Assuming that there are not multiple non-trivial roots of we have the " exact formula " by the residue theorem:

Assuming that f '( x ) < 0, there are no distinct roots.

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 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.

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

Assuming now without loss of generality that P is the origin, take a smooth bump function h with value 1 on the interval and quickly tending to 0 outside it.

Assuming process P in the KPN above is constructed so that it first reads data from channel A, then channel B, computes something and then writes data to channel C, the execution model of the process can be modeled with the Petri net shown on the right.

Assuming now that light travels along the x < sub > 3 </ sub > axis, the path of a light ray may be parametrized as and

Assuming a function that is defined where, form the definite integral from 0 to x.

Assuming y ≤ x, the result will always be greater or equal to and dropping the initial ' 1 ' is the same as subtracting, making the result or just, the desired result.

Assuming there exists an eigenpair ( λ, y ) for A, such that vector y is positive, and given ( r, x ), where x-is the right Perron-Frobenius eigenvector for A ( i. e. eigenvector for A < sup > t </ sup >), then

Assuming both the hydraulic conductivity and the horizontal components of flow are uniform along the entire saturated thickness of the aquifer ( i. e., and ), we can express Darcy's law in terms of integrated discharges, Q < sub > x </ sub > and Q < sub > y </ sub >:

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.

NOTE: Assuming a resonance equation of F = 1 /( 2 x Pi x sqrt ( L x C ) ) I believe the above math needs reviewed.

Assuming an adjustment to the July 1 to June 30 fiscal year, the required adjustment of the tax collection years and the towns involved are shown in Table 3.

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

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

Assuming that 100 engineers are needed to design a CPU and the project takes 4 years.

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 the above are done one after another, minimum plane turnaround time is:

Assuming that the six factors are present and Miranda applies, the statement will be subject to suppression unless the prosecution can demonstrate

Assuming that the six factors are present, the Miranda rule would apply unless the prosecution can establish that the statement falls within an exception to the Miranda rule.

Assuming that a Miranda violation occurred — the six factors are present and no exception applies — the statement will be subject to suppression under the Miranda exclusionary rule.

Assuming hydrogen and oxygen are standard weights in this image ( as opposed to deuterium oxide ) the molecular mass should be 18. 01528 u.

Assuming there are no complications, the remaining portion of the first day's dose is then given.

Assuming that the leaders in the social hierarchy are perfectly conformed to the ruler, who is perfectly submissive to Heaven, conformity in speech and behaviour is expected of all people.

Assuming enharmonicity, many accidentals will create equivalences between pitches that are written differently.

Assuming that Ictis, Mictis and Corbulo are the same, Diodorus appears to have read Timaeus, who must have read Pytheas, whom Polybius also read.

* Assuming that an individual had no choice in who, when and where to come into being: How are the choices of existence determined by what he is?

* Assuming that not all possible choices are available to him: How capable is the individual to desire all choices available, in order to choose from among them?

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

Assuming Chavez was approximately 10 years old in 1979, that places the events of Debt of Honor to be in or near 2000, although the overall technology presented in the novel and its successive novels Executive Orders and Rainbow Six ( especially in regards to the sophistication of internet technology ) are more consistent with the mid-1990's.

Assuming that there are seven players on the field, and that a cup is in effect, this leaves four players to cover the rest of the field.

Assuming that the masses are constant, the virial G is one-half the time derivative of this moment of inertia

Assuming no high-grade obstruction or associated infection is found in the urinary tract, and symptoms are relatively mild, various nonsurgical measures can be used to encourage the passage of a stone.

Assuming that the routing tables are consistent, the simple algorithm of relaying packets to their destination's next hop thus suffices to deliver data anywhere in a network.

Assuming linear variation of glaze and decoration with time, and that these variables are independent,

* January 1 – Assuming that the copyright laws are not changed further, all works published in 1923 enter the public domain in the U. S., the first works to do so since the passage of the 1998 Sonny Bono Copyright Term Extension Act.

Assuming these are in general position, i. e. four distinct intersections, we get another interpretation of the linear system as the conics passing through the four given points ( note that the codimension four here matches the dimension, one, in the five-dimensional space of conics ).

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.

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