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Region above a graph
In mathematics, the epigraph or supergraph of a function f : X → [ − ∞ , ∞ ] {\displaystyle f:X\to [-\infty ,\infty ]} valued in the extended real numbers
Epigraph_(mathematics)
Topics referred to by the same term
epigraphy Epigraph (literature), a phrase, quotation, or poem that is set at the beginning of a document or component Epigraph (mathematics), the set
Epigraph
Region underneath a graph
domain Epigraph (mathematics) – Region above a graph Proper convex function – Concept in convex analysis Wikimedia Commons has media related to epigraphs und
Hypograph_(mathematics)
Topics referred to by the same term
epi- in Wiktionary, the free dictionary. EPI or Epi may refer to: Epigraph (mathematics) Epimorphism Entropy power inequality, a result that relates to
EPI
American mathematician
theory Epigraph (mathematics) Wets, Roger J-B Rockafeller, Ralph Tyrell (12 January 1997). Convex Analysis: (PMS-28) (Princeton Landmarks in Mathematics and
R._Tyrrell_Rockafellar
In geometry, set whose intersection with every line is a single line segment
set, such as the epigraph of a concave function, is sometimes called a reverse convex set, especially in the context of mathematical optimization. Given
Convex_set
Mathematics of convex functions and sets
study of nonsmooth problems. The tools of convex analysis include the epigraph of a function, the subdifferential, the Legendre–Fenchel transform, and
Convex_analysis
degree of curvature is called the convexity. Duality (optimization) Epigraph (mathematics) - for a function f : Rn→R,[check spelling] the set of points lying
List_of_convexity_topics
convex function – Concept in convex analysis Epigraph (mathematics) – Region above a graph Hypograph (mathematics) – Region underneath a graph Rockafellar
Effective_domain
Representation of a mathematical function
Concave function Convex function Contour plot Critical point Derivative Epigraph Normal to a graph Slope Stationary point Tetraview Vertical translation
Graph_of_a_function
following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology. This list is limited to abbreviations
List of mathematical abbreviations
List_of_mathematical_abbreviations
Generalization of the Legendre transformation
In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex
Convex_conjugate
Complement of an open subset
In topology, a branch of mathematics, a closed set is a set that contains all of its boundary points. An example is the closed interval [ a , b ] {\displaystyle
Closed_set
Smallest convex set containing a given set
polygons, Brownian motion, space curves, and epigraphs of functions. Convex hulls have wide applications in mathematics, statistics, combinatorial optimization
Convex_hull
Adage that anything that can go wrong will go wrong
said to exhibit a high degree of malice toward humans. In 1952, as an epigraph to the mountaineering book The Butcher: The Ascent of Yerupaja, John Sack
Murphy's_law
Series of four mathematics textbooks
Lectures in Analysis is a series of four mathematics textbooks, each covering a different area of mathematical analysis. They were written by Elias M.
