( Note that by designating cardinal directions for 1 ,-1,, and, complex numbers such as are considered constructible.

Note: This table represents active equipment only ; there are large numbers of equipment in reserve status.

Note that the points must all be different numbers for them to count towards the fire bet.

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 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.

Note that the hex numbers in the following tables are in little-endian byte order, as the format specification prescribes.

Note that ƒ cannot be extended to a homomorphism of rings ( from the complex numbers to the real numbers ), since it does not preserve addition:

Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J < sup > PC </ sup >( m ), where J is the spin quantum number, P the intrinsic parity ( or P-parity ), and C, the charge conjugation ( or C-parity ), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks ; rather, due to mass – energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.

Note: Chapters Zero, and all " in-between " chapters with halves in the numbers are not included in the softcover collection in North America.

Note that these numbers are one more than the formal ordinal numbers according to the isomorphic order, because these are equal to the number of earlier objects ( which corresponds to counting from zero ).

A set T of real numbers ( red and green balls ), a subset S of T ( green balls ), and the infimum of S. Note that for finite set s the infimum and the minimum are equal.

Note: Routing tables are constructed with no duplicate numbers, so that direct dial service can be provided to all network subscribers.

The path loss for the first ten kilometers may be 150 -- 190 dB ( Note: These values are very approximate and are given here only as an illustration of the range in which the numbers used to express the path loss values can eventually be, these are not definitive or binding figures -- the path loss may be very different for the same distance along two different paths and it can be different even along the same path if measured at different times.

Note that numbers are not exact, and may change slightly in the future, as nuclides are observed to be radioactive, or new half-lives are determined to some precision.

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 there is no to terminate this program so it produces an endless stream of random numbers from 1 to 9.

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: many American texts have B. pendula and B. pubescens confused, though they are distinct species with different chromosome numbers.

Note however that for prime numbers the function also returns-1, and that.

Note that this usage of the term linear is not the same as the above, because linear polynomials over the real numbers do not in general satisfy either additivity or homogeneity.

Note that although s and S are infinite, this works for finite matrices by only considering Stirling numbers up to some number N.

Note systems involve the use of sequential numbers in the text which refer to either footnotes ( notes at the end of the page ) or endnotes ( a note on a separate page at the end of the paper ) which gives the source detail.

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 the changes in subpixel intensity that are used to increase effective resolution when ClearType is enabled — without ClearType, all sub-pixels of a given pixel have the same intensity.

Note that, because of the overhead from determining nearest neighbor pairs, exact resolution of long-range, compared with particle size, forces can increase computational cost or require specialized algorithms to resolve these interactions.

Note the way steam allowed an increase in the rate of growth

Note that the ABOVE figure does not show any Virtual LAN tags, which increase the size of the frame by 32-bits per tag.

During the Panic of 1907, President Theodore Roosevelt attempted to increase liquidity in the markets by authorizing the Treasury to issue more Greenbacks, but the Aldrich-Vreeland Act provided for the needed flexibility in the National Bank Note supply instead.

Note cuffs fitted to propeller blade roots of Grumman F4F-3 to increase airflow to the engine, avoiding engine cooling problems.

Note that part of that profit results from turning the company around, and part results from the general increase in share prices in a buoyant stockmarket, the latter often being the greater component.

Note that in this regard both parasympathetic and sympathetic stimuli result in an increase in salivary gland secretions.

In addition, as of 2008 there were approximately 7, 000, 000 undocumented Mexicans living in the United States which if included in the count would increase the US share to over 28 % of the world's Mexican origin population ( Note that some of the undocumented would be captured in the US Census count depending on their willingness to provide information ).

Note that this growth is not due to an increase in fertility ( or birth rates ) but to a decline in deaths.

Note that the actual increase in the global surface temperature during the 100 years ending in 2005 was 0. 74 ± 0. 18 ° C.

Following Loving v. Virginia, The Changing Nature of Interracial Marriage in Georgia: A Research Note states " there was a 448 per cent increase in the number of interracial marriages ( from 21 in 1967 to 115 in 1970 )" ( Aldridge, 1973 ).

) Note that the increase in the speed of sound as waves approach the center of the sun causes a corresponding increase in the acoustic wavelength.

Note: This was the first full season in which all networks, on every day of the week except for Sunday, started airing programs at 8: 00 instead of 7: 30, as dictated by the FCC under its Prime Time Access Rule, intended to increase diversity in programming.

( Note: If the moisture later condenses inside the house, the latent heat will be converted back into ambient heat which could increase the temperature of the air in the room slightly.

Note that Lanchester's Square Law does not apply to technological force, only numerical force ; so it takes an N-squared-fold increase in quality to make up for an N-fold increase in quantity.

Note that in the sequence above,, and increase monotonically, but first decreases from 1 to 0, then increases from 0 to infinity.

Note Müller-Thurgau's increase and decrease.

The lake has been raised twice to increase storage capacity ( 9m in the 1940s, 37m in the 1970s ), submerging Five Pound Note Island, which once appeared on New Zealand's five pound note.

Note, that as such, this does not imply that an increase in savings must lead directly to an increase in investment.

* HW 35 Has been in production for many years with a unique barrel lock, the HW35E A more expensive version with walnut stock and longer barrel ( Note: longer barrel did not increase power ) and the HW35 " K " ( Carbine ) type with a short barrel.