different between meromorphic vs pole
meromorphic
English
Etymology
mero- +? -morphic
Adjective
meromorphic (not comparable)
- (complex analysis, of a function) That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).
- 1993, Joel L. Schiff, Normal Families, Springer, page 71,
- Normal families of meromorphic functions are most naturally studied using the spherical metric (§1.2), an approach initiated by Ostrowski [1926]. Some results for meromorphic functions, such as the FNT, are immediate extensions from the analytic case, whereas others, such as Landau's or Julia's theorem are set in a much broader context than their analytic counterparts. Normality criteria pertinent to families of meromorphic functions, such as Marty's theorem, have not yet been encountered.
- 2000, Werner Balser, Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations, Springer, page 39,
- Note that such a transformation is holomorphic at the origin, but is essentially singular at infinity. However, since commutes with , the transformed system has coefficient matrix and hence is again meromorphic at infinity.
- 2012, Marius van der Put, Michael F. Singer, Galois Theory of Linear Differential Equations, Springer, page 147,
- A point is singular for if the equation cannot be made regular at with a local meromorphic transformation.
- 1993, Joel L. Schiff, Normal Families, Springer, page 71,
Derived terms
Related terms
- holomorphic
- meromorphism
meromorphic From the web:
- what meromorphic functions
pole
English
Pronunciation
- (UK) IPA(key): /p??l/, /p??l/
- (US, Canada) IPA(key): /po?l/
- IPA(key): [p?o???], [p?o??]
- (US) IPA(key): [p?o???]
- (General Australian) IPA(key): /p??l/
- Rhymes: -??l
- Homophones: Pole, poll
Etymology 1
From Middle English pole, pal, from Old English p?l (“a pole, stake, post; a kind of hoe or spade”), from Proto-Germanic *palaz, *p?laz (“pole”), from Latin p?lus (“stake, pale, prop, stay”) from Old Latin *paxlus, from Proto-Indo-European *peh??- (“to nail, fasten”).
Noun
pole (plural poles)
- Originally, a stick; now specifically, a long and slender piece of metal or (especially) wood, used for various construction or support purposes.
- (fishing) A type of basic fishing rod.
- A long sports implement used for pole-vaulting; now made of glassfiber or carbon fiber, formerly also metal, bamboo and wood have been used.
- (slang, spotting) A telescope used to identify birds, aeroplanes or wildlife.
- (historical) A unit of length, equal to a rod (1?4 chain or 5 1?2 yards).
- (motor racing) Pole position.
- (US, African-American Vernacular, slang) A gun.
- (vulgar) A penis
Synonyms
- See also Thesaurus:stick
- (unit of length): rod
Derived terms
Translations
Verb
pole (third-person singular simple present poles, present participle poling, simple past and past participle poled)
- To propel by pushing with poles, to push with a pole.
- To identify something quite precisely using a telescope.
- (transitive) To furnish with poles for support.
- (transitive) To convey on poles.
- (transitive) To stir, as molten glass, with a pole.
- (transitive, baseball) To strike (the ball) very hard.
Translations
Etymology 2
From Middle French pole, pôle, from Latin polus, from Ancient Greek ????? (pólos, “axis of rotation”).
Noun
pole (plural poles)
- Either of the two points on the earth's surface around which it rotates; also, similar points on any other rotating object.
- A point of magnetic focus, especially each of the two opposing such points of a magnet (designated north and south).
- (geometry) A fixed point relative to other points or lines.
- (electricity) A contact on an electrical device (such as a battery) at which electric current enters or leaves.
- (complex analysis) For a meromorphic function , any point for which as .
- (obsolete) The firmament; the sky.
- 1634, John Milton, Comus, 1817, Paradise Regained... To which is added a complete collection of his miscellaneous poems, page 211,
- And the slope sun his upward beam / Shoots against the dusky pole,
- 1634, John Milton, Comus, 1817, Paradise Regained... To which is added a complete collection of his miscellaneous poems, page 211,
- Either of the states that characterize a bipolar disorder.
Antonyms
- (complex analysis): zero
Derived terms
Translations
Verb
pole (third-person singular simple present poles, present participle poling, simple past and past participle poled)
- (transitive) To induce piezoelectricity in (a substance) by aligning the dipoles.
