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Two closely related series in number theory
number theory, the ruler function of an integer n {\displaystyle n} can be either of two closely related functions. One of these functions counts the number
Ruler_function
Function that is discontinuous at rationals and continuous at irrationals
names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function (not to be confused
Thomae's_function
Mathematical fractal pattern
each letter with their respective numbers yields the ruler function. Sierpinski triangle: ABACABA Ruler, excluding 1 and 2: ABACABADABACABA excluding 2: EABACABADABACABA
ABACABA_pattern
Arithmetical function
the Kempner function. Therefore, computing the Kempner function can in general be no easier than factoring composite numbers. Ruler function, a simpler
Kempner_function
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Head of the Emirate of Dubai
The ruler of Dubai (Arabic: حاكم دبي) is the position of the hereditary monarch and head of government of the Emirate of Dubai. The Ruler is also considered
Ruler_of_Dubai
Mathematical puzzle game
1, ... (sequence A001511 in the OEIS), a sequence also known as the ruler function, or one more than the power of 2 within the move number. In the Wolfram
Tower_of_Hanoi
Head of state of Malaysia
Special Court, he is required to stop exercising the functions of a ruler. In the event of a ruler being sentenced to imprisonment for more than one day
King_of_Malaysia
Set of marks along a ruler such that no two pairs of marks are the same distance apart
In mathematics, a Golomb ruler is a set of marks at integer positions along a ruler such that no two pairs of marks are the same distance apart. The number
Golomb_ruler
Leader of the anti-Bolshevik White Movement during the Russian Civil War
existence, and the only one to officially adopt the titles and functions of the Supreme Ruler, was Admiral Alexander Kolchak, who was elected to the position
Supreme_Ruler_of_Russia
Society of Japan from 1603 to 1868
the official ruler of Japan at the very top of the Tokugawa class hierarchy. However, the Emperor was only a de jure ruler, functioning as a figurehead
Edo_society
Council of Malaysian Rulers
Conference of Rulers (also known as Council of Rulers or Durbar, Malay: Majlis Raja-Raja; Jawi: مجليس راج٢) is a council comprising the nine rulers of the Malay
Conference_of_Rulers
Swiss software company
compatibility; scene merging in the Editor; AutoCAD integration; 2D Map and Ruler functions in the Viewer and Editor; a WebGL Viewer for web use; and the option
Revizto
Castrated male human
where physical access to the ruler could wield great influence. Seemingly lowly domestic functions—such as making the ruler's bed, bathing him, cutting his
Eunuch
Number of partitions of an integer
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because
Partition function (number theory)
Partition_function_(number_theory)
Word meaning "ruler" in the Yoruba language
Nigeria, and Togo, are those with obas who generally wear beaded crowns; the rulers of many of the 'second generation' settlements are also often obas. Those
Oba_(ruler)
Ruler of a Mesoamerican āltepētl (city-state)
Tlacopan. Each āltepētl had its own tlahtoāni who would concurrently function as its ruler, high priest and commander-in-chief. The tlahtoāni wielded ultimate
Tlatoani
and trees by adjusting the altitude of a Polygon in 3D, or use the Ruler function to measure the height of an object in a 3D path in Google Earth Pro
Tree_height_measurement
Abstract ruler in which some of the distance marks may be missing
A sparse ruler is a ruler in which some of the distance marks may be missing. More abstractly, a sparse ruler of length L {\displaystyle L} with m {\displaystyle
Sparse_ruler
Rulers of the Duchy- and Kingdom of Bohemia
1126, when his father died, he was too young to assume power. The rulers appointed by Sobeslaus I in the period 1126–40 could be functioning as regents.
