional clans, including Yong, Gao, Zhu and Meng, had taken control of some cities in the south, so Zhuge Liang led an expedition force to Nanzhong. Ma Su proposed that they should attempt to win the hearts of the Nanman and rally their support instead of using military force to subdue them. Zhuge Liang heeded Ma Su's advice and defeated the rebel leader, Meng Huo, on seven different occasions, as it was claimed in later histories such as the "Chronicles of Huayang". He released Meng Huo each time in order to achieve Meng's genuine surrender. The story about Meng Huo's seven captures is recently questioned by many modern academics, including historians such as Miao Yue, Tan Liangxiao, and Zhang Hualan.  Realising he had no chance to win, Meng Huo pledged allegiance to Shu, and was appointed by Zhuge Liang as governor of the region to keep the populace content and secure the southern Shu border. This would ensure that the future Northern Expeditions would proceed without internal disruptions. Rich and abundant resources acquired from Nanzhong were used to fund Shu's military and the state became more prosperous.

Northern Expeditions and death.

After pacifying the Nanman, Zhuge Liang ordered the Shu military to make preparations for a large scale offensive on Wei. In 227, while in Hanzhong, he wrote a memorial, titled "Chu Shi Biao", to Liu Shan, stating his rationale for the campaign and giving advice to the emperor on good governance. From 228 until his death in 234, Zhuge Liang launched a total of five Northern Expeditions against Wei, all except one of which failed. During the first Northern Expedition, Zhuge Liang persuaded Jiang Wei, a young Wei military officer, to surrender and defect to his side. Jiang Wei became a prominent general of Shu later and continued Zhuge Liang's legacy of an aggressive foreign policy against Wei. The other permanent gains by Shu were the conquests of the impoverished Wudu and Yinping commanderies, as well as the relocation of Wei citizens to Shu territories on occasion.  In the spring of 231, Zhuge Liang finally met his nemesis, Sima Yi (the newly appointed Wei commander), at the Battle of Mount Qi, the deadliest campaign of the five expeditions in terms of death toll. In late 234, Zhuge Liang and Sima Yi reached a stalemate at the Battle of Wuzhang Plains. Straining his energy on military matters big and small, Zhuge Liang fell seriously ill and eventually died in camp at the age of 53. Before his death, Zhuge Liang recommended Jiang Wan and Fei Yi to succeed him as regent of Shu. He was buried on Mount Dingjun according to his dying wish and posthumously granted the title "Marquis Zhongwu" (忠武侯; literally "loyal and martial marquis") by Liu Shan.

Family and descendants.

Zhuge Liang's ancestor, Zhuge Feng (), served as the Colonel-Director of Retainers during the reign of Emperor Yuan of the Han dynasty. Zhuge Liang's father, Zhuge Gui (), served as an assistant officer in Mount Tai Commandery in the late Han dynasty. Zhuge Liang's cousin-uncle, Zhuge Xuan, who raised Zhuge Liang and Zhuge Jun, served as the Administrator of Yuzhang Commandery before serving under Liu Biao, the Governor of Jing Province.  Zhuge Liang had an elder brother, a younger brother, and two elder sisters. His elder brother, Zhuge Jin, served under the warlord Sun Quan and later in the state of Eastern Wu. His younger brother, Zhuge Jun (), served in the state of Shu Han. One of Zhuge Liang's sisters married Pang Shanmin, a cousin of Pang Tong, while the other sister married a member of the prominent Kuai family headed by Kuai Liang and Kuai Yue in Xiangyang Commandery.  Zhuge Liang married the daughter of Huang Chengyan. She was a maternal niece of Liu Biao and Lady Cai because her mother (Huang Chengyan's wife) was Lady Cai's younger sister. Although her name was not recorded in history, she is commonly referred to by the name "Huang Yueying" in popular culture.  Zhuge Liang had at least two sons. His elder son, Zhuge Zhan, served as a general in Shu and was killed in action during the Conquest of Shu by Wei. His younger son, Zhuge Huai (), lived as a commoner during the Jin dynasty. Zhuge Liang initially had no sons, so he adopted his nephew, Zhuge Qiao (Zhuge Jin's son). Zhuge Qiao served in Shu and died at a relatively young age. According to legend, Zhuge Liang had a daughter, Zhuge Guo (), but her existence is disputed by historians.  Zhuge Qiao's son, Zhuge Pan (), returned to Eastern Wu after Zhuge Ke's death to continue Zhuge Jin's family line there. Zhuge Zhan had three sons. The eldest, Zhuge Shang, served Shu and was killed in action together with his father. The second, Zhuge Jing (), moved to Hedong Commandery in 264 with Zhuge Pan's son, Zhuge Xian (), and came to serve the Jin dynasty later. The youngest was Zhuge Zhi ().  Zhuge Dan, one of Zhuge Liang's cousins, served in the state of Cao Wei and masterminded the third of the Three Rebellions in Shouchun. He was killed after his defeat.

Legacy.

Inventions.

Although the invention of the repeating crossbow has often been attributed to Zhuge Liang, he had nothing to do with it. This misconception is based on a record attributing improvements to the multiple bolt crossbows to him.  Zhuge Liang is also credited with constructing the Stone Sentinel Maze, an array of stone piles that is said to produce supernatural phenomena, located near Baidicheng.  An early type of hot air balloon used for military signalling, known as the Kongming lantern, is also named after him. It was said to be invented by Zhuge Liang when he was trapped by Sima Yi in Pingyang. Friendly forces nearby saw the message on the lantern paper covering and came to Zhuge Liang's aid. Another belief is that the lantern resembled Zhuge Liang's headdress, so it was named after him.

Literary works.

Some books popularly attributed to Zhuge Liang can be found today. For example, the "Thirty-Six Stratagems", and "Mastering the Art of War" (not to be confused with Sun Tzu's "The Art of War") are two commonly available works attributed to Zhuge Liang. Supposedly, his mastery of infantry and cavalry formation tactics, based on the Taoist classic "I Ching", were unrivalled. His memorial, the "Chu Shi Biao", written prior to the Northern Expeditions, provided a salutary reflection of his unwavering loyalty to the state of Shu. The memorial moved some readers to tears. In addition, he wrote "Admonition to His Son" () in which he reflected on his humbleness and frugality in pursuit of a meaningful life.  Zhuge Liang is also the subject of many Chinese literary works. A poem by Du Fu, a prolific Tang dynasty poet, was written in memory of Zhuge Liang whose legacy of unwavering dedication seems to have been forgotten in Du Fu's generation (judging by the description of Zhuge Liang' unkept temple). Some historians believe that Du Fu had compared himself with Zhuge Liang in the poem. The full text is:  Du Fu's quatrain "Eightfold Battle Formation" () about Zhuge Liang's Stone Sentinel Maze, is collected in the "Three Hundred Tang Poems".

Notable quotes.

The phrase "The Han and the Evil do not stand together" () from the Later "Chu Shi Biao" is often used to draw a line in the sand and declare a situation where one cannot stand with evil. Notably, this phrase was Generalissimo Chiang Kai-shek's favorite quote to invoke to justify his anti-communism ideology.  Another phrase "with deference and prudence, to the state of one's depletion; it's never finished until one's death" () from the Later "Chu Shi Biao" is often used to describe one's commitment and perseverance to strive to the utmost.  One famous line of poem, "Who is the first, awakened from the Great Dream? As always, I'm the one who knows." (), was also attributed to Zhuge Liang.  "Without modest simplicity, one cannot brighten volition; Without tranquility and serenity, one cannot reach far" (), a well-known maxim authored by Zhuge Liang, has been popular in educational institutions in China for thousands of years.

In "Romance of the Three Kingdoms".

The wisdom of Zhuge Liang was popularised by the historical novel "Romance of the Three Kingdoms", written by Luo Guanzhong during the Ming dynasty. In it, Zhuge Liang is described to be able to perform fantastical achievements such as summoning advantageous winds and devising magical stone mazes.  There is great confusion on whether the stories are historical or fictional. At least, the Empty Fort Strategy is based on historical records, albeit not attributed to Zhuge Liang historically. For Chinese people, the question is largely irrelevant, as the Zhuge Liang of lore is regardless seen as a mastermind, whose examples continue to influence many layers of Chinese society. They are also argued, together with Sun Tzu's "The Art of War", to still greatly influence the modern Chinese strategical, military and everyday thinking.  See the following for the stories in "Romance of the Three Kingdoms" involving Zhuge Liang.

Events before Zhuge Liang's death.

When Zhuge Liang fell critically ill during the Battle of Wuzhang Plains, he attempted to extend his lifespan by 12 years through a ritual. However, he failed when the ritual was disrupted by Wei Yan, who rushed in to warn him about the enemy's advance. Before his death, Zhuge Liang also passed his "24 Volumes on Military Strategy" () to Jiang Wei, who would continue his legacy and lead another eleven campaigns against the state of Cao Wei.()

Worship of Zhuge Liang.

There are many temples and shrines built to commemorate Zhuge Liang. Some of the most famous ones include the Temple of the Marquis of Wu in Chengdu, and the Temple of the Marquis of Wu in Baidicheng.  In 760, when Emperor Suzong of the Tang dynasty built a temple to honour Jiang Ziya, he had sculptures of Zhuge Liang and another nine famous historical military generals/strategists – Bai Qi, Han Xin, Li Jing, Li Shiji, Zhang Liang, Tian Rangju, Sun Tzu, Wu Qi and Yue Yi – placed in the temple flanking Jiang Ziya's statue.  Zhuge Liang is also sometimes venerated as a door god at Chinese and Taoist temples, usually in partnership with Sima Yi of Wei.

In popular culture.

Film and television.

Notable actors who have portrayed Zhuge Liang in film and television include: Adam Cheng, in "The Legendary Prime Minister – Zhuge Liang" (1985); Li Fazeng, in "Zhuge Liang" (1985); Tang Guoqiang, in "Romance of the Three Kingdoms" (1994); Pu Cunxin, in "" (2008); Takeshi Kaneshiro, in "Red Cliff" (2008–09); Lu Yi, in "Three Kingdoms" (2010); Raymond Lam, in "Three Kingdoms RPG" (2012).

