* Historia Augusta, The Life of Antoninus Pius, English version of Historia Augusta Note that the Historia Augusta includes pseudohistorical elements.

Note that the first element in a sequence has the index one and that $ refers to the length ( i. e. total number of elements ) of the sequence.

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

Note that the end tag's name is preceded by a slash character, "/", and that in empty elements the end tag is neither required nor allowed.

Note that the operators operate on elements from the domain and range, respectively, of the " one-to-one " and " onto " function ƒ.

Note that the bilinearity and alternating properties imply anticommutativity, i. e., for all elements x, y in, while anticommutativity only implies the alternating property if the field's characteristic is not 2.

Note this does not restrict dormant forms of life to these environments, so this argument only contradicts the widest interpretation of panspermia — that life is ongoing and is spread across many different environments throughout the Universe — and presupposes that any life needs those elements, which the proponents of alternative biochemistries do not consider certain.

Note that in this vector dotted with Pauli vector operation the Pauli matrices are treated in a scalar like fashion, commuting with the vector basis elements.

Note that many of the common polyatomic anions are conjugate bases of acids derived from the oxides of non-metallic elements.

Note that elements up to E118 have now been experimentally produced and that there are chemical studies on an increasing number of them.

Note: The principal applications of off-axis optical systems are to avoid obstruction of the primary aperture by secondary optical elements, instrument packages, or sensors, and to provide ready access to instrument packages or sensors at the focus.

Note 1: The PCS switching center represents a collection of one or more network elements.

Note that only the 253 have any claim to stability, but that only 90 nuclides from the first 40 elements are theoretically stable to any process but proton decay.

Note that all elements are written in their standard states, and one mole of product is formed.

Note that this is stated in terms of maps – product and inverse must be maps in the category – and without any reference to underlying " elements " of group – categories in general do not have elements to their objects.

Note: Work function can change for crystalline elements based upon the orientation.

( Note that categorical syllogisms have elements traditionally called middles, predicates, and subjects.

Note for completeness that condition ( 1 ) fails: any map t: B → A must map every two-cycle to the identity because the map has to be a group homomorphism, while the order of a two-cycle is 2 which can not be divided by the order of the elements in A other than the identity element, which is 3 as A is the alternating subgroup of, or namely the cyclic group of order 3.

Note that an iterator performs traversal and also gives access to data elements in a container, but does not perform iteration ( i. e., not without some significant liberty taken with that concept or with trivial use of the terminology ).

Note that while both the elements of the Cantor space ( regarded as sets of integers ) and subsets of the Cantor space are classified in arithmetic hierarchies but these are not the same hierarchy.

Note that not every relation which is not reflexive is irreflexive ; it is possible to define relations where some elements are related to themselves but others are not related to themselves ( i. e., neither all nor none ).

Note that although bulk materials differentiate outward or inward according to their density, the elements that are chemically bound in them fractionate according to their chemical affinities, " carried along " by more abundant materials that they're associated with.

Note that we can also define the arithmetic hierarchy of subsets of the Cantor and Baire spaces relative to some set of integers.

Note that, commonly, 2 < sup > ω </ sup > is referred to simply as the Cantor set, while the term Cantor space is reserved for the more general construction of D < sup > S </ sup > for a finite set D and a set S which might be finite, countable or possibly uncountable.

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 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 that, in a metric space, every compact subset is closed and bounded.

Note that completeness is a property of the metric and not of the topology, meaning that a complete metric space can be homeomorphic to a non-complete one.

Note that if the operations are performed in a colour space where γ is not equal to 1 then the operation will lead to non-linear effects which can potentially be seen as aliasing artifacts ( or ' jaggies ') along sharp edges in the matte.

Note: The above definition of group velocity is only useful for wavepackets, which is a pulse that is localized in both real space and frequency space.

Note that an eight-dimensional vector can be specified in many different ways depending on what basis is chosen for the space.

Note that the ordinary sphere is a 2-sphere, because it is a 2-dimensional surface ( which is embedded in 3-dimensional space ).

Note that every part of the machine — its state and symbol-collections — and its actions — printing, erasing and tape motion — is finite, discrete and distinguishable ; it is the potentially unlimited amount of tape that gives it an unbounded amount of storage space.

Note that this is also true if the boundary is the empty set, e. g. in the metric space of rational numbers, for the set of numbers of which the square is less than 2.

Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events is finite ( see above section on asymptotic behaviour of the posterior ).

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 the distinction with virtual memory systems ; in this case, the entirety of a process's addressable space must be in core memory, must be contiguous, and its size cannot be larger than the real memory capacity.

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 the fact that the set of points mapped into any hyperplane can be quite convoluted as a result, allowing much more complex discrimination between sets which are not convex at all in the original space.

( Note that the king never starts on the a-or h-files, since this would leave no space for a rook.

) Note that Pearson's original paper was entitled " On Lines and Planes of Closest Fit to Systems of Points in Space " – " in space " implies physical Euclidean space where such concerns do not arise.

( Note that on the 80186 and earlier, the first kibibyte of the address space, starting at address 0, is the permanent, immovable location of the interrupt vector table.

Note: Indoor distances are less standardized as many facilities run shorter or occasionally longer distances depending on available space.

Note that these depictions of two-dimensional surfaces are merely easily visualizable analogs to the 3-dimensional structure of ( local ) space.

( Note that the I / O register space may be larger on some more extensive devices, in which case the memory mapped I / O registers will occupy a portion of the SRAM address space.