List_of_Bohemian_monarchs
Rulers of loose chiefdoms in pre-Spanish Colombia
Muisca rulers were so-called "aggrandizers", that is charismatic leaders at the head of various factions, who forged alliances and relations of subordination
Muisca_rulers
Meeting of noblemen and princes in pre-20th-century India
of a king or ruler or a formal meeting where the king held all discussions regarding the state. It was used in South Asia for a ruler's court or feudal
Durbar_(court)
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Theories about a de facto leadership in Iran
Minister Benjamin Netanyahu and the IDF said that Larijani was the real ruler of Iran and that he was part of a gang which ruled Iran. Reportedly the
2025–2026 Iranian de facto leadership speculations
2025–2026_Iranian_de_facto_leadership_speculations
reduced to a nominal ruler. Their power rapidly dwindled during the 19th century and later Peshwas also were reduced to nominal ruler under various Maratha
List_of_Maratha_rulers
Visual artifact that depicts or records perception
It may represent an abstract concept, such as the political power of a ruler or ruling class, a practical or moral lesson, an object for spiritual or
Image
Division of Herod the Great's kingdom
Antipas ruled Galilee and Perea until 39 CE. The last notable Herodian ruler with some level of independence was King Herod Agrippa I. He was given the
Herodian_tetrarchy
Countries in Asia which are monarchies
and Ruler of Abu Dhabi Sheikh Mohammed bin Rashid, Vice President and Prime Minister of the UAE and Ruler of Dubai Sheikh Sultan bin Muhammad, Ruler of
Monarchies_in_Asia
Cylindrical conformal map projection
non-secant projection). Therefore, interpreting ruler measurements on the equator is: True distance = ruler distance / RF (equator) For the above model
Mercator_projection
Concept in Chinese philosophy favouring inaction
functions of government". Xun Kuang's Xunzi, a Confucian adaptation to Qin Legalism, defines the ruler in much the same sense, saying that the ruler "need
Wu_wei
Pro Dutch militia in Indonesia
The Legion of the Just Ruler (Dutch: Legioen van de Rechtvaardige Vorst, Indonesian: Angkatan Perang Ratu Adil; APRA) or the Legion of Ratu Adil was a
Legion_of_the_Just_Ruler
This is a list of rulers of Bengal. For much of its history, Bengal was split up into several independent kingdoms, completely unifying only several times
List_of_rulers_of_Bengal
Indian regnal title
Maharaja (also spelled Maharajah or Maharaj; lit. 'great ruler'; feminine: Maharani or Maharajin) is a royal title in the Indian subcontinent of Sanskrit
Maharaja
the ruler Boris I (852–889) was using the title knyaz (prince). For much of its later history under the first and second empires, Bulgaria functioned as
List_of_Bulgarian_monarchs
Central deity in Aztec religion
ruler of the mythico-historic city of Tollan. Historians debate to what degree, or whether at all, these narratives about this legendary Toltec ruler
Quetzalcōātl
Archaeological site in Sindh, Pakistan
13 mm (0.005 in). A ruler found at Lothal (2400 BCE) is calibrated to about 1.6 mm (1⁄16 in). The decimal subdivision on the ruler is noteworthy, as it
Mohenjo-daro
Pharaoh's duties in the Ancient Egypt
Thutmesis to his newly promoted vizier. The ruler is fully aware of the unpleasantness of the vizier's function. The official must always satisfy his master
Functions_of_the_Pharaoh
4th-century BCE Syncretic philosophy text
and his disciple Zixia, "Kong Zi said: 'Zixia, do you know how rulers function as rulers?' Zixia replied: '(If) fish lose the water (they are in), then
Shizi_(book)
with the Odd Job the functions of scribing, squaring, level/plumb, and the sliding and locking ruler (originally a 12 inch wooden ruler with a built-in trammel
Stanley_Odd_Jobs
Nubian king
Meroe, are the only known records of the ruler. Also significant is the gold cylinder discovered with the ruler in this pyramid, not unlike those found
Amaninatakilebte
Fluctuations in the density of the normal matter of the universe
systematics. The BAO signal is a standard ruler such that the length of the sound horizon can be measured as a function of cosmic time. This measures two cosmological
Baryon_acoustic_oscillations
Island country in Southeast Asia
