The people of Cyprus are broadly divided into two main ethnic communities, Greek Cypriots and Turkish Cypriots, who share many cultural traits but maintain distinct identities based on ethnicity, religion and close ties with their respective motherlands. Before the dispute started in 1964 the peoples of Cyprus were dispersed over the entire island; the Turkish invasion of Cyprus in 1974 de facto partitioned the island into two political areas: 99.5% of Greek Cypriots now live in the Republic of Cyprus while 98.7% of Turkish Cypriots live in Northern Cyprus. Greek is predominantly spoken in the South, where the majority are Greek Cypriots, Turkish in the north, where the majority are Turkish Cypriots. English is used throughout the island, as a common language; the total population of Cyprus as of the end of 2006 is over 1 million, comprising 789,300 in the territory controlled by the government of the Republic of Cyprus and 294,406 in Northern Cyprus. The population of Northern Cyprus includes some 150,000–160,000 Turkish immigrants who are regarded as illegal settlers by the Republic of Cyprus government and are not included in the population statistics of the Republic of Cyprus Statistical Service.

838,897 in Republic of Cyprus controlled area 294.906 in Northern Cyprus. 1,133,803 total population of Cyprus Population by citizenship Republic of Cyprus government controlled area: 1992 census: 95.8% Cypriot, 4.2% Non-Cypriot 2001 census: 90.6% Cypriot, 9.4% Non-Cypriot 2011 census: 78.6% Cypriot, 21.4% Non-Cypriot Northern Cyprus: 2006 census: 66.7% NC, 29.3% Turkey, 4.0% other Historical data about main demographic indicators from 1901 to 1990, for the entire island: 1 The numbers of births and deaths 1901–1932 are estimates calculated from the birth and death rates. Historical data about main demographic indicators from 1990 to 2018, for the southern part of the island: Source: UN World Population Prospects Structure of the population: Turkish Cypriots were the majority of the population registered for taxation between 1777 and 1800. However, it is that the Muslim population never exceeded 35-40 per cent of the total population of Cyprus. Rather, many Orthodox Christians registered as Muslims in order to reduce taxation from their occupiers.

In the census from 1881 to 1960, all Muslims are counted as Turks, only Greek Orthodox are counted as Greeks. There were small populations of Turkish-speaking Greek Orthodox. In total, between 1955 and 1973, 16,519 Turks and 71,036 Greeks emigrated from the country. Of the emigrated Turkish Cypriots in this period, only 290 went to Turkey. In the 2011 census, 208 people stated their ethnic origin as being Latin. Large-scale demographic changes have been caused since 1964 by the movements of peoples across the island and the influx of settlers from Turkey to Northern Cyprus. According to the 2011 Census there are 170,383 non-citizens living in Cyprus, of whom 106,270 are EU citizens and 64,113 are from third countries; the largest EU groups by nationality are Greeks, British and Bulgarians. The largest non-EU groups are Filipinos, Sri Lankans and Vietnamese. There are an estimated 20–25,000 undocumented migrants from third countries living in the Republic, though migrant rights groups dispute these figures.

The demographic changes in society have led to some racist incidents, the formation of the charity KISA in response. The demographic character of Northern Cyprus changed after the Turkish invasion in 1974 and during the last 10–15 years. TRNC census carried out in April 2006 showed that out of a total population of 256,644 in Northern Cyprus, 132,635, or 52%, were Turkish Cypriots in the sense that they were born in Cyprus of at least one Cyprus-born parent. In addition, 43,062 so called TRNC citizens had at least one non-Cypriot Turkish-born parent, 2,334 so called TRNC citizens had parents born in other countries, 70,525 residents had Turkish citizenship, 8,088 were citizens of other countries. Based on these census data, it is estimated that 113,687 Northern Cyprus residents, or 44% of the population, are not Turkish Cypriots properly speaking, but are in fact "Turkish immigrants" or "Turkish settlers" from Anatolia. Alternative sources suggest that there are 146,122 Turkish settlers from Anatolia in Northern Cyprus and that the Turkish Cypriots in Northern Cyprus are today outnumbered by the Turkish settlers, contrary to the picture presented by the 2006 so called TRNC census.