Video games.

Zhuge Liang's reputation for being an unparalleled genius is also emphasised in his portrayal in video games. Reflecting his status as the most highly regarded strategist in "Romance of the Three Kingdoms", games such as "Destiny of an Emperor" and Koei's "Romance of the Three Kingdoms" game series place Zhuge Liang's intelligence statistic as the highest of all characters. He is also a playable character in Koei's "Dynasty Warriors", "Dynasty Tactics" and "Kessen II". He also appears in "Warriors Orochi", a crossover between "Dynasty Warriors" and "Samurai Warriors".  Zhuge Liang is the protagonist in Koei's tactical role-playing game "Sangokushi Koumeiden", where he can die at the Battle of Wuzhang Plains, as he did historically, or proceed to restore the Han dynasty under Emperor Xian.  Zhuge Liang appears in the turn-based strategy games "Civilization IV" and "Civilization V" as a great general along with Cao Cao.  Zhuge Liang appears as two separate spirits in the game "Destiny of Spirits".  Zhuge Liang appears in at least two forms in the mobile game "Puzzle & Dragons".  Zhuge Liang appears as a summonable Pseudo-Servant in the mobile game "Fate/Grand Order", with most of his skills portraying him as a skilled tactician.  Zhuge Liang is featured in the sequel to Level-5's game and anime "", as well as Cao Cao, Liu Bei, Guan Yu and Zhang Fei. Notably, both adaptations portray Zhuge Liang as a woman.  Zhuge Liang is a legendary strategist in Creative Assembly's turn-based strategy game "".  Zhuge Liang is the fable hero of scholar class in the mobile game Royal Chaos, where he deals great amount of Area of Effect (AOE) damage as well as skilled in deployment.

Zhuge Liang ( ; 181–234), courtesy name Kongming, was a Chinese politician, military strategist, writer, engineer and inventor. He served as the chancellor and regent of the state of Shu Han during the Three Kingdoms period. He is recognised as the most accomplished strategist of his era, and has been compared to Sun Tzu, the author of "The Art of War". His reputation as an intelligent and learned scholar grew even while he was living in relative seclusion, earning him the nickname "Wolong" or "Fulong", meaning "Crouching Dragon" or "Sleeping Dragon". Zhuge Liang is often depicted wearing a Taoist robe and holding a hand fan made of crane feathers.

诸葛亮(181年-234年-10月8日),字孔明,东汉末年徐州琅琊阳都(今山东省临沂市沂南县)人。三国蜀汉(季汉)丞相,是中国历史上著名的政治家、军事家、发明家、及散文家。隐居隆中,自比管仲、乐毅,人称「卧龙」。刘备三顾始见之,为备画据荆益、联孙权、拒曹操之策,佐备取荆州,定益州,遂与魏、吴成鼎足之势。曹丕代汉,备称帝于成都,以亮为丞相。备死,亮辅后主刘禅,以丞相封武乡侯,兼领益州牧。整官制,修法度,志复中原。屡次北伐,与魏相攻战。建兴十二年卒于五丈原军中,年五十四,谥为忠武侯。《三国志·蜀志》。诸葛亮的才能、品格备受后世敬仰,故常被尊称为武侯、诸葛武侯。后民间小说、戏曲谓其通晓阴阳,料事如神。其一生“鞠躬尽瘁、死而后已”,是中国传统文化里忠臣与智者之代表。明罗贯中《三国演义》所刻画者,流传众口,最为著称。与汉昭烈帝刘备在统治蜀汉期间,提拔诸多名将与能臣,并奠定基础。


Discovery.

In 1846, Pierre Philippe Émile Matheron, a French geologist and paleontologist, described several large bones from Provence, France. In the spring of 1869, Matheron formally described these remains, including a partial femur, fibula and possible tibia and a pair of associated caudal vertebrae, as the holotype specimen of a new taxon, "Hypselosaurus priscus". Among the bones, portions of the femur shaft are not preserved, along with a majority of the tibia, while both the fibula and vertebrae are entirely preserved. The layer the fossils came from is likely from the late Late Cretaceous, specifically 70 million years ago.  Since its original description, several specimens have been referred to "Hypselosaurus". One of these, originally described in 1957 by Albert de Lapparent, includes a caudal vertebra, as well as another vertebra described in 1960 by Bataller. In 1993, a review of European sauropods stated that "Hypselosaurus" was a "nomen dubium", and that its holotype could not be verifiably distinguished from other sauropods in the same, and many other, regions. Based on this, the material that was referred to "Hypselosaurus" by several other authors would have to be considered an intermediate titanosaur.  In addition to the holotype skeleton, Matheron described two fragments of a spherical or ellipsoid fossil in 1869. These fragments were studied for some time by Matheron and his contemporary French paleontologists, and the only probable conclusion was that they were fragments of eggshells. The eggs were proposed to have been significantly larger than those of "Aepyornis" when complete, and Matheron suggested that they either were a very large bird egg, or belonged to "Hypselosaurus".  When originally named, Matheron proposed that "Hypselosaurus" was an aquatic crocodile, as was suggested for similar taxa like "Pelorosaurus", "Cetiosaurus", "Streptospondylus" and "Steneosaurus" by their describers. Matheron noted that the long bones, particularly the femur, lacked medullary bone, and thus proposed that it could not have been terrestrial like "Iguanodon".

Description.

"Hypselosaurus" was a proposed to be in length, when it was considered a crocodilian, which would have made it one of the largest of the group. However, a modern estimate as a titanosaur has put "Hypselosaurus" at around, with a very rough weight estimate of. One of the smaller titanosaurs, "Neuquensaurus", measures only long.

Limb bones.

The left femur of "Hypselosaurus", at in length, is quite eroded, with both the femoral head and the distal condyles being eroded and distorted by sediment. The femur is slightly sinuous, and narrows antero-posteriorly, becoming a subquadrangular oval wide and only long. The internal shaft is fairly spongey, although the internal bone is only loosely attached, and the femur clearly lacks a medullary canal.  As preserved, the left tibia is largely incomplete, with only a small section of the shaft, just proximal to the distal condyles, known. Like the femur, there is no medullary canal present, and the spongey internal bone is asymmetrically dense. Few other features can be identified, among those the dimensions and cross-section of the bone. The tibia is ovoid in cross-section, with the anterior diameter long, and wide.  The fibula, at in length, corresponds well with the size of the femur and tibia. The fibula is approximately an equilateral triangle in cross-section, with the inner face slightly concave and outer face convex. The flatter surface of the fibula is wide, and opposite ridge protrudes from this.

Vertebrae.

Two caudal vertebrae were preserved, although there would have been a much larger number in the tail. Both bones are nearly identical in every feature, but the anterior has is slightly larger dimensions. The vertebrae are not compressed laterally, instead being compressed vertically to a width of and a height of in the posterior vertebra. Both vertebrae are procoelous, with the anterior articular face being concave, and the posterior face being convex. The larger vertebra is at its widest, but it narrows towards the middle of its length until it is only wide. Both vertebrae preserved the zygapophyses, articular processes that connect the consecutive vertebrae. The vertebrae are overall very similar to those of "Pelorosaurus"

Palaeobiology.

Eggs.

Eggs attributed to "Hypselosaurus" by Matheron and Paul Gervais have been found in France since 1846, and were the earliest dinosaur eggs actually discovered, although they were not recognized as being dinosaurian for several decades. The eggs are unusually large; measuring at around in length. Age determination studies performed on the fossilized remains have been inconclusive, with results ranging from a few decades to several hundred years.  Eggs with abnormally thin shells have been attributed to "Hypselosaurus priscus". Some experts have speculated that this was the cause of the species' extinction, with vegetation changes, climatic change and overcrowding being the original impetus for the shell thinning. However, there are alternative explanations for the thin eggshell not dependent on pathology. Later researchers found evidence that the eggs in question successfully hatched. Some researchers postulated that the thinner ""Hypselosaurus priscus"" eggshells came from different taxa than the thicker eggshells, and subsequent researchers have come to support this idea. Another potential explanation for variation in eggshell thickness is that the thinner eggs were laid by younger individuals than the thicker shell eggs laid by older individuals or that it was a consequence of natural variations of eggshell thickness within a single species.

Ecology.

"Hypselosaurus" has been found only in the Grès à Reptiles Formation, in the Provence region of southern France. This formation, dating to the early Maastrichtian approximately 70 mya, has provided fossils of several different groups of dinosaurs. The theropods "Variraptor" and "Pyroraptor", both considered to be within the family Dromaeosauridae, have been found in the Grés á Reptiles Formation, in addition to the nodosaurid ankylosaurian "Rhodanosaurus" (a dubious genus); a bone fragment potentially belonging to Abelisauridae; and the rhabdodontid ornithopod "Rhabdodon". Although the material between "Variraptor" and "Pyroraptor" cannot be compared, and they may in fact belong to the same taxon, there are at least two separate dromarosaurids present in the formation. In addition, a new titanosaur, "Atsinganosaurus" was described from the formation, based on several dorsal vertebrae. There are also indeterminate crocodilians known from the same strata as "Hypselosaurus", although they are only represented by unnamed fragments.

Hypselosaurus (meaning 'highest lizard', from Greek ὑψηλός meaning 'high' or 'lofty' and σαυρος meaning 'lizard') was a dubious titanosaurian sauropod that lived in southern France during the Late Cretaceous, approximately 70 million years ago in the early Maastrichtian. "Hypselosaurus" was first described in 1846, but was not formally named until 1869, when Phillip Matheron named it under the binomial Hypselosaurus priscus. The holotype specimen includes a partial hindlimb and a pair of caudal vertebrae, and two eggshell fragments were found alongside these bones. Because of the proximity of these eggshells to the fossil remains, many later authors, including Matheron and Paul Gervais, have assigned several eggs from the same region of France all to "Hypselosaurus", although the variation and differences between these eggs suggest that they do not all belong to the same taxon. "Hypselosaurus" has been found in the same formation as the dromaeosaurids "Variraptor" and "Pyroraptor", the ornithopod "Rhabdodon", and the ankylosaurian "Rhodanosaurus", as well as indeterminate bones from other groups.

