Since every equivalence relation over X corresponds to a partition of X, and vice versa, the number of possible equivalence relations on X equals the number of distinct partitions of X, which is the nth Bell number B < sub > n </ sub >:

Since each element of X belongs to a unique cell of any partition of X, and since each cell of the partition is identical to an equivalence class of X by ~, each element of X belongs to a unique equivalence class of X by ~.

Since those fluid waves move the cochlear partition that separates the scalae up and down, the waves have a corresponding symmetric part in perilymph of the scala tympani, which ends at the round window, bulging out when the oval window bulges in.

Since partition, the Gurkha regiments that were transferred to the Indian Army have established themselves as a permanent and vital part of the newly independent Indian Army.

Since the partition of Ireland, the term generally refers to support for a united Ireland.

Since reinstalling Windows ( or installing a new version ) often requires deleting the contents of the C: drive, it is advantageous to create multiple partitions so only one partition needs to be deleted during the installation.

Since this range looks like a well designed partition that splits river Godavari, this name was coined.

Since partition, the residents of Baltistan have remained essentially people of Baltistan ’ s soil.

Since the three colors partition the n vertices of the polygon, the color with the fewest vertices forms a valid guard set with at most guards.

Since the partition of 1947, more work ( kar Seva ) has been done on Darbar Sahib Tarn Taran.

Since the partition in 1947, both countries have been constantly locked in skirmishes and wars mainly in this Himalayan region with the highest mountains in the world.

Since all side curtain airbags are contiguous from the " A " pillar to the " C " pillar, there is a deployment zone intrusion conflict when there is a partition installed.

Since Windows Vista, the first partition usually starts after a gap of 2, 047 sectors at LBA 2, 048 as part of its new 1 MiB partition alignment policy, so no large-sector misalignment occurs by default, but serious compatibility problems with older operating systems and disk tools exist.

Since the partition, the theory has been subjected to debates and interpretations on several grounds.

Since partition began, a key aspiration of Irish nationalists has been to bring about a united Ireland, with the whole island forming one independent state.

Since the Bishop of London refused to ordain ministers in the British American colonies, this constituted an emergency, and as a result, on 2 September 1784, Rev.

Since the English Reformation, the Church of England has been more explicitly a state church and the choice is legally that of the British crown ; today it is made in the name of the Sovereign by the Prime Minister, from a shortlist of two selected by an ad hoc committee called the Crown Nominations Commission.

Since Henry VIII broke with Rome, the Archbishops of Canterbury have been selected by the English ( British since the Act of Union in 1707 ) monarch.

Since the Admiralty no longer exists as a department, these are now used as an " office bank " by the British government:

Since 2001, financial services in the British Virgin Islands have been regulated by the independent Financial Services Commission.

Since 1999, the German parliament has again assembled in Berlin in its original Reichstag building, which dates from the 1890s and underwent a significant renovation under the lead of British architect Sir Norman Foster.

Since the introduction of the comic book format in 1933 with the publication of Famous Funnies, the United States has produced the most titles, along with British comics and Japanese manga, in terms of quantity of titles.

Since first being aired, it has been one of the most financially lucrative programmes on British commercial television, underpinning the success of its broadcaster ITV and its franchise Granada Television.

Since its release the album has itself become part of British popular culture.

Since FINA refused to rescind recognition of the ASA as the British governing body for all aquatic sports including diving, this meant that the elite divers had to belong to ASA-affiliated clubs to be eligible for selection to international competition.

Since its premiere in 1985, EastEnders has had a large impact on British popular culture.

Since then Mullan and Edwards have travelled to Flanders and the site of the World War One Christmas Truce and the legendary football game between British and German soldiers.

Since the days of the Second World War, US and British intelligence have shared information.

Since 1714, the succession of the British monarchs of the houses of Hanover and Saxe-Coburg and Gotha ( Windsor ) has been due to their descent from James VI and I of the House of Stuart.

Since Greece, a maritime country, could not oppose the mighty British navy, and citing the need for a respite after two wars, King Constantine favored continued neutrality, while Venizelos actively sought Greek entry in the war on the Allied side.

Since the 1950s and 1960s in particular, the Irish have become assimilated into the British population.

Since antiquity in various parts of the world, and since the 17th century in England, it had been known that citrus fruit had an antiscorbutic effect, when John Woodall ( 1570 – 1643 ), an English military surgeon of the British East India Company recommended them but their use did not become widespread.