Princeton Lectures in Analysis
Princeton_Lectures_in_Analysis
5th-century BC Greek philosopher
came into this world to see the Sun” is attributed to Anaxagoras in the epigraph to Russian Silver Age poet Konstantin Balmont's sixth book of poetry, Let
Anaxagoras
Subfield of mathematical optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently
Convex_optimization
Property of functions which is weaker than continuity
function on a domain X {\displaystyle X} is lower semi-continuous if its epigraph { ( x , t ) ∈ X × R : t ≥ f ( x ) } {\displaystyle \{(x,t)\in X\times \mathbb
Semi-continuity
Latin axiom in natural philosophy
sometimes attributed to Gottfried Leibniz. Natura non facit saltum is also the epigraph of Alfred Marshall's 1890 Principles of Economics. He most likely borrowed
Natura_non_facit_saltus
American scientist (1839–1903)
on his doctoral dissertation, in which he used as epigraph a remark attributed to Gibbs: "Mathematics is a language." Samuelson later explained that in
Josiah_Willard_Gibbs
Mathematical transformation
In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface
Legendre_transformation
Mathematical physicist
2022. "Universes as Big Data". Youtube. 27 November 2020. "Muß Es Sein? – Epigraph to a String Quartet". ICMS NEWS. 2014-05-09. Retrieved 2021-10-11. "慕校"
Yang-Hui_He
Real function with secant line between points above the graph itself
function between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set
Convex_function
Topics referred to by the same term
supersymmetric theory using the advantages of the superspace formalism. Synonym for epigraph, i.e. the set of points lying on or above a function's graph. This disambiguation
Supergraph
8th episode of the 4th season of The Wire
authority figures. The next day Prez takes his class through their state mathematics test. Calvin and Charlene struggle with the change in the particulars
Corner_Boys
1864 novella by Fyodor Dostoevsky
writers of the natural school in Petersburg. Following the title there is an epigraph containing the opening lines from Nekrasov's poem "When from the darkness
Notes_from_Underground
Subset of a function's domain on which its value is equal
convexity of all the sublevel sets characterizes quasiconvex functions. Epigraph Level-set method Level set (data structures) Simionescu, P.A. (2011). "Some
Level_set
associated imagery is considered a popular and proverbial illustration of the mathematics of probability, widely known to the general public because of its transmission
Infinite monkey theorem in popular culture
Infinite_monkey_theorem_in_popular_culture
Terms in Maths
{\mbox{dom}}f\vert f(x)\leq \alpha \}} is a closed set. Equivalently, if the epigraph defined by epi f = { ( x , t ) ∈ R n + 1 | x ∈ dom f , f ( x ) ≤ t } {\displaystyle
Closed_convex_function
11th century Chola Empire general
queen of his called Alagiyamanavalini Mangai Ālvār is known to us from an epigraph in the Varadarajaswami temple in Kanchi. The Sri Lankan vassal of the Chola
Karunakara_Tondaiman
1963 paper by Jacques Derrida
dream and not something real, unlike the incontrovertible truths of mathematics. But even the latter are attacked, with the use of the further objection
Cogito and the History of Madness
Cogito_and_the_History_of_Madness
Italian polymath (1452–1519)
May 2022. Retrieved 27 March 2021. Michael Rocke, Forbidden Friendships epigraph, pp. 148 & 298, N120. Ana Finel Honigman. "Universal Leonardo". Artnet
Leonardo_da_Vinci
1759–1767 novel by Laurence Sterne
of Martinus Scriblerus. The title page of the first volume features an epigraph in untranslated Greek. The unattributed quotation is from the Stoic philosopher
The Life and Opinions of Tristram Shandy, Gentleman
The_Life_and_Opinions_of_Tristram_Shandy,_Gentleman
Type of convergence for functionals
Kuratowski-convergence of sets. Let epi ( F ) {\displaystyle {\text{epi}}(F)} denote the epigraph of a function F {\displaystyle F} and let F n : X → R ¯ {\displaystyle
Γ-convergence
watches the watchmen (or modern, 'watchers')?" This translation is a common epigraph, such as of the Tower Commission and Alan Moore's Watchmen comic book series
List_of_Latin_phrases_(full)