Historical sources also indicate that around the end of the 14th century, its ruler Parameswara was attacked by either the Majapahit or the Siamese, forcing
Singapore
Egyptian pharaoh of the late 18th Dynasty (14th century BCE)
It is speculated that he was the power behind the throne during child ruler Tutankhamun's reign, although there is no evidence for this aside from Tutankhamun's
Ay_(pharaoh)
King of Norway from 1046 to 1066
co-rule ended abruptly the next year as Magnus died: Harald became the sole ruler of Norway. Domestically, Harald crushed opposition, and outlined the unification
Harald_Hardrada
King of England from 1509 to 1547
accomplished king. He has been described as "one of the most charismatic rulers to sit on the English throne" and his reign described as the "most important"
Henry_VIII
Queen of England, Scotland, and Ireland from 1689 to 1694
powerful, firm, and effective ruler. Mary's early death from smallpox in 1694 at the age of 32 left William as sole ruler until his death in 1702, when
Mary_II
List of characters appearing in the Marvel Cinematic Universe
spiritual leader of the Eternals, who possesses healing abilities and functions as the "bridge" between the Eternals and the Celestial Arishem. Based
Characters of the Marvel Cinematic Universe: A–L
Characters_of_the_Marvel_Cinematic_Universe:_A–L
Country in West Asia
the control of a local Arab ruler known as the Sharif of Mecca, but at most times the Sharif owed allegiance to the ruler of one of the major Islamic
Saudi_Arabia
Country in Eurasia from 1922 to 1991
struggle saw Joseph Stalin emerge as the country's undisputed personalist ruler. He initiated rapid industrialization and forced collectivization that led
Soviet_Union
Character from Arabian Nights
suspense, and thematic selection, she gradually transforms Shahryar from a ruler driven by vengeance and misogyny into a just and stable king. Her role establishes
Scheherazade
Country in Northwestern Europe and the Caribbean
Lothair I of Middle Francia acknowledged the Viking Rorik of Dorestad as ruler of most of Frisia. When the kingdom of Middle Francia was partitioned in
Netherlands
of state Portale Storia (in Italian)—a list of current rulers by country Rulers—a list of rulers throughout time and places United Nations Protocol and
List of current heads of state and government
List_of_current_heads_of_state_and_government
Turkish Empire (c. 1299–1922)
in northern Hungary. After further advances by the Turks, the Habsburg ruler Ferdinand officially recognised Ottoman ascendancy in Hungary in 1547. Suleiman
Ottoman_Empire
Northwest Semitic supreme deity
1350 BCE in one of the Amarna Letters EA333, found in Tell-el-Hesi from the ruler of Lachish to 'The Great One' A Phoenician inscribed amulet of the 7th century BCE
El_(deity)
Former princely state of British India and Pakistan
seven rulers of the Rais period may be a recent invention, as there is no mention of them in any known source or oral tradition. The last three rulers are
Kingdom_of_Chitral
Aspect of Philippine history
The term Paramount Ruler, or sometimes Paramount Datu, is a term used by historians[who?] to describe the highest ranking political authorities in the
Paramount rulers in early Philippine history
Paramount_rulers_in_early_Philippine_history
Pyramid structure in Mexico
of another pyramid layer over the existing one. The passing of several rulers, and rapid changes in ideologies, led to the Pyramid of the Moon's exponential
Pyramid_of_the_Moon
Country in Europe
Kingdom of Germany and the Holy Roman Empire emerged from it. The Ottonian rulers (919–1024) consolidated several major duchies. In 996, Gregory V became
Germany
Maharaja of Jammu and Kashmir from 1925 to 1952
final days in Bombay, he died on 26 April 1961. Singh was a controversial ruler. He faced an agitation in Kashmir in 1931 and successful rebellions in Poonch
Hari_Singh
Internal organ in the male reproductive system
(an orchidometer) of known sizes. Another method is to use calipers, a ruler, or an ultrasound image to obtain the three measurements of the x, y, and
Testicle
Country in Central Europe
process of establishing statehood coincided with the conversion of a pagan ruler of the Polans to Christianity in 966 under the auspices of the Roman Catholic
Poland
Subdivision of the United Arab Emirates