高桥龙属(学名:"Hypselosaurus")是蜥脚下目泰坦巨龙类恐龙的一属,生存于白垩纪(麦斯特里希特阶,距今约7000万)的法国、西班牙、罗马尼亚。学名的意思是「最高的蜥蜴」。


Prehistoric Croatia.

The area known today as Croatia was inhabited throughout the prehistoric period. Fossils of Neanderthals dating to the middle Palaeolithic period have been unearthed in northern Croatia, with the most famous and the best presented site in Krapina. Remnants of several Neolithic and Chalcolithic cultures were found in all

Roman provinces of Pannonia and Dalmatia.

Dalmatia was the northern part of the Illyrian kingdom between the 4th century BC until the Illyrian Wars in the 220s BC and 168 BC when the Roman Republic established its protectorate south of the river Neretva. The area north of the Neretva was slowly incorporated into Roman possession until the province of Illyricum was formally established c. 32–27 BC.  The Dalmatia region then became part of the Roman province of Illyricum. Between 6 and 9 AD the Dalmatians raised the last in a series of revolts together with the Pannonians, but it was finally crushed and in 10 AD Illyricum was split into two provinces, Pannonia and Dalmatia. The province of Dalmatia spread inland to cover all of the Dinaric Alps and most of the eastern Adriatic coast. Dalmatia was the birthplace of the Roman Emperor Diocletian, who, upon retirement from Emperor in AD 305, built a

Early Medieval Croatia (until 925).

According to the work "De Administrando Imperio" written by the 10th-century Byzantine Emperor Constantine VII, the Croats had arrived in what is today Croatia, from southern Poland, south of Kraków in the early 7th century, however that claim is disputed and competing hypotheses date the event between the 6th and the 9th centuries. Eventually two dukedoms were formed—Duchy of Pannonia and Duchy of

Kingdom of Croatia (925–1102).

Tomislav was the first ruler of Croatia who was styled a king in a letter from the Pope John X, dating kingdom of Croatia to year 925. Tomislav defeated Hungarian and Bulgarian invasions, spreading the influence of Croatian kings.

Personal union with Hungary (1102–1527) and Republic of Venice.

The consequences of the change to the Hungarian king included the introduction of feudalism and the rise of the native noble families such as Frankopan and Šubić. The later kings sought to restore some of their previously lost influence by giving certain privileges to the towns. For the next four centuries, the Kingdom of Croatia was ruled by the Sabor (parliament) and a Ban (viceroy) appointed by the king.  The princes of Bribir from the Šubić family became particularly influential, asserting control over large parts of Dalmatia, Slavonia and Bosnia. Later, however, the Angevins intervened and restored royal power. The period saw rise of native nobility such as the Frankopans and the Šubićs to prominence and

Croatia in the Habsburg Monarchy (1527–1918).

As the Turkish incursion into Europe started, Croatia once again became a border area. The Croats fought an increasing number of battles and gradually lost increasing swathes of territory to the Ottoman Empire. Ottoman conquests led to the 1493 Battle of Krbava field and 1526 Battle of Mohács, both ending in decisive Ottoman victories. King Louis II died at Mohács, and in November 1526, a Hungarian parliament elected János Szapolyai as the new king of Hungary. In December 1526, another Hungarian parliament elected Ferdinand Habsburg as King of Hungary. On the other side, the Croatian Parliament met in Cetin and chose Ferdinand I of the House of Habsburg as new ruler of Croatia, under the condition that he provide protection to Croatia against the Ottoman Empire while respecting its political rights. A few years later both crown would be again united in Habsburgs hands and the union would be restored. The Ottoman Empire further expanded in the 16th century to include most of Slavonia, western Bosnia (then called Turkish Croatia) and Lika. Ottoman Croatia initially was part of Rumelia Eyalet, and later was parts of Budin Eyalet, Bosnia Eyalet and Kanije Eyalet.  Later in the same century, Croatia was so weak that its parliament authorized Ferdinand Habsburg to carve out large areas of Croatia and Slavonia adjacent to the Ottoman Empire for the creation of the Military Frontier ("Vojna Krajina", German: "Militaergrenze") which would be ruled directly from Vienna's military headquarters. The area became rather deserted and was subsequently settled by Serbs, Vlachs, Croats and Germans and others. As a result of their compulsory military service to the Habsburg Empire during conflict with the Ottoman Empire, the population in the Military Frontier was free of

Kingdom of Yugoslavia (1918–1941).

The creation of Yugoslavia happened in late 1918: after Srijem left Croatia-Slavonia and joined Serbia together with Vojvodina, shortly followed by a referendum to join Bosnia and Herzegovina to Serbia, the People's Council of Slovenes, Croats and Serbs ("Narodno vijeće"), guided by what was by that time a half a century long tradition of pan-Slavism and without sanction of the Croatian sabor, joined the Kingdom of Serbia into the Kingdom of the Serbs, Croats and Slovenes.  Although the state inherited much of Austro-Hungary's military arsenal, including the entire fleet, the Kingdom of Italy moved rapidly to annex the state's most western territories, promised to her by the Treaty of London of 1915. An Italian Army eventually took Istria, started to annex the Adriatic islands one by one, and even landed in Zadar. Partial resolution to the so-called Adriatic Question would come in 1920 with the Treaty of Rapallo.  The Kingdom underwent a crucial change in 1921 to the dismay of Croatia's largest political party, the Croatian Peasant Party (Hrvatska seljačka stranka). The new constitution abolished the historical/political entities, including Croatia and Slavonia, centralizing authority in the capital of Belgrade. The Croatian Peasant Party boycotted the government of the Serbian People's Radical Party throughout the period,

World War II and the Independent State of Croatia (1941–1945).

The Axis occupation of Yugoslavia in 1941 allowed the Croatian radical right Ustaše to come into power, forming the "Independent State of Croatia" ("Nezavisna Država Hrvatska", NDH), led by Ante Pavelić, who assumed the role of "Poglavnik". Following the pattern of other fascist regimes in Europe, the Ustashi enacted racial laws, formed eight concentration camps targeting minority Serbs, Romas and Jewish populations, as well as Croatian and Bosnian Muslim partisans. The biggest concentration camp was Jasenovac in Croatia. The NDH had a program, formulated by Mile Budak, to purge Croatia of Serbs, by "killing one third, expelling the other third and assimilating the remaining third". The main targets for persecution were the Serbs, with approximately 330,000 were killed.  The anti-fascist communist-led Partisan movement, based on pan-Yugoslav ideology, emerged in early 1941, under the command of Croatian-born Josip Broz Tito, spreading quickly into many parts of Yugoslavia. The 1st Sisak Partisan Detachment, often hailed

Socialist Yugoslavia (1945–1991).

Tito's leadership of the LCY (1945–1980).

Croatia was a Socialist Republic part of a six-part Socialist Federative Republic of Yugoslavia. Under the new communist system, privately owned factories and estates were nationalized, and the economy was based on a type of planned market socialism. The country underwent a rebuilding process, recovered from World War II, went through industrialization and started developing tourism.  The country's socialist system also provided free apartments from big companies, which with the workers' self-management investments paid for the living spaces. From 1963, the citizens of Yugoslavia were allowed to travel to almost any country because of the neutral politics. No visas were required to travel to eastern or western countries, or to capitalist or communist nations.  Such

Until the breakup of Yugoslavia (1980–1991).

In 1980, after Tito's death, economic, political, and religious difficulties started to mount and the federal government began to crumble. The crisis in Kosovo and, in 1986, the emergence of Slobodan Milošević in Serbia provoked a very negative reaction in Croatia and Slovenia; politicians from both republics feared that his motives would threaten their republics' autonomy. With the climate of change throughout Eastern Europe during the 1980s, the communist hegemony was challenged (at the same time, the Milošević government began to gradually concentrate Yugoslav power in Serbia and calls for free multi-party elections were becoming louder).  In

Republic of Croatia (1991–present).

Political changes.

On 22 April and 7 May 1990, the first free multi-party elections were held in Croatia. Franjo Tuđman's Croatian Democratic Union (HDZ) won by a 42% margin against Ivica Račan's reformed communist Party of Democratic Change (SDP) who won 26%. However, Croatia's first-past-the-post election system enabled Tuđman to form the government relatively independently as the win translated into 205 mandates (out of 351 total). The HDZ's intentions were to secure independence for Croatia, contrary to the wishes of a part of the ethnic Serbs in the

War of Independence (1991–1995).

The civilian population fled the areas of armed conflict "en masse": generally speaking, hundreds of thousands of Croats moved away from the Bosnian and Serbian border areas. In many places, masses of civilians were forced out by the Yugoslav National Army (JNA), who consisted mostly of conscripts from Serbia and Montenegro, and irregulars from Serbia, in what became known as ethnic cleansing.  The border city of Vukovar underwent a three-month siege – the Battle of Vukovar – during which most of the city was destroyed and a majority of the population was forced to flee. The city fell to the Serbian forces on 18 November 1991 and the Vukovar massacre occurred.  Subsequent UN-sponsored cease-fires followed, and the warring parties mostly entrenched. The Yugoslav People's Army retreated from Croatia into Bosnia and

Since the end of the war.

Croatia became a member of the Council of Europe in 1996. The years 1996 and 1997 were a period of post-war recovery and improving economic conditions. However, in 1998 and 1999 Croatia experienced an economic depression, which brought unemployment for thousands of citizens.  The remaining part of former "Krajina", areas adjacent to FR Yugoslavia, negotiated a peaceful reintegration process with the Croatian government. The so-called Erdut Agreement made the area a temporary protectorate of the UN Transitional Administration for Eastern Slavonia, Baranja and Western Sirmium. The area was formally re-integrated into Croatia by 1998.