One-third of the Turkish settlers in Northern Cyprus have been granted TRNC citizenship by the authorities of Northern Cyprus and have thus been naturalized. The Republic of Cyprus regards settlement in Northern Cyprus if accompanied by naturalization, as a violation of the Geneva Conventions Protocol of 1977, since the Turkish occupation has been declared illegal by the UN, it therefore considers these Turkish immigrants to be "illegal settlers" and does not include them in the population estimates for the entire island published by the Republic of Cyprus Statistical Service. Greek 98.8%, Other 1% Unspecified 0.2% Greek and Turkish are the official languages according to Article 3 of the Constitution of C

The Mencius is a collection of anecdotes and conversations of the Confucian thinker and philosopher Mencius on topics in moral and political philosophy between Mencius and the rulers of the various Warring States. Mencius was a disciple of one of the students of Zisi, a grandson of Confucius, the Mencius records his travels and audiences with the various rulers of the Warring States period, his students, his other contemporaries. A number of linguistic and textual clues suggest that the text was not written by Mencius himself but by his disciples during the late 4th century BC; the Mencius comprises seven chapters, each divided into two halves, with alternating short sayings and extensive dialogues on specific philosophical arguments. Its fundamental positions, such as Mencius' famous argument in chapter 6A that human nature is inherently good, are presented as conversations between Mencius and contemporaneous thinkers, while arguments on specific issues appear in records of his advice and counsel to various rulers.

His argument that inborn potential tends towards virtue contrasts with the position of contemporary figure Yang Zhu, who argued that that human nature is motivated by self-interest. The Mencius was one of the most important texts of early Confucianism, represents a notable advance over the Analects of Confucius in terms of sophistication of argument. Notwithstanding its early importance to Confucianism, the Mencius was not canonized as one of the Chinese Classics until over 1,000 years in Song-dynasty Neo-Confucianism; the famous saying "live in peril, die in comfort" comes from the following passage of Mencius: Mencius said,'Shun rose from among the channelled fields. Fu Yue was called to office from the midst of his building frames. Thus, when Heaven is about to confer a great office on any man, it first exercises his mind with suffering, his sinews and bones with toil, it exposes his body to hunger, subjects him to extreme poverty. It confounds his undertakings. By all these methods it stimulates his mind, hardens his nature, supplies his incompetencies.

Men for the most part err, are afterwards able to reform. They are distressed in mind and perplexed in their thoughts, they arise to vigorous reformation; when things have been evidenced in men's looks, set forth in their words they understand them. If a prince have not about his court families attached to the laws and worthy counsellors, if abroad there are not hostile States or other external calamities, his kingdom will come to ruin. From these things we see how life springs from sorrow and calamity, death from ease and pleasure.' Legge, James. The Works of Mencius; the Chinese Classics, vol. 2. Reprinted, Oxford: Clarendon Press. Couvreur, Séraphin. Oeuvres de Meng Tzeu, in Les Quatres Livres. Ho Kien Fou: Mission Catholique. Wilhelm, Richard. Mong Dsi. Jena: Eugen Diderichs. Lyall, Leonard A.. Mencius. London: Longmans, Green and Co. Ware, James R.. The Sayings of Mencius. New York: Mentor Books. Dobson, W. A. C. H.. Mencius, A New Translation Annotated for the General Reader. London: Oxford University Press.

