However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

However, a common and well-accepted metric is the half power points ( i. e. frequency where the power goes down by half its peak value ) on the output vs. frequency curve.

However, a turbine's power output and efficiency both drop dramatically with rotational speed, unlike a piston engine, which has a comparatively flat power curve.

However, it moves so quickly that the central body will curve away beneath it.

However, the net effect of entry by new firms and adjustment by existing firms will be to shift the supply curve outward.

However, it is possible to find round-shaped electric stove elements that will fit the curve of a wok, which allows the wok to be heated at its bottom along with part of its sides.

However, later it was shown that such model of closed timelike curve can have internal inconsistencies as it will lead to strange phenomena like distinguishing non orthogonal quantum states and distinguishing proper and improper mixture.

However, as the weight of the curve adds 12 dB of gain to the critical midband, making THD + N measurements bigger, manufacturers object to its use and have widely prevented its adoption in American and Asian markets.

However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of the dynamic, small-signal, or incremental resistance, defined as the one over the slope of the V – I curve at the average value ( DC operating point ) of the voltage ( that is, one over the derivative of current with respect to voltage ).

However, the work was completed before the appearance of the ogee curve, an S-shaped double curve which was extensively used at the end of this period.

However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.

However, for a time the Comford and High Peak Railway did have the sharpest curve out of all railways in Britain and the steepest incline for vehicles without steam power.

However, this brace is not available for all curve patterns.

However, positional accuracy could usually be computed to within 100-meters for a slow-moving ship, even with reception of just one two-minute Doppler curve.

However, the total area under the curve y = 1 / x from 1 to infinity is given by an improper integral:

) However, this bound is small enough that any single odd number below the bound can be verified by existing primality tests such as elliptic curve primality proving, which generates a proof of primality and has been used on numbers with as many as 26, 643 digits.

However, the cross-flow turbine has a flat efficiency curve under varying load.

However, Phillips ' original curve described the behavior of money wages.

However, according to the NAIRU, exploiting this short-run tradeoff will raise inflation expectations, shifting the short-run curve rightward to the " New Short-Run Phillips Curve " and moving the point of equilibrium from B to C. Thus the reduction in unemployment below the " Natural Rate " will be temporary, and lead only to higher inflation in the long run.

However, if gcd ( v, n ) is neither 1 nor n, then the-addition will not produce a meaningful point on the curve, which shows that our elliptic curve is not a group ( mod n ), but, more importantly for now, gcd ( v, n ) is a non-trivial factor of n.

However, considering the same curve and operation over /~ with not a prime does not give a group.

However, wherever a minimum occurs in the dispersion relation, the minimum can be approximated by a quadratic curve in the small region around that minimum, for example:

However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist.

However, his subject matter and basic themes have remained surprisingly consistent, and these, together with certain key poetic images, may be traced through all his work, including the new jazz experiments.

However, a narrow strip may be very practical for small developments, or to provide additional stream frontage for a fisherman's trail, or include scenic strips within the park unit.

However, Af adsorbs water from the atmosphere and this may account for the low chromium analysis and high total weight loss.

However, the dynamics of airflow, from morphologic considerations alone, may conceivably be different in the monkey than in the horse.

However, because of Church laws, lately more stringently enforced, which forbid the marriage of cousins closely related consanguineously, a means of facilitating the goal of in-group relations may be that of recourse to illegitimate unions.

However, the teacher who understands the influence of emotions on behavior may be highly influential in helping pupils gain confidence, security, and satisfaction.

However that may be, people are known to go to mediums for diverse reasons.

However, by cultivating a wine dealer and accepting his advice, one will soon enough ascertain whether he has any knowledge of wines ( as opposed to what he may have been told by salesmen and promoters ) and, better yet, whether he has a taste for wine.

However needed this may be, the fundamental problem is not information but active commitment to the total mission of the church of Christ in the world.

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 story may reflect a cultural influence which had the reverse direction: Hittite cuneiform texts mention a Minor Asian god called Appaliunas or Apalunas in connection with the city of Wilusa attested in Hittite inscriptions, which is now generally regarded as being identical with the Greek Ilion by most scholars.

However, certain critical interlocutory court orders, such as the denial of a request for an interim injunction, or an order holding a person in contempt of court, can be appealed immediately although the case may otherwise not have been fully disposed of.

However, appeals may be costly, and the appellate court must find an error on the part of the court below that justifies upsetting the verdict.

However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand.

Experiments have been conducted to attempt the synthesis of ununennium ( Uue ), which is likely to be the next member of the group, but they have all met with failure .< ref name =" link "> However, ununennium may not be an alkali metal due to relativistic effects, which are predicted to have a large influence on the chemical properties of superheavy elements.

However, actual rainfall from year to year is irregular and occasionally may be less than, leading to severe reductions in crop yields for both rain-fed and irrigated agriculture.

However, some experimental evidence suggests astatine may have lower melting and boiling points than those implied by the halogen trend.

However, when anxiety becomes overwhelming, it may fall under the classification of an anxiety disorder.

However, there is no evidence to support this practice and it may in fact delay healing.

However other process philosophers such as David Ray Griffin have written that people may have subjective experience after death.

However, if the excited atom has been previously ionized, in particular if one of its inner shell electrons has been removed, a phenomenon known as the Auger effect may take place where the quantity of energy is transferred to one of the bound electrons causing it to go into the continuum.

But on meeting Mackenzie, Dufferin revised his opinions: " However narrow and inexperienced Mackenzie may be, I imagine he is a thoroughly upright, well-principled, and well-meaning man.

However, there are certain limitations: they may not administer the sacraments and related functions whose celebration is reserved to bishops, priests, deacons, or seminarians ( the male clergy ), namely, Holy Orders ( they may make provision for an ordained cleric to help train and to admit some of their members, if needed, as altar servers, Eucharistic ministers, or lectors-the minor ministries which are now open to the non-ordained ).

However, in the Coulomb field of a nucleus the translational invariance is broken and single-photon annihilation may occur.