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, 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, this equation only applies if the source resistance cannot be adjusted, e. g., with antennas ( see the first line in the proof stating " fixed source resistance ").

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, for most alloys there is a particular proportion of constituents ( in rare cases two )— the eutectic mixture — which gives the alloy a unique melting point.

However, Odysseus proves to be more eloquent, and the council gives him the armor.

However, the relatively high altitude of the country and its continental situation gives it a subtropical climate.

However, another interpretation is that Job's silence is defiant, and that what he gives up is not his belief that justice be done, but his confidence that God will behave justly.

However, custom gives the legislation little strength and all graduates keep their titles, and those with a doctorate are referred as Professor Doutor.

However, that would convey the idea of the physical body of people, whereas using the name of the language as the basis of the word gives it the more abstract connotation of a cultural sphere.

" However, in his review for the Chicago Reader, Dave Kehr, wrote " it fails to satisfy – it gives us too little of too much.

However, when he sees Achilles he is seized by fear, and turns to flee, as Achilles gives chase to him three times around the city.

However, modern technology gives pilots the ability to soar for hours, gain thousands of metres of altitude in thermal updrafts, perform aerobatics, and glide cross-country for hundreds of kilometres.

However, slightly leaning the blade over and digging one of its edges into the ice (" rock over and bite ") gives skaters the ability to increase friction and control their movement at will.

) However, the fundamental theorem of arithmetic gives no insight into how to obtain an integer's prime factorization ; it only guarantees its existence.

However, any inclusion of lead or lead solder will cause an English Assay office ( the building which gives English jewellery its stamp of approval, the Hallmark ) to destroy the piece.

However, every experiment to date has shown these values to be proportional, and this proportionality gives rise to the abstract concept of mass.

However, it was also argued that muscular tension resulting from holding down buttons could be exploited in user interface design as it gives constant feedback that the user is in a temporary state, or mode ( Buxton, 1995 ).

However each of these two configurations in fact gives rise to a set of states at different energies.

However, in the real world, many bodies rotate, and this introduces oblateness and distorts the gravity field, and gives a quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body.

However, while riding on horseback she gives birth, thus exposing her gender.

However, this distribution of meanings between the two terms used to be precisely inverse at the time they were coined: The Oxford English Dictionary defined “ racialism ” as “ belief in the superiority of a particular race ” and gives a 1907 quote as the first recorded use.

However, having four bonding electrons gives it, like carbon, many opportunities to combine with other elements or compounds under the right circumstances.

However the Oxford English Dictionary gives this etymology " no claim to consideration ".

However, the New American Standard Bible gives, " Also to Shem, the father of all the children of Eber, and the older brother of Japheth, children were born.

However, he knows that he has been seen and so leaves, on pretense of finishing a task, and gives the key to his room to the abbot, who then goes to see the girl for himself.

However, an Icelandic law text gives a very specific explanation of " eykt ", with reference to Norse navigation techniques.

However, Pausanias gives another place called " Museum ," namely a small hill in Classical Athens opposite the Akropolis.

However, the fact that Melbourne is significantly closer than Sydney and the fact that Victorian television broadcasts in the region, resulting ( among other things ) in the predominance of Australian rules football in the local media outlets, gives Albury close cultural and psychological links to Victoria, despite its location in southern New South Wales.