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In

Definitions

  • View of the Oasis Of Wady FeÎkÂn in The Peninsula Of Sinai
    View of the Oasis Of Wady FeÎkÂn in The Peninsula Of Sinai
  • WordNet 3.6
    • adj in currently fashionable "the in thing to do","large shoulder pads are in"
    • adj in directed or bound inward "took the in bus","the in basket"
    • adj in holding office "the in party"
    • adv in to or toward the inside of "come in","smash in the door"
    • n IN a state in midwestern United States
    • n in a unit of length equal to one twelfth of a foot
    • n In a rare soft silvery metallic element; occurs in small quantities in sphalerite
    • ***

Additional illustrations & photos:

242b THE SITTING SCRIBE IN THE GÎZEH MUSEUM 242b THE SITTING SCRIBE IN THE GÎZEH MUSEUM
a View in the FayÛm In The Neighbourhood of The Village of FidemÎn a View in the FayÛm In The Neighbourhood of The Village of FidemÎn
Statue of HarsÛf in the Vienna Museum Statue of HarsÛf in the Vienna Museum
A Scene in Clissold Park A Scene in Clissold Park
"Valeria sleeps in peace." "Valeria sleeps in peace."
In Moor Park In Moor Park
A Street in Oxted A Street in Oxted
Tools used in Logging Tools used in Logging

