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Nowhere analytic, infinitely differentiable function
the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by Jaap Fabius (1966). This function satisfies
Fabius_function
Degree of differentiability of a function or map
example is the Fabius function. Although it might seem that such functions are the exception rather than the rule, analytic functions form a small subclass
Smoothness
Mathematical functions which are smooth but not analytic
infinitely many times in every neighbourhood of the origin. Bump function Fabius function Flat function Mollifier Exercise 12 on page 418 in Walter Rudin, Real
Non-analytic_smooth_function
Type of differential equation
1\end{cases}}} with F ( t ) {\displaystyle F(t)} the Fabius function, known as Rvachëv up function. Dynamics of diabetes Epidemiology Population dynamics
Delay_differential_equation
Counterintuitive mathematical object
dense but has positive measure. The Fabius function is everywhere smooth but nowhere analytic. Volterra's function is differentiable with bounded derivative
Pathological_(mathematics)
Prime Minister of France from 1984 to 1986
1986. Fabius was 37 years old when he was appointed and is, after Gabriel Attal, the second youngest prime minister of the Fifth Republic. Fabius was also
Laurent_Fabius
Infinite binary sequence generated by repeated complementation and concatenation
the consecutive criterion can be evaded forever. Dejean's theorem Fabius function First difference of the Thue–Morse sequence Gray code Komornik–Loreti
Thue–Morse_sequence
confirms the hypothesis of seafloor spreading at mid-ocean ridges. The Fabius function is published. Chen Jingrun publishes Chen's theorem: every sufficiently
1966_in_science
Roman orator and rhetorician (c. 35 – c. 100)
Marcus Fabius Quintilianus (Latin: [kʷiːntɪliˈaːnʊs]; c. 35 – c. 100 AD) was a Roman educator and rhetorician born in Hispania, widely referred to in medieval
Quintilian
Fabius Ambustus was a name used by ancient Roman men from a branch of the gens Fabia, including: Quintus Fabius Ambustus, consul 412 BC; son of Quintus
Fabius_Ambustus
Jewish Women's Studies & Gender Issues. Oktober 2008 16(16):174–195 Fabius Schach, Todesfallanzeige Ghetto Theresienstadt Fabius Schach, bei holocaust.cz
Fabius_Schach
Carthaginian general and statesman (247–183/181 BC)
Quintus Fabius Maximus Verrucosus, demanded Carthage choose between war and peace, to which his audience replied that Rome could choose. Fabius chose war
Hannibal
victories credited to Gaius Poetelius Libo Visolus to "Κόιντος Φάβιος" (Quintus Fabius) instead. The fasti consulares list Gaius Sulpicius Longus as the dictator
List_of_Roman_dictators
Most beautiful woman in Greek mythology
earlier states that Helen, Castor and Pollux were produced from a single egg. Fabius Planciades Fulgentius also states that Helen, Castor and Pollux are born
Helen_of_Troy
British socialist organisation founded in 1884
as Fabius did most patiently when warring against Hannibal, though many censured his delays; but when the time comes you must strike hard, as Fabius did
Fabian_Society
First member by precedence of the Roman Senate
Quintus Fabius Maximus Verrucosus instead of Titus Manlius Torquatus, the senior ex-censor. Tuditanus justified his choice by saying that Fabius was the
Princeps_senatus
Extraordinary magistrate of the Roman Republic
perhaps except in cases with a non-consular nominator. In the case of Quintus Fabius Maximus Verrucosus, the people may have created him dictator directly by
Roman_dictator
3rd century BC Roman politician and general
including opposition from Quintus Fabius Maximus, a rival of Flaminius, although Cicero notes that Spurius Carvilius, Fabius Maximus' colleague for his second
Gaius Flaminius (consul 223 BC)
Gaius_Flaminius_(consul_223_BC)
Public square in a Roman municipium
name, such as Forum Popili or Forum Livi. In addition to its standard function as a marketplace, a forum was a gathering place of great social significance
Forum_(Roman)
Chief deity of Roman state religion
between 26 and 22 BC. Iuppiter Victor had a temple dedicated by Quintus Fabius Maximus Gurges during the third Samnite War in 295 BC. It was probably on
