Note that the acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.

Note that this case in this example implies that the user was next to the solid object, and not inside it.

( 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 that the result of partial function application in this case is a function that takes two arguments.

Note that this statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass.

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

Note that the probability of finding particles in the same state is relatively larger than in the distinguishable case.

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 that the plural suffix "- s " can also influence the form taken by the preceding morpheme, as in the case of the words leaf and knife, which end with in the singular, but have in the plural ( leaves, knives ).

Note that, although capitalization can aid in recognizing named entities in languages such as English, this information cannot aid in determining the type of named entity, and in any case is often inaccurate or insufficient.

Note that in the case of hybrid offences, the Crown must make a binding decision as to whether to proceed summarily or by indictment prior to the defendant making his or her plea.

( Note that A Uachtaráin ( vocative case ) would be the correct address in Irish.

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 the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied ( this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any ).

) Note that in this case, as in many cases with the term, tough shit is often said as a way of pointing out someone's fault in his / her own current problem.

Note that these nutrients become available because of the sapling's decomposition, rather than from the living sapling, which would be a case of parasitism.

Note: An example of bit pairing occurs in the International Alphabet No. 5 and the American Standard Code for Information Interchange ( ASCII ), where the upper case letters are related to their respective lower case letters by the state of bit six.

Note: In DSB-RC transmission, the carrier is usually transmitted at a level suitable for use as a reference by the receiver, except for the case in which it is reduced to the minimum practical level, i. e. the carrier is suppressed.

:: Note: In networks that are based upon the partially connected mesh topology, the data that is transmitted between nodes in the network takes many shortest paths between nodes using a technology like Shortest Path Bridging, except in the case of a failure or break in one of the links, in which case the network uses the remaining alternative paths to the destination.

: Note: partitive case has to be distinguished from partitive meaning which refers to the selection of a part or quantity out of a group or amount, see Partitive.

Note that this is only the case if the source is close to an ideal point source.

Note that in the special case where A is the empty set the meet of A will be the greatest element of L. Likewise, the join of the empty set yields the least element.

**** Note that this axiom precludes the possibility that the consumer cannot decide, and that a consumer is able to make this comparison with respect to every conceivable bundle of goods.

Note that there is one axiom for every such predicate φ ; thus, this is an axiom schema.

Note that the existence of the Cartesian product can be proved without using the power set axiom, as in the case of the Kripke – Platek set theory.

Note that there is no corresponding axiom of intersection.

Note, that the third axiom is actually redundant, because the second and fourth axioms imply is also an identity, and identities are unique.

Note that modern set-theoretic definitions usually define operations as maps between sets, so adding closure to a structure as an axiom is superfluous, though it still makes sense to ask whether subsets are closed.

It is then a theorem that there are in fact infinitely many such lines through P. Note that this axiom still does not uniquely characterize the hyperbolic plane uniquely up to isometry ; there is an extra constant, the curvature K < 0, which must be specified.

Note how, applying the reduction substitution axiom, occurrences of are now labeled as.

) Note that even without such an axiom we could form the first n terms of such a sequence, for any natural number n ; the axiom of dependent choices merely says that we can form a whole sequence this way.

Note that the translation axiom implies Ta =

Note also that there exists a number of alternative axiomatizations of S5 which do not employ the axiom 5 ( of course, 5 remains a theorem of S5 independently of a given axiomatization ).

Note that an everywhere defined extension exists for every operator, which is a purely algebraic fact explained at Discontinuous linear map # General existence theorem and based on the axiom of choice.

Note that the points must all be different numbers for them to count towards the fire bet.

Note that is a monotone function in γ and that the solution γ must satisfy.

The subgroup of generated by all commutators is called the derived group or the commutator subgroup of G. Note that one must consider the subgroup generated by the set of commutators because in general the set of commutators is not closed under the group operation.

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.

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 polystyrene peanuts must be used ; biodegradable packing peanuts will decompose into a sludge.

#* 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 the above calculation, the square-root, must be positive.

Note: In children there must be evidence of the capacity for age-appropriate social relationships with familiar people and the anxiety must occur in peer settings, not just in interactions with adults.

Note that a sample of random variables ( i. e. a set of measurable functions ) must not be confused with the realizations of these variables ( which are the values that these random variables take, formally called random variates ).

Note that any element of I must have the form αω, by virtue of our assumption that.

( Note that the boiling point of water varies with pressure, so this must be controlled.

Note 1: A duplexer must be designed for operation in the frequency band used by the receiver and transmitter, and must be capable of handling the output power of the transmitter.

Note 2: A duplexer must provide adequate rejection of transmitter noise occurring at the receive frequency, and must be designed to operate at, or less than, the frequency separation between the transmitter and receiver.

Note 3: A duplexer must provide sufficient isolation to prevent receiver desensitization.

Note that the earth itself has no role in this fault-clearing process since current must return to its source, not the earth as is sometimes believed ( see Kirchhoff's circuit laws ).

Note: must be positive.

Note that the arguments of the binomial coefficient are decremented due to order: the last " failure " must occur last, and so the other events have one fewer positions available when counting possible orderings.

Note that is the location to jump to, not the address of a handler, and so must be skipped () whether or not the branch is taken.

Note that this leaves the fuel at atmospheric pressure, and therefore it cannot travel into a throat which has been pressurized by a supercharger mounted upstream ; in such cases, the entire carburetor must be contained in an airtight pressurized box to operate.

Note that if a < sub > 2 </ sub > were non-zero there would be no way to cancel the M value — therefore a < sub > 2 </ sub > must be zero.