See also.

General:

Croatia first appeared as two duchies in the 7th century, the Duchy of Croatia and the Duchy of Pannonian Croatia, which were united and elevated into the Kingdom of Croatia which lasted from 925 until 1918. From the 12th century the Kingdom of Croatia entered a Personal Union with the Kingdom of Hungary, it remained a distinct state with its ruler ("Ban") and Sabor, but it elected Royal dynasties from neighboring powers, primarily Hungary, Naples and the Habsburg Monarchy.

克罗地亚首先出现在历史上是8世纪,以大公国形式存在。10世纪成为一个王国。


Early life and education.

Kernighan was born in Toronto. He attended the University of Toronto between 1960 and 1964, earning his Bachelor's degree in engineering physics. He received his Ph.D. in electrical engineering from Princeton University in 1969, completing a doctoral dissertation titled "Some graph partitioning problems related to program segmentation" under the supervision of Peter G. Weiner.

Career and research.

Kernighan has held a professorship in the Department of Computer Science at Princeton since 2000. Each fall he teaches a course called "Computers in Our World", which introduces the fundamentals of computing to non-majors.  Kernighan was the software editor for Prentice Hall International. His "Software Tools" series spread the essence of "C/Unix thinking" with makeovers for BASIC, FORTRAN, and Pascal, and most notably his "Ratfor" (rational FORTRAN) was put in the public domain.  He has said that if stranded on an island with only one programming language it would have to be C.  Kernighan coined the term Unix and helped popularize Thompson's Unix philosophy. Kernighan is also known as a coiner of the expression "What You See Is All You Get" (WYSIAYG), which is a sarcastic variant of the original "What You See Is What You Get" (WYSIWYG). Kernighan's term is used to indicate that WYSIWYG systems might throw away information in a document that could be useful in other contexts.  Kernighan's original 1978 implementation of Hello, World! was sold at The Algorithm Auction, the world's first auction of computer algorithms.  In 1996, Kernighan taught CS50 which is the Harvard University introductory course in Computer Science.  Kernighan was elected as a member of the National Academy of Engineering in 2002 and a member of the American Academy of Arts and Sciences in 2019.  Other achievements during his career include:

Brian Wilson Kernighan (; born January 1, 1942) is a Canadian computer scientist.

布莱恩·威尔森·柯林汉(英语:Brian Wilson Kernighan,1942年),生于加拿大多伦多,加拿大计算机科学家,曾服务于贝尔实验室,为普林斯顿大学教授。他曾参与Unix的研发,也是AMPL与AWK的共同创造者之一。


From prehistory to the sovereign country.

The area of current day Angola was inhabited during the paleolithic and neolithic eras, as attested by remains found in Luanda, Congo, and the Namibe desert. At the beginning of recorded history other cultures and people also arrived.  The first ones to settle were the San people. This changed at the beginning of the sixth century AD, when the Bantu, already in possession of metal-working technology, ceramics and agriculture began migrating from the north. When they reached what is now Angola they encountered the San and other groups. The establishment of the Bantu took many centuries and gave rise to various groupings that took on different ethnic characteristics.  The first large political entity in the area, known to history as the Kingdom of Kongo, appeared in the thirteenth century and stretched from Gabon in the north to the river Kwanza in the south, and from the Atlantic in the west to the river Cuango in the east.  The wealth of the Kongo came mainly from agriculture. Power was in the hands of the Mani, aristocrats who occupied key positions in the kingdom and who answered only to the all-powerful King of the Kongo. Mbanza was the name given to a territorial unit administered and ruled by a Mani; Mbanza Congo, the capital, had a population of over fifty thousand in the sixteenth century.  The Kingdom of Kongo was divided into six provinces and included some dependent kingdoms, such as Ndongo to the south. Trade was the main activity, based on highly productive agriculture and increasing exploitation of mineral wealth. In 1482, Portuguese caravels commanded by Diogo Cão arrived in the Congo and he explored the extreme north-western coast of what today is Angola in 1484. Other expeditions followed, and close relations were soon established between the two states. The Portuguese brought firearms and many other technological advances, as well as a new religion (Christianity); in return, the King of the Congo offered plenty of slaves, ivory, and minerals.  The Portuguese colony of Angola was founded in 1575 with the arrival of Paulo Dias de Novais with a hundred families of colonists and four hundred soldiers. Its center at Luanda was granted the status of city in 1605.  The King of the Kongo soon converted to Christianity and adopted a similar political structure to the Europeans. He became a well-known figure in Europe, to the point of receiving missives from the Pope.  To the south of the Kingdom of the Kongo, around the river Kwanza, there were various important states. The most important of these was the Kingdom of Ndongo or Dongo, ruled by the ngolas. At the time of the arrival of the Portuguese, Ngola Kiluange was in power. By maintaining a policy of alliances with neighbouring states, he managed to hold out against the foreigners for several decades but was eventually beheaded in Luanda. Years later, the Ndongo rose to prominence again when Jinga Mbandi (Queen Jinga) took power. A wily politician, she kept the Portuguese in check with carefully prepared agreements. After undertaking various journeys she succeeded in 1635 in forming a grand coalition with the states of Matamba and Ndongo, Kongo, Kassanje, Dembos and Kissamas. At the head of this formidable alliance, she forced the Portuguese to retreat.  Meanwhile, Portugal had lost its King and the Spanish took control of the Portuguese monarchy. By this time, Portugal's overseas territories had taken second place. The Dutch took advantage of this situation and occupied Luanda in 1641. Jinga entered into an alliance with the Dutch, thereby strengthening her coalition and confining the Portuguese to Massangano, which they fortified strongly, sallying forth on occasion to capture slaves in the Kuata! Kuata! Wars. Slaves from Angola were essential to the development of the Portuguese colony of Brazil, but the traffic had been interrupted by these events. Portugal having regained its independence, a large force from Brazil under the command of Salvador Correia de Sá retook Luanda in 1648, leading to the return of the Portuguese in large numbers. Jinga's coalition then fell apart; the absence of their Dutch allies with their firearms and the strong position of Correia de Sá delivered a deadly blow to the morale of the native forces. Jinga died in 1663; two years later, the King of the Congo committed all his forces to an attempt to capture the island of Luanda, occupied by Correia de Sá, but they were defeated and lost their independence. The Kingdom of Ndongo submitted to the Portuguese Crown in 1671.  Trade was mostly with the Portuguese colony of Brazil; Brazilian ships were the most numerous in the ports of Luanda and Benguela. By this time, Angola, a Portuguese colony, was in fact like a colony of Brazil, paradoxically another Portuguese colony. A strong Brazilian influence was also exercised by the Jesuits in religion and education. War gradually gave way to the philosophy of trade. Slave-trading routes and the conquests that made them possible were the driving force for activities between the different areas; independent states were subjugated to the demands of American slavery. In the high plains (the Planalto), the most important states were those of Bié and Bailundo, the latter being noted for its production of foodstuffs and rubber. The interior remained largely free of Portuguese control as late as the 19th century. The slave trade was not abolished until 1836, and in 1844 Angola's ports were opened to foreign shipping. This facilitated the continuation of slave smuggling to the United States and Brazil. By 1850, Luanda was one of the largest Portuguese cities in the Portuguese Empire outside Mainland Portugal exporting (together with Benguela) palm and peanut oil, wax, copal, timber, ivory, cotton, coffee, and cocoa, among many other products – almost all the produce of a continued forced labour system.  The Berlin Conference compelled Portugal to move towards the immediate occupation of all the territories it laid claim to but had been unable to effectively conquer. The territory of Cabinda (province), to the north of the river Zaire, was also ceded to Portugal on the legal basis of the Treaty of Simulambuko Protectorate, concluded between the Portuguese Crown and the princes of Cabinda in 1885. In the 19th century they slowly and hesitantly began to establish themselves in the interior. Angola as a Portuguese colony encompassing the present territory was not established before the end of the 19th century, and "effective occupation", as required by the Berlin Conference (1884) was achieved only by the 1920s.  Colonial economic strategy was based on agriculture and the export of raw materials. Trade in rubber and ivory, together with the taxes imposed on the population of the Empire (including the mainland), brought vast income to Lisbon.  Portuguese policy in Angola was modified by certain reforms introduced at the beginning of the twentieth century. The fall of the Portuguese monarchy and a favourable international climate led to reforms in administration, agriculture, and education. In 1951, with the advent of the New State regime ("Estado Novo") extended to the colony, Angola became a province of Portugal (Ultramarine Province), called the "Província Ultramarina de Angola" (Overseas Province of Angola).  However, Portuguese rule remained characterized by deep-seated racism, mass forced labour, and an almost complete failure to modernize the country. By 1960, after 400 years of colonial rule, there was not a single university in the entire territory. To counter this lack of education facilities, overtly political organizations first appeared in the 1950s, and began to make organized demands for human and civil rights, initiating diplomatic campaigns throughout the world in their fight for independence. The Portuguese regime, meanwhile, refused to accede to the nationalist's demands for independence, thereby provoking the armed conflict that started in 1961 when guerrillas attacked colonial assets in cross-border operations in northeastern Angola. The war came to be known as the Colonial War.  In this struggle, the principal protagonists were the MPLA (Popular Movement for the Liberation of Angola), founded in 1956, the FNLA (National Front for the Liberation of Angola), which appeared in 1961, and UNITA (National Union for the Total Independence of Angola), founded in 1966. After many years of conflict, the nation gained its independence on 11 November 1975, after the 1974 coup d'état in Lisbon, Portugal. Portugal's new leaders began a process of democratic change at home and acceptance of the independence of its former colonies.

Civil war.

