Assuming that the quantum particle started in orbit number n, emitted a photon, then ended up in orbit number m, the energy of the photon is E < sub > n </ sub > − E < sub > m </ sub >, which means that its frequency is.

Average growth approximation: Assuming that two stocks have the same earnings growth, the one with a lower P / E is a better value.

Assuming E

Assuming the energy required scales with the mass of the fusion plasma ( E < sub > laser </ sub > ~ ρR < sup > 3 </ sup > ~ ρ < sup >- 2 </ sup >), compressing the fuel to 10 < sup > 3 </ sup > or 10 < sup > 4 </ sup > times solid density would reduce the energy required by a factor of 10 < sup > 6 </ sup > or 10 < sup > 8 </ sup >, bringing it into a realistic range.

Assuming that the system is symmetrical in the x and y directions ( around and along the axon, respectively ), only the z direction need be considered ; thus, the voltage E < sub > m </ sub > is the integral of the z component of the electric field across the membrane.

Assuming the lower figure for the big blast and one shot estimated by the Japanese at 10 megatons, a conservative computation is that the 24 announced tests produced a total yield of at least 60 megatons.

Assuming the weather is halfway decent that day, hundreds of thousands of persons will mass along this thoroughfare as President John F. Kennedy and retiring President Dwight D. Eisenhower leave Capitol Hill following the oath-taking ceremonies and ride down this historic ceremonial route.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

Assuming that the pixel color is expressed using straight ( non-premultiplied ) RGBA tuples, a pixel value of ( 0. 0, 0. 5, 0. 0, 0. 5 ) implies a pixel which has 50 % of the maximum green intensity and 50 % opacity.

Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.

Assuming that 10 – 15 % of bread is thrown away as stale, if it could be made to stay fresh another 5 – 7 days then perhaps 2 million tons of flour per year would be saved.

Assuming average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.

Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

:< u > The Copenhagen Interpretation </ u >: Assuming wave functions are not real, wave-function collapse is interpreted subjectively.

Assuming the Axiom of choice, is regular for each α.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

Assuming that the rule is known, one can derive the function that is used above in the classical heat calculation with respect to pressure.

Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.

Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.

Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this.

Assuming a specific Nazi usage of the term " Vaterland " ( which in fact never existed ), the direct English translation " fatherland " featured in news reports associated with Nazi Germany and in domestic anti-Nazi propaganda during World War II.

Assuming office in 1770, he had a controversial career during which land title disputes and factional conflict slowed the initial attempts to populate and develop the island under a feudal system.

Assuming both sidebands are symmetric, which is the case for a normal AM signal, no information is lost in the process.

Assuming that it is possible to distinguish an observation corresponding to one of the discrete probability masses from one which corresponds to the density component, the likelihood function for an observation from the continuous component can be dealt with as above by setting the interval length short enough to exclude any of the discrete masses.

Assuming the gamma-ray explosion to be spherical, the energy output of GRB 080319B would be within a factor of two of the rest-mass energy of the Sun ( the energy which would be released were the Sun to be converted entirely into radiation ).

Assuming a Unix-style scenario in which one machine ( the client ) requires access to data stored on another machine ( the NFS server ):

Assuming that the Earth is a uniform sphere ( which is not correct, but is close enough to get an order-of-magnitude estimate ) with M

Assuming that the radius of the star does not change over this interval, the long term variation in activity level appears to produce a temperature variation of 15 K, which corresponds to a variation in visual magnitude ( V ) of 0. 014.

Assuming each character equals one byte, there are about 2 < sup > 320 </ sup > such passwords, which is about 2 × 10 < sup > 96 </ sup >.

Assuming a modern PC could output 1 billion strings per second, it would take one billionth of 2 × 10 < sup > 96 </ sup > seconds, or 2 × 10 < sup > 87 </ sup > seconds to complete its task, which is about 6 × 10 < sup > 79 </ sup > years.

If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group, which means that if we test all a from a set which generates, one of them must be a witness for the compositeness of n. Assuming the truth of the generalized Riemann hypothesis ( GRH ), it is known that the group is generated by its elements smaller than O (( log n )< sup > 2 </ sup >), which was already noted by Miller.

Assuming that the scene contains objects which reflect all red light, and ( other ) objects which reflect all green light and still others which reflect all blue light, one can then deduce that the illuminating light source is described by ( r < sub > max </ sub >, g < sub > max </ sub >, b < sub > max </ sub >).

Assuming the validity of Bell's theorem, any deterministic hidden-variable theory which is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster-than-light relations ( correlations ) between physically separated entities.

