Note: Step ( in the description below ) is defined as: a transfer / change of weight to the opposite foot while hopping ( this is usually minimal ; almost more of a scoot than a literal hop ).

Note that this description is meant only as an heuristic ; a proper understanding requires a quantum-mechanical description.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Some such books include a separate ' Note about the type ', which will identify the names of the primary typefaces used, provide a brief description of the type's history and a brief statement about its most identifiable physical characteristics.

Note that this definition of entropy can even be viewed as equivalent to the previous one ( unknown information ) if we take a meta-perspective, and say that for observer A to " know " the state of system B means simply that there is a definite correlation between the state of observer A and the state of system B ; this correlation could thus be used by a meta-observer ( that is, whoever is discussing the overall situation regarding A's state of knowledge about B ) to compress his own description of the joint system AB.

( Note: the below description of Prince He's life as Prince of Changyi are based on description of him written after he was deposed, and may very well be biased or fabricated.

Note that this description creates an exaggerated hobble often seen with newer dancers.

Note: The following description is based on the player making the correct choices and successfully completing the game.

where is the number of ways to distribute cards between hands of two cards each .< ref name =" prod " group =" Note "> See " Capital Pi notation for multiplication " for a description of the ( capital π or pi ) symbol .</ ref > is the factorial # Double factorial | double factorial operator: ( 2n-1 )!!

Note the Apostle Paul's description of this process, that the disciple " not be conformed to this world, but be transformed by the renewing of your minds, so that you may discern what is the will of God — what is good and acceptable and perfect.

Note that virtually all computer software implementing these spaces use a very rough approximation to calculate the value they call " saturation ", such as the formula described for HSV and this value has little, if anything, to do with the description shown here.

Note on the taxonomy of the family Notobranchaeidae and description of Notobranchaea bleekerae n. sp., a species new to science ( Gastropoda, Pteropoda ).

Note that this is an astronomical description of the precessional movement and the vernal equinox position in a given constellation may not imply the astrological meaning of an Age carrying the same name, as they ( ages and constellations ) only have an exact alignment in the " first point of Aries ", meaning once in each ca.

Note that some imaging scientists will include additional " links " in their description of the imaging chain.

* Note: this description of federated databases does not accurately reflect the McLeod / Heimbigner definition of a federated database.

Note: This description is not of a drum circle, in the sense that the term is commonly used.

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

Note: this description of the life of François Bernier is abstracted from a French introduction by France Bhattacharya to an edition of " Voyage dans les Etats du Grand Mogol " ( Paris: Fayard, 1981 ).

Note: The above is a description of what the game SAYS, in reality the Wizard gets more spell POINTS then any other class, but cannot cast priestly spells ( like the hugely important protection from level drain ).

Note: The above is a description of what the game SAYS, in reality the Sage does not gain experience for exploring, but CAN use weapons and items ( unlike the monk ) AND can learn all spells in the game.

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 this model assumes the particle is a point mass, which is certainly known to be false in many cases in which we use this model ; for example, as a model of planetary motion.

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, 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: