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 also that ' br ' is an empty element in that, while it may have attributes, it can take no content and it may not have an end tag.

Note that during the sort, the largest element is at the root of the heap at a, while at the end of the sort, the largest element is in a.

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

Note, however, that a language wishing to index arrays from 1 could simply adopt the convention that every " array address " is represented by a ′ = a – s ; that is, rather than using the address of the first array element, such a language would use the address of an imaginary element located immediately before the first actual element.

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.

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 the zero morphism in item 3 can be identified as the identity element of the hom-set Hom ( A, B ), which is an abelian group by item 1 ; or as the unique morphism A → O → B, where O is a zero object, guaranteed to exist by item 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 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 the ( Hg ) symbol indicating it contains mercury ( element ) | mercury.

Note that this element lies in the center of Dic < sub > n </ sub >.

A functional defined on some appropriate space of functions with norm < ref group =" Note "> The dot in this norm expression is a placeholder for an element of V, e. g. .</ ref > is said to have a weak minimum at the function if there exists some such that, for all functions with < math >

Note that avian creatures, linked to the element of air, were considered superior to aquatic creatures linked to the element of water.

Note that the result is a scalar ( an element of k ).

( Note: So far as State Police cars are concerned, only their replacement is under this division ).

Note, however, that it is six inches shorter at the forward end.

Note another piece of wood six inches wide is fastened to the transom between these pieces.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.

Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large.

Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;

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

Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.

Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by

Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.

Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

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 that there is no directly corresponding concept in the German language.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.

Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.

Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.

Note that this is subtly different to the ' thanks ' list in the original BBC Model B.

Note that the continuous crossover between the dilute and dense regimes of attracting pairs of fermions is still an open problem, which now attracts a lot of attention within the field of ultracold gases.

Note that a hack might be a kludge, but that ' hack ' could be, at least in computing, ironic praise, for a quick fix solution to a frustrating problem.

) 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, however, that unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time.

Note that the tautology problem for positive Boolean formulae remains co-NP complete, even though the satisfiability problem is trivial, as every positive Boolean formula is satisfiable.

( Note that for LZ77 compression such as gzip, this is much easier, as the problem reduces to " Is t in s ?".

Note that the definition of PSPACE-completeness is based on asymptotic complexity: the time it takes to solve a problem of size n, in the limit as n grows without bound.

Note that the subproblems must be only slightly smaller ( typically taken to mean a constant additive factor ) than the larger problem ; when they are a multiplicative factor smaller the problem is no longer classified as dynamic programming.

Note that if the u < sup > 2 </ sup > term were replaced with u, the problem would be linear ( the exponential decay problem ).

Note also that graphically this problem would involve a shift of the curve and a movement along the shifted curve.

Note that owing to the symmetrical nature of the problem space, R ( r, s ) results in the same solution as R ( s, r ).

Note that intersecting the server and client's permissions does not solve the problem either, because the server may then have to be given very wide permissions ( all of the time, rather than those needed for a given request ) in order to act for arbitrary clients.

Note the tacit assumption here that no intelligence or insight is brought to bear on the problem.

* The baby's shoulders are stuck ( shoulder dystocia ), or a bony association ( Note that the episiotomy does not directly resolve this problem, but it is indicated to allow the operator more room to perform maneuvers to free shoulders from the pelvis )

Note that the gimbal lock problem does not make Euler angles " wrong " ( they always play at least their role of a well-defined coordinates system ), but it makes them unsuited for some practical applications.

Note that a problem like this can be solved by block sampling the entire 100-bit vector at once.

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

Note that any coloring of a graph with the minimum number of colors must be a complete coloring, so minimizing the number of colors in a complete coloring is just a restatement of the standard graph coloring problem.