Jupiter_(god)
Warfare by small groups against regular forces
guerrilla-style tactics in The Art of War. The 3rd century BC Roman general Quintus Fabius Maximus Verrucosus is also credited with inventing many of the tactics of
Guerrilla_warfare
(12.3.1) inserts a new pair of consuls, L. Quinctius Cincinnatus and M. Fabius Vibulanus, between the colleges of 457 and 456. Taylor 1951, pp. 74, 78
List_of_Roman_consuls
the Romans' own gods remain obscure, known only by name and sometimes function, through inscriptions and texts that are often fragmentary. This is particularly
List_of_Roman_deities
Wars between Rome and Carthage (264–146 BC)
panicked by these heavy defeats, appointed Fabius Maximus as dictator, with sole charge of the war effort. Fabius introduced the Fabian strategy of avoiding
Punic_Wars
Salafi jihadist militant organisation
uses the Arabic acronym Dāʻish or Daesh. France's Foreign Minister Laurent Fabius said: "This is a terrorist group and not a state. I do not recommend using
Islamic_State
Prefecture of the Late Roman Empire
Catullinus Philomathius (341, uncertain whether he was prefect of Gaul) Fabius Titianus (341-350) Vulcacius Rufinus (353-354) Gaius Ceionius Rufius Volusianus
Praetorian_prefecture_of_Gaul
Ancient Roman goddess of love, sex and fertility
temple, on August 19 in 295 BC during the Third Samnite War by Quintus Fabius Maximus Gurges. It was sited somewhere near the Aventine Hill and Circus
Venus_(mythology)
Attitudes and behaviors towards sex in ancient Rome
(conceived of as a humor) and pneuma (the "vital air" required by organs to function) formed within the man's coiled spermatic vessels, with the humor turning
Sexuality_in_ancient_Rome
French politician (born 1951)
Dominique Strauss-Kahn]. By logic, I conclude that Laurent Fabius should be the candidate. […] Fabius has been a minister; he is capable of leading the country
Jean-Luc_Mélenchon
Ceres (University of Texas Press, 1996), p. 36. Servius cites the historian Fabius Pictor (late 3rd century BC) as his source. Michael Lipka, Roman Gods: A
List of Roman agricultural deities
List_of_Roman_agricultural_deities
Loss of political control in antiquity
leadership in battle. City governments with their own properties and revenues functioned effectively at a local level; membership of city councils involved lucrative
Fall of the Western Roman Empire
Fall_of_the_Western_Roman_Empire
Theorem in stochastic analysis
Øksendal (2003), Example 7.4.2, p127. Sources Dynkin, Eugene B.; trans. J. Fabius; V. Greenberg; A. Maitra; G. Majone (1965). Markov processes. Vols. I, II
Dynkin's_formula
President of France from 1995 to 2007
public companies, renewing the liberalisation initiated under Laurent Fabius's Socialist government of 1984–1986, and abolished the solidarity tax on
Jacques_Chirac
Roman emperor from AD 14 to 37
himself, and the histories of contemporaries such as Marcus Cluvius Rufus, Fabius Rusticus and Pliny the Elder (all of which are lost). Tacitus's narrative
Tiberius
War in the Roman Republic (49–45 BC)
impression. He also permitted two of his legates, Quintus Pedius and Quintus Fabius Maximus, to hold triumphs as well. None of these celebrations were popular
Caesar's_civil_war
Period of Roman history (c. 753 – c. 509 BC)
centuries. The traditional chronology, as codified by Varro (116 – 27 BC) and Fabius Pictor (c. 270 – c. 200 BC), allows 243 years for their combined reigns
Roman_Kingdom
Numbers in the Roman numeral system
(seven ten) and nonaginta septem (ninety seven), respectively. The ROMAN() function in Microsoft Excel supports multiple subtraction modes depending on the
Roman_numerals
Continuation of the Roman Empire (330–1453)
territories from 400 AD. Greek had begun to replace it even in those functions by the time of Justinian I (r. 527–565), who may have tried to arrest
Byzantine_Empire
Type of traditional narrative
was then borrowed into Late Latin, occurring in the title of Latin author Fabius Planciades Fulgentius' 5th-century Mythologiæ to denote what is now referred
Myth
Twin-engine light utility helicopter