Assuming the fulfillment of certain technical criteria ( such as the sentencing of the accused whose punishment was not yet executed ), wherever it is possible to punish the conspirators with exactly the same punishment through which they had planned to harm their fellow, the court carries out this direct reciprocal justice ( including when the punishment constitutes the death penalty ).

Assuming that the northern part of M82 is nearer to us, which most literature assumes, the observed sense of rotation implies trailing arms.

Assuming you have Verdana version 5. 01 installed, which supports the locl feature for the latn / ROM ( Romanian ) script, a quick demonstration ( on Linux ) is:

Assuming dark energy remains constant ( an unchanging cosmological constant ), so that the expansion rate of the universe continues to accelerate, there is a " future visibility limit " beyond which objects will never enter our observable universe at any time in the infinite future, because light emitted by objects outside that limit can never reach points that expand away from us at less than the speed of light.

Assuming a court finds no contract, tax-payer is only liable for the fair market value of tax preparation services, which is not inflated up to account for the unusually large refund he enjoyed.

Assuming perfect combustion conditions, such as complete combustion under adiabatic conditions ( i. e., no heat loss or gain ), the adiabatic combustion temperature can be determined.

( Assuming the axiom of choice ), the following are equivalent.

Assuming Ignatius ' view was the Apostolic teaching and practice, the line of succession was unbroken and passed through the four ancient Patriarchal sees ( those local churches known to be founded by apostles ), Rome, Jerusalem, Antioch and Alexandria.

), the total human biomass is the average weight multiplied by the current human population of approximately 6. 5 billion ( see, e. g., ): Assuming 60 – 70 kg to be the average human mass ( approximately 130 – 150 lb on the average ), an approximation of total global human mass of between 390 billion ( 390 × 10 < sup > 9 </ sup >) and 455 billion kg ( between 845 billion and 975 billion lb, or about 423 million – 488 million short tons ).

For instance, raising the note B to B is equal to the note C. Assuming all such equivalences, the complete chromatic scale adds five additional pitch classes to the original seven lettered notes for a total of 12 ( the 13th note completing the octave ), each separated by a half-step.

Assuming that a TNT explosion releases 1, 000 small ( thermochemical ) calories per gram ( 4. 2 kJ / g ), one tonne of TNT is equivalent to 4. 2 gigajoules.

* Assuming that the Atlantic multidecadal oscillation runs through a 70-year quasi-cycle ( after peaks in ≈ 1880 and ≈ 1950 ), its current warm phase is likely to peak during this decade.

Assuming a full-scale sine wave signal ( that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal ), the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level and uniform distribution.

Assuming opener bids 1 and partner responds 2 ; opener will know from this bid that partner has 9 losers ( using basic LTC ), if opener has 5 losers rather than the systemically assumed 7, then the calculation changes to ( 5 + 9

Assuming that the transcriptions are not intended to be precise, only 11 of the 26 — Bravo, Echo, Hotel, Juliet ( t ), Kilo, Mike, Papa, Quebec, Romeo, Whiskey, and Zulu — are given English pronunciations by all these agencies, though not always the same English pronunciations.

Assuming that birthdays are equally likely to happen on each of the 365 days of the year, the probability, P ( 2 ), that Person 2 has a different birthday than Person 1 is 364 / 365.

Assuming zero empirical mean ( the empirical mean of the distribution has been subtracted from the data set ), the principal component w < sub > 1 </ sub > of a data set X can be defined as:

Assuming the identity of " John Smith " ( the English equivalent of his natural German name ), Skull decided that he would reinvent himself and his quest for absolute power as a means to celebrate his cheating death.

Assuming the responsibility of mediator between the two sides, and with Erasmus ' willing participation ( the robot being left as the leader and controlling-force of the thinking machines ), Duncan does something similar to Bene-Gesserit Sharing with the robot ; possibly along with what seems to be a physical-bonding ( similar to what Leto II did with the sandtrout ) into something of a human-machine hybrid.

Assuming the material expands with temperature ( enriched Uranium-235 at room temperature for example ), at an exactly critical state, it will become subcritical if warmed to lower density or become supercritical if cooled to higher density.

Assuming all of the voters vote sincerely ( strategic voting is discussed below ), the results would be as follows, by percentage:

Assuming the medium is linear, isotropic, and homogeneous ( see polarization density ), we have the constitutive equation:

Assuming further for simplicity ( all arrows are lost after just one shot, so that they are circulating capital ), the absolute competitive prices of beavers and deer become:

Assuming the title of samdech ( prince ), Sihanouk explained that this action was necessary in order to give him a free hand to engage in politics.

* Assuming the shadow position ( with any handhold ), the leader leads the follower into chicken walks.