Since the Early Modern period, the title of knight is purely honorific, usually bestowed by a monarch, as in the British honours system, often for non-military service to the country.

Since 1611, the British Crown has awarded a hereditary title in the form of the Baronetcy.

Since Victoria's reign, the stone has generally been worn by the British Queen Consort, never by a male ruler.

* Christine Clark, The British Malting Industry Since 1830, Hambledon Continuum ( 1 July 1998 ), ISBN 1-85285-170-8

Since the privatisation of British Rail there is no longer a single approach to design on railways in Great Britain.

Since January 2006, the NATO International Security Assistance Force undertook combat duties from Operation Enduring Freedom in southern Afghanistan, the NATO force chiefly made up of British, Canadian and Dutch forces ( and some smaller contributions from Denmark, Romania and Estonia and air support from Norway as well as air and artillery support from the U. S .) ( see the article Coalition combat operations in Afghanistan in 2006 ).

" Jamie Reid ", in Communicate: Independent British Graphic Design Since the Sixties, ed.

Since the American, British and Soviet Occupation Zones converged there, people theoretically only had to walk a few paces across sector boundaries to avoid the respective Police officials.

Since the collapse of the Taliban government in 2001, new trade relations are emerging with the United States, Pakistan, Iran, Turkmenistan, the EU, Japan, Uzbekistan, India and other countries.

" Since these tablets predate the Sulbasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India.

Since the 1990s, Canadian born musician Nadaka who has spent most of his life in India, has been creating music that is an acoustic fusion of Indian classical music with western styles.

Since World War II the United Kingdom was forced to withdraw from the area, to be replaced by India, the USSR, and the United States.

Since the independence of India from British rule, the British fantasy of an " Aryan Invasion and subjugation of the dark skinned Dravidians in India " has become a staple polemic in South Asian geopolitics, including the propaganda of Indophobia in Pakistan.

Since becoming the viceroy of the Indies, he took Goa in India in 1510, and Malacca on the Malay peninsula in 1511.

Since then, and as a result of the Arab trade activities, the site has been strategically important as a crossroads for the Arab caravan routes passing between Europe and India through lands controlled by the Arabs.

* Since the establishment of its presidencies in 1689, the British East India Company has been under constant pressure from traders who are not members of the company and are not licensed by the Crown to trade.

Since the 14th century the Deccan ( Southern Peninsular region of India ) was divided into two entities: on the one side stood the Muslim Bahmani Sultanate and on the other stood the Hindu kings rallied around the Vijayanagara Empire.

Since the late 1940s with the dissolution of British India and creation of Pakistan, some rigid Pashtun nationalists proposed merging with Afghanistan or creating Pashtunistan as a future sovereign state for the local Pashtun inhabitanits of the area.

Since Bangladesh is almost entirely encircled by India via a land border which stretches, its relations with India are vital for economic reasons.

Since the classicists of the early 20th century, biblical archeologists often identify the place-name Tarshish in the Hebrew Bible with Tartessos, though others connect it to Tarsus in Anatolia or other places as far as India.

Since then, it underwent many changes, and the modern sitar evolved in the 18th century India.

Since, according to the learned researches of Sir William Jones, Odin and Buddha are probably the same person, it is curious to see the names of Bondvar, Wodansdag, and Votan designating in India, Scandinavia, and in Mexico the day of a brief period.

Since, moreover, Dharma was made the central subject of a literary tradition which was to become vast and extensive throughout India, while the conception of Ṛta remained largely confined to the Vedas and their commentaries, it naturally took possession of brāhmaṇical thinking even at the expense of older, exalted concepts and conceptions.

Since, at that time, Australia was preparing to attack the Ottoman Empire, those people were first speculated to be Turkish, but later identified as being from British colony of India ( modern day Pakistan ).

Since then he has walked the entire length of the river Ganges in India ( the 3000 km walk is recounted in A Walk Along the Ganges ) and travelled extensively in the Amazon and ( journeys that were described in Amazon and Savages: The Life and Killing of the Yanomami ).

Since the time of the Charyapada, Assamese has been influenced by the languages belonging to the Sino-Tibetan and Austroasiatic families in Northeast India, and share many common characteristics with them.

Since the 1960s, the mantra has been made well known outside of India by A. C. Bhaktivedanta Swami Prabhupada and his International Society for Krishna Consciousness ( commonly known as " the Hare Krishnas ").

Since 1950, the President of India has lived in this building.