2025. "CORRECTED-France, Saudi Arabia to sign contracts worth $12 bln – Fabius". reuters.com. 24 June 2015. Retrieved 24 June 2015. "Republic of Serbia
Eurocopter_EC145
King of Rome from 753 to 716 BC
Troezen, is widely disputed. Livy, Dionysius, and Plutarch rely on Quintus Fabius Pictor as a source. Other significant sources include Ovid's Fasti, and
Romulus
President of France from 1981 to 1995
political crisis. It was abandoned and Mauroy resigned in July 1984. Laurent Fabius succeeded him, and the Communists left the cabinet. In terms of foreign
François_Mitterrand
Non-standard Latin spoken in ancient Rome
sprachbund. The term ille may have evolved from its initial demonstrative function, broadening to convey semantic prominence by directing the attention of
Vulgar_Latin
Ancient Roman circus in Rome
Described by Dionysius of Halicarnassus, 7.72.1–13, supplemented by Quintus Fabius Pictor's history. Aedileship was a rung on the cursus honorum, available
Circus_Maximus
Mass surveillance program run by the NSA
American servers. On October 21, 2013, the French Foreign Minister, Laurent Fabius, summoned the U.S. Ambassador, Charles Rivkin, to the Quai d'Orsay in Paris
PRISM
Age of the ancient Greeks and Romans
during this period eventually evolved into strong Greek city-states, functioning independently of their metropolis. The Etruscans had established political
Classical_antiquity
citing Livy 22.23.6–8, 22.60.3–4, 22. 61.3, 7, and 34.50.3–7; Plutarch, Fabius 7.4–5. Matthew Leigh, Comedy and the Rise of Rome (Oxford University Press
Slavery_in_ancient_Rome
Roman general and dictator (100–44 BC)
membership [in the Senate] would certainly make the house incapable of functioning properly, but it enabled Caesar to show favour to many". Meier 1995,
Julius_Caesar
Roman emperor from AD 54 to 68
of historians. A few of the contemporary historians are known by name. Fabius Rusticus, Cluvius Rufus and Pliny the Elder all wrote condemning histories
Nero
Random process independent of past history
Grundlehren der mathematischen Wissenschaften. Vol. I (121). Translated by Fabius, Jaap; Greenberg, Vida Lazarus; Maitra, Ashok Prasad; Majone, Giandomenico
Markov_chain
Political institution in ancient Rome
of Rome. During the years of the monarchy, the senate's most important function was to elect new kings. While the king was nominally elected by the people
Roman_Senate
Chief magistrate of the Roman Kingdom
ruler of the Roman Kingdom, a legendary period of Roman history that functioned as an elective monarchy. According to legend, the first king of Rome was
King_of_Rome
Army officer in Imperial Rome
similar to that of commissioned officers but that centurions "combined the function and prestige of a modern company commander and sergeant-major." Professor
Centurion
Science of Roman historical writing
Second Punic War with Carthage, Rome's earliest known annalists Quintus Fabius Pictor and Lucius Cincius Alimentus recorded history in Greek, and relied
Roman_historiography
Prime Minister of France from 1991 to 1992
programme from which vast sums went missing. When Cresson took up her functions, she intended to appoint dental surgeon Philippe Berthelot, one of her
Édith_Cresson
Narrow strait in northwestern Turkey
Heritage Dictionary's online version has only this spelling and its search function does not find anything for the spelling Bosphorus. The Columbia Encyclopedia
Bosporus
Roman hereditary name
Flavius, and other names became quite common, including Valerius, Claudius, Fabius, Julius and Junius. Those names no longer had any utility in indicating
Nomen_gentilicium
Method of execution/torture
Plb. 1.11.5, al., Plu.Fab.6, al. 2. crucify afresh, Ep.Hebr.6.6. Plutarch Fabius Maximus 6.3 "Hannibal now perceived the mistake in his position, and its
Crucifixion
French economist and politician (born 1949)
Strauss-Kahn's position inside the PS,[citation needed] while left-wing Laurent Fabius, who had campaigned for a 'No' vote, was reinforced.[citation needed] Strauss-Kahn
Dominique_Strauss-Kahn
Period of Roman history (c. 509 – 27 BC)
province of Gallia Narbonensis was established after the victory of Quintus Fabius Maximus over a coalition of Arverni and Allobroges in southern Gaul in 123
