However, some biological substances commonly called " monosaccharides " do not conform to this formula ( e. g., uronic acids and deoxy-sugars such as fucose ), and there are many chemicals that do conform to this formula but are not considered to be monosaccharides ( e. g., formaldehyde CH < sub > 2 </ sub > O and inositol ( CH < sub > 2 </ sub > O )< sub > 6 </ sub >).

However, a few American businessmen got around the patent by using a slightly different formula.

However, if the sequence itself is definable in the sense that we can specify a single formula for all its terms, then its limit will necessarily be a definable number.

However, the phase of this contribution at any given point along the path is determined by the action along the path ( see Euler's formula ):

However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Legendre canonical forms ( i. e. the elliptic integrals of the first, second and third kind ).

However the definition expressed by this formula is not recursive.

However, the use of Female Gothic and Supernatural Explained, are a “ good example of how the formula novel changes to suit the interests and needs of its current readers ”.

However, suppose that for every formula φ there is some formula ψ taken from a more restricted class of formulas C, such that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable ".

However, Kepler later rejected this formula, because it was not precise enough.

However, the previous formula can still apply by generalizing the definition of x ( F ):

However, when deconstructed, each individual letter may refer to some universal concept found in the system that the formula appears.

However, one can obtain an explicit formula for majority of polynomial size using a sorting network of Ajtai, Komlós, and Szemerédi.

However, a consumer backlash led to Coca-Cola quickly reintroducing the original formula as Coke " Classic ".

However, instead of writing the solution as a pair of numbers, it may be written using the formula

However, the subsequent discovery of the Kuiper belt, and in particular of the object, which is larger than Pluto yet does not fit Bode's law, have further discredited the formula.

However, according to Hofstadter, a formal system will often simply define all of its well-formed formula as theorems.

However it is consistent with ZFC that a definable well-ordering of the reals exists — for example, it is consistent with ZFC that V = L, and it follows from ZFC + V = L that a particular formula well-orders the reals, or indeed any set.

However a more theoretical thermodynamic definition of an ideal solution is one in which the chemical potential of each component is given by the above formula.

However, they can also be thought of as unstable particles, with the formula above valid if the is the decay rate and replaced by the particle's mass M. In that case, the formula comes from the particle's propagator, with its mass replaced by the complex number.

However, according to him, there is less duality, in the sense of opposition, than synthesis ( one is the limit of the other ) and the effort of synthesis is constant according to him, like in his first formula, in which the first member pertains to mechanics and the second to optics:

However, the formula, abstract-negative-concrete, suggests a flaw, or perhaps an incomplete-ness, in any initial thesis — it is too abstract and lacks the negative of trial, error and experience.

However, this formula still provides a good approximation for long thin conductors such as wires.

However, in recent decades, for what doubtless are multiple reasons, an unannounced but nonetheless readily observable shift has occurred in both facets of national activity.

However, for convenience we will stick to the idea that information can be classified according to Table 1.

However, it seems axiomatic that the government has an obligation `` to exercise its mandate reasonably, equitably and with full regard for the disruptions which it inevitably causes ''.

However, the surface temperature gradient can produce erroneous vapor-pressure measurements for the bulk liquid helium unless precautions are taken to isolate the tube ( which passes through the surface to the vapor pressure bulb ) from the liquid helium surface.

However, it determined that neither this factor, nor `` the fact that all concerned in high executive posts in both companies acted honorably and fairly, each in the honest conviction that his actions were in the best interests of his own company and without any design to overreach anyone, including Du Pont's competitors '', outweighed the Government's claim for relief.

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, first I thoughtfully study my sketch for improvement of color and design along the lines I have described.

However while in his cell awaiting trial for theft, Barco, in a fit of apprehension, made an attempt to take his own life.

However one looks at it, therefore, I'd say that your horoscope for this autumn is the reverse of rosy.

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

However, the statistical offices of both governments were assigned responsibility for the planning and analysis of these statistics.

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, if Federal funds are used, it would be entirely appropriate to train workers for jobs which could be obtained elsewhere as well as for jobs in the area of chronic unemployment.

However, as witnessed by the large corporate bond calendar at present, as well as the record amount of municipal bond issues approved by voters, the over-all demands for capital funds seem likely to remain high, so that any downward pressure on rates from reduced demand should not be great.

However, to the extent that the monetary authorities, in their effort to ease credit in the next several months, conduct their open market operations in longer-term Government bonds, they will certainly act to accentuate any tendency for long-term interest rates to ease as a result of market forces.

However, a similar privilege was not specifically provided in section 168 for a person acquiring emergency facilities.

However, as we have seen, in later childhood the child begins to substitute the standards of the peer group for those of parents and teachers.

However, the proposed correlation of the many interrelated properties of crystals will reveal discrepancies in the recorded data and suggest areas for reinvestigation.

However, in the actual assessment of the cutting force by instrumental methods for any thickness of coating a number of spurious effects occur which must be taken into account and which make the measured value larger than the true cutting force indicated by eqn. ( 1 ).

However, electrostatic focus, important for many applications, has not been realized for these devices.

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