1943 lithograph by M. C. Escher
released in 1969. In 1993, Graham Waterhouse composed a piano trio, Four Epigraphs after Escher, in four movements, with the final one based on Reptiles
Reptiles_(M._C._Escher)
Book by the Scottish D'Arcy Wentworth Thompson 1917
On Growth and Form is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is 793 pages in the first edition of
On_Growth_and_Form
American science fiction media franchise
some idea of the power of melange." Each chapter of Dune begins with an epigraph excerpted from the fictional writings of the character Princess Irulan
Dune_(franchise)
French mathematician (born 1944)
analysis, the calculus of variations, and mathematical economics, as well as popular books on mathematics, which have been published in French, English
Ivar_Ekeland
Empire in southern India (1336–1646)
all epigraphs inscribed during the Tuluva period. Despite the popularity of Telugu language as a literary medium, the majority of the epigraphs in the
Vijayanagara_Empire
Fictional technology
massive retaliation from any number of the other Houses. As Paul notes via epigraph in Dune Messiah (1969), "any Family in my Empire could so deploy its atomics
List of technology in the Dune universe
List_of_technology_in_the_Dune_universe
and exile Shaddam. Shaddam is described as "red-haired" by Irulan via epigraph in Dune, and noted to be 72 years old yet looking no older than 35. He
List_of_Dune_characters
The epigraph of f is a convex set if and only if f is a convex function. The following theorems present some functions f for which the epigraph has an
Self-concordant_function
American crime drama television series (2002–2008)
rarely seen in the title sequence. At the end of the sequence, a quotation (epigraph) is shown on-screen that is spoken by a character during the episode. The
The_Wire
Italian theoretical physicist and writer (born 1956)
quote from Rovelli's The Order of Time (L'ordine del tempo, 2017) as the epigraph for his book. The 2023 film The Order of Time, directed by Liliana Cavani
Carlo_Rovelli
2001 short story by David Foster Wallace
The original version of the story published in Conjuctions contained an epigraph with text from "Avatars of the Tortoise" by Jorge Luis Borges, although
Good_Old_Neon
Type of reference work
media offer new capabilities for search, indexing and cross reference. The epigraph from Horace on the title page of the 18th century Encyclopédie suggests
Encyclopedia
of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set
Glossary_of_calculus
Word appearing only once in a text or record
referred to the sun and signifying "one born in the east", appears only in an epigraph found in Castellammare di Stabia (the ancient Stabiae). Paland (پلند, "Poland";
Hapax_legomenon
1965 science fiction novel by Frank Herbert
reading to close the gap between what the epigraph says and what is happening in the main narrative. The epigraphs also give the reader the feeling that the
Dune_(novel)
Largest pyramid in the Giza Necropolis, Egypt
ancient texts with the search for material evidence, such as statues, epigraphs and monuments, reporting information about them in his travel diaries
Great_Pyramid_of_Giza
1997 novel by Thomas Pynchon
Transit might make him a candidate for the post. Episode 44 The episode's epigraph quotes the Reverend on the properties of ley lines and recalls Dixon's
Mason_&_Dixon
Approach to software development
about the Battle of Flodden in 1513. – the actual citation appeared as an epigraph in a May 1986 article by Jon Bentley and Donald Knuth in one of the classical
Literate_programming
King of Castile and León from 1252 to 1284
Secretary of State, 1949–1953) used it as the basis for the title and epigraph of his memoir Present at the Creation. Alfonso also commissioned a compilation
Alfonso_X_of_Castile
French applied mathematician
problem — that is, the problem defined by the closed convex hull of the epigraph of the original problem. Following Ekeland and Aubin, similar applications
Claude_Lemaréchal
Mathematical operator
(f)}}} , where epi ( f ) {\displaystyle \operatorname {epi} (f)} is the epigraph of a function f {\displaystyle f} . The relative interior ri {\displaystyle