Roman_Republic
Prime Minister of France since 2025
Jospin in 1997 of not combining an executive mandate with a government function; he was authorized to do so "for a time" by Emmanuel Macron and Jean Castex
Sébastien_Lecornu
Prime Minister of France from 1981 to 1984
Secretary of the PS against the will of Mitterrand, who supported Laurent Fabius. The following year, Mauroy called for (as noted by one study) “an “ideological”
Pierre_Mauroy
Currency of the European Union
made by Wim Duisenberg, European Central Bank Governor, in 1998, Laurent Fabius, French Finance Minister, in 2000, and Romano Prodi, President of the European
Euro
2014 revolution in Ukraine
three visiting EU foreign ministers—Radosław Sikorski of Poland, Laurent Fabius of France, and Frank-Walter Steinmeier of Germany—were due to meet with
Revolution_of_Dignity
Indo-European language of the Italic branch
grammatical functions of words entered. Online results. Aversa, Alan. "Latin Inflector". Retrieved 8 June 2023. Identifies the grammatical functions of all
Latin
Monumental structure in the form of an archway
built on the Capitoline Hill by Scipio Africanus in 190 BC, and Quintus Fabius Maximus Allobrogicus constructed one in the Roman Forum in 121 BC. None
Triumphal_arch
Personification of Earth in ancient Rome
(edition of Cardauns), Servius Danielis, note to Georgics "1.21", citing Fabius Pictor[clarification needed] Rüpke, Jörg (2012). Religion in Republican
Terra_(mythology)
Roman goddess of safety and well-being
dedicated on 5 August 302, and adorned with frescos at the order of Gaius Fabius Pictor. The high antiquity and importance of the cult of Salus is testified
Salus
Chief high priest in ancient Rome
sacred river (and a deity): only prestigious authorities with sacral functions could be allowed to "disturb" it with mechanical additions. However, it
Pontifex_maximus
Play by William Shakespeare
relation to a serpent signifying "original sin". The symbol of the serpent "functions, at the symbolic level, as a means of her submission, the phallic appropriation
Antony_and_Cleopatra
Western half of the Roman Empire (395–476)
Greek culture of the East and the predominantly Latin culture of the West functioned effectively as an integrated whole, political and military developments
Western_Roman_Empire
Roman civilisation from the 8th century BC to the 5th century AD
vestigial rex sacrorum was retained to exercise the monarch's former priestly functions. The Romans believed that their monarchy was elective, with seven legendary
Ancient_Rome
Bodyguards of the Roman emperors
escort or reserve military force, they housed adaptable equipment for each function. For heavy packed combat infantry lines (Triplex Acies System), they mounted
Praetorian_Guard
Settlement established on the current site of the City of London around 43–50 AD
measuring about 100 m × 50 m (330 ft × 160 ft). The basilica would have functioned as the city's administrative heart, hearing law cases and seating the
Londinium
Roman emperor from 198 to 217
to be mundane. She may have taken on one of the more important civil functions of the emperor; receiving petitions and answering correspondence. The
Caracalla
French statesman and clergyman (1585–1642)
Edward Porter. Museums in Motion: an introduction to the history and functions of museums. Lanham: Rowman and Littlefield. (1996) Auchincloss, Louis
Cardinal_Richelieu
Political party in France
autonomy of its members and local levels of the party. Consequently, the function of secretary general, held by Louis Dubreuilh until 1918, was essentially
French Section of the Workers' International
French_Section_of_the_Workers'_International
Archaeological site in Tunisia
could not be used as a base by a hostile power again. It also continued to function as an episcopal see. The regional power shifted to Kairouan and the Medina
Carthage
Ancient Roman goddess of the hearth, home, and family
between Promathion's version of Romulus' birth and that of the more credible Fabius Pictor which he describes in a detailed narrative and lends support to.