Anagrams
- LEPO, lope, olpe, pleo-
Aiwoo
Verb
pole
- to work (in a garden or field)
References
- Ross, M. & Næss, Å. (2007) , “An Oceanic origin for Äiwoo, the language of the Reef Islands?”, in Oceanic Linguistics, volume 46, issue 2. Cited in: "Äiwoo" in Greenhill, S.J., Blust, R., & Gray, R.D. (2008). The Austronesian Basic Vocabulary Database: From Bioinformatics to Lexomics. Evolutionary Bioinformatics, 4:271-283.
Alemannic German
Etymology
From Middle High German boln.
Verb
pole
- (Uri) to make noise, clatter, rumble
References
- Abegg, Emil, (1911) Die Mundart von Urseren (Beiträge zur Schweizerdeutschen Grammatik. IV.) [The Dialect of Urseren], Frauenfeld, Switzerland: Huber & Co., page 35.
Czech
Etymology
From Proto-Slavic *po?e.
Pronunciation
- IPA(key): [?pol?]
Noun
pole n
- (agriculture) field
- (physics) field
- (algebra) field
- (computing) field
- (programming) array
Declension
Synonyms
- komutativní t?leso n (algebra)
Further reading
- pole in P?íru?ní slovník jazyka ?eského, 1935–1957
- pole in Slovník spisovného jazyka ?eského, 1960–1971, 1989
Esperanto
Pronunciation
Adverb
pole
- in Polish
Estonian
Etymology
Contraction of ep ole (Modern: ei ole). ep is the old 3rd person singular form of the negative verb.
Verb
pole
- Alternative form of ei ole
Galician
Etymology 1
From Latin pollen.
Noun
pole m (plural poles)
- pollen
- (motor racing) Pole position.
Synonyms
- primeira posición
Etymology 2
See pulir.
Verb
pole
- Third-person singular (el, ela, vostede?) present indicative of pulir
Latin
Noun
pole
- vocative singular of polus
References
- pole in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition, 1883–1887)
- pole in Harry Thurston Peck, editor (1898) Harper's Dictionary of Classical Antiquities, New York: Harper & Brothers
Polish
Etymology
From Proto-Slavic *p??e, from Proto-Indo-European *pleh?- (whence English plain, plane, plan, piano, clan, plant, planet, place, floor, and flake).
Pronunciation
- IPA(key): /?p?.l?/
Noun
pole n (diminutive poletko)
- field (land area; wide open space)
- (regional, singular only) outside
- (geometry) area
- (physics) field
- (computing) field
Declension
Derived terms
- pole namiotowe
- szuka? wiatru w polu
Related terms
- Polska
- English: Poland
Further reading
- pole in Wielki s?ownik j?zyka polskiego, Instytut J?zyka Polskiego PAN
- pole in Polish dictionaries at PWN
Serbo-Croatian
Noun
pole (Cyrillic spelling ????)
- vocative singular of pol
Spanish
Etymology
From English pole.
Noun
pole m (plural poles)
- (motor racing) Pole position
- Synonym: primera posición
Verb
pole
- Informal second-person singular (tú) affirmative imperative form of polir.
- Formal second-person singular (usted) present indicative form of polir.
- Third-person singular (él, ella, also used with usted?) present indicative form of polir.
Swahili
Pronunciation
Interjection
pole (plural poleni)
- sorry
See also
- samahani
Adjective
-pole (declinable)
- calm, gentle
Inflection
Derived terms
- Nominal derivations:
- upole (“gentleness”)
pole From the web:
- what polenta
- what polenta is made of
- what pole are penguins on
- what pole is colder
- what pole are polar bears on
- what polearm for zhongli
- what pole to use for string lights
- what pokemon am i
you may also like
- meromorphic vs pole
- mesomorph vs undefined
- mesomorphy vs mesomorph
- fat vs mesomorph
- muscular vs mesomorph
- mesomorph vs pyknic
- mesomorph vs ectomorph
- mesomorph vs endomorph
- leptosomatic vs leptosomatid
- ecomorph vs ectomorph
- ectomorphy vs ectomorph
- body vs ectomorph
- muscular vs ectomorph
- lean vs ectomorph
- ectomorph vs endomorph
- circuitry vs circuitries
- circuity vs circuitry
- circuitry vs motherboard
- design vs circuitry
- device vs circuitry