Closure_operator
was little, if any, religion in his films: even his tombstone bears no epigraph, save only for an ancient Chinese character signifying 'Nothingness', ('mu')
List of atheists in film, radio, television and theater
List_of_atheists_in_film,_radio,_television_and_theater
Principle in mathematical optimization
non-convex function with its convex closure, that is the function that has the epigraph that is the closed convex hull of the original primal objective function
Duality_(optimization)
French physicist, philosopher and author
lefigaro. Retrieved 6 August 2015. Bernard d’Espagnat, physicist - obituary Epigraph of the article "The Quantum Theory and Reality, by Bernard d'Espagnat"
Bernard_d'Espagnat
Sums of sets of vectors are nearly convex
arguments x and function evaluations f(x) Graph(f) = { (x, f(x) ) } The epigraph of a real-valued function f is the set of points above the graph Epi(f)
Shapley–Folkman_lemma
French poet, essayist, and philosopher (1871–1945)
Le Moigne in his description of constructivist history. One of three epigraphs in Cormac McCarthy's novel Blood Meridian is from Valéry's "Writing at
Paul_Valéry
In mathematics, contour sets generalize and formalize the everyday notions of everything superior to something everything superior or equivalent to something
Contour_set
Character from Mary Shelley's 1818 novel
promote me?", X, 773-745, a quotation that appears in Frankenstein as an epigraph on the title page. Stupeo, Atonitus : I'm stunned, as if struck by thunder
Victor_Frankenstein
a certificate in case there is no solution. If K is represented as the epigraph of some computable convex function, then SMEM is trivial; if a subgradient
Algorithmic problems on convex sets
Algorithmic_problems_on_convex_sets
tradition of all languages of India. Current estimates of the total number of epigraph present in Karnataka range from 25,000 by the scholar Sheldon Pollock to
Languages_of_India
1818 book by Arthur Schopenhauer
remedies for this condition include contemplative, ascetic activities. The epigraph to volume one is a quotation from Johann Wolfgang von Goethe: Ob nicht
The World as Will and Representation
The_World_as_Will_and_Representation
convergence. Here, epi f {\displaystyle \operatorname {epi} f} is the epigraph of the function f {\displaystyle f} . If f n {\displaystyle f_{n}} epi-converges
Epi-convergence
Algorithms for solving convex optimization problems
(or maximizing) a linear function over a convex set by converting to the epigraph form. The idea of encoding the feasible set using a barrier and designing
Interior-point_method
Ottoman Greek scholar and physician (1657–1719)
novissimom liber, and this was probably also the period when he composed four epigraphs on behalf of Tsar Peter the Great (r. 1682–1725) and his brother Ivan
John_Komnenos_Molyvdos
In mathematics, Kuratowski convergence or Painlevé-Kuratowski convergence is a notion of convergence for subsets of a topological space. First introduced
Kuratowski_convergence
English epic poem by Edmund Spenser
Faerie Queene aloud to Marianne Dashwood. Quotes from the poem are used as epigraphs in Troubled Blood by Robert Galbraith, a pen name of J. K. Rowling. In
The_Faerie_Queene
Rashtrakuta Emperor from 814 to 878
(1999), p. 214 Desai, P.B. (1957). Jainism in South India and Some Jaina Epigraphs. Sholapur(sonnalagi): Jaina Samshodhana Sangha. pp. 10–15. Jain (1987)
Amoghavarsha
Jesuit university in New York City, New York, US
the center of the H, and the three nails of the Crucifixion beneath the epigraph. These elements dressed in gold lay on the purple shield framed in maroon
Fordham_University
Short story collection by Dan Simmons
The actual story is classic Simmons in its literary allusions, with epigraphs from Ezra Pound's Cantos; the protagonist's father is a Pound scholar
Prayers_to_Broken_Stones
Ancient script of Central and South Asia
for instance, how they had deciphered the Brahmi letters of various epigraphs from Samudragupta's Allahabad pillar inscription, to the Karle cave inscriptions
Brahmi_script
British statesman (1749–1806)
Baily was erected in Westminster Hall in 1857. Fox was the subject of the epigraph in John F. Kennedy's Pulitzer-prize winning book Profiles in Courage: "He
