Assuming all references are to the same person, as some ( but by no means all ) of the Church fathers did, the earliest reference to him is the canonical Acts of the Apostles, this is his only appearance in the New Testament.

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.

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.

Example: Assuming that is a numeric variable, the assignment means that the content of the variable is doubled after the execution of the statement.

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.

Assuming we connect New York with Los Angeles by means of an electronic telecommunication network that operates in strong transmission ranges, as well as with continental satellites, wave guides, bundled coaxial cable, and later also via laser beam fiber optics: the expenditure would be about the same as for a Moon landing, except that the benefits in term of by-products would be greater.

Assuming that the landowner has correctly identified the host tree ( s ) and symptom ( s ), has submitted a sample to a local authority to send to an approved laboratory for testing, and has received confirmation that the tree ( s ) are indeed infected with P. ramorum — or, alternatively, assuming that the landowner knows that P. ramorum-infected trees are nearby and wants to protect the resources on his or her property — he or she can attempt control by cultural ( individual-tree ), chemical, or silvicultural ( stand-level ) means.

Assuming a completely susceptible population, that means that the basic reproduction number ( R < sub > 0 </ sub >) of the infection must equal 1.

Assuming that the results of c1 () and c2 () are independent, that means that the function as presented above contains a bug.

Assuming each atom liberates its 3 valence electrons, this means that there are 40 electrons present, which is one of the magic numbers noted above for sodium, and implies that these numbers are a reflection of the noble gases.

Assuming a yield for a 10 year-old tree is a reliable conservative estimate, though some exceptional specimens of that age have yielded.

Assuming that the heights are normally ( Gaussian ) distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population.

Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function:

Assuming that one had taken the necessary prerequisite courses, one could complete an OAC course before the OAC year, and so in many schools it was common for Grade 11 or Grade 12 students to have taken some OAC courses.

Assuming that he had been on the continent with the Duke of Bedford, Dunstaple would have been introduced to French fauxbourdon ; borrowing some of the sonorities, he created elegant harmonies in his own music using thirds and sixths.

Assuming an example with a particular property exists, one shows that another exists that is in some sense ' smaller ' as measured by a natural number.

Assuming such a state were to exist at some point, any departure of the diver from its current depth, however small, will alter the pressure exerted on the bubble in the diver due to the change in the weight of the water above it in the vessel.

Assuming that the prophecy took place after Uzziah became sole regent in 768 / 767, Amos's prophecy can be dated to some time after that and some time before Jeroboam's death in 753 BC, with the earthquake two years after that.

Assuming athletic careers are partly based on random factors, attributing this to a " jinx " rather than regression, as some athletes reportedly believed, would be an example of committing the regression fallacy.

Assuming a genetic distance of 2 % in hierofalcons corresponds to a divergence roughly 200, 000-130, 000 years ago, the 0. 6-0. 7 % genetic distance in the Peregine-Barbary Falcon (" peregrinoid ") complex suggests its current taxa evolved in the Late Pleistocene some 100, 000 years ago or less, but before the Upper Paleolithic.

Assuming that Richard A. Locke was the author, his intentions were probably, first, to create a sensational story which would increase sales of the New York Sun, and, second, to ridicule some of the more extravagant astronomical theories that had recently been published.

Assuming for convenience that a is horizontal, corresponding to the angle a with respect to some suitable reference direction, the dividing circle will be in a vertical plane.

Assuming Sharchops still outnumber Ngalops some three to two, the total population is around 212, 500.

Assuming the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius < var > r </ var >, which intercepts some of the power which is spread over the surface of a sphere of radius < var > D </ var >.

Assuming Sharchops still outnumber Ngalops some three to two, the total Ngalop population is around 141, 700.

Assuming one is hired by a company that is fairly well known and established, there would be some type of creative department or management that the director would work with.

Assuming that some nodes in the network have enough memory to know of all nodes in the network, there is no practical limitation to network size.

