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

Note the range of tones, fading toward the edges.

Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off (" saturated ") states.

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: List of Urdu language poets provides pen names for a range of Urdu poets.

Note that the occurrence of brown recluses in a single building ( such as a warehouse ) outside of the native range is not considered a successful colonization ; such single-building populations can occur ( e. g., several such cases in Florida ), but do not spread, and can be easily eradicated.

Note that this notion of image may not correspond to the usual notion of image, or range, of a function, even assuming that the morphisms in the category are functions.

Note: The listed measurements of this system range from the lowest to highest acceptable halachic value, in terms of conversion to either metric or Imperial units.

Note also that Unicode includes non-graphical language tag characters in the range U + E0000 – U + E007F for plain text language tagging.

Note that the sine function is such that there are two solutions for for a given range.

Note that for purposes of computer programming, this table should start at 0 instead of 1 and thus use all of the 7-bit range ( 0-127 ) allowed by the MIDI Program Change message.

Blue Note offered better pay and more artistic control than other labels, and his work for this organization is highly regarded and includes leadership and sideman dates with a wide range of musicians, including Donald Byrd, Sonny Clark, Lee Morgan, Ornette Coleman, Dexter Gordon, Billy Higgins, Freddie Hubbard, Grachan Moncur III, Bobby Hutcherson, Mal Waldron, and many others.

Note that this may be difficult to arrange in practice with simple linkages, and designers are advised to draw or analyze their steering systems over the full range of steering angles.

Note that the μ and ν summation indices range from 0 to 3: see Einstein notation.

Note, however, that although temperature reconstructions from proxy data help us understand the character of natural climate variability, attribution of recent climate change relies on a broad range of methodologies of which the proxy reconstructions are only a small part.

Note that we do not count the time needed to find the largest pancake, only the number of flips ; if we wished to create a real machine to execute this algorithm in linear time, it would have to both perform prefix reversal ( flips ) and be able to find the maximum of a range of consecutive numbers in constant time.

Note that audible sound has a very wide frequency range ( from 20 to about 17000 Hz ), and thus a very wide range of wavelengths ( from about 20 mm to 17 m ).

* Info on the range ( Note: the western range separated from the rest is actually the range of Eumeces callicephalus.

Note that the exponent range for this format is only about a quarter as large as the corresponding IEEE binary format.

Note that the image of the pole ’ s top will overlay that of some terrain point which is on the same slant range arc but at a shorter horizontal range (“ ground-range ”).

( 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: Marker tapes Makavejev circulating among the guests of a party in his honor as much jovial backslapping abounds ( Film comment ).

Note that the velocities are much higher at the upper surface than at the lower surface.

Note that these statistics only show officially registered residents, and that the actual number of foreign citizens living in Shanghai is likely much higher.

Note that much of history from 1800-1950 is often not reflected well in general parlance as they are overshadowed by the ' big three ', games on other subjects in this era are often referred to by the actual war they deal with.

Note that the wavelengths in audible sound are much longer than those in visible light.

Note that this formula ( equivalent to Newton's law of heat flow ) is analogous to, and much older than, Ohm's law of electric flow:

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

( Note that the same equation applies for recoil energy losses in x-rays, but the photon energy is much less, resulting in a lower energy loss, which is why gas-phase resonance could be observed with x-rays.

(* Note that menigitis, sinusitis and pneumonia can all be caused by Group A Strep, but are much more commonly associated with Streptococcus pneumoniae and should not be confused.

Note that the reason this works is that the bit line input-drivers are designed to be much stronger than the relatively weak transistors in the cell itself, so that they can easily override the previous state of the cross-coupled inverters.

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 an air source heat pump is more efficient in hotter climates than cooler ones, so when the weather is much warmer the unit will perform with a higher COP ( as it has less work to do ).

There has been much sampling of classic Blue Note tracks by both hip hop artists and for mashing projects.

Note: The early history of historical Williamsburg Township includes a much wider area than the current Williamsburg County

( Note: Lake Gusher was formed when Taft began its early drills, first finding water, which was very much needed in the area and one of the few reason along with prostitution and booze that Taft survived while surrounding towns vanished overnight.

Note also, that in the case of air, this convention is much less accurate.

Note: most players will declare a Grand game with the above hand, as it will be much more lucrative than a suit game in Hearts ( declarer will concede at most one Club trick, achieving Schneider for a score of at least 144 points ).

Note that may be much lower than the actual number of empty places in the queue, for example in the case where many producers have decremented it but are waiting their turn on before filling empty places.

From 1965-1973 he switched from Blue Note to Prestige Records but stayed very much on the hard-bop track ; while the rest of the jazz world was getting funky, Gordon was making classic bop albums like 1972's Tangerine with Thad Jones, Freddie Hubbard, and Hank Jones.

Note that in the interaction of color the constituent colors retain much of the own identity even though they may be altered somewhat by contrast.

Note that much of this anatomy does not apply to gastropods in other clade s or groups.

Note that much of this anatomy does not apply to gastropods in other clades. Light yellow-bodyBrown-Gastropod shell | shell and Operculum ( gastropod ) | operculum Green-digestive systemLight purple-gills Yellow-osphradium Red-heartPink-Dark violet-1. foot 2. cerebral ganglion 3. pneumostome 4. upper commissura 5. osphradium 6. gills 7. pleural ganglion 8. atrium of heart 9. visceral ganglion 10. ventricle 11. foot 12.

Note that, for r much greater than σ, the erf function approaches unity and the potential φ ( r ) approaches the point charge potential

Note that the DECstation systems used MIPS processors and predate the much later Alpha-based systems.