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 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 we have g ( 1 ) = 1.

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 that runs of zero bytes, which will be very common, can be ignored, as an exclusive or of any byte value to a byte of zero will not alter the original byte value.

Note that the first operator,, is just a special case of this operator in which the return value of the first action is ignored and the selected second action is always the same.

Note that in the calculations used to make this graph, the activation of fission products was ignored and the fission was assumed to occur in a single moment rather than a length of time.

Note: In the default configuration, any User Style code will be ignored.

Note that R might not be a subgroup, let alone a normal subgroup of F < sub > S </ sub >, so we cannot take a quotient by R. The solution is to take the normal closure N of R in F < sub > S </ sub >.

Note that the quotient D-topology is the D-topology of the quotient diffeology.

Note that unlike the general linear group, which is generally defined axiomatically as " invertible functions preserving the linear ( vector space ) structure ", the projective linear group is defined constructively, as a quotient of the general linear group of the associated vector space, rather than axiomatically as " invertible functions preserving the projective linear structure ".

:: Note that the notation does not denote the modular multiplication of times the modular multiplicative inverse of but rather the quotient of divided by, i. e., the largest integer value to satisfy the relation.

Note that the slash (/) denotes here quotient group.

Note that, as profinite groups are compact, the open subgroups are exactly the subgroups of finite index, so that the discrete quotient group is always finite.

Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.

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: ∇< sup > 2 </ sup > F represents, in this case, the vector formed by the individual Laplacian of each component of the vector in question )

Note, however, that it is acceptable to define two relative terms in respect of each other.

Note how the word endings do not coincide with the end of a metrical foot ; for the early part of the line this forces the natural accent of each word to lie in the middle of a foot, playing against the natural rhythm of the ictus.

Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together

< cite id =" demographics "> Note I </ cite >-There were around 300, 000 people () working as electrical engineers in the US ; in Australia, there were around 17, 000 () and in Canada, there were around 37, 000 (), constituting about 0. 2 % of the labour force in each of the three countries.

Note: In the following discussion, only one or two common pronunciations of American and British English varieties are used in this article for each word cited.

For future editions of the book, in 1917 Conrad wrote an " Author's Note " where he discusses each of the three stories, and makes light commentary on the character Marlow-the narrator of the tales within the first two stories.

Note the different check digits in each.

Note: if the product resulting from the labor process is homogeneous ( all similar in quality and traits, for example, all cups of coffee ) then the value of the period ’ s product can be divided by the total number of items ( use-values ) produced to derive the unit value of each item.

Note that while the associations indicated between the concepts in each item in that list is very strong, it is not absolute.

Note also that in most spoken languages, the sounds representing successive letters blend into each other in a process termed coarticulation, so the conversion of the analog signal to discrete characters can be a very difficult process.

Note that the ball becomes significantly non-spherical after each bounce, especially after the first.

Note that in between some cases, the roles and labels of the nodes are exchanged, but in each case, every label continues to represent the same node it represented at the beginning of the case.

Note that there are many languages where the features voice, aspiration, and length reinforce each other, and in such cases it may be hard to determine which of these features predominates.

Note 2: One user making two 75-second calls is equivalent to two users each making one 75-second call.

Note: In the table of allocation, the first two characters of each call sign ( whether two letters or one number and one letter, in that order ) identify the nationality of the station.

Note 2: The DTG may be used as a message identifier if it is unique for each message.

Note: The multiplexing function is performed in the D-4 framing structure by interleaving bits of consecutive bytes as they are presented from individual circuits into each D-4 frame.

Note that every signaling system can be characterized along each of the above axes of classification.

( Note, however, that in multiprocessing systems, many processes may run off of, or share, the same reentrant program at the same location in memory — but each process is said to own its own image of the program.