Note that the two-sample test checks whether the two data samples come from the same distribution.

( Note: if 19a or 19b is answered " NO " that ends the due process analysis-the totality of circumstances test is not reached )

Under the Miller test, a work is obscene if: Note that " community " standards — not national standards — are applied whether the material appeals to the prurient interest ; thus, material may be deemed obscene in one locality but not in another.

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 ".

With this choice of a hyperplane, the points in the feature space that are mapped into the hyperplane are defined by the relation: Note that if becomes small as grows further away from, each element in the sum measures the degree of closeness of the test point to the corresponding data base point.

In response to the " temporary dispensation " theory, they point to Hirsch in Collected Writings as continually stressing the philosophical and religious imperative of Torah im Derech Eretz for all times ( Note that Hirsch himself addressed this contention: " Torah im Derech Eretz ... is not part of troubled, time bound notions ; it represents the ancient, traditional wisdom of our sages that has stood the test everywhere and at all times.

( Note that running time is measured in terms of the size of the input, which in this case is ~ log n, that being the number of bits needed to represent the number n .) The elliptic curve primality test can be proven to run in O (( log n )< sup > 6 </ sup >), but only if some still unproven ( but widely assumed to be true ) statements of analytic number theory are used.

Note that the last phrase is not required to be said if the speaker has a personal or moral objection, as is true of all oaths administered by the United States government ; Article Six of the United States Constitution requires that there be no religious test for public office.

( Note that knowing where to find needed information in such specialized books is itself an effective component of the test.

**( Note: not all the codes in the search result are suitable for this test.

" Note that the test of the constitutional functioning of the government was not required for the President to dissolve the National Assembly.

Note that for positive semidefinite and negative semidefinite Hessians the test is inconclusive ( yet a conclusion can be made that f is locally convex or concave respectively ).

( Note that Hirsch himself addressed this contention: " Torah im Derech Eretz … is not part of troubled, time bound notions ; it represents the ancient, traditional wisdom of our sages that has stood the test everywhere and at all times.

Note that the true distribution of the test statistic actually depends ( slightly ) on the two unknown variances: see Behrens – Fisher problem.

As she enumerates in her " Author's Note ", Fraser aims ( 1 ) to test the truth or falsehood of the many legends surrounding the subject ; and ( 2 ) to set Queen Mary in the context of the age in which she lived.

Note that Proteus vulgaris can also test Urease negative in solid media ( such as in Enterotube ), but will be Urease positive in liquid media.

Note that resetting test logic doesn't necessarily imply resetting anything else.

Note that " CAPTCHA " is an acronym for " Completely Automated Public Turing test to tell Computers and Humans Apart " so that the original designers of the test regard the test as a Turing test, not specifically a reverse one.

Note the possibility for restriction of range both in test scores and performance scores: The incumbent employees are likely to be a more homogeneous and higher performing group than the applicant pool at large.

He is one of the musicians who test and talk about the piano in the documentary Note by Note: The Making of Steinway L1037, released in November 2007.

( Note: The CIA did not include the Baltic states in its statistic calculations.

Note the crucial feature: the unknown parameter p interacts with the data x only via the statistic T ( x )

Note that the dimension of the random variable need not match the dimension of the parameter vector, nor ( in the case of a curved exponential function ) the dimension of the natural parameter and sufficient statistic.

Note that is a function of and the observation, so that, in general, it is not a statistic.

Note also that the estimated return period below is a statistic: it is computed from a set of data ( the observations ), as distinct from the theoretical value in an idealized distribution.

* OTL – Overtime losses – Games the team has lost in overtime ( Note: Many leagues do not separate overtime losses and regulation losses, including all losses in the losses statistic )

Note that some texts use an alternative notation, in which the statistic

Note that since the hold is not an official Major League Baseball statistic, the definition above can vary.

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.