Webster's Revised Unabridged Dictionary
  • Interesting fact: The longest freshwater shoreline in the world is located in the state of Michigan
    • In A reëntrant angle; a nook or corner. "All the ins and outs of this neighborhood."
    • In Not out; within; inside. In, the preposition, becomes an adverb by omission of its object, leaving it as the representative of an adverbial phrase, the context indicating what the omitted object is; as, he takes in the situation (i. e., he comprehends it in his mind); the Republicans were ini. e.in office); in at one ear and out at the other (i. e.in or into the head); his side was ini. e.in the turn at the bat); he came ini. e., into the house. "Their vacation . . . falls in so pat with ours."
    • In One who is in office; -- the opposite of out.
    • prep In The specific signification of in is situation or place with respect to surrounding, environment, encompassment, etc. It is used with verbs signifying being, resting, or moving within limits, or within circumstances or conditions of any kind conceived of as limiting, confining, or investing, either wholly or in part. In its different applications, it approaches some of the meanings of, and sometimes is interchangeable with, within into on at of, and among.
    • v. t In ĭn To inclose; to take in; to harvest. "He that ears my land spares my team and gives me leave to in the crop."
    • In (Law) With privilege or possession; -- used to denote a holding, possession, or seisin; as, in by descent; in by purchase; in of the seisin of her husband.
    • In With reference to a limit of time; as, in an hour; it happened in the last century; in all my life.
    • In With reference to a whole which includes or comprises the part spoken of; as, the first in his family; the first regiment in the army.
    • In With reference to character, reach, scope, or influence considered as establishing a limitation; as, to be in one's favor.
    • In With reference to circumstances or conditions; as, he is in difficulties; she stood in a blaze of light.
    • In With reference to movement or tendency toward a certain limit or environment; -- sometimes equivalent to into; as, to put seed in the ground; to fall in love; to end in death; to put our trust in God.
    • In With reference to physical surrounding, personal states, etc., abstractly denoted; as, I am in doubt; the room is in darkness; to live in fear.
    • In With reference to space or place; as, he lives in Boston; he traveled in Italy; castles in the air.
    • ***
Century Dictionary and Cyclopedia
  • Interesting fact: The only popcorn museum in the world is lcoated in Marion, Ohio, USA
    • in A word used to express the relation of presence, existence, situation, inclusion, action, etc., within limits, as of place, time, condition, circumstances, etc.
    • in Of place or situation: Within the bounds or limits of; within: as, in the house; in the city; to keep a subject in mind.
    • in Among; in the midst of.
    • in Of time: Of a point of time, or a period taken as a point: At.
    • in Of a course or period of time: Within the limits or duration of; during: as, in the present year; in two hours.
    • in Of a limit of time: At the expiration of: as, a note due in three months.
    • in Of action: Under process of; undergoing the process or running the course of: used especially before verbal nouns proper, or the same used participially.
    • in Of being: Within the power, capacity, or possession of: noting presence within as an inherent quality, distinguishing characteristic, or constituent element or part, or intimacy of relation: as, he has in him the making of a great man; it is not in her to desert him.
    • in Of state, condition, circumstance, or manner: In the condition, state, etc., of: as, in sickness and in health; painted in yellow; in arms (armed); in doubt; in very deed; paper in quires; grain in bulk; the party in power.
    • in Of range, purview, or use: With regard to; within the range of: as, in politics; in theology or philosophy; in botany, etc.
    • in Of number, amount, quantity, etc.: Within the body or whole of; existing or contained in: as, there are ten tens in a hundred; four quarts in a gallon; the good men in a community.
    • in To the amount of; for or to the payment of, absolutely or contingently: as, to amerce, bind, fine, or condemn in a thousand dollars.
    • in Of material, form, method, etc.: Of; made of; consisting of; with: as, a statue in bronze; a worker in metal; to paint in oils; a book written in Latin; a volume in leather or cloth; music in triple time.
    • in Of means or instruments: By means of; with; by; through.
    • in Of cause or occasion: From; because of; on account of; for the sake of: as, to rejoice in an ancient lineage; in the name of God.
    • in Of end: With respect to; as regards; concerning.
    • in Of proportion or partition: From among; out of: as, one in ten.
    • in Of motion or direction: Into: as, to break a thing in two; to put in operation.
    • in Of purpose, intent, or result: For; to; by way of: as, to act in self-defense; in conclusion.
    • in According to: as, in all likelihood.
    • in Occupied with.
    • in On; upon: as, in the whole; in guard: in various archaic uses now more commonly expressed by on.
    • in In law. See the extract.
    • in Having the top carriage run forward to the front end of the chassis: applied to heavy guns in the firing position.
    • in With the name only: said of the indorsement of a bill or note by merely writing one's name on it.
    • in Bound with boards. See board, 11.
    • in In or into some place, position, or state indicated by the context: an elliptical use of the preposition in: as, the master is not in (in the house, or at home); the ship is in (in port); come in (into the room, house, etc.); to keep one's temper in (in restraint, or within bounds).
    • in Inward; coming in, as to a place.
    • in Close; home.
    • in In law, in possession; in enjoyment; invested: used in expressing the nature or the mode of acquiring an estate, or the right upon which a seizin is founded: thus, a tenant is said to be in by the lease of his lessor (that is, his title or estate is derived from the lease).