A 1974 coup d'état in Portugal established a military government led by President António de Spínola. The Spínola government agreed to give all of Portugal's colonies independence, and handed power in Angola over to a coalition of the three largest nationalist movements, the MPLA, UNITA, and the FNLA, through the Alvor Agreement. The coalition quickly broke down, however, and the country descended into civil war. The MPLA gained control of the capital Luanda and much of the rest of the country. With the support of the United States, Zaïre and South Africa intervened militarily in favour of the FNLA and UNITA with the intention of taking Luanda before the declaration of independence. In response, Cuba intervened in favor of the MPLA. In the meantime the South Africans and UNITA had come as close as 200 km to the south of the capital, the FNLA and Zairian forces as far as Kifangondo, 30 km to the east.  With Cuban support, the MPLA held Luanda and declared independence as the Angolan People's Republic on November 11, 1975, the day the Portuguese left the country. Agostinho Neto became the first president. FNLA and UNITA proclaimed their own short-lived republics (the Angolan Democratic Republic and the Angolan Social Democratic Republic) on November 24, 1975, for the zones they controlled with Holden Roberto and Jonas Savimbi as co-presidents of the Angolan People's Democratic Republic in Huambo. This joint FNLA-UNITA government was dissolved on February 11, 1976 after a MPLA offensive. By the end of January 1976 the MPLA army (FAPLA) and the Cubans had all but crushed FNLA, Zairians and UNITA, and the South African forces withdrew.  On May 27, 1977, a coup attempt, including some former members of the MPLA government such as Nito Alves, led to retaliation by the government and Cuban forces, resulting in the execution of thousands, if not tens of thousands. Alves was tortured and killed. The movement is known as Fraccionismo.  The proxy war continued. The MPLA government, recognized internationally (although not by the United States), requested that Cuban forces remain in the country. Led by Jonas Savimbi, UNITA received clandestine support from the U.S. and other nations and took up military resistance in the southeast of the country while the MPLA government was supported by the USSR and Eastern Bloc countries. South Africa continued to pursue South-West Africa People's Organisation (SWAPO) forces in Southern Angola, soon established bases and increased support of UNITA, which gained control of more and more territory. In an effort to deliver a final blow to UNITA and to drive South Africa out of the country, in 1987 the People's Armed Forces for the Liberation of Angola (FAPLA), with Soviet support, launched a campaign fraught with failures and defeats. Again, the Cubans intervened, stopping UNITA and South African advances, leading to the Battle of Cuito Cuanavale from January 13 to March 23, the largest battle in African history since World War II.  The MPLA and the U.S. had been in negotiations for a peaceful solution since June 1987. The U.S. agreed to include Cuba in direct talks. Cuba joined the negotiations January 28, 1988; South Africa joined March 9. Angola, Cuba and South Africa signed the Tripartite Accord on December 22, 1988, in which the withdrawal of Cuban troops from Angola was linked to the retreat of South African soldiers from Angola and Namibia.  The Bicesse Accord in 1991 spelled out an electoral process for a democratic Angola under the supervision of the United Nations. MPLA won the first round with 49% of the votes, against 40% for UNITA. UNITA leader Jonas Savimbi rejected the results and returned to war. From October 30 to November 1, 1992 the Halloween Massacre occurred in which thousands of UNITA and FNLA supporters in Luanda were killed by MPLA troops. Estimates for the death toll nationwide reach 25,000 to 30,000. A second peace accord, the Lusaka Protocol, was brokered in Lusaka, Zambia and signed on November 20, 1994.  The peace accord between the government and UNITA provided for the integration of former UNITA insurgents into the government and armed forces. However, in 1995, localized fighting resumed. A national unity government was installed in April 1997, but serious fighting resumed in late 1998 when Savimbi renewed the war for a second time, claiming that the MPLA was not fulfilling its obligations. The UN Security Council voted on August 28, 1997, to impose sanctions on UNITA. The Angolan military launched a massive offensive in 1999 that destroyed UNITA's conventional capacity and recaptured all major cities previously held by Savimbi's forces. Savimbi then declared that UNITA would return to guerrilla tactics, and much of the country remained in turmoil..  The extended civil war rendered hundreds of thousands of people homeless. Up to 1 million lives may have been lost in fighting over the past quarter century. It only ended when Savimbi was killed in 2002

2000s and 2010s.

A Russian freighter delivered 500 tons of Ukrainian 7.62 mm ammunition to Simportex, a division of the Angolan government, with the help of a shipping agent in London on September 21, 2000. The ship's captain declared his cargo "fragile" to minimize inspection. The next day, the MPLA began attacking UNITA, winning victories in several battles from September 22–25. The government gained control over military bases and diamond mines in Lunda Norte and Lunda Sul, hurting Savimbi's ability to pay his troops.  Angola agreed to trade oil to Slovakia in return for arms, buying six Sukhoi Su-17 attack aircraft on April 3, 2000. The Spanish government in the Canary Islands prevented a Ukrainian freighter from delivering 636 tons of military equipment to Angola on February 24, 2001. The captain of the ship had inaccurately reported his cargo, falsely claiming the ship carried automobile parts. The Angolan government admitted Simportex had purchased arms from Rosvooruzhenie, the Russian state-owned arms company, and acknowledged the captain might have violated Spanish law by misreporting his cargo, a common practice in arms smuggling to Angola.  Government troops captured and destroyed UNITA's Epongoloko base in Benguela province and Mufumbo base in Cuanza Sul in October 2001. The Slovak government sold fighter jets to the Angolan government in 2001 in violation of the European Union Code of Conduct on Arms Exports.  Government troops killed Savimbi on February 22, 2002, in Moxico province. UNITA Vice President António Dembo took over, but died from diabetes twelve days later on March 3, and Secretary-General Paulo Lukamba became UNITA's leader. After Savimbi's death, the government came to a crossroads over how to proceed. After initially indicating the counter-insurgency might continue, the government announced it would halt all military operations on March 13. Military commanders for UNITA and the MPLA met in Cassamba and agreed to a cease-fire. However, Carlos Morgado, UNITA's spokesman in Portugal, said that the UNITA's Portugal wing had been under the impression General Kamorteiro, the UNITA general who agreed to the ceasefire, had been captured more than a week earlier. Morgado did say that he had not heard from Angola since Savimbi's death. The military commanders signed a Memorandum of Understanding as an addendum to the Lusaka Protocol in Luena on April 4, Dos Santos and Lukambo observing.  The United Nations Security Council passed Resolution 1404 on April 18, extending the monitoring mechanism of sanctions by six months. Resolutions 1412 and 1432, passed on May 17 and August 15 respectively, suspended the UN travel ban on UNITA officials for 90 days each, finally abolishing the ban through Resolution 1439 on October 18. UNAVEM III, extended an additional two months by Resolution 1439, ended on December 19.  In August 2002, UNITA declared itself a political party and officially demobilised its armed forces. That same month, the United Nations Security Council replaced the United Nations Office in Angola with the United Nations Mission in Angola, a larger, non-military, political presence.  The civil war internally displaced four million people (IDPs), one third of Angola's population. The government spent $187 million settling IDPs between April 4, 2002 and 2004, after which the World Bank gave $33 million to continue the settling process. Militant forces laid approximately 15 million landmines by 2002. The HALO Trust charity began demining in 1994, destroying 30,000 by July 2007. There are 1,100 Angolans and seven foreign workers who are working for HALO Trust in Angola, with operations expected to finish sometime between 2011 and 2014.  Human Rights Watch estimates UNITA and the government employed more than 86,000 and 3,000 child soldiers respectively, some forcibly impressed, during the war. Human rights analysts found 5,000 to 8,000 underage girls married to UNITA militants. Some girls were ordered to go and forage for food to provide for the troops. If the girls did not bring back enough food as judged by their commander, then the girls would not eat. After victories, UNITA commanders would be rewarded with women who were often then sexually abused. The government and UN agencies identified 190 child soldiers in the Angolan army and relocated seventy of them by November 2002, but the government continued to knowingly employ other underage soldiers.  Fernando Vendrell produced and Zézé Gamboa directed "The Hero", a film about the life of average Angolans after the civil war, in 2004. The film follows the lives of three individuals; Vitório, a war veteran crippled by a landmine who returns to Luanda, Manu, a young boy searching for his soldier father, and Joana, a teacher who mentors the boy and begins a love affair with Vitório. "The Hero" won the 2005 Sundance World Dramatic Cinema Jury Grand Prize. A joint Angolan, Portuguese, and French production, Gamboa filmed "The Hero" entirely in Angola.

References.

Attribution:

Angola is a country in southwestern Africa. The country's name derives from the Kimbundu word for king. It was first settled by San hunter-gatherer societies before the northern domains came under the rule of Bantu states such as Kongo and Ndongo. From the 15th century, Portuguese colonists began trading, and a settlement was established at Luanda during the 16th century. Portugal annexed territories in the region which were ruled as a colony from 1655, and Angola was incorporated as an overseas province of Portugal in 1951. After the Angolan War of Independence, which ended in April 1974 with an army mutiny and leftist coup in Lisbon, Angola achieved independence on November 11, 1975 through the Alvor Agreement. A few months before independence, Angola entered a period of civil war that lasted up until 2002.

安哥拉为非洲西南部国家。安哥拉这个词是来源于金邦杜语中的王。从考古学的角度来看,安哥拉历史开始于旧石器时代。


Statement of the problem.

Consider the following operation on an arbitrary positive integer:  In modular arithmetic notation, define the function as follows:  Now form a sequence by performing this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next.  In notation:  (that is: is the value of applied to recursively times; ).  The Collatz conjecture is: "This process will eventually reach the number 1, regardless of which positive integer is chosen initially."  That smallest such that is called the total stopping time of. The conjecture asserts that every has a well-defined total stopping time. If, for some, such an doesn't exist, we say that has infinite total stopping time and the conjecture is false.  If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found.

Examples.