States. Each emirate maintains its own sovereignty over its territory and functions in parallel with the federal government of the United Arab Emirates as
Emirates of the United Arab Emirates
Emirates_of_the_United_Arab_Emirates
Kingdoms established by barbarian tribes in the former Western Roman Empire
barbarian rulers slowly lost the habit of waiting for the Western Roman Empire to again function properly. Left to their own devices, barbarian rulers instead
Barbarian_kingdoms
Hellenistic state in West Asia (312–63 BC)
kingdom (βασιλεία, basileía). Similarly, Seleucid rulers were described as kings in Babylonia. The rulers did not describe themselves as being of any particular
Seleucid_Empire
American research psychologist
The acronym RULER refers to the five key emotion skills of Recognizing, Understanding, Labeling, Expressing, and Regulating emotions. RULER intends to
Marc_Brackett
Highest constitutional authority in the UAE
general. Any other functions stipulated in this Constitution or federal laws. The Federal Supreme Council consists of the rulers of the seven emirates:
Federal_Supreme_Council
Country in North Africa
society did so after the conquest in 698 and others were welcomed by Norman rulers to Sicily or Italy in the 11th and 12th centuries – the logical destination
Tunisia
Mechanical analog computer
position on the ruler as each function's input. Calculations that can be reduced to simple addition or subtraction using those precomputed functions can be solved
Slide_rule
Country in Southeastern Europe and West Asia
languages", forming the Anatolian sub-group. Hattian rulers were gradually replaced by Hittite rulers. The Hittite kingdom was a large kingdom in Central
Turkey
27 BC–476/1453 AD state and civilization
vote of the Senate. The Roman imperial cult, influenced by Hellenistic ruler cult, became one of the major ways Rome advertised its presence in the provinces
Roman_Empire
Head of government of Pakistan
minister nominates the members of the Cabinet who supervise the important functions and ministries of the Government of Pakistan and communicates to the president
Prime_Minister_of_Pakistan
Sex toy
Kammerer-Doak, Dorothy; Rogers, Rebecca G. (June 2008). "Female Sexual Function and Dysfunction". Obstetrics and Gynecology Clinics of North America. 35
G-spot_vibrator
1438–1533 empire in South America
individuals, groups, and Inca rulers. "Taxes" consisted of a labour obligation of a person to the Empire. The Inca rulers (who theoretically owned all
Inca_Empire
Title of the ruler of Kievan Rus' (10th–13th centuries)
of Rurik, suggesting the author was "more interested in the first Rus' ruler to reside in Kiev than with any founder of a dynasty". Kiev was captured
Grand_Prince_of_Kiev
Official in the Kingdom of Mosquitia
coast of Central America, included several high-ranking hereditary regional rulers appointed or recognized by the Miskito king: Governor, General, and Admiral
Miskito_regional_rulers
Country in northern Europe
Götaland were united under a single ruler. Svealand was described by Tacitus in 98 AD as being under a single ruler, though it is unknown how long this
Sweden
Word processor
the general public. It was also notable for its very fast cut-and-paste function and unlimited number of undo operations, which are due to its usage of
Microsoft_Word
Country in North America
Guatimotzin, a romanticized account of the defense of Mexico by its last Aztec ruler, Cuauhtémoc. The most well-known Mexican composer of the twentieth century
Mexico
Japanese light novel series
The chief assistant of the Sun Castle's ruler and Gou's creator. She was imprisoned by the castle's original ruler and is tasked with gifting the person
Farming_Life_in_Another_World
Roman emperor from 198 to 217
Septimius Severus and Empress Julia Domna. Severus proclaimed Caracalla co-ruler in 198, doing the same with his other son Geta in 209. The two brothers
Caracalla
Indian vassal states under the British Raj
all powers would be transferred to the people and he would function as a constitutional Ruler. Although this process successfully integrated the vast majority
Princely_state
30–375 CE empire in Central and South Asia
the Kushan Empire." The earliest documented ruler, and the first one to proclaim himself as a Kushan ruler, was Heraios. He calls himself a "tyrant" in
Kushan_Empire
Princess of Kiev, Orthodox saint (c. 890–925)
