Note that the process of a string splitting ( or strings connecting ) is a global process of the worldsheet, not a local one: Locally, the worldsheet looks the same everywhere, and it is not possible to determine a single point on the worldsheet where the splitting occurs.

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 determining anywhere on Earth by this formula requires to be known everywhere on Earth.

( 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 symmetric everywhere defined operators are necessarily self-adjoint, so this theorem can also be stated that an everywhere defined self-adjoint operator is bounded.

Note that based on this form for B we can see that A is constant along any given magnetic field line, since is everywhere perpendicular to B.

Note from the form of this equation that we also know p is a constant along any field line, ( again since is everywhere perpendicular to B. Additionally, the two-dimensional assumption () means that the z-component of the left hand side must be zero, so the z-component of the magnetic force on the right hand side must also be zero.

Note however that both in algebra and model theory the binary operations considered are defined on all of S × S.

Note that arrows between categories are called functors, subject to specific defining commutativity conditions ; moreover, categorical diagrams and sequences can be defined as functors ( viz.

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 the Bernoulli numbers are defined as B < sub > n </ sub > = B < sub > n </ sub >( 0 ), and that these vanish for odd n greater than 1.

Note that sometimes the elliptic integral of the third kind is defined with an inverse sign for the characteristic,

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.

Methods PUT and DELETE are defined to be idempotent, meaning that multiple identical requests should have the same effect as a single request ( Note that idempotence refers to the state of the system after the request has completed, so while the action the server takes ( e. g. deleting a record ) or the response code it returns may be different on subsequent requests, the system state will be the same every time ).

: is a spherical harmonic function of degree ℓ and order m. Note that the generalized Laguerre polynomials are defined differently by different authors.

Note that not every probability distribution has a defined mean ; see the Cauchy distribution for an example.

Note that this also differs subtly from the molecular mass in that the choice of isotopes is defined and thus is a single specific molecular mass of the many possible.

Note that despite its name, Great Barrier Island not a sandbar barrier which is often defined as the correct use of the term.

Note that typically, the reference point for jitter is defined such that the mean jitter is 0.

Note that the trace is only defined for a square matrix ( i. e., n × n ).

Note that the crude death rate as defined above and applied to a whole population can give a misleading impression.

Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).

Note that the Apple ISO 9660 Extensions do not technically follow the SUSP standard ; however the basic structure of the AA and AB fields defined by Apple are forward compatible with SUSP ; so that, with care, a volume can use both Apple extensions as well as RRIP extensions.

Note, however, that the DCT-I is not defined for N less than 2.

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.

( Note that the contact X on the second rung serves no useful purpose, as X is already defined in the ' AND ' function of S from the 1st rung.

( Note that the term " equinox " here refers to a point on the celestial sphere so defined, rather than the moment in time when the Sun is overhead at the Equator, though the two meanings are related.

Note: avg is defined above using a train of three verbs ("", "", and "") known as a fork.

( Note that X < sup > T </ sup > is defined here and not X itself, and what we are calling X < sup > T </ sup > is often alternatively denoted as X itself.

Note that this means that two non-equal points can be used to define a plane so long as they are ordered and used according to an agreed convention: for example, the first point sits on the plane and the normal vector is defined implicitly from (-).

Note that the matrix defined as above has the following properties:

Note that, although ' flight number ' is the term used colloquially, the official term as defined in the Standard Schedules Information Manual ( SSIM ) published annually by the International Air Transport Association ( IATA ) Schedules Information Standards Committee ( SISC ), is flight code.

Note, this is not true of the extension of propositional logic to other logics like first-order logic.

Note: As of Mac OS X version 10. 4. 9, the system will sometimes incorrectly display the AIFC icon for files with the. aif extension, whether or not the actual file format is AIFF or AIFF-C.

Note that the file extension abbreviations are different from the codecs which have the same name.

Note that it also creates a class from the extension of the intensional set.

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 ).

* WordPerfect (. wpd,. wp,. wp7,. doc ) ( Note: possible confusion with Word format extension )

( Note: That there was an extension of the " Hunding Stellung " further south from Verdun to Metz, called the " Michel Stellung ".

: Note: The. dat extension is commonly used for data files ( files that are not human-readable and do not hold a document-based binary file ).

Note the extension up the Wei valley.

Note that a conservative extension of a consistent theory is consistent.

Note that Chaos, and by extension Maria, is the Ghost Sweeper whose dire financial straits are most often displayed.

: Note that a set and a class having the same extension are identical.

Note that if has characteristic q ≡ 2 ( mod 3 ), then every element of has a unique cube root ; otherwise, it is necessary to consider an extension field of K.