Charles_James_Fox
Rock-cut tomb in Old City Jerusalem
City in East Jerusalem. It contained ten ossuaries, six inscribed with epigraphs, including one interpreted as Yeshua bar Yehosef ("Jeshua, son of Joseph")
Talpiot_Tomb
Metropolitan municipality in Turkey
Pasha of Darende. From records, it is known that there was formerly an epigraph on the south gate written by Kusuri; however, this inscription is not in
Gaziantep
Short story by Edgar Allan Poe
with an intense desire for life may have led to her revival. The opening epigraph, which is repeated in the body of the story, is attributed to Joseph Glanvill
Ligeia
493–553 kingdom centered in Italy
Well-educated and also from a distinguished family, he wrote works on mathematics, music and philosophy. His most famous work, Consolatio philosophiae
Ostrogothic_Kingdom
Belgian American mathematician (1937–2025)
including metric spaces of sets, which he used to study the convergence of epigraphs; Wets's ideas of epigraphical convergence was used to study the convergence
Roger_J-B_Wets
non-convex function with its convex closure, that is the function that has the epigraph that is the closed convex hull of the original primal objective function
Duality_gap
German aristocrat and polymath (1772–1801)
for himself. This metaphoric sense of his pen name can be seen in the epigraph of Pollen, the first work he published as Novalis: "Friends, the soil is
Novalis
3rd-century BCE inscriptions in South Asia
centuries had concealed the character and the language of the earliest epigraphs". The Edicts are divided into four categories, according to their size
Edicts_of_Ashoka
French philosopher and writer (1713–1784)
the unfavorable (gods) Vertumnuses, however many they are") appear as epigraph. According to Nicholas Cronk, Rameau's Nephew is "arguably the greatest
Denis_Diderot
Uruguayan-born French author (1846–1870)
story "The Other Heaven", which also uses quotations from Maldoror as epigraphs. French philosopher Gilles Deleuze and psychiatrist Félix Guattari cited
Comte_de_Lautréamont
Russian brothers, writer duo
quotation is conducted through epigraphs, each serving as a commentary on the events of each chapter. The epigraph technique was also used in other
Arkady_and_Boris_Strugatsky
Public university in Berlin, Germany
with empty shelf space for 20,000 volumes, along with a plaque bearing an epigraph taken from an 1820 work by the great German-Jewish writer Heinrich Heine:
Humboldt_University_of_Berlin
Book series by Samuel Delany
well as critical theory in general. Each of the stories begins with an epigraph from a theoretical thinker. Other literary sources that Delany himself
Return_to_Nevèrÿon_(series)
City and comune in the region of Lombardy, Italy
while their interior walls are now a lapidarium displaying ancient Roman epigraphs collected in the 19th century. In front of the cellae, is a fragmentary
Brescia
Romanian mathematician and academic
optimization theory. Together with Wanka, he introduced a weaker conjugate epigraph-based regularity condition that ensured Fenchel duality in infinite-dimensional
Radu_I._Boț
Italian public university
Antonelli, former rector of the University of Naples Federico II, and a marble epigraph reading "Hic mors gaudet succurrere vitae" ("Here Death rejoices to help
University of Campania Luigi Vanvitelli
University_of_Campania_Luigi_Vanvitelli
Early medieval Indian dynasty (753–982)
families. The system of shaving the heads of widows was infrequent as epigraphs note that widows were allowed to grow their hair but decorating it was
Rashtrakuta_Empire
Association football club in Monza, Italy
the badge became a stylised golden Corona Ferrea with red details. The epigraph of the club's name was placed in the inner circle. In 1984, Monza's logo
AC_Monza
South Indian dynasty (1163–1323)
information about Prataparudra's relations with the Kampili kingdom. Besides epigraphs and literature, the forts, temples and tanks constructed during the Kakatiya
Kakatiya_dynasty
Early Indian medieval empire
to determine. Based on their different interpretations of the various epigraphs and historical records, different historians estimate the Pala chronology
