Any prime p ≡ 1 mod 4 splits into two distinct prime ideals in Z ; this is a manifestation of Fermat's theorem on sums of two squares.

Any two Ford circles are congruent in hyperbolic geometry.

Any finite set of lines in the Euclidean plane has a combinatorially equivalent arrangement in the hyperbolic plane ( e. g. by enclosing the vertices of the arrangement by a large circle and interpreting the interior of the circle as a Klein model of the hyperbolic plane ).

* The quasi-isometry classification of rank one lattices: Any quasi-isometry of a hyperbolic lattice is equivalent to a commensurator.

Any other cost price would yield an arbitrage opportunity and riskless profit ( see rational pricing for the arbitrage mechanics ).

Any discrepancy that may exist in pricing perfectly tradable goods because of foreign exchange market movements, for instance, is called an arbitrage opportunity.

He merely said, `` Any good decorator these days can make you a tasteful home ''.

Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any free elections that were to be held in Poland would have to produce a government in which Moscow had complete confidence, and all pressure from the West for free voting by anti-Soviet elements in Poland would be met by restrictions on voting by these elements.

Any shareholder of any of these funds who finds a mistake in his account certainly should get in touch with the bank.

Any little dose of radiation might knock off these critters ''.

Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.

Any of these body styles can optionally incorporate a " cutaway ".

Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical ( i. e. non-quantum ) mechanics.

Any of these may be sources of essential amino acids.

Any of these ways can be criticized for ...

Any of these reactions may be used in LPCVD, but the silane reaction is also done in APCVD.

Any trade in these species requires export and import permits.

# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.

Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.

Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.

Any theory in which these principles apply produces the inequalities.

Any of these may hurt the handler or bystanders through burning or impact damage.

Any list of these would have to include the Night of the Living Houses ( said to be the first comic strip to enter the collection of the Louvre ) wherein Nemo and a friend are chased down a city street by a gang of tenement houses on legs ; the Walking Bed, in which Nemo and Flip ride over the rooftops on the increasingly long limbs of Nemo's bed ( see illustration ); and the Befuddle Hall sequence, wherein Nemo and his friends attempt to find their way out of a funhouse environment of a Beaux-Arts interior turned topsy-turvy.

Any number of these monomer units may be indicated by the appropriate Greek prefix ; e. g. a decamer is formed from 10 monomers.

Any of these properties can be modified in accordance with a low frequency signal to obtain the modulated signal.

Any communication to another system in the galaxy has to be recorded on a physical disc which is transported through the wormhole ; chains of these are referenced in Diplomatic Immunity ( Chapter 9 ) where messages are ' squirted ' to a station on one side of a wormhole, flown ( on a physical medium ) through the wormhole and re-squirted to a similar arrangement at the next wormhole in the sequence.

Any of these changes might have an effect that is highly advantageous or highly disadvantageous, but large effects are very rare.

Any racial elements from these influences have not remained part of the Anthroposophical Society as contemporary adherents of the society have either not adopted or repudiated these beliefs.

Any of these causes is linked with an increase in the risk of thrombosis.

Any measures derogating from obligations under the Covenant, however, must only be to the extent required by the exigencies of the situation, and must be announced by the State Party to the Secretary-General of the United Nations.

Any rights or obligations arising from the vocals created by the software belong to the software user.

Any posse riding down the street to demand Blue Throat's surrender would be wiped out with one deadly burst of fire.

Any retaliatory gas attack would be airborne.

Any other reaction would have been reported instantly.

" Any threat of war Clovis could make would only be effective if they were neighbors ; " it is nowhere written that Syagrius was handed over in 486 or 487.

Jo Walton wrote: " Any one of the ideas in A Fire Upon the Deep would have kept an ordinary writer going for years.

Any form of intelligent life would do ; so, specifying carbon-based life, per se, is irrelevant.

Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.

Any civilian caught participating in cannibalism would have been immediately executed.

Any other craters that might have formed in the Tethys Ocean would have been obscured by tectonic events like the relentless northward drift of Africa and India.

Any new flag would also quickly become unlawful, due to wear and tear.

Note: Any nonlinear electronic block driven by two signals with frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub > would generate intermodulation ( mixing ) products.

# Any player who would qualify from the Interzonal to play in the Candidates but who was excluded because of a limitation on the number of participants from his Federation.

Any slight deformation in the antique telescopic lenses would lead to a dramatic decrease in optical performance, a phenomenon that is not observed.

Any given individual or organization attempting to implement this model in a real situation would be unable to comply with the three requirements.

Any foreigners who came to Paraguay during his rule ( which would have been very difficult ) were not allowed to leave for the rest of their life.

Any customer who opted to keep theirs was required to sign a waiver indicating their understanding that no more software would be written for the system and which absolved Intellivision of any future responsibility for technical support.

" Any attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre.

Any overbid or underbid loses the number of points their bid was off ( a player bidding 3 tricks that wins only 2 would lose a point, as would a player bidding 2 and winning 3 ).

Any agency wanting to read PGP messages would probably use easier means than standard cryptanalysis, e. g. rubber-hose cryptanalysis or black-bag cryptanalysis i. e. installing some form of trojan horse or keystroke logging software / hardware on the target computer to capture encrypted keyrings and their passwords.

Any damages would then be divided according to the market share ratio.

Any invader penetrating the destroyer and frigate protection would have been swarmed by almost 900 fast-attack craft.