For instance, starting with, one gets the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. , for example, takes longer to reach 1: 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. The sequence for, listed and graphed below, takes 111 steps (41 steps through odd numbers, in large font), climbing to a high of 9232 before descending to 1.  Numbers with a total stopping time longer than that of any smaller starting value form a sequence beginning with:  The starting values whose maximum trajectory point is greater than that of any smaller starting value are as follows:  Number of steps for to reach 1 are  The longest progression for any initial starting number  These numbers are the lowest ones with the indicated step count, but not necessarily the only ones below the given limit. As an example, has 1132 steps, as does.  The powers of two converge to one quickly because is halved times to reach 1, and is never increased.

Cycles.

In this part, consider the "shortcut" form of the Collatz function A "cycle" is a sequence of distinct positive integers where,,..., and.  The only known cycle is of length 2, called the trivial cycle.

Cycle length.

The length of a non-trivial cycle is known to be at least. In fact, Eliahou (1993) proved that the period of any non-trivial cycle is of the form where, and are non-negative integers, and. This result is based on the continued fraction expansion of.  A similar reasoning that accounts for the recent verification of the conjecture up to leads to the improved lower bound (or without the "shortcut"). This lower bound is consistent with the above result, since formula_5.

-cycles.

A -cycle is a cycle that can be partitioned into contiguous subsequences: increasing sequences of odd numbers alternating with decreasing sequences of even numbers. For instance, if the cycle consists of a single increasing sequence of odd numbers followed by a decreasing sequence of even numbers, it is called a "1-cycle".  Steiner (1977) proved that there is no 1-cycle other than the trivial. Simons (2004) used Steiner's method to prove that there is no 2-cycle. Simons & de Weger (2005) extended this proof up to 68-cycles: there is no -cycle up to. Beyond 68, this method gives upper bounds for the elements in such a cycle: for example, if there is a 75-cycle, then at least one element of the cycle is less than. Therefore, as exhaustive computer searches continue, larger cycles may be ruled out. To state the argument more intuitively: we need not look for cycles that have at most 68 trajectories, where each trajectory consists of consecutive ups followed by consecutive downs.

Supporting arguments.

Although the conjecture has not been proven, most mathematicians who have looked into the problem think the conjecture is true because experimental evidence and heuristic arguments support it.

Experimental evidence.

, the conjecture has been checked by computer for all starting values up to. All initial values tested so far eventually end in the repeating cycle, which has only three terms. From this lower bound on the starting value, a lower bound can also be obtained for the number of terms a repeating cycle other than must have. When this relationship was established in 1981, the formula gave a lower bound of terms.  This computer evidence is not a proof that the conjecture is true. As shown in the cases of the Pólya conjecture, the Mertens conjecture, and Skewes' number, sometimes a conjecture's only counterexamples are found when using very large numbers.

A probabilistic heuristic.

If one considers only the "odd" numbers in the sequence generated by the Collatz process, then each odd number is on average of the previous one. (More precisely, the geometric mean of the ratios of outcomes is.) This yields a heuristic argument that every Hailstone sequence should decrease in the long run, although this is not evidence against other cycles, only against divergence. The argument is not a proof because it assumes that Hailstone sequences are assembled from uncorrelated probabilistic events. (It does rigorously establish that the 2-adic extension of the Collatz process has two division steps for every multiplication step for almost all 2-adic starting values.)  And even if the probabilistic reasoning were rigorous, this would still imply only that the conjecture is almost surely true for any given integer, which does not necessarily imply that it is true for all integers.  Terence Tao (2019) proved using probability that almost all Collatz orbits are bounded by any function that diverges into infinity. Responding to this work, Quanta Magazine wrote that Tao "came away with one of the most significant results on the Collatz conjecture in decades."

Rigorous bounds.

In a computer-aided proof, Krasikov and Lagarias showed that the number of integers in the interval that eventually reach 1 is at least equal to for all sufficiently large.

Other formulations of the conjecture.

In reverse.

There is another approach to prove the conjecture, which considers the bottom-up method of growing the so-called "Collatz graph". The "Collatz graph" is a graph defined by the inverse relation  So, instead of proving that all positive integers eventually lead to 1, we can try to prove that 1 leads backwards to all positive integers. For any integer, if and only if. Equivalently, if and only if. Conjecturally, this inverse relation forms a tree except for the 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function defined in the Statement of the problem section of this article).  When the relation of the function is replaced by the common substitute "shortcut" relation, the Collatz graph is defined by the inverse relation,  For any integer, if and only if. Equivalently, if and only if. Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above).  Alternatively, replace the with where and is the highest power of 2 that divides (with no remainder). The resulting function maps from odd numbers to odd numbers. Now suppose that for some odd number, applying this operation times yields the number 1 (that is, ). Then in binary, the number can be written as the concatenation of strings where each is a finite and contiguous extract from the representation of. The representation of therefore holds the repetends of, where each repetend is optionally rotated and then replicated up to a finite number of bits. It is only in binary that this occurs. Conjecturally, every binary string that ends with a '1' can be reached by a representation of this form (where we may add or delete leading '0's to ).

As an abstract machine that computes in base two.

Repeated applications of the Collatz function can be represented as an abstract machine that handles strings of bits. The machine will perform the following three steps on any odd number until only one "1" remains:

Example.

The starting number 7 is written in base two as 111. The resulting Collatz sequence is:

As a parity sequence.

For this section, consider the Collatz function in the slightly modified form  This can be done because when is odd, is always even.  If is the parity of a number, that is and, then we can define the Collatz parity sequence (or parity vector) for a number as, where, and.  Which operation is performed, or, depends on the parity. The parity sequence is the same as the sequence of operations.  Using this form for, it can be shown that the parity sequences for two numbers and will agree in the first terms if and only if and are equivalent modulo. This implies that every number is uniquely identified by its parity sequence, and moreover that if there are multiple Hailstone cycles, then their corresponding parity cycles must be different.  Applying the function times to the number will give the result, where is the result of applying the function times to, and is how many increases were encountered during that sequence (e.g. for there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is ; for there is only 1 increase as 1 rises to 2 and falls to 1 so the result is ). When is then there will be rises and the result will be. The factor of 3 multiplying is independent of the value of ; it depends only on the behavior of. This allows one to predict that certain forms of numbers will always lead to a smaller number after a certain number of iterations, e.g. becomes after two applications of and becomes after 4 applications of. Whether those smaller numbers continue to 1, however, depends on the value of.

As a tag system.

For the Collatz function in the form  formula_9  Hailstone sequences can be computed by the extremely simple with production rules  In this system, the positive integer is represented by a string of copies of, and iteration of the tag operation halts on any word of length less than 2. (Adapted from De Mol.)  The Collatz conjecture equivalently states that this tag system, with an arbitrary finite string of as the initial word, eventually halts (see "" for a worked example).

Extensions to larger domains.

Iterating on all integers.

An extension to the Collatz conjecture is to include all integers, not just positive integers. Leaving aside the cycle 0 → 0 which cannot be entered from outside, there are a total of 4 known cycles, which all nonzero integers seem to eventually fall into under iteration of. These cycles are listed here, starting with the well-known cycle for positive :  Odd values are listed in large bold. Each cycle is listed with its member of least absolute value (which is always odd) first.  The generalized Collatz conjecture is the assertion that every integer, under iteration by, eventually falls into one of the four cycles above or the cycle 0 → 0. The 0 → 0 cycle is often regarded as "trivial" by the argument, as it is only included for the sake of completeness.

Iterating on rationals with odd denominators.

The Collatz map can be extended to (positive or negative) rational numbers which have odd denominators when written in lowest terms. The number is taken to be 'odd' or 'even' according to whether its numerator is odd or even. Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added. A closely related fact is that the Collatz map extends to the ring of 2-adic integers, which contains the ring of rationals with odd denominators as a subring.  When using the "shortcut" definition of the Collatz map, it is known that any periodic parity sequence is generated by exactly one rational. Conversely, it is conjectured that every rational with an odd denominator has an eventually cyclic parity sequence (Periodicity Conjecture ).  If a parity cycle has length and includes odd numbers exactly times at indices, then the unique rational which generates immediately and periodically this parity cycle is  For example, the parity cycle has length 7 and four odd terms at indices 0, 2, 3, and 6. It is repeatedly generated by the fraction as the latter leads to the rational cycle  Any cyclic permutation of is associated to one of the above fractions. For instance, the cycle is produced by the fraction  For a one-to-one correspondence, a parity cycle should be "irreducible", i.e., not partitionable into identical sub-cycles. As an illustration of this, the parity cycle and its sub-cycle are associated to the same fraction when reduced to lowest terms.  In this context, assuming the validity of the Collatz conjecture implies that and are the only parity cycles generated by positive whole numbers (1 and 2, respectively).  If the odd denominator of a rational is not a multiple of 3, then all the iterates have the same denominator and the sequence of numerators can be obtained by applying the "" generalization of the Collatz function

2-adic extension.

The function is well-defined on the ring of 2-adic integers, where it is continuous and measure-preserving with respect to the 2-adic measure. Moreover, its dynamics is known to be ergodic.  Define the "parity vector" function acting on as  The function is a 2-adic isometry. Consequently, every infinite parity sequence occurs for exactly one 2-adic integer, so that almost all trajectories are acyclic in formula_16.  An equivalent formulation of the Collatz conjecture is that

Iterating on real or complex numbers.

The Collatz map can be viewed as the restriction to the integers of the smooth real and complex map  If the standard Collatz map defined above is optimized by replacing the relation with the common substitute "shortcut" relation, it can be viewed as the restriction to the integers of the smooth real and complex map  The point of view of iteration on the real line was investigated by. He showed that the conjecture does not hold for real numbers since there are infinitely many fixed points, as well as orbits escaping monotonically to infinity. He also showed that there is, at least, another attracting cycle: 1.1925 → 2.1386.  On the complex plane, it was investigated by Most points of the plane diverge to infinity, as seen in blue on the illustration below. The boundary between diverging and non-diverging regions show a fractal pattern called the "Collatz fractal".

Optimizations.

Time–space tradeoff.