Vesta_(mythology)
Political instability c. 134–30 BC
stopped regularly establishing Roman colonies in Italy. One of the major functions of these colonies was to provide land for the urban and rural poor, increasing
Crisis_of_the_Roman_Republic
President of Syria from 2000 to 2024
Assad for crimes against humanity, with French Foreign Minister Laurent Fabius stating "Faced with these crimes that offend the human conscience, this
Bashar_al-Assad
Roman goddess of agriculture
Georgics, 1.21. Cited in Spaeth, 1996, p. 36. Servius cites the historian Fabius Pictor (late 3rd century BC) as his source. Wilhelm Heinrich Roscher, Ausführliches
Ceres_(mythology)
the husband's name and uxor for "wife". N. Fabius Q. f. M. n. Furia gnatus Maximus means "Numerius Fabius Maximus, son of Quintus, grandson of Marcus
Roman_naming_conventions
victory: Rome's first known temple to Venus was vowed by the consul Q. Fabius Gurges in the heat of battle against the Samnites, and dedicated in 295
Religion_in_ancient_Rome
French satirical weekly newspaper
magazine to protect it against possible attacks. Foreign Minister Laurent Fabius criticised the magazine's decision, saying, "In France, there is a principle
Charlie_Hebdo
Communication used to influence opinion
humanity and would soon lose the favour of gods. At the same time, led by Q. Fabius Maximus, they organized elaborate religious rituals to protect Roman morale
Propaganda
Sexuality in ancient Rome
Festus provides a definition and illustrates with a comic anecdote. Quintus Fabius Maximus Eburnus, a consul in 116 BC and later a censor known for his moral
Homosexuality_in_ancient_Rome
Roman historian (c. AD 69 – after AD 122)
112. Under Trajan he served as secretary of studies (a studiis (precise functions are uncertain)) and director of Imperial archives (a bibliotecis); while
Suetonius
1163/15692060260289707 – via EBSCO. Yeo, Cedric A. (1959). "The Founding and Function of Roman Colonies". The Classical World. 52 (4): 104–130. doi:10.2307/4344123
Social_class_in_ancient_Rome
French politician and lawyer (1878–1966)
business community, arguing that "We live in a capitalist system. For it to function we must obey its laws. These are the laws of profits, individual risk,
Paul_Reynaud
Form of non-verbal/non-vocal communication
Gestures have been studied throughout time from different philosophers. Marcus Fabius Quintilianus was a Roman Rhetorician who studied in his Institutio Oratoria
Gesture
Prefecture of Gard, Occitanie, France
indigenous sculpture in southern Gaul. In 123 BCE, the Roman general Quintus Fabius Maximus launched a campaign against Gallic tribes in the area, eventually
Nîmes
Chemical compound
CABI Publishing. ISBN 0-85199-910-7. Borodovsky A, Salmasi V, Turcan S, Fabius AW, Baia GS, Eberhart CG, et al. (October 2013). "5-azacytidine reduces
Azacitidine
French diplomat, political philosopher and historian (1805–1859)
within the United States. Tocqueville's main purpose was to analyze the functioning of political society and various forms of political associations, although
Alexis_de_Tocqueville
Decorative style in ancient Rome
Damophilus as the first known artists to make paintings in Italy. Gaius Fabius Pictor, a little later, was celebrated as a historical painter and the first
Painting_in_ancient_Rome
Calendar used in Ancient Rome
the increasing use of such date phrases as an absolute phrase able to function as the object of another preposition, or simply originated in a mistaken
Roman_calendar
Ruler of the Roman Empire
sons Honorius and Arcadius. The two halves of the Empire, while later functioning as de facto separate entities, were always considered and seen, legally
Roman_emperor
unskilled. Especially under the empire, architecture often served a political function, demonstrating the power of the Roman state in general, and of specific
Ancient_Roman_architecture
French politician (1943–2010)
President of the Court of Audit of France : 2004–2010 (death). Governmental function Minister of Social Affairs and Employment : 1986–1988. Electoral mandates
Philippe_Séguin
Concept in ancient Roman ethic
Flight of Pudicitia: Juvenal’s Vision of the Past and the Programmatic Function of the Prologue in the Sixth Satire.” Mnemosyne, vol. 65, no. 1, 2012,
Pudicitia
FABIUS FUNCTION
FABIUS FUNCTION
Male
English
Anglicized form of Greek Abioud, ABIUD means "my father is majesty." In the bible, this is the name of the son of Bela.