Christianity and made it the state religion, she was the first Rurikid ruler to be baptized. Olga is venerated as a saint in the Eastern Orthodox Church
Olga_of_Kiev
Skyscraper in Dubai, United Arab Emirates
organised federal financial support. For his support, Mohammad bin Rashid, Ruler of Dubai, changed the name from "Burj Dubai" to "Burj Khalifa" during inauguration
Burj_Khalifa
Topics referred to by the same term
operator (M operator), a function-building operator for General recursive function Möbius function, a multiplicative function in number theory and combinatorics
MU
Identification of emperors with divine authority
and on forms of the Hellenistic ruler cult developed in the eastern provinces of the Empire. The nature and function of imperial cult remain contentious
Roman_imperial_cult
Intelligence of machines
tendency to classify images with a ruler as "cancerous", because pictures of malignancies typically include a ruler to show the scale. Another machine
Artificial_intelligence
Eighteenth Dynasty Egyptian pharaoh
ancient Egyptian pharaoh reigning c. 1353–1336 or 1351–1334 BC, the tenth ruler of the Eighteenth Dynasty. Originally named Amenhotep IV (Ancient Egyptian:
Akhenaten
Historical semi-nomadic Turkic ethnic group
the powerful Kievan Rus' in the north. By 969, Sviatoslav I of Kiev, the ruler of Kievan Rus', along with his allies, conquered the Khazar capital of Atil
Khazars
Catholic Church and Bishop of Rome; he is an elected rather than hereditary ruler. The Pope need not be a citizen of the territory prior to his election by
List_of_current_monarchies
Country in Southeast Europe
much of present-day Albania. Together with the Dardanian ruler Cleitus, Glaucias, the ruler of the Taulantian kingdom, fought against Alexander the Great
Albania
Senior military title in various ancient Greek city states
('war') and archon ('ruler, leader') and translates as 'warleader' or 'warlord'. The name indicates that the polemarch's original function was to command the
Polemarch
Canaanite deity or form of human sacrifice
"Moloch", the Septuagint translates the instances of Moloch in Leviticus as "ruler" (ἄρχων), and as "king" (βασιλεύς) at 1 Kings 11:7. The Greek version of
Moloch
Spiritual leader of Tibet since 1940
age of 15, the 14th Dalai Lama assumed full temporal (political) power as ruler of Tibet. The Dalai Lama's formal rule as head of the government in Tibet
14th_Dalai_Lama
thinking machines as a human trustee, his primary function being to deliver updates of the thinking machine ruler, the evermind Omnius, to machine-controlled
List_of_Dune_characters
Indian surname
from Karnataka Kempe Gowda I (1510–1569), Founder of Bengaluru & feudatory ruler of the Vijayanagara Empire. Venkate Gopala Gowda (born 1951), Indian Supreme
Gowda_(surname)
Abrahamic monotheistic religion
Ottoman Empire and its claims were strengthened in 1517 as Selim I became the ruler of Mecca and Medina. The Shia Safavid dynasty rose to power in 1501 and
Islam
Emperor of Russia from 1894 to 1917
view among historians is that Nicholas was a well-intentioned yet poor ruler who proved incapable of handling the challenges facing his nation. He and
Nicholas_II
Country in East Asia
says the four goals of the Chinese revolution were "to expel the Manchu rulers, to revive Chunghwa, to establish a Republic, and to distribute land equally
Taiwan
Founder of Buddhism
during the Mahajanapada period, specifically during the reign of Bimbisara, ruler of Magadha, and died during the reign of Bimbisara's successor Ajatashatru
The_Buddha
RULER FUNCTION
RULER FUNCTION
Boy/Male
Australian, French, German, Italian, Teutonic
Rules the Estate; Estate Ruler; Ruler of an Estate
Boy/Male
Australian, Czechoslovakian, French, German, Polish, Russian, Slavic
Rule with Glory; Has Glory; Splendid Rule; To Rule with Glory; The Glorious Ruler; Glorious Ruler
Boy/Male
Australian, Dutch, Scandinavian
Rules the Home; Home Ruler
Boy/Male
French, German, Latin
Famous Wolf
Boy/Male
American, Anglo, British, English, German, Norse
Ruler of All; Rule with Mercy; Ruler; Noble Leader
Boy/Male
American, Australian, Chinese, German, Jamaican, Portuguese, Spanish
Rules with Counsel; Form of Ronald; Well Advised Ruler; Ruler Advisor; Wise Ruler
Boy/Male
Hindu
Boy/Male
Scottish
World ruler; rules the world.
Boy/Male
Latin French
Ruler.
