Assuming we restrict our measurements to the z-and x-axes, such a hidden variable theory is experimentally indistinguishable from quantum mechanics.

Assuming normalization ( i. e. that all probabilities in the set do total 100 %), the probability density in quantum mechanics is equal to the square of the absolute value of the amplitude of the waveform.

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 normalization Δ ( 1 )= 0, the quantum master equation reads

Assuming that the second particle is at rest before the collision, the angles of deflection of the two particles, and, are related to the angle of deflection in the system of the center of mass by

Assuming a Gaussian distribution of particle positions and impulses, a charged particle beam ( or a bunch of the beam ) is characterized by

Assuming that the particle is spherical, a simple analysis to calculate critical separation particle sizes can be established.

Assuming Stokes ' law, the drag force on any particle in this inlet stream is therefore given by the following equation:

Assuming no change in the height of the particle, this will be the total gravitational potential energy of the particle at all times.

Assuming victory, Haldimand pledged that after the war ended, the British government would restore the Mohawk to their lands as stated before the conflict started.

Assuming that Jeconiah's reign ended on the day that the Babylonians captured Jerusalem the first time, 2 Adar ( 16 March ) 597 BC, and further assuming that the Jewish calendar in the sixth century BC had the same number of days in the two preceding months as in the modern Jewish calendar, Jehoiachin's reign of three months and ten days () would have started on 21 Heshvan ( 9 December ) 598 BC.

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 Hunnic forces were roughly the same size as the Romano-Gothic, the number involved in battle is just under 100, 000 combatants in total.

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 the axiom of choice, every other infinite cardinal number is either regular or a ( weak ) limit.

Assuming that the dimensionless constants in the theory do not get too large, one can group calculations by inverse powers of the cutoff, and extract approximate predictions to finite order in the cutoff that still have a finite number of free parameters.

Assuming that the four centres of each colour are indistinguishable, the number of permutations is reduced to 24 !/( 4 !< sup > 6 </ sup >) arrangements.

Assuming the cube does not have a fixed orientation in space, and that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced by a factor of 24.

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 the number of available trucks ( capital ) is fixed, then the amount of the variable input labour could be varied and the resultant efficiency determined.

Assuming a purely random distribution of wars between states, regardless of their democratic character, the predicted number of conflicts between democracies would be around ten.

Assuming we know on which day a century starts ( from above ), if we add the number of years elapsed since the start of the century, plus the number of leap years that have elapsed since the start of the century, we get the day of the week on which the year starts.

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 we have a sorting network of size n, we can construct a network of size by " inserting " an additional number into the already sorted subnet ( using the principle behind insertion sort ).

Assuming T * is arithmetically definable, there is a natural number n such that T * is definable by a formula at level of the arithmetical hierarchy.

Assuming that the online casino is using an appropriately programmed random number generator, table games like blackjack have an established house edge.

" Assuming this is a reference to Mick, this is a slight discontinuity with Skinny Dip, in which he lists his number of ex-wives as six: the five mentioned in Skin Tight, plus Christina.

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

Assuming each test case takes one path, the number of cases needed to achieve path coverage is equal to the number of paths that can actually be taken.

Assuming that the four centers of each color in each set are indistinguishable, the number of permutations of each set is reduced to 24 !/( 4 !< sup > 6 </ sup >) arrangements, all of which are possible.

Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2 < sup > n </ sup >/ 1.

Assuming the columns of A ( and hence R ) are independent, the projection solution is found from A < sup > T </ sup > Ax = A < sup > T </ sup > b. Now A < sup > T </ sup > A is square ( n × n ) and invertible, and also equal to R < sup > T </ sup > R.

Assuming that the series converges to a value n, the Turing machine would complete an infinite execution in n time units.

Assuming that all of an individual's ancestors are otherwise unrelated to each other, that individual has 2 < sup > n </ sup > ancestors in the nth generation before him and a total of about 2 < sup > g + 1 </ sup > ancestors in the g generations before him.

Assuming that two individuals share the same 32 ancestors of n =

Assuming that this is the same level as the DC input voltage then an n stage multiplier will ( ideally ) output nV < sub > in </ sub >.

Assuming substitution of genes to take place slowly, one gene at a time over n generations, the fitness of the species will fall below the optimum ( achieved when the substitution is complete ) by a factor of about 30 / n, so long as this is small-small enough to prevent extinction.

Assuming that the n points needed for estimating a model are selected independently, is the probability that all n points are inliers and is the probability that at least one of the n points is an outlier, a case which implies that a bad model will be estimated from this point set.

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 that L denotes radiance, we have that at each particular position and direction, the outgoing light ( L < sub > o </ sub >) is the sum of the emitted light ( L < sub > e </ sub >) and the reflected light.

Assuming energy demand does not change, this reduces the carbon dioxide emitted.