Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.

Note however that both in algebra and model theory the binary operations considered are defined on all of S × S.

Note that unlike Hypatia he did not study ' mathematics, philosophy and astronomy ', thus he and his followers came into conflict with the ancient University of Alexandria which pursued all forms of knowledge including science and human anatomy, politics and history according to the model inaugurated by Alexander the Great, the founder of Alexandria.

Note that in this model, the two fission fragments are the same size.

Note that the force balance itself creates drag and potential turbulence that will affect the model and introduce errors into the measurements.

Those trials were sanctioned and supervised by NASCAR. Note: between 1964 and 1966, Oldsmobile named its least expensive full size model the Oldsmobile Jetstar 88 which the Jetstar I was not related to, and priced $ 500 –$ 600 below the Jetstar I.

Note that the adjective ' hidden ' refers to the state sequence through which the model passes, not to the parameters of the model ; even if the model parameters are known exactly, the model is still ' hidden '.

Note that the use of natural numbers both in S and the existential quantification merely reflects the usual applications in computability and model theory.

Note that in the standard Shakura-Sunyaev model, viscosity is proportional to the total pressure since

Note the ' grid squares thus formed are far larger than the city blocks described earlier, and the road layouts within the grid squares are generally ' organic ' in form — matching the ' street hierarchy model described above

Note that unlike the liar paradox or Russell's paradox, this paradox does not depend on what model of negation is used, as it is completely negation-free.

Note that many simpler levels of climate model exist ; some are of only heuristic interest, while others continue to be scientifically relevant.

Note that to include a constant in the model above, one can choose to include the variable X < sub > K </ sub > all of whose observed values are unity: X < sub > iK </ sub > = 1 for all i.

a function that associates a header with each relation name in R. ( Note that this is a simplification from the full relational model where there is more than one domain and a header is not just a set of column names but also maps these column names to a domain.

Note: Cisco recommends that all Cisco IOS devices implement the authentication, authorization, and accounting ( AAA ) security model.

( Note that the model can be described mathematically and that words like " predict ", " surprise ", and " expect " are only used to help explain the model.

Note that all Jones vectors and matrices on this page assumes that the phase of the light wave is, which is used by Hecht.

Note that the following is a classical ( Newtonian ) analysis of orbital mechanics, which assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible.

( Note: Astronomy should not be confused with astrology, which assumes that people's destiny and human affairs in general are correlated to the apparent positions of astronomical objects in the sky -- although the two fields share a common origin, they are quite different ; astronomers embrace the scientific method, while astrologers do not.

Note that this article generally assumes Western ( Latin-based, Cyrillic, or Greek ) writing systems.

Note that the examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow a normal distribution, but this is not correct.

Note also that this rule assumes that the host which is acting as the firewall will not be sending email itself, such as to the email server.

: Note: This article assumes an understanding of the tensor product of vector spaces without chosen bases.

Note that the chain rule assumes the existence of total derivative of the inside function H, while

Note also that the function A ( θ ) or equivalently g ( θ ) is automatically determined once the other functions have been chosen, and assumes a form that causes the distribution to be normalized ( sum or integrate to one over the entire domain ).

Let k be a field and L and K be two extensions of k. The compositum, denoted KL is defined to be where the right-hand side denotes the extension generated by K and L. Note that this assumes some field containing both K and L. Either one starts in a situation where such a common over-field is easy to identify ( for example if K and L are both subfields of the complex numbers ); or one proves a result that allows one to place both K and L ( as isomorphic copies ) in some large enough field.

The structure of the ring can be analysed by considering all ways of embedding both K and L in some field extension of N. Note that the construction here assumes the common subfield N ; but does not assume a priori that K and L are subfields of some field M ( thus getting round the caveats about constructing a compositum field ).

( Note that this explanation assumes that the atmosphere starts in a geostrophically unbalanced state and describes how such a state would evolve into a balanced flow.

While the story can stand on its own, independent of Matsumoto's other works, it mostly assumes that the viewer has seen the other Harlock titles, especially Galaxy Express 999 ( the TV series and the movies ), which featured Maetel, Emeraldas ' sister, but had the occasional appearance of Emeraldas ( Note: Maetel, for some reason in the English dub is referred to as Mataire, possibly as a translation error ).

Note that this description assumes the checks are being done in world space.

Note, however, that this algorithm assumes that acceleration only depends on position, and does not depend on velocity.

Note that Haldane's model assumes independence of genes at different loci ; if the selection intensity is 0. 1 for each gene moving towards fixation, and there are N such genes, then the reproductive capacity of the species will be lowered to 0. 9 < sup > N </ sup > times the original capacity.

Note that this expression assumes that the conductivity and temperature have both been recast in units

Note that this analysis of the performance of a packrat parser assumes that enough memory is available to hold all of the memoized results ; in practice, if there were not enough memory, some parsing functions might have to be invoked more than once at the same input position, and consequently the parser could take more than linear time.

Note that the second definition assumes that the depth of field is symmetric around H ( which is roughly correct for normal lenses ) and therefore assumes a setting in which only half the depth of field is utilized ( i. e., for a lens focused at infinity, the depth of field is 10. 4 m to infinity ).

Note that the use of the phrase generally assumes that the returns were the product of a legitimate election ; show elections to fraudulent legislatures regularly produce incredibly strong majorities for the ruling party ( s ).

Note that this implementation assumes the join attributes are unique, i. e., there is no need to output multiple tuples for a given value of the key.

Note that the nD version, which is based on the graph generalization of the Laplacian, assumes all neighbors to be at an equal distance, and hence, leads to the following 2D-filter with diagonals included, rather than the version above:

Note, however, that the description of the problem assumes it is possible to surprise someone who is performing backward induction.

Note the similarity of the above formula to the ideal gas law and also that osmotic pressure is not dependent on particle charge.

Note that, with the opposite sign convention ( used in Physics ), this is the potential generated by a point particle, for an inverse-square law force, arising in the solution of Poisson equation.

Note that, with the opposite sign convention, this is the potential generated by a pointlike sink ( see point particle ), which is the solution of the Euler equations in two-dimensional incompressible flow.

Note that, because of the overhead from determining nearest neighbor pairs, exact resolution of long-range, compared with particle size, forces can increase computational cost or require specialized algorithms to resolve these interactions.

Note that at point the curve is parallel to the flow velocity vector, where the velocity vector is evaluated at the position of the particle at that time.

Note that since buoyant force increases as R ^ 3 and Stokes drag increases as R, the terminal velocity increases as R ^ 2 and thus varies greatly with particle size.

Note again that the particle verb constructions ( in orange ) qualify as catenae in both the a-and b-trees.

Note that the cross section is simply proportional ( by a numerical factor ) to the square of the classical radius of a point particle of mass m and charge q:

Note that if the densities of the particle and fluid are equal, the solution is and cyclonic separation is not possible.

Note that some authors use the particle velocity v instead of momentum p ; they are related in the definition of momentum by p

Note that not all particles follow geodesics, as they may experience external forces, for example, a charged particle may experience an electric field — in such cases, the worldline of the particle will still be timelike, as the tangent vector at any point of a particle's worldline will always be timelike.

< tr align = center bgcolor =# eeeeee >< td rowspan = 2 > Characteristic </ td >< td colspan = 3 > Space plasma density categories ( Note that density does not refer to only particle density )</ td >< td rowspan = 2 > Ideal comparison </ td ></ tr >