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

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 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 the demand for labor to be a given monotonically decreasing function of the real wage rate, the theory then predicted that, in the long-run equilibrium of the system, labor supply ( i. e. population ) will be equated to the numbers demanded at the subsistence wage.

Assuming smallness of | ψ | and smallness of its gradients, the free energy has the form of a field theory.

Assuming smoothness the existence of a Heegard splitting also follows from the work of Smale about handle decompositions from Morse theory.

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 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 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 identification of Æthelweard as the brother of Ælfgifu is correct, his mother was the Æthelgifu whose company Eadwig enjoyed along with her daughter whilst escaping his coronation.

Assuming the foundational premise is correct, the optimal option for all governments would be an agreement to maintain tax harmonization.

Assuming that the degree of does not exceed, the criterion is correct however, and somewhat stronger than the formulation given above, since if is irreducible modulo, it certainly cannot decompose in into non-constant factors.

Assuming the date of death of Cossa is correct, this one must have been completed prior to the others.

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

Assuming that the matrix W is irreducible, then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate.

Assuming the only safe place for power is in many hands, social credit is a distributive philosophy, and its policy is to disperse power to individuals.

Assuming genetic drift is the only evolutionary force acting on an allele, after t generations in many replicated populations, starting with allele frequencies of p and q, the variance in allele frequency across those populations is

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 carfentanil and remifentanil were the only active constituents ( which has not been verified by the Russian military ), the primary acute toxic effect to the theatre victims would have been opioid-induced apnea ; in this case mechanical ventilation and / or treatment with opioid antagonists would have been life-saving for many or all victims.

Assuming that Malaysia can afford the same sustainable practices used in “ the North ” potentially neglects the importance of economic growth for a developing country, and for many commentators, weighs environmental considerations heavier than those for human life.

Assuming they'd be among many drag queens, they found themselves to be the only ones.

Assuming that this was due to his displeasure about his contract situation, many Red Sox fans and reporters, including Dan Shaughnessy of the Boston Globe, called for Ramirez to be traded.

*" Assuming the RHP of the combatants to be equal, there are many instances of fitness pay-off imbalances between holder and attacker which should weight the dispute outcome in favour of one or other opponent by allowing it a greater expendable fitness budget.

Assuming that the number of colonies in an area remains constant over time, on average only one queen among the many thousands sent out by a colony successfully founds a new one.

Assuming the trilemma to be accurate, the argument proceeds in stating that neither a charlatan or a madman could be considered a great moral teacher and that therefore the possibility of Jesus being merely a great moral teacher is excluded.