Lau, D. C.. Mencius. London: Penguin Books. ———. Mencius. Hong Kong: Chinese University Press. Van Norden, Bryan. Mencius: With Selections from Traditional Commentaries. Indianapolis: Hackett Publishing Company. Bloom, Irene. Mencius. New York: Columbia University Press. Works related to Mencius at Wikisource The Works of Mencius: Legge's English translation Mengzi Chinese text with Legge's English translation Mencius, translated by A. Charles Muller Mencius 《孟子》 Chinese and English text with matching English vocabulary at Chinese Notes

In mathematics, the Rankin–Selberg method, introduced by and Selberg known as the theory of integral representations of L-functions, is a technique for directly constructing and analytically continuing several important examples of automorphic L-functions. Some authors reserve the term for a special type of integral representation, namely those that involve an Eisenstein series, it has been one of the most powerful techniques for studying the Langlands program. The theory in some sense dates back to Bernhard Riemann, who constructed his zeta function as the Mellin transform of Jacobi's theta function. Riemann used asymptotics of the theta function to obtain the analytic continuation, the automorphy of the theta function to prove the functional equation. Erich Hecke, Hans Maass, applied the same Mellin transform method to modular forms on the upper half-plane, after which Riemann's example can be seen as a special case. Robert Alexander Rankin and Atle Selberg independently constructed their convolution L-functions, now thought of as the Langlands L-function associated to the tensor product of standard representation of GL with itself.

Like Riemann, they used an integral of modular forms, but one of a different type: they integrated the product of two weight k modular forms f, g with a real analytic Eisenstein series E over a fundamental domain D of the modular group SL2 acting on the upper half plane ∫ D f g ¯ E y k − 2 d x d y. The integral converges if one of the two forms is cuspidal; the analytic continuation and functional equation boil down to those of the Eisenstein series. The integral was identified with the convolution L-function by a technique called "unfolding", in which the definition of the Eisenstein series and the range of integration are converted into a simpler expression that more exhibits the L-function as a Dirichlet series; the simultaneous combination of an unfolding together with global control over the analytic properties, is special and what makes the technique successful. Hervé Jacquet and Robert Langlands gave adelic integral representations for the standard, tensor product L-functions, earlier obtained by Riemann, Maass and Selberg.

They gave a complete theory, in that they elucidated formulas for all local factors, stated the functional equation in a precise form, gave sharp analytic continuations. Nowadays one has integral representations for a large constellation of automorphic L-functions, however with two frustrating caveats; the first is that it is not at all clear which L-functions have integral representations, or how they may be found. The second is that in general it is difficult or even impossible to compute the local integrals after the unfolding stage; this means that the integrals may have the desired analytic properties, only that they may not represent an L-function. Thus, having an integral representation for an L-function by no means indicates its analytic properties are resolved: there may be serious analytic issues remaining. At minimum, though, it ensures the L-function has an algebraic construction through formal manipulations of an integral of automorphic forms, that at all but a finite number of places it has the conjectured Euler product of a particular L-function.

In many situations the Langlands–Shahidi method gives complementary information. Standard L-function on GL; the theory was resolved in the original manuscript. Standard L-function on classical groups; this construction was known as the doubling method and works for non-generic representations as well. Tensor product L-function on GL × GL, due to Jacquet, Piatetski-Shapiro, Shalika; the theory was resolved by Moeglin–Waldspurger, was reverse-engineered to establish the "converse theorem". Symmetric square on GL due to Shimura, Gelbart–Jacquet, Piatetski-Shapiro and Patterson, Bump–Ginzburg. Exterior square on GL, due to Jacquet -- Bump -- Ginzburg. Triple Product on GL × GL × GL. Symmetric cube on GL. Symmetric fourth power on GL. Standard L-function of E6 and E7. Standard L-function of G2. Bump, Daniel, "The Rankin-Selberg method: a survey", Number theory, trace formulas and discrete groups, Boston, MA: Academic Press, pp. 49–109, MR 0993311 Bump, Daniel, "The Rankin-Selberg method: an introduction and survey", in Cogdell, James W..

Math. Res. Inst. Publ. 11, Berlin: de Gruyter, pp. 41–73, ISBN 978-3-11-017939-2, MR 2192819 Rankin, Robert A. "Contributions to the theory of Ramanujan's function τ and similar arithmetical functions. I; the zeros of the function Σn=1∞τ/ns on the line R s=13/2. II. T