Note that we need not know the value of p, for the experiment to be binomial.

Note that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.

Note that after calling, we are left with a function that takes a single argument and returns another function, not a function that takes two arguments.

( Note that we are imagining the vector field to be like the velocity vector field of a fluid ( in motion ) when we use the terms flow, sink and so on.

Note that by reversing the equation, we can swap < math > < </ math > and, for example:

Alice now discards three of her own cards, and replaces them with three from the top of the deck ( Note: in a player-dealt casino game there is often a rule that the dealer must discard before picking up the deck, but this is a home game so we won't worry about such details ).

Note that we ignored the quotient in each step except to notice when the remainder reached 0, signalling that we had arrived at the answer.

) Note that we have omitted the Π < sub > j </ sub > n < sub > j </ sub > term, because each single-particle state can appear only once in a fermionic state.

Note that we have to restrict the sum to ordered values of m < sub > 1 </ sub >, ..., m < sub > N </ sub > to ensure that we do not count each multi-particle state more than once.

Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

Note: In cases where the optical design of a microscope produces an appreciable lateral separation of the two beams we have the case of classical interference microscopy, which does not result in relief images, but can nevertheless be used for the quantitative determination of mass-thicknesses of microscopic objects.

: 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.

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.

Note that we require the domains of G < sub > 2 </ sub >, G < sub > 3 </ sub > to be broad enough to make the above properties meaningful.

Note that here we are not concerned about the number of computational steps, or the size of the computer memory used.

Note that the shells exist for both protons and neutrons individually, so that we can speak of " magic nuclei " where one nucleon type is at a magic number, and " doubly magic nuclei ", where both are.

A subset T is totally ordered if for any s, t in T we have s ≤ t or t ≤ s. Such a set T has an upper bound u in P if t ≤ u for all t in T. Note that u is an element of P but need not be an element of T. An element m of P is called a maximal element ( or non-dominated ) if there is no element x in P for which m < x.

Note that, if the language is infinite, the enumerating algorithm provided can be chosen so that it avoids repetitions, since we can test whether the string produced for number n is " already " produced for a number which is less than n. If it already is produced, use the output for input n + 1 instead ( recursively ), but again, test whether it is " new ".

Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

Note that quite a few of the plants that were once included in family Alliaceae have been assigned to the subfamily Brodiaeoideae ( rather than the subfamily Allioideae ).

Note, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.

Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

Note that the officials have one eye, a sign of Odin.

Note the forward wings have not been installed yet ( 2003 )

* Note: Botswana does not have a westernmost point as the western section is formed by the 22nd meridian of longitude east of Greenwich.

* Note: technically Chad does not have an easternmost point, the northern section of the border being formed by the 24 ° of latitude

) Note that the same set of points would not have, as an accumulation point, any point of the open unit interval ; hence that space cannot be compact.

Note: it is reported in the scientific literature that some " shock " features, such as small shatter cones, which are often reported as being associated only with impact events, have been found in terrestrial volcanic ejecta.

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

Note the changes in subpixel intensity that are used to increase effective resolution when ClearType is enabled — without ClearType, all sub-pixels of a given pixel have the same intensity.

Note that the so-called Kinshasa Highway is not a physical road but a metaphor applied to the route by which AIDS is believed to have been spread east through Uganda and Kenya and neighbouring countries by truck drivers from the Congo.

( Note that, technically, Wisda's damages would be the lost profits only — if Wisda would have had $ 35 per hour in wages, materials and other expenses, its actual damages are only $ 15 per hour

Note: This study only involved male subjects which may be significant as sex steroids may have different effects in the responses to cortisol administration.

Note that a dominatrix does not necessarily dominate a male partner ; a dominatrix may well have female submissives, nor must the role of a dominatrix involve pain toward the submissive ; her domination can be verbal, involving humiliating tasks and servitude.

Note: Many of the essays found in these works have been individually translated and can be found in the English collections.

By Rule 1. 04, Note ( a ), all parks built after 1958 have been required to have foul lines at least long and a center-field fence at least from home plate.

Note: the fasces depicted have no axes, possibly because in the Roman Republic, the blade was always removed from the bundle whenever the fasces were carried inside the city, in order to symbolize the rights of citizens against arbitrary state power ( see above ).

* * Note: Guinea does not have a northern-most point, this section of the border being formed by a straight horizontal line

* * Note: Guinea-Bissau does not have a northern-most point, the border here being formed by a straight horizontal line

Note that with this definition, two elements a and b may very well have several greatest common divisors, or none at all.

Note that not all worlds have the same objects: some objects exist in some worlds and not in others.

Note that due to the reduced number of colors in the image, there are obvious display issues. GIF is palette-based: the colors used in an image ( a frame ) in the file have their RGB values defined in a palette table that can hold up to 256 entries, and the data for the image refer to the colors by their indexes ( 0 – 255 ) in the palette table.