Note that using a hierarchical system like this ( assuming it is done carefully ) changes the intersection computational time from a linear dependence on the number of objects to something between linear and a logarithmic dependence.

: Note: For ease of understanding, this discussion uses the terms intersection, road and map — however, formally these terms are vertex, edge and graph, respectively.

Note that there is no corresponding axiom of intersection.

Note that these properties are also satisfied if " interior ", " subset ", " union ", " contained in ", " largest " and " open " are replaced by " closure ", " superset ", " intersection ", " which contains ", " smallest ", and " closed ", respectively.

Let there be a right angle ABC, r a line parallel to BC passing by A and s a line parallel to AB passing by C. Let D be the point of intersection of lines r and s ( Note that it has not been proven that D lies on the circle )

This proves that all points in the intersection are the same distance from the point E in the plane P, in other words all points in the intersection lie on a circle with center E. Note that OE is the axis of the circle.

Note that the definition of the intersection number does not depend on the order of the divisors.

( Note that if we use the nullary intersection convention, then there is no need to include X in the second definition.

Note that if t and u, t ≠ u are two values of the parameter then the intersection of the curves C < sub > t </ sub > and C < sub > u </ sub > is given by

Note however that it is not compositional with respect to the intersection operator.

Note that unlike possibility, fuzzy logic is compositional with respect to both the union and the intersection operator.

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

Note the use of zero at the beginning an end of the two cycles.

Note the gravitational lens ing effect, which produces two enlarged but highly distorted views of the Cloud.

Note that after calling, we are left with a function that takes a single argument and returns another function, not a function that takes two arguments.

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

Note that positions on a surface in navigation use latitude and longitude in a similar two dimensional system.

Note, however, that it is acceptable to define two relative terms in respect of each other.

Note however that working with the current two form itself and the exterior derivative is usually easier than working with the vector field and divergence, because unlike the divergence, the exterior derivative commutes with a change of ( curvilinear ) coordinate system.

Note the two Danish flags.

Note that-is a long syllable, u a short syllable, and U either one long or two shorts:

Note: Any nonlinear electronic block driven by two signals with frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub > would generate intermodulation ( mixing ) products.

Note: In the following discussion, only one or two common pronunciations of American and British English varieties are used in this article for each word cited.

( Note: On most location-based television shows, there will be two Assistant Location Managers that alternate episodes, allowing one to prep an upcoming episode while the other is on-set with the current one.

Note that reflection by a window is from the front side as well as the back side, and that some of the light bounces back and forth a number of times between the two sides.

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

For future editions of the book, in 1917 Conrad wrote an " Author's Note " where he discusses each of the three stories, and makes light commentary on the character Marlow-the narrator of the tales within the first two stories.

Note that the dipole – dipole interaction between two atoms is usually zero, because atoms rarely carry a permanent dipole.

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

Note that there is no contradiction among these two results ; both computations are correct.

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: there are two closely related equations which are called Faraday's law.

Note that Karachentsev divides this group into two subgroups centered around IC 342 and Maffei 1.

Note that in this model, the two fission fragments are the same size.

Note two hydroxyl (- OH ) groups attached to the D ring ( rightmost ring ).

Note that the orange circles appear of different sizes, even though equal.

Note that the two circles are totally separate — none of the vowel-sounds made by speakers of one language is made by speakers of the other.

Note that a Möbius transformation does not necessarily map circles to circles and lines to lines: it can mix the two.

Note the analogy to the classification of conic sections by eccentricity: circles ε

* 1974-1978 — Yellow, orange, red and purple label with " abc Records " ( black " abc " circle logo ) between two black lines at top ( Note: The other ABC labels would also adopt this label, such as Dunhill, Dot, Blue Thumb with its logo next to the " abc " logo, Impulse-The Impulse label had a green background rather than a yellow background, but the circles were the same, etc.

Note: In the figure, there are 36 circles whose centers are spaced 10 degrees apart on the base circle.

Note: In the figure, there are 60 circles corresponding to the parameter t taking on values which are multiples of 6.

Note that Pennying accompanies the International Drinking Rules observed in some social circles.

Note the comfort offered by the mortal King Elessar to his elvish bride Arwen as his death approaches: " we are not bound forever to the circles of the world.