    • in Nautical, furled or stowed: said of sails.
    • in In advance or in addition; beyond what was the case, was expected, or the like; to the good; thrown in: as, he found himself five dollars in.
    • in Into the bargain: as, ten cents a dozen and one thrown in.
    • in To be or keep on terms of friendship, familiarity, or intimacy with.
    • n in A person in office; specifically, in politics, a member of the party in power.
    • n in A nook or corner; used chiefly in the phrase ins and outs.
    • n in Hence— All the details or intricacies of a matter: as, the ins and outs of a question.
    • in To get in; take or put in; house.
    • in A Latin preposition. cognate with English in. It occurs in many phrases more or less current in English use, as in loco parentis, in absentia, in esse, in posse, in statu quo, etc.
    • n in An obsolete spelling of inn.
    • n in In chem., the symbol for indium.
    • n in An abbreviation of inch or inches.
    • n in A prefix of Anglo-Saxon origin, being the preposition and adverb in so used. It is ultimately identical with in- of Latin origin; but the latter in English apprehension is often unmeaning, while in- always conveys the distinct sense of ‘in’ or ‘into,’ as in inborn, inbred, income, inland, inlet, inmate, inside, insight, insnare, inwrap, etc. In ingot, however, the prefix is unfelt, the word being no longer recognized as a compound. In consequence of its formal and original identity with in-, it may assume the same phases, becoming im- before a labial, as in impark, impen, imbitter, imbody, immesh, immingle, or varying to en-, as in encloud, enfetter, before a labial to em-, as in embed, embody, embitter, etc., the distinction being purely historical and depending on the origin, native or foreign of the primitive. In the etymologies of this dictionary it depends on the origin of the primitive whether the prefix in-, meaning ‘in,’ is marked in- or in-.
    • n in A prefix of Latin origin, being the Latin preposition in so used. It is ultimately identical with in- of English origin, having the same literal sense; but it is often merely intensive, and in many words has in modern apprehension no assignable force. Before a labial in- in later Latin, and hence in Romance, English, etc., becomes im-, as in imbibe, imperil, immanent, etc.; before l it becomes il-, as in illation, illude, illumine, etc.; before r it becomes ir-, as in irradiate, irrigate, etc. In many words derived in fact or form through the French, in- interchanges with or has displaced the earlier English and French en-, the tendency being to use in- whenever there is a corresponding Latin form in in-, as in inclose or enclose, inquire or enquire, etc. See in-, en-, en-. This prefix occurs unfelt, with the accent, as en- in envy.
    • n in A prefix of Latin origin, having a negative or privative force, ‘not, -less, without.’ It is cognate with the English prefix un-, with which it may interchange in English formations: but the rule is to use in- with an obvious Latin primitive and un- with a native or thoroughly naturalized primitive, as in inanimate, incredulous, inaccessible, inequality, as against unliving, unbelieving, unapproachable, unequal, etc. The two forms coexist in inedited, unedited, incautious, uncautious, etc. This prefix in- assumes the same phonetic phases as in-, in-, as in impartial, immense, immeasurable, illiterate, irregular, etc.; it is reduced to i- in ignore, ignorant, etc. It occurs unfelt, with the accent, in enemy, enmity.
    • n in A suffix of Latin (or Greek) origin forming, in Latin, adjectives, and nouns thence derived, from nouns, many of which formations have come into or are imitated in modern Latin and English. The proper English spelling, when the vowel is short, is -in, which was formerly in use, alongside of -ine, in all cases, as in genuin, feminin, etc.; but in present spelling -ine prevails, whether the vowel is short, as in genuine, feminine, masculine, etc., or long as in canine, divine, equine, etc. The form -in occurs in a few words, especially old contracted forms, as matin, a., matins, coffin, cousin, pilgrim (for *pilgrin), alongside of -ine, as in lupin, lupine. In proper names -ine is found, as in Augustine, Collatine, but regularly -in, as iu Augustin, Austin, Calvin, Crispin, Justin, etc.
    • n in A suffix of Latin origin occurring, unfelt in English, in nouns formed as nouns in Latin, as in ravin or raven (doublet rapine), ruin, discipline, doctrine, medicine, etc. It occurs also in its Latin form -ina (which see), and is ultimately identical with -in, -ine.
    • n in A suffix of Latin or Greek origin, ultimately identical with the fem. of the preceding (-in, -ine), occurring as a feminine formative in heroine.
    • n in The same suffix used in a special manner in chemical and mineralogical nomenclature, forming names of some of the elements, as in bromine, chlorin, etc., but usually derivatives, as in glycerin, acetin, etc. In spelling usage wavers between -in and -ine. In this dictionary. in accordance with the proper pronunciation, and with the best recent usage in chemistry, the form -in is generally used in preference to -ine when both forms are in use. In chemistry a certain distinction of use is attempted, basic substances having the termination -ine rather than -in, as aconitine, aniline, etc., and -in being restricted to certain neutral compounds, glycerides, glucosides, and proteids, as albumin, palmitin, etc.; but this distinction is not observed in all cases. In names of minerals -ine is generally used. From its chemical use the suffix has come to be much used in the formation of tradenames, more or less absurd, of proprietary “remedies,” “cures,” soaps, powders, etc.
    • in A simplified spelling of inn.
    • ***
Chambers's Twentieth Century Dictionary
  • Interesting fact: In 1962, the first Wal-Mart opened up in Rogers, Arkansas
    • prep In in denotes presence or situation in place, time, or circumstances—within, during: consisting of: because of: by or through
    • adv In within: not out: in addition to, thrown in
    • n In in politics, a member of the party in office: a corner
    • n In a game with four dice
    • ***