Assuming that we don ’ t have a commitment to one ' set theory ' ( all toposes are in some sense equally set theories for some intuitionistic logic ) it is possible to state everything relative to some given set theory which acts as a base topos.

→ Assuming for simplicity no technological progress or labor force growth, diminishing returns implies that at some point the amount of new capital produced is only just enough to make up for the amount of existing capital lost due to depreciation.

Assuming there is no future question as to the status of such a species, the absence of a type specimen does not invalidate the name, but it may be necessary in the future to designate a neotype for such a taxon, should any questions arise.

Assuming the source to be " rotationally invariant " ( to produce all possible states λ with equal probability ), the probability of a given type of coincidence will clearly be proportional to the corresponding area, and these areas will vary linearly with the angle between a and b. ( To see this, think of an orange and its segments.

Assuming this crate was the common type, its size would appear to support de Loys ’ measurement of the creature, although others say the crate is only 15 inches tall and the ape would measure under 4 feet-smaller than de Loys ' claims.

Assuming that such constructions ran counter to the traditional Byzantine type, the Patriarch Nikon declared them un-canonical.

Assuming that the underlying field is, the inner product becomes symmetric, and we obtain

Assuming that and have zero expected values, i. e.,, their covariance matrices and can be viewed as Gram matrices in an inner product, see Covariance # Relationship_to_inner_products, for the columns of and, correspondingly.

Assuming the manifold M is smooth, the intersection product is computed by perturbing the homology classes to be transverse and computing their oriented intersection number.

Assuming that is the semidirect product of the normal subgroup K and complement H, then the following restrictions on centralizers are equivalent to G being a Frobenius group with Frobenius complement H:

Assuming a frame with unitary vectors ( X, Y, Z ) as in the main diagram, it can be seen that

It is sometimes called a tickler oscillator because the feedback needed to produce oscillations is provided using a tickler coil ( T in the circuit diagram ) via magnetic coupling between coil L and coil T. Assuming the coupling is weak, but sufficient to sustain oscillation, the frequency is determined primarily by the tank circuit ( L and C in the illustration ) and is approximately given by.

Assuming no loss of time when moving a car from one station to another, the longest stage on the assembly line determines the throughput ( 20 minutes for the engine installation ) so a car can be produced every 20 minutes, once the first car taking 35 minutes has been produced.

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 all the particles start from the origin at the initial time t = 0, the diffusion equation has the solution

Assuming one has overcome the mind's initial flight response in those first torturous minutes, the body fights back by invoking a " blood rush ".

Assuming initially has value, two consecutive evaluations of the expression yield, respectively, and.

Assuming that the display screen has a fixed size, higher magnification results from reducing the size of the raster on the specimen, and vice versa.

Assuming the mark in question meets certain other standards of protectibility, it is protected from infringement on the grounds that other uses might confuse consumers as to the origin or nature of the goods once the mark has been associated with a particular supplier.

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 the woman still has a uterus, menopause is defined as the day after her final episode of menstrual flow finishes.

) Assuming the student has read the case and can articulate the court's argument, the professor then asks whether the student agrees with the argument.

Assuming that the newly found path to that destination has a total distance of 10, the router will transition back to Passive state and update both its RD and FD to the new shortest path length, in this case, 10.

Assuming, the general second-order PDE in two independent variables has the form

Assuming 4 trials, Worm has the nuts 2 times, and has a busted draw 2 times.

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 that has an inverse in a neighbourhood of and that its derivative at that point is non-zero, its inverse is guaranteed to be differentiable at and have a derivative given by the above formula.

Assuming the subject has been under guard, the screener often can get valuable information about the subject's behavior from the guards.

Assuming a trump suit of Hearts in a suit game, this hand will have a different valuation before and after the Skat has been examined.

Assuming that the relic anti-neutrino is at rest, the energy of the incident cosmic neutrino has to be:

Assuming the goal of a system has been articulated and its measurements defined, the steps are:

Assuming something to be true for all numbers when it has been shown for over 906 million cases would not generally be considered hasty, but in mathematics a statement remains a conjecture until it is shown to be universally true.