Boy/Male
Anglo, Australian, British, English, French, German, Teutonic
Ruler of All; Highborn Ruler; Rules All
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, English, German, Indian, Norse, Teutonic
Ruler of All; Sacred Ruler; Ruler; Rule with Mercy; Noble Leader; Ever Ruler
Girl/Female
Australian, British, English, Slavic
Gypsy
Girl/Female
Christian, English, German, Indian
Ruler of All; Rules All
Surname or Lastname
English
English : from the medieval personal name Roul (see Rollo, Rolf).Scottish : habitational name from a place in Roxburghshire, so named from the stream on which it stands. This name is of uncertain origin, possibly from Welsh rhull ‘hasty’, ‘rash’.Probably an altered spelling of German Ruhl.
Girl/Female
French, German, Norse, Scandinavian, Swedish, Teutonic
Renowned Ruler; Spirited Warrior; Famous Ruler; Power; Rule
Boy/Male
German, Teutonic
Highborn Ruler; Noble Rule
Girl/Female
American, Australian, Irish
One who Rules; Ruler
Boy/Male
German, Teutonic
Estate Ruler; Rules an Estate
Boy/Male
French, German, Spanish
Rules All; Highborn Ruler; Ruler of All; Powerful
Boy/Male
American, Anglo, British, English, German, Norse
Ruler of All; Rule with Mercy; Ruler
RULER FUNCTION
RULER FUNCTION
Girl/Female
Egyptian Muslim
Loved.
Girl/Female
Hebrew
Plant.
Surname or Lastname
English
English : variant of Hilburn.
Boy/Male
Tamil
Eye liner
Male
Italian
Italian and Spanish form of Roman Latin Flavius, FLAVIO means "yellow hair."
Girl/Female
Bengali, Indian
God Gift; Relationship with God; God's Blessing
Girl/Female
Greek
Loving.
Girl/Female
Hindu, Indian, Tamil
Creative
Male
Italian
Italian form of Latin Eligius, ELIGIO means "to choose."
Male
English
Pet form of English Sacheverell, SACHIE means "roe-buck leap."
RULER FUNCTION
RULER FUNCTION
RULER FUNCTION
RULER FUNCTION
RULER FUNCTION
n.
To mark with lines made with a pen, pencil, etc., guided by a rule or ruler; to print or mark with lines by means of a rule or other contrivance effecting a similar result; as, to rule a sheet of paper of a blank book.
a.
That may be ruled; subject to rule; accordant or conformable to rule.
n.
A straight or curved strip of wood, metal, etc., with a smooth edge, used for guiding a pen or pencil in drawing lines. Cf. Rule, n., 7 (a).
imp. & p. p.
of Rule
n.
To require or command by rule; to give as a direction or order of court.
a.
A determinate method prescribed for performing any operation and producing a certain result; as, a rule for extracting the cube root.
n.
To establish or settle by, or as by, a rule; to fix by universal or general consent, or by common practice.
a.
Not comprehended within a rule or rules.
a.
Ordibary course of procedure; usual way; comon state or condition of things; as, it is a rule to which there are many exeptions.
a.
That which is prescribed or laid down as a guide for conduct or action; a governing direction for a specific purpose; an authoritative enactment; a regulation; a prescription; a precept; as, the rules of various societies; the rules governing a school; a rule of etiquette or propriety; the rules of cricket.
n.
One who rules; one who exercises sway or authority; a governor.
n.
A stickler for rules; a slave of rules
a.
A general principle concerning the formation or use of words, or a concise statement thereof; thus, it is a rule in England, that s or es , added to a noun in the singular number, forms the plural of that noun; but "man" forms its plural "men", and is an exception to the rule.
v. i.
To keep within a (certain) range for a time; to be in general, or as a rule; as, prices ruled lower yesterday than the day before.
n.
The act of one who rules; ruled lines.
a.
A composing rule. See under Conposing.
v. i.
To lay down and settle a rule or order of court; to decide an incidental point; to enter a rule.
a.
The office of ruler; rule; authority; government.
a.
A straight strip of wood, metal, or the like, which serves as a guide in drawing a straight line; a ruler.
a.
One who rules or reigns; a governor; a ruler.