The section "As a parity sequence" above gives a way to speed up simulation of the sequence. To jump ahead steps on each iteration (using the function from that section), break up the current number into two parts, (the least significant bits, interpreted as an integer), and (the rest of the bits as an integer). The result of jumping ahead steps can be found as:  The (or better ) and arrays are precalculated for all possible -bit numbers, where is the result of applying the function times to, and is the number of odd numbers encountered on the way. For example, if, one can jump ahead 5 steps on each iteration by separating out the 5 least significant bits of a number and using:  This requires precomputation and storage to speed up the resulting calculation by a factor of, a space–time tradeoff.

Modular restrictions.

For the special purpose of searching for a counterexample to the Collatz conjecture, this precomputation leads to an even more important acceleration, used by Tomás Oliveira e Silva in his computational confirmations of the Collatz conjecture up to large values of. If, for some given and, the inequality  holds for all, then the first counterexample, if it exists, cannot be modulo. For instance, the first counterexample must be odd because, smaller than ; and it must be 3 mod 4 because, smaller than. For each starting value which is not a counterexample to the Collatz conjecture, there is a for which such an inequality holds, so checking the Collatz conjecture for one starting value is as good as checking an entire congruence class. As increases, the search only needs to check those residues that are not eliminated by lower values of. Only an exponentially small fraction of the residues survive. For example, the only surviving residues mod 32 are 7, 15, 27, and 31.

Syracuse function.

If is an odd integer, then is even, so with odd and. The Syracuse function is the function from the set of odd integers into itself, for which.  Some properties of the Syracuse function are:  The Collatz conjecture is equivalent to the statement that, for all in, there exists an integer such that.

Undecidable generalizations.

In 1972, John Horton Conway proved that a natural generalization of the Collatz problem is algorithmically undecidable.  Specifically, he considered functions of the form  and are rational numbers which are so chosen that is always an integer.  The standard Collatz function is given by,,,,. Conway proved that the problem:  is undecidable, by representing the halting problem in this way.  Closer to the Collatz problem is the following "universally quantified" problem:  Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer but might be easier to justify a negative one). Kurtz and Simon proved that the above problem is, in fact, undecidable and even higher in the arithmetical hierarchy, specifically -complete. This hardness result holds even if one restricts the class of functions by fixing the modulus to 6480.

In popular culture.

In the movie "Incendies", a graduate student in pure mathematics explains the Collatz conjecture to a group of undergraduates. She puts her studies on hold for a time to address some unresolved questions about her family's past. Late in the movie, the Collatz conjecture turns out to have foreshadowed a disturbing and difficult discovery that she makes about her family.

The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of, the sequence will always reach 1.

考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。


Definition.

According to the historian Rashid-al-Din Hamadani, Kublai Khan granted Hulagu (Hülegü) the title of Ilkhan after his defeat of Ariq Böke. The term "ilkhan" here means "khan of the tribe, khan of the 'ulus'" and this inferior "khanship" refers to the initial deference to Möngke Khan and his successor Great Khans of the Mongol empire. The title "Ilkhan", borne by the descendants of Hulagu and later other Borjigin princes in Persia, does not materialize in the sources until after 1260.

History.

Origin.

When Muhammad II of Khwarazm executed a contingent of merchants dispatched by the Mongols, Genghis Khan declared war on the Khwārazm-Shāh dynasty in 1219. The Mongols overran the empire, occupying the major cities and population centers between 1219 and 1221. Iran was ravaged by the Mongol detachment under Jebe and Subutai, who left the area in ruin. Transoxiana also came under Mongol control after the invasion.  Muhammad's son Jalal ad-Din Mingburnu returned to Iran in c. 1224 after fleeing to India. The rival Turkic states, which were all that remained of his father's empire, quickly declared their allegiance to Jalal. He repulsed the first Mongol attempt to take Central Persia. However, Jalal ad-Din was overwhelmed and crushed by Chormaqan's army sent by the Great Khan Ögedei in 1231. During the Mongol expedition, Azerbaijan and the southern Persian dynasties in Fars and Kerman voluntarily submitted to the Mongols and agreed to pay tribute. To the west, Hamadan and the rest of Persia was secured by Chormaqan. The Mongols invaded Armenia and Georgia in 1234 or 1236, completing the conquest of the Kingdom of Georgia in 1238. They began to attack the western parts of Greater Armenia, which was under the Seljuks, the following year. By 1237 the Mongol Empire had subjugated most of Persia (including modern-day Azerbaijan), Armenia, Georgia (excluding Abbasid Iraq and Ismaili strongholds), as well as all of Afghanistan and Kashmir. After the battle of Köse Dağ in 1243, the Mongols under Baiju occupied Anatolia, while the Seljuk Sultanate of Rûm and the Empire of Trebizond became vassals of the Mongols.  In 1236 Ögedei commanded Greater Khorasan to be restored and the city of Herat repopulated. The Mongol military governors mostly made camp in the Mughan plain in what is now Azerbaijan. Realizing the danger posed by the Mongols, the rulers of Mosul and Cilician Armenia submitted to the Great Khan. Chormaqan divided the Transcaucasia region into three districts based on the Mongol military hierarchy. In Georgia, the population was temporarily divided into eight tumens. In 1244, Güyük Khan stopped raising of revenue from districts in Persia as well and offered tax exemptions to others. In accordance with a complaint by the governor Arghun the Elder (Arghun agha), Möngke Khan prohibited "ortog"-merchants (Mongol-contracted Muslim traders) and nobles from abusing relay stations and civilians in 1251. He ordered a new census and decreed that each man in the Mongol-ruled Middle East must pay in proportion to his property. Persia was divided between four districts under Arghun. Möngke Khan granted the Kartids authority over Herat, Jam, Pushang (Fushanj), Ghor, Khaysar, Firuz-Kuh, Gharjistan, Farah, Sistan, Kabul, Tirah, and Afghanistan.

Hulagu Khan.

Hulagu Khan, third son of Tolui, grandson of Genghis Khan, and brother of both Möngke Khan and Kublai Khan, was the first khan of the Ilkhanate. Immediately after his brother Möngke's accession as Great Khan in 1251, Hulagu was appointed as administrator of North China, however in the following year, North China was assigned to Kublai and Hulagu tasked with conquering the Abbasid Caliphate. He was given a fifth of the entire Mongol army for the campaign and he took his sons Abaqa and Yoshmut along with him. Hulagu also took with him many Chinese scholars and astronomers, from whom the famous Persian astronomer Nasir al-Din al-Tusi learned about the mode of the Chinese calculating tables. An observatory was built on a hill of Maragheh. Taking over from Baiju in 1255, Hulagu established Mongol rule from Transoxiana to Syria. He destroyed the Nizari Ismaili state and the Abbasid Caliphate in 1256 and 1258 respectively. In 1258, Hulagu proclaimed himself Ilkhan (subordinate khan). After that he advanced as far as Gaza, briefly conquering Ayyubid Syria and Aleppo in 1260. Möngke's death forced Hulagu to return to Mongolia to attend the kuriltai for the next Great Khan. He left a small force of around 10,000 behind in Palestine that was defeated at the battle of Ain Jalut by the Mamluks of Egypt.  Due to the suspicious deaths of three Jochid princes in Hulagu's service, Berke of the Golden Horde declared war on Hulagu in 1262. According to Mamluk historians, Hulagu might have massacred Berke's troops and refused to share his war booty with Berke. Berke sought a joint attack with Baybars and forged an alliance with the Mamluks against Hulagu. The Golden Horde dispatched the young prince Nogai to invade the Ilkhanate but Hulagu forced him back in 1262. The Ilkhanid army then crossed the Terek River, capturing an empty Jochid encampment, only to be routed in a surprise attack by Nogai's forces. Many of them were drowned as the ice broke on the frozen Terek River.  In 1262, Hulagu gave Greater Khorasan and Mazandaran to Abaqa and northern Azerbaijan to Yoshmut. Hulagu himself spent his time living as a nomad in southern Azerbaijan and Armenia. During his early rule, the Ilkhanate experienced mass revolts by its subjects, with the exception of the Seljukids and Artuqids in Anatolia and Mardin. It was not until Shams al-Din Juvayni was appointed as vizier after 1262 that things started calming down and a more sustainable administration was implemented.  Hulagu fell ill in February 1265 after several days of banquets and hunting. He died on 8 February and his son Abaqa succeeded him in the summer.

Middle period (1265–1291).

Upon Abaqa's accession, he immediately faced an invasion by Berke of the Golden Horde, which ended with Berke's death in Tiflis. In 1270, Abaqa defeated an invasion by Ghiyas-ud-din Baraq of the Chagatai Khanate. Abaqa's brother Tekuder sacked Bukhara in retaliation. In 1277, the Mamluks invaded Anatolia and defeated the Mongols at the Battle of Elbistan. Stung by the defeat, Abaqa executed the local regent Mu'in-ad-Din Pervane and replaced him with the Mongol prince Qongqortai. In 1281, Abaqa sent Mongke Temur against the Mamluks, but he too was defeated at Homs.  Abaqa's death in 1282 triggered a succession struggle between his son Arghun, supported by the Qara'unas, and his brother Tekuder, supported by the Chinggisid aristocracy. Tekuder was elected khan by the Chinggisids. Tekuder was the first Muslim ruler of the Ilkhanate but he made no active attempt to proselytize or convert his realm. However he did try to replace Mongol political traditions with Islamic ones, resulting in a loss of support from the army. Arghun used his religion against him by appealing to non-Muslims for support. When Tekuder realized this, he executed several of Arghun's supporters, and captured Arghun. Tekuder's foster son, Buaq, freed Arghun and overthrew Tekuder. Arghun was confirmed as Ilkhan by Kublai Khan in February 1286.  During Arghun's reign, he actively sought to combat Muslim influence, and fought against both the Mamluks and the Muslim Mongol emir Nawruz in Khorasan. To fund his campaigns, Arghun allowed his viziers Buqa and Sa'd-ud-dawla to centralize expenditures, but this was highly unpopular and caused his former supporters to turn against him. Both viziers were killed and Arghun was murdered in 1291.