Quotations

  • William R. Alger
    William R. Alger
    “Men often make up in wrath what they want in reason.”
  • Edward G. Bulwer-Lytton
    Edward%20G.%20Bulwer-Lytton
    “In science read the newest works, in literature read the oldest.”
  • Robert Frost
    Robert%20Frost
    “No tears in the writer, no tears in the reader.”
  • Friedrich Nietzsche
    Friedrich%20Nietzsche
    “It is my ambition to say in ten sentences; what others say in a whole book.”
  • Orson Welles
    Orson%20Welles
    “They teach anything in universities today. You can major in mud pies.”
  • Indian Proverb
    Indian Proverb
    “There is nothing noble in being superior to some other person. The true nobility is in being superior to your previous self.”

Idioms

A hitch in your giddy-up - If you have a hitch in your giddy-up, you're not feeling well. ('A hitch in your gittie-up' is also used.)
***
A lost ball in the high weeds - A lost ball in the high weeds is someone who does not know what they are doing, where they are or how to do something.
***
Ace in the hole - An ace in the hole is something other people are not aware of that can be used to your advantage when the time is right.
***
Air your dirty laundry in public - If you air your dirty laundry in public, you reveal aspects of your private life that should really remain private, by telling a secret, arguing in public, etc.
***
All cats are grey in the dark - Things are indistinguishable in the dark so appearances don't matter.('All cats are grey at night' is also used.)
***
All in a day's work - If something is all in a day's work, it is nothing special.
***
All in your head - If something is all in your head, you have imagined it and it is not real.
***
All the tea in China - If someone won't do something for all the tea in China, they won't do it no matter how much money they are offered.
***
All your eggs in one basket - If you put all your eggs in one basket, you risk everything at once, instead of trying to spread the risk. (This is often used as a negative imperative- 'Don't put all your eggs in one basket'. 'Have your eggs in one basket' is also used.)
***
All's fair in love and war - This idiom is used to say that where there is conflict, people can be expected to behave in a more vicious way.
***
Almost only counts in horseshoes and hand grenades - (USA) Used in response to someone saying "almost" in a win/lose situation. The full expression is "Almost only counts in horseshoes and hand grenades." An alternate form puts "and flinging shit from a shovel" at the end.
***
Ants in your pants - If someone has ants in their pants, they are agitated or excited about something and can't keep still.
***
Any port in a storm - This means that in an emergency any solution will do, even one that would normally be unacceptable.
***
Arrow in the quiver - An arrow in the quiver is a strategy or option that could be used to achieve your objective.
***
Babe in arms - A babe in arms is a very young child, or a person who is very young to be holding a position.
***

Etymology

Webster's Revised Unabridged Dictionary
AS. in,; akin to D. & G. in, Icel. ī, Sw. & Dan. i, OIr. & L. in, Gr. 'en. √197. Cf. 1st In- Inn

Usage

In literature:

In 1886 the universal depression, which was first manifest in this Colony in 1884, still continued.
"The Philippine Islands" by John Foreman
She was forward in acquirements, in manner, in general intelligence, and in powers of conversation.
"Orley Farm" by Anthony Trollope
It is higher in the young animal than in the old, and is higher in hot weather than in cold.
"Special Report on Diseases of the Horse" by United States Department of Agriculture
Julyman had missed the latter in his absorbed interest in the return of these folk from Deadwater.
"The Heart of Unaga" by Ridgwell Cullum
For a time he traveled in Italy and in the south of France.
"The History of Sir Richard Calmady" by Lucas Malet
Peace in the in-group.+ Government, law, order, peace, and institutions were developed in the in-group.
"Folkways" by William Graham Sumner
That law acknowledges his property in any sense in which you please to take it, or in any sense in which it is applicable.
"A Report of the Debates and Proceedings in the Secret Sessions of the Conference Convention" by Lucius Eugene Chittenden
At last it was performed in Rouen in 1890, and in November 1892 the Grand Opera in Paris followed suit.
"The Standard Operaglass" by Charles Annesley
In the first place, you won't see me; in the next, if you did, you would feel me as wax in your hands.
"Robert Elsmere" by Mrs. Humphry Ward
He was confined first in the Gate-house, and then in the Tower, in Ralegh's old cell, and in due course was tried.
"Sir Walter Ralegh" by William Stebbing
I've heard they lived in England, in London, in fact, but we knew nothing about them.
"The Day of Judgment" by Joseph Hocking
Should he succeed in killing any, he would bring it in; and should he not, he would return in proper time without it.
"Popular Adventure Tales" by Mayne Reid
There is to be a dinner in the same place, in the same week, to which I have had an invitation with every known name in America appended to it.
"The Life of Charles Dickens, Vol. I-III, Complete" by John Forster
It found pleasure in bathing itself, in dressing itself, in brushing its hair.
"The Creators" by May Sinclair
Those used in the artillery by the men in pulling the gun backwards and forwards in practice and in action.
"The Sailor's Word-Book" by William Henry Smyth
In Kansas such an amendment in 1867 received 9,070 ayes, 19,857 noes; in 1894, 95,302 ayes, 130,139 noes.
"The History of Woman Suffrage, Volume IV" by Various
I store some apples for winter in bulk, in boxes and in barrels in a cellar.
"The Apple" by Various
The book in question, however, was no other than the treatise of Doctor Tilingius upon the rhubarb plant, published in Germany in 1679.
"Toilers of the Sea" by Victor Hugo
In its complete form it appeared in 4 volumes in 1806 and was reprinted in 1809 and 1812.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 6" by Various
Espoused the royal cause in the Revolution; in 1777 a lieutenant in the Loyal Virginians, and in 1782 a captain in the Queen's Rangers.
"The Makers of Canada: Index and Dictionary of Canadian History" by Various
***