Boy/Male
Indian
Male
French
French form of Latin Fabianus, FABIEN means "like Fabius."Â
Male
Babylonian
, man of Nabium.
Boy/Male
Australian, British, English, Finnish, French, Latin, Shakespearean, Swedish
Happy; Rejoice; Lord; Similar to Gaius which is a More Common Form of the Name in Britain
Male
English
English form of Latin Fabianus, FABIAN means "like Fabius."Â
Boy/Male
French, German, Latin, Swedish
Bean Farmer; A Bean
Male
Spanish
Spanish form of Latin Fabianus, FABIÃN means "like Fabius."Â
Surname or Lastname
English, French, German, Italian (Venetian), Polish, Czech and Slovak (Fabián), and Hungarian (Fábián)
English, French, German, Italian (Venetian), Polish, Czech and Slovak (Fabián), and Hungarian (Fábián) : from a personal name, Latin Fabianus, a derivative of the Roman family name Fabius. The personal name achieved considerable popularity in Europe in the Middle Ages, having been borne by a 3rd-century pope and saint.Americanized or Italianized spelling of Slovenian Fabjan or Fabijan (see 1).Jewish : adoption of the non-Jewish surname under the influence of the Yiddish personal name Fayvish.
Surname or Lastname
English
English : probably an altered form of Irish or Scottish Ferris, or of English Farrar.
Boy/Male
Australian, French, German, Latin, Swiss
Derived from the Roman Clan Name Fabius; One who Grows Beans
Boy/Male
English American Latin Shakespearean Swedish
Derived from the Roman clan name Fabius; a name given several Roman emperors and 16 saints.
Boy/Male
American, Australian, British, English, French, Latin
Bean Grower; Derived from the Roman Clan Name Fabius; A Name Given Several Roman Emperors and 16 Saints
Girl/Female
Australian, French, German, Italian, Latin, Portuguese, Swiss
Bean Farmer; Form of Fabian
Boy/Male
Australian, French, German, Japanese, Latin, Portuguese, Spanish, Swiss
Derived from the Roman Clan Name Fabius; One who Grows Beans; Bean Grower
Boy/Male
Latin Biblical
To rejoice. Famous bearer: Roman dictator Gaius Julius Caesar.
Boy/Male
Latin
Bean farmer.
Male
Italian
Italian name derived from Roman Latin Fabius, FABIO means "bean."
Surname or Lastname
English
English : patronymic from Sabin.
Boy/Male
English Latin
Derived from the Roman clan name Fabius; a name given several Roman emperors and 16 saints.
FABIUS FUNCTION
FABIUS FUNCTION
Girl/Female
Tamil
Name of a Nakshathra, Months name
Boy/Male
Tamil
Shiv
Biblical
a willing brother; brother of a vow
Girl/Female
Muslim
Praise of Allah swt
Boy/Male
American, British, English, Norse
From Thor's Hill
Girl/Female
Indian
Princess
Boy/Male
English
From the cold spring.
Boy/Male
Hebrew
Dearly loved.
Boy/Male
Basque, French, German, Portuguese
Baptist; To Dip
Boy/Male
English
From the brook.
FABIUS FUNCTION
FABIUS FUNCTION
FABIUS FUNCTION
FABIUS FUNCTION
FABIUS FUNCTION
n.
pl. of Radius.
n.
See Ignis fatuus.
pl.
of Faunus
a.
Famous; notorious.
a.
Famous.
n.
The movable limb of a sextant or other angular instrument.
a.
Popular; famous.
pl.
of Labium
pl.
of Labium
n.
The front median plate of the labium in insects. See Labium.
pl.
of Labrus
pl.
of Radius
n. pl.
See Labium.
n.
Radiating organs, or color-markings, of the radiates.
pl.
of Radius
pl.
of Ignis fatuus
a.
Of, pertaining to, or in the manner of, the Roman general, Quintus Fabius Maximus Verrucosus; cautious; dilatory; avoiding a decisive contest.
a.
Celebrated in fame or public report; renowned; mach talked of; distinguished in story; -- used in either a good or a bad sense, chiefly the former; often followed by for; as, famous for erudition, for eloquence, for military skill; a famous pirate.
n.
Practice; habits.