Religious shift (1291–1316).

The Ilkhanate started crumbling under the reign of Arghun's brother, Gaykhatu. The majority of Mongols converted to Islam while the Mongol court remained Buddhist. Gaykhatu had to buy the support of his followers and as a result, ruined the realm's finances. His vizir Sadr-ud-Din Zanjani tried to bolster the state finances by adopting paper money from the Yuan dynasty, which ended horribly. Gaykhatu also alienated the Mongol old guard with his alleged sexual relations with a boy. Gaykhatu was overthrown in 1295 and replaced with his cousin Baydu. Baydu reigned for less than a year before he was overthrown by Gaykhatu's son, Ghazan.  Hulagu's descendants ruled Persia for the next eighty years, tolerating multiple religions, including Shamanism, Buddhism, and Christianity, and ultimately adopting Islam as a state religion in 1295. However, despite this conversion, the Ilkhans remained opposed to the Mamluks, who had defeated both Mongol invaders and Crusaders. The Ilkhans launched several invasions of Syria, but were never able to gain and keep significant ground against the Mamluks, eventually being forced to give up their plans to conquer Syria, along with their stranglehold over their vassals the Sultanate of Rum and the Armenian kingdom in Cilicia. This was in large part due to civil war in the Mongol Empire and the hostility of the khanates to the north and east. The Chagatai Khanate in Moghulistan and the Golden Horde threatened the Ilkhanate in the Caucasus and Transoxiana, preventing expansion westward. Even under Hulagu's reign, the Ilkhanate was engaged in open warfare in the Caucasus with the Mongols in the Russian steppes. On the other hand, the China-based Yuan Dynasty was an ally of the Ikhanate and also held nominal suzerainty over the latter (the Emperor being also Great Khan) for many decades.  Ghazan converted to Islam under influence of Nawrūz and made Islam the official state religion. Christian and Jewish subjects lost their equal status and had to pay the "jizya" protection tax. Ghazan gave Buddhists the starker choice of conversion or expulsion and ordered their temples to be destroyed; though he later relaxed this severity. After Nawrūz was deposed and killed in 1297, Ghazan made religious intolerance punishable and attempted to restore relations with non-Muslims.  In terms of foreign relations, the Ilkhanate's conversion to Islam had little to no effect on its hostility towards other Muslim states, and conflict with the Mamluks for control of Syria continued. The Battle of Wadi al-Khazandar, the only major victory by the Mongols over the Mamluks, ended the latter's control over Syria for a few months. For the most part, Ghazan's policies continued under his brother Öljeitü despite suggestions that he might begin to favor the Shi'a brand of Islam after he came under the influence of Shi'a theologians Al-Hilli and Maitham Al Bahrani.  Öljeitü, who had been baptised in Christianity as an infant, had flirted with Buddhism, became a Hanafi Sunni, though he still retained some residual shamanism. In 1309-10, he became a Shi'ite Muslim. An Armenian scribe in 1304 noted the death of "benevolent and just" Ghazan, who was succeeded by Khar-Banda Öljeitü "who too, exhibits good will to everyone." A colophon from 1306 reports conversion of Mongols to Islam and "they coerce everyone into converting to their vain and false hope. They persecute, they molest, and torment," including "insulting the cross and the church". Some of the Buddhists who survived Ghazan's assaults made an unsuccessful attempt to bring Öljeitü back into Dharma, showing they were active in the realm for more than 50 years.  The conversion of Mongols was initially a fairly superficial affair. The process of establishment of Islam did not happen suddenly. Öljeitü's historian Qāshāni records that Qutlugh-Shah, after losing patience with a dispute between Hanafis and Shafi'is, expressed his view that Islam should be abandoned and Mongols should return to the ways of Genghis Khan. Qāshani also stated that Öljeitü had in fact reverted for a brief period. As Muslims, Mongols showed a marked preference for Sufism with masters like Safi-ad-din Ardabili often treated with respect and favour.

Disintegration (1316–1357).

Öljaitü's son, the last Ilkhan Abu Sa'id Bahadur Khan, was enthroned in 1316. He was faced with rebellion in 1318 by the Chagatayids and Qara'unas in Khorasan, and an invasion by the Golden Horde at the same time. An Anatolian emir, Irenchin, also rebelled. Irenchin was crushed by Chupan of the Taichiud in the Battle of Zanjan-Rud on 13 July 1319. Under the influence of Chupan, the Ilkhanate made peace with the Chagatais, who helped them crush the Chagatayid revolt, and the Mamluks. In 1327, Abu-Sai'd replaced Chupan with "Big" Hasan. Hasan was accused of attempting to assassinate the khan and exiled to Anatolia in 1332. The non-Mongol emirs Sharaf-ud-Din Mahmud-Shah and Ghiyas-ud-Din Muhammad were given unprecedented military authority, which irked the Mongol emirs. In the 1330s, outbreaks of the Black Death ravaged the Ilkhanate and both Abu-Sai'd and his sons were killed by 1335 by the plague. Ghiyas-ud-Din put a descendant of Ariq Böke, Arpa Ke'un, on the throne, triggering a succession of short-lived khans until "Little" Hasan took Azerbaijan in 1338. In 1357, Jani Beg of the Golden Horde conquered Chupanid-held Tabriz for a year, putting an end to the Ilkhanate remnant.

Franco-Mongol alliance.

The courts of Western Europe made many attempts to form an alliance with the Mongols, primarily with the Ilkhanate, in the 13th and 14th centuries, starting from around the time of the Seventh Crusade (West Europeans were collectively called Franks by Muslims and Asians in the era of the Crusades). United in their opposition to the Muslims (primarily the Mamluks), the Ilkhanate and the Europeans were nevertheless unable to satisfactorily combine their forces against their common enemy.

Government.

The Ilkhanate Mongols remained nomadic in their way of life until the end of the dynasty. Their nomadic routes covered central Iraq, northwest Iran, Azerbaijan, and Armenia. The Mongols administered Iraq, the Caucasus, and western and southern Iran directly with the exception of Georgia, the Artuqid sultan of Mardin, and Kufa and Luristan. The Qara'unas Mongols ruled Khorasan as an autonomous realm and did not pay taxes. Herat's local Kart dynasty also remained autonomous. Anatolia was the richest province of the Ilkhanate, supplying a quarter of its revenue while Iraq and Diyarbakir together supplied about 35 percent of its revenue.  In 1330, the annexation of Abkhazia resulted in the reunification of the Kingdom of Georgia. However, tribute received by the Il-Khans from Georgia sank by about three-quarters between 1336 and 1350 because of wars and famines.

Legacy.

The emergence of the Ilkhanate had an important historical impact in the Middle Eastern region. The establishment of the unified Mongol Empire had significantly eased trade and commerce across Asia. The communications between the Ilkhanate and the Yuan Dynasty headquartered in China encouraged this development. The dragon clothing of Imperial China was used by the Ilkhanids, the Chinese Huangdi (Emperor) title was used by the Ilkhanids due to heavy clout upon the Mongols of the Chinese system of politics. Seals with Chinese characters were created by the Ilkhanids themselves besides the seals they received from the Yuan dynasty which contain references to a Chinese government organization.  The Ilkhanate also helped to pave the way for the later Safavid dynastic state, and ultimately the modern country of Iran. Hulagu's conquests had also opened Iran to Chinese influence from the east. This, combined with patronage from his successors, would develop Iran's distinctive excellence in architecture. Under the Ilkhans, Iranian historians also moved from writing in Arabic to writing in their native Persian tongue.  The rudiments of double-entry accounting were practiced in the Ilkhanate; merdiban was then adopted by the Ottoman Empire. These developments were independent from the accounting practices used in Europe. This accounting system was adopted primarily as the result of socio-economic necessities created by the agricultural and fiscal reforms of Ghazan Khan in 1295-1304.

Ilkhan as a tribal title in 19th/20th century Iran.

The title Ilkhan resurfaced among the Qashqai nomads of Southern Iran in the 19th century. Jan Mohammad Khan started using it from 1818/19 and this was continued by all the following Qashqai leaders. The last Ilkhan was Naser Khan, who in 1954 was pushed into exile after his support of Mossadeq. When he returned during the Islamic Revolution in 1979, he could not regain his previous position and died in 1984 as the last Ilkhan of the Qashqai.

Ilkhans.

House of Hulagu (1256–1335; Ilkhanate Mongol kings).

After the Ilkhanate, the regional states established during the disintegration of the Ilkhanate raised their own candidates as claimants.

House of Hasar.

"Claimants from eastern Persia (Khurasan):"

The Ilkhanate, also spelled Il-khanate (, "Ilxānān"), known to the Mongols as Hülegü Ulus (, "Hu’legīn Uls") was a khanate established from the southwestern sector of the Mongol Empire, ruled by the Mongol House of Hulagu. Hulagu Khan, the son of Tolui and grandson of Genghis Khan, inherited the Middle Eastern part of the Mongol Empire after his brother Möngke Khan died in 1260. Its core territory lies in what is now part of the countries of Iran, Azerbaijan, and Turkey. At its greatest extent, the Ilkhanate also included parts of modern Iraq, Armenia, Georgia, Turkmenistan, Afghanistan, Pakistan, part of modern Dagestan, part of modern Tajikistan. Later Ilkhanate rulers, beginning with Ghazan in 1295, converted to Islam. In the 1330s, the Ilkhanate was ravaged by the Black Death. Its last khan Abu Sa'id died in 1335, after which the khanate disintegrated.

伊儿汗国(;拉丁转写:"Hülegü-yn Ulus";波斯语:;阿塞拜疆语:Hülakülər dövləti;英语:Ilkhanate),1220/1256–1357年,又译伊利汗国或伊尔汗国,是蒙古四大汗国之一,由成吉思汗之孙、拖雷的第六子旭烈兀及其子阿八哈与他的后人统治。