However, if the equation were based on the natural numbers for example, some of these operations ( like division and subtraction ) may not be valid as negative numbers and non-whole numbers are not allowed.

However, this equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid.

However a more simple equation relating only the different energies in the fluid, known as Bernoulli's equation can be used.

However, globally human-made pollutants from combustion, construction, mining, agriculture and warfare are increasingly significant in the air pollution equation.

However, Bernoulli's equation states:

However, it is not yet clear what the full field equation will govern the dilaton in higher dimensions.

However, this equation may not be applicable to a comparator circuit which is non-linear and operates open-loop ( no negative feedback ).

However, when he explains in detail what he means, it is clear that he actually believes that his assertion is always true ; for instance, he shows that the equation x < sup > 4 </ sup > = 4x − 3, although incomplete, has four solutions ( counting multiplicities ): 1 ( twice ), − 1 + i √< span style =" text-decoration: overline "> 2 </ span >, and − 1 − i √< span style =" text-decoration: overline "> 2 </ span >.

However, the equation gives no information on the function's dependence on the variable y.

However, when we set corresponding coefficients equal in this case, the equation for x < sup > 3 </ sup > is

However, the Schrödinger equation predicts that there is a small probability that the ball will get to the other side of the hill, even if it has too little energy to reach the top.

However, since the Schrödinger equation is a wave equation, a single particle fired through a double-slit does show this same pattern ( figure on left ).

However, the Schrödinger equation does not directly say what, exactly, the wavefunction is.

However in general, the equation is non-linear, and may lead to chaotic behaviour depending on how sensitive the system is to the initial conditions.

However, because is so much smaller than, the second term on the right in the above equation is small compared to the first, so doesn't have to be determined with high accuracy, and the balancing procedure described above is sufficient to give accurate results.

However, the equation of time can still be calculated for any time of the year, so an analemma can be graphed with this information.

However, the Council for Community and Economic Research ranked Fort Bend County as America's 3rd wealthiest county when the local cost of living was factored into the equation with median household income.

However, iconographically, such an equation is questionable, since what is considered the Classic Maya moon goddess, identifiable through her crescent, is always represented as a fertile young woman.

However, even in this simple example it may be observed that for ( arbitrarily ) small there are four other solutions to the equation ( with very large magnitude ).

However, there remains a further possible source of cancellation when computing and indeed this can lead to up to half of significant figures being lost: to correct for this requires to be computed in extended precision, of twice the precision of the final result ( see quadratic equation for details ).

) However, this was understood ( only ) in the language of equivalence classes of quadratic forms, so that in particular the analogy between quadratic forms and the Fermat equation seems not to have been perceived.

However, power consumption by a chip is given by the equation P = C × V < sup > 2 </ sup > × F, where P is power, C is the capacitance being switched per clock cycle ( proportional to the number of transistors whose inputs change ), V is voltage, and F is the processor frequency ( cycles per second ).

However, only Illinois, Oregon, Louisiana and Rhode Island have a situation in which the sundry units of government vary widely in relation to fiscal uniformity.

However, the possible absence of a center of symmetry not only moves the hydrogen atom off Af, but also allows the oxygen atoms to become nonequivalent, with Af at Af and Af at Af ( space group Af ), where Af represents the oxygens on one side of the Af layers and Af those on the other side.

However, since the pencil contains a secant of **zg it actually contains only Af singular lines.

However, any such suggestion accounts for only some of the difficulties in hearing tone, or in developing a realistic attitude about tone, but not for the analytic difficulties that occur even when tone is meticulously recorded.

However, the teacher can only go so far if the attitude of the community and the family is anti-intellectual.

However, the confession, which was the only evidence against him, was retracted before the trial.

However much we may have to criticize liberal theology's constructive formulations, the theology we ourselves must strive to formulate can only go beyond liberalism, not behind it.

However, this only highlights certain aspects of alchemy.

However, while Apollo has a great number of appellations in Greek myth, only a few occur in Latin literature, chief among them Phoebus ( ; Φοίβος, Phoibos, literally " radiant "), which was very commonly used by both the Greeks and Romans in Apollo's role as the god of light.

However, only a very small percentage of all these people has remained in Angola, either for personal reasons ( intermarriage ) or as professionals ( e. g. medical doctors ).

However, it was held by the Supreme Court that an affidavit can be used as an evidence only if the Court so orders for sufficient reasons.

However, this name is used to refer to the brown vine snake, Ahaetulla pulverulenta, a slender, arboreal species that grows to five feet ( 152 cm ) at most and feeds only on small vertebrates.

However, in digital systems, degradation can not only be detected but corrected as well.

However, the latter figures only represent cash remittances processed through Armenian commercial banks.

However, data from the National Statistical Service shows that there were only 65, 000 foreigners staying in Armenian hotels in 2009.

However, the rail link between Abkhazia and Georgia proper has been closed for a number of years, forcing Armenia to receive rail cars laden with cargo only through the relatively expensive rail-ferry services operating between Georgian and other Black Sea ports.

However, he spends only nine months in jail, during which he writes Mein Kampf.

However, in general, the books only feature mental battles when there is some reason for mind-to-mind contact ( for example, Trump contact ) and magic or Trump is involved in all three of the above conflicts, so it is not clear whether Zelazny intended his characters to have such a power ; the combination of Brand's " living trump " powers and his high Psyche ( as presented in the roleplaying game ) would have guaranteed him victory over Corwin.

However, using pure mass to resist the forces of a storm only works well as a permanent mooring ; a large enough rock would be nearly impossible to move to a new location.

However, tyrannosaurid forelimbs were extremely small for their body size and retained only two digits.

However, Sargon took this process further, conquering many of the surrounding regions to create an empire that reached westward as far as the Mediterranean Sea and perhaps Cyprus ( Kaptara ); northward as far as the mountains ( a later Hittite text asserts he fought the Hattite king Nurdaggal of Burushanda, well into Anatolia ); eastward over Elam ; and as far south as Magan ( Oman ) — a region over which he reigned for purportedly 56 years, though only four " year-names " survive.

However, Wolfram points out that at the time " Clovis got no farther than the Seine ; only after several more years did the Franks succeed in occupying the rest of the Gallo-Roman buffer state north of the Loire.

However, the temple of Ares to which he refers had only been moved from Acharnes and re-sited in the Agora in Augustus's time, and statues known to derive from Alcamenes ' statue show the god in a breastplate, so the identification of Alcamenes ' Ares with the Ares Borghese is not secure.

However, in practice they proved to be too large to manoeuvre well in the close waters of estuaries and rivers, the only places in which a ' naval ' battle could occur.

However, they are only distantly related to the true lily, Lilium.