Pala_Empire
Kulin written on 29 August 1189. The text is written is an Old Slavic epigraph in Bosnian Cyrillic script, and dated to the end of the 10th or the beginning
Literature of Bosnia and Herzegovina
Literature_of_Bosnia_and_Herzegovina
Arabic poetry composed between 540 and 620 AD
although it is difficult to assess their authenticity and, compared to epigraphs, are more difficult to date and are subject to later influences of Islamicization
Pre-Islamic_Arabic_poetry
One of the ancient Sanskrit scriptures of Hinduism
states in Europe. A verse in the Upanishad inspired the title and the epigraph of W. Somerset Maugham's 1944 novel The Razor's Edge, later adapted, twice
Katha_Upanishad
EPIGRAPH MATHEMATICS
EPIGRAPH MATHEMATICS
Boy/Male
Australian, Vietnamese
Complete; Mathematics
Boy/Male
Irish
The name is given to boys as a mark of respect to the great Irish orator and patriot Robert Emmet who was a leader of the unsuccessful 1798 rebellion against the British. He was captured on August 25, 1803 and tried for high treason and sentenced to be hanged, drawn and quartered. When asked if he had any thing to say in response to this sentence Emmet gave what is considered to be one of the most moving speeches of the period “â€â€¦When my country takes her place among the nations of the earth, then, and not till then, let my epitaph be written. I have done.â€â€
EPIGRAPH MATHEMATICS
EPIGRAPH MATHEMATICS
Boy/Male
French, German, Latin
Lion
Surname or Lastname
Scottish, English, and German
Scottish, English, and German : nickname for a calm man, from Middle English, Middle High German stille ‘calm’, ‘still’. The German name may also have denoted a (deaf) mute, from the same word in the sense ‘silent’.English : topographic name for someone who lived by a fish trap in a river, from Middle English still, stell ‘fish trap’.German : habitational name from a place so named, in Alsace, near Strasbourg.
Boy/Male
Hindu, Indian, Marathi
Faultless
Boy/Male
African, Arabic, Egyptian, Swahili
Handsome
Girl/Female
Tamil
Arunangi | à®…à®°à¯à®¨à®¾à®¨à®•à¯€
Name of a Raga
Boy/Male
Teutonic Polish
Rules an estate.
Boy/Male
Scottish
Son of the fair born.
Boy/Male
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Gold; Lord Shiva; Silver; Closeness
Girl/Female
Indian
Precious thing, Gem, Princess, Refined, Pure, Exquisite
Surname or Lastname
English (chiefly West Yorkshire)
English (chiefly West Yorkshire) : habitational name from Stead in West Yorkshire, or from some other place taking its name from Old English stede ‘estate’, ‘farm’, ‘place’.English (chiefly West Yorkshire) : from Middle English steed ‘stud horse’, ‘stallion’, applied as a nickname to a lusty person or as an occupational name to someone responsible for looking after stallions.
EPIGRAPH MATHEMATICS
EPIGRAPH MATHEMATICS
EPIGRAPH MATHEMATICS
EPIGRAPH MATHEMATICS
EPIGRAPH MATHEMATICS
n.
Any inscription set upon a building; especially, one which has to do with the building itself, its founding or dedication.
v. t.
To represent by epigrams; to express by epigrams.
n.
The science of inscriptions; the art of engraving inscriptions or of deciphering them.
v. i.
To write or speak after the manner of an epitaph.
n.
A student of, or one versed in, epigraphy.
a.
Pertaining to an epitaph; epitaphian.
n.
A digraph.
v. t.
To commemorate by an epitaph.
n.
Same as Trigraph.
n.
The style of the epigram.
a.
Of or pertaining to epigraphs or to epigraphy; as, an epigraphic style; epigraphical works or studies.
n.
A citation from some author, or a sentence framed for the purpose, placed at the beginning of a work or of its separate divisions; a motto.
n.
An epitaph.
a.
Of or pertaining to a digraph.
n.
Three letters united in pronunciation so as to have but one sound, or to form but one syllable, as -ieu in adieu; a triphthong.
n.
A short poem treating concisely and pointedly of a single thought or event. The modern epigram is so contrived as to surprise the reader with a witticism or ingenious turn of thought, and is often satirical in character.
n.
One who composes epigrams, or makes use of them.
n.
The science or study of epigraphs.