In poetry:

In shadow and in sunshine,
In sighing and in song,
May heaven bless your union,
Throughout your whole life long.
"Just Married" by Frank Barbour Coffin
Thy presence in the shade is seen,
As in the sunshine; in a worm,
As in a world; in eve serene,
As in the thunder of the storm.
"Summer: Monday Morning" by John Bowring
In field and hall, in valor and in grace,
In wisdom's livery,
Gentle and brave, he moved with knightly pace,
A worthy son of thee!
"M. W. Ransom" by John Charles McNeill
No change in these; the waves still break
In ripple or in foam upon
The green shore of Saint Mary's Lake
As in the ages dead and gone.
"By Saint Mary's Lake" by Alexander Anderson
Then in the autumn's woe rejoice,--
Rejoice in calm, rejoice in storm;
In either hear God's tender voice,
For both his holy will perform.
"November" by Nancy Rebecca Campbell Glass
In vain that all things changed around,
No change in my own heart was found.
In sad or gay, in dark or fair,
My spirit found a likeness there.
"The Troubadour. Canto 3" by Letitia Elizabeth Landon

In news:

Carlucci's career includes tenures at Riot in Santa Monica, FSM in Sydney, Rumblefish in Milano, and most recently, Fame in Bangkok, where he headed a newly-launched data grading department.
Ivan Mendel ate 10 dumplings in half a minute to win first place and a one-liter jar of sour cream in the contest held in the town of Tokmak in the southeastern Zaporizhya region on September 18, Fakty I Kommentarii newspaper said.
ClassNK, the Japanese-based classification society has opened an office in Durban, Republic of South Africa in response to a significant increase in survey business in the Durban and Richards Bay area.
Founded in 1856, the church building was dedicated in 1858, renovated in 1886, 1901 and 1920, and closed in 1934.
However, there's been another revolution of sorts in the last five years, specifically in industrial manufacturing and in the area of quality control, in particular.
The barefoot running phenomenon has cycled around three times in the past 30 years: once in the 1960s, again in the 1980s and reappearing in the late 2000s.
After four months in a temporary location in Endicott, the Lourdes Owego Family Practice and Walk-In has re-opened on 5th Avenue in Owego.
The defending MLS champion is last in the conference standings, tied for last in the West in wins, has the second-most losses in the league and trails just one other MLS team in goals allowed.
Operations, troubleshooting and even design may require sampling a multiphase stream — ie, a solid in gas, solid in liquid, liquid in gas or liquid in liquid.
In a photo shot from a surveillance video, an unidentified man has a cat in a dog crate in front of Dogtopia in Bayonne.
The party's founding unfolded, amid police harassment, in three acts: the first in a garden house, the second in a cafe, the third in an apartment.
Using a light bulb as his campaign symbol, Kucinich won a seat in the Ohio State Senate in 1994 and then a seat in the US House in 1996.
After back-to-back leads romancing Cate Blanchett in "Elizabeth" and Gwyneth Paltrow in "Shakespeare in Love," Joseph Fiennes was a shoo-in for A-list Hollywood hunkery.
We were seated in a dark subterranean booth at Meridian Pint in Columbia Heights, receiving instructions on how to pour our own beers from two shiny tap handles installed in the table in front of us.
Ingested fat is transported in the blood in the form of triglycerides, whose removal by the muscle is increased in obese compared to healthy individuals, and in parallel with an increase in the uptake of the ingested fat into the muscle.
***

In science:

In the present version 5 of hep-ph/0506298 a bug in the propagated fluxes of antineutrinos from the Sun has been fixed, leading to corrections of the order of 10% in the fluxes presented in Fig. 9 and, as a consequence, in the spectra presented in Figures 10 → 12.
Spectra of neutrinos from dark matter annihilations
It is worth remarking that in the result found for the flux in Eq. (9), the combination R − c′ l enters in the time-dependent correction in the same form as in the steady-state term — that is, the extrapolation-length idea also figures in the asymptotically large-time behavior of the system.
Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap
In addition, there is a long-standing mystery as to why the distribution of RSG spectral subtypes in the MCs is skewed towards earlier types in the MCs (Elias et al. 1985), with the average RSG being K5-K7 in the SMC, M1 in the LMC, and M2 in the Milky Way (Massey & Olsen 2003).
The Effective Temperatures and Physical Properties of Magellanic Cloud Red Supergiants: The Effects of Metallicity
To put this in a more physical way, a star in the same place in the H-R diagram that is called an M2 I in the Milky Way, would be of M1.5 I type in the LMC, and M0 I in the SMC.
The Effective Temperatures and Physical Properties of Magellanic Cloud Red Supergiants: The Effects of Metallicity
Basically, decrease in cluster size can occur as a result of decrease in magnetic correlation length ξ, which in turn implies reduction in MS in the system hence an expected signature is decrease in corresponding absolute value of χ2 .
Direct evidence of random field effect on magnetic ordering of La_(0.5)Gd_(0.2)Sr_(0.3)MnO_(3) manganite system
We distinguish two situations: (1) (α, β ) induces opposite orientations in two of the three intersection points (without loss of generality we can assume that (α, β ) induces opposite orientations in A and in B ), (2) (α, β ) induces the same orientation in A, in B and in C .
Minimal length of two intersecting simple closed geodesics
Just as edge-reinforced random walk on finite graphs, the edge-reinforced random walk on infinite ladders turns out to be equivalent to a random walk in a random environment, as studied in Section 3: In particular, there is an infinitevolume analogue to Theorem 3.3 for the infinite graphs N0 × G and Z × G.
Linearly edge-reinforced random walks
In accordance with the long-time behavior of the random walk itself, in Theorem A, we have the following picture for the behavior of the free energies: in the sub-ballistic regime, the walker remains near the origin in the annealed case and in regions with small potential in the quenched case.
Coincidence of Lyapunov exponents for random walks in weak random potentials
However, in cases where φ extends to a meromorphic function in a larger domain (for example, when φ is rational), we may include such λ too in Λ; this makes no difference in Theorem 3.1. (In Theorem 3.4, we include all roots in the complex plane.) We will use Λ(s) only for s ≥ 0, where there is no ambiguity.
The size of random fragmentation trees
Let ǫn > 0 (in place of δ), Gn (in place of G ) be a finite subset of B (in place of A) and Pn ⊂ K (B ) be required in 5.1 for 1/n (in place of ǫ) and Fn (in place of F ) (and for j in place of h there).
AF-embedding of crossed products of AH-algebras by $\Z$ and asymptotic AF-embedding
We do this by requiring that supp(ηi ) should be supported in the union of Im ψ i and a thin neighbourhood in X of supp(ζi−1 ) in ∂X, and supp(ηj i ) should be supported in the union of V ij and a thin neighbourhood in V j of supp(ζ j−1 i−1 ) in ∂ V j .
Kuranishi homology and Kuranishi cohomology
This bivariant framework is likely to be valuable in situations in which one is forced to work with (co)chains rather than just with (co)homology, for example, in defining A∞ -algebras in Lagrangian Floer cohomology, as in and sketched in §6.6.
Kuranishi homology and Kuranishi cohomology
This is because if d(x, ∞) = ∞ then as flow of v moves at speed at most C then it must take infinite time to reach infinity, and if d(x, ∞) is finite then log d(x, ∞) decreases with speed at most C, so log d(x, ∞) → −∞ in infinite time, and the flow of v takes infinite time to reach infinity in V i .
Kuranishi homology and Kuranishi cohomology
We can now follow the old Steps 4 and 5 to complete the proof. (b) In the proof of Theorem 4.8 we use the fact that R is a Q-algebra in two different ways: firstly, in (260) of Step 2 the |Γac |−1 must lie in R, and secondly, in (272) of Step 4 the |Oa |−1 must lie in R, so for both we need Q ⊆ R.
Kuranishi homology and Kuranishi cohomology
Sc. degrees in astrophysics and experimental physics at the University of Utrecht in the Netherlands in 1991 and 1992, and his Ph.D. degree in astrophysics at Lund University in Sweden in 1998.
Study of the Dynamics of Large Reflector Antennas with Accelerometers
***