Although the law can be used to tell whether any quadratic equation modulo a prime number has a solution, it does not provide any help at all for actually finding the solution.

Although in its basic form radiosity is assumed to have a quadratic increase in computation time with added geometry ( surfaces and patches ), this need not be the case.

Although this notation is compact and convenient for some purposes, the most useful notation is the Legendre symbol, also called the quadratic character, which is defined for all integers a and positive odd prime numbers p as

Although their definition involved a choice of basis and consideration of the corresponding real symmetric matrix A, Sylvester's law of inertia means that they are invariants of the quadratic form q.

Although quickselect is linear-time on average, it can require quadratic time with poor pivot choices ( consider the case of pivoting around the smallest element at each step ).

Although each step is linear in the sampled values and in the position, the interpolation as a whole is not linear but rather quadratic in the sample location ( details below ).

Although quadratic TFRs offer perfect temporal and spectral resolutions simultaneously, the quadratic nature of the transforms creates cross-terms.

Although the derivative of a quadratic function is linear, matrix operations and trigonometric operations make it highly non-linear.

Although the best model adds a quadratic term to defined International Atomic Time, the team encountered problems with this theory.

Although it offered credible 3D performance, its use of quadratic surfaces was anything but popular, and was quite different than typical polygon rendering.

Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity.

Although enzymes can consist of hundreds of amino acids, it is usually only a small fraction of the residues that come in contact with the substrate, and an even smaller fraction — three to four residues on average — that are directly involved in catalysis.

Although initially scheduled for 2008, the reaction looking at the synthesis of evaporation residues has not been conducted to date.

Although the exact mechanism of the event is unknown, key amino acid residues identified include tyrosine at positions 80 and 123, glutamic acid at position 177, and arginine at position 180.

Although this method requires about p modular multiplications, rendering it impractical, theorems about primes and modular residues form the basis of many more practical methods.

Although it makes things tidier, this article does not insist that residues must be coprime to the modulus.

Although the average liver concentrations of polychlorinated biphenyls ( PCBs ) in Eurasian Sparrowhawks were lower in birds that died in 2005 compared to those that died in 2004, there was not a significant or consistent decline in residues between 2000 – 2005.

Although this bird eats rice on the wintering grounds, where it can make up nearly 40 % of its diet, it takes mainly waste and residues from cropping and threshing, not harvestable grain.

Although there is growing concern that hormone residues in meat and milk might be harmful to human and animal health, the quantities of hormones found in a serving of meat are far below the level considered to be a risk to the development of cancer.

Although it is not enzymatically active, it is structurally related to several serine proteases of the coagulation cascade: factors VII, IX, X and protein C. The carboxyglutamate residues ( which require vitamin K ) bind protein Z to phospholipid surfaces.

Although vinclozolin is not registered for use by homeowners, it is still possible for people to come in to contact with the fungicide and its residues.

Although crop residues contain both macro-and micronutrients,

Although these disease residues would persist for a few months, tungiasis is no longer present.

Although he uses the terms interchangeably, remarks that, for example, the final glides of English par and buy differ from French par (' through ') and baille (' tub ') in that, in the latter pair, the approximants appear in the syllable coda, whereas, in the former, they appear in the syllable nucleus.

Although officially declassified, the original film taken by U. S. Corona spy satellite in the 1960s has been altered prior to declassification ; in answer to freedom of information queries, the government responds that these exposures ( which map to Groom and the entire NAFR ) appear to have been destroyed .< ref >

Although the permanency of acrylics is sometimes debated by conservators, they appear more stable than oil paints.

Although the butterfly effect may appear to be an esoteric and unlikely behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill may roll into any of several valleys depending on, among other things, slight differences in initial position.

Although possibly Celtic-speaking in 179 BC, the Bastarnae probably were Germanic in language and culture during the 1st century AD, but appear to have become assimilated by their neighbouring Sarmatians by the 3rd century.

Although his name does not appear in any other part of the Jewish Bible, Rabbinic tradition holds Habakkuk to be the Shunammite woman's son, who was restored to life by Elisha in 2 Kings 4: 16.

Although there is no proof, the name " Thomas Corbett " does appear on the list of dead and missing.

Although dream sleep and non-dream sleep appear very similar to an outside observer, each is associated with a distinct pattern of brain activity, metabolic activity, and eye movement ; each is also associated with a distinct pattern of experience and cognition.

Although a coma patient may appear to be awake, they are unable to consciously feel, speak, hear, or move.

Although privacy-advocates have questioned such methods, they appear to serve the interests of the organisations using them.

Although especially common in stories told by southwestern Native American nations, such as the Diné and Apache, stories about Coyote appear in dozens of Native American nations from Canada to Mexico.

Although Triatominae bugs feed on them, birds appear to be immune to infection and therefore are not considered to be a T. cruzi reservoir.

Although many psychologists believe that the entire brain is involved with memory, the hippocampus and surrounding structures appear to be most important in declarative memory specifically.

Although its decisions are accepted by all Christians, and still observed in full by the Greek Orthodox, and later definitions of an ecumenical council appear to conform to this sole biblical Council, no Christian church calls it a mere ecumenical council, instead it is called the " Apostolic Council " or " Council of Jerusalem ".

Although perennialism may appear similar to essentialism, perennialism focuses first on personal development, while essentialism focuses first on essential skills.

Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force.

Although verse 7 does not appear in any version of the Greek text prior to the ninth century, it appears in most of the Latin manscripts, especially in the Vetus Itala ( Old Latin predating Jerome ).

Although a male deity existed as well, “… statues of a female deity far outnumber those of the male deity, who moreover, does not appear to be represented at all after Level VI ”.

Although theoretically a significant blow to John's legitimacy, this did not appear to greatly worry the king.

Although Luthor would not appear until two years after Superman's debut, a central theme to his character — a dichotomy of science versus superpowers — was in place.

Although they reign under constitutions, the monarchs of Brunei, Oman, Qatar, Saudi Arabia and Swaziland appear to continue to exercise more political influence than any other single source of authority in their nations, either by constitutional mandate or by tradition.

Although he conducted some of his studies using vivisection and others through the dissection of corpses, his most illustrative efforts appear to have been based on the use of the microscope.

Although outwardly masts may appear irrational or even insane, Baba indicated that their spiritual status was actually quite elevated, and that by meeting with them he helped them to move forward spiritually while enlisting their aid in his spiritual work.

Although there exist occasional reports of opposition to the government, these appear to be isolated, and there is no evidence of major internal threats to the current regime.