These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

Note that for a Euclidean function that is so established there need not exist an effective method to determine q and r in ( EF1 ).

Note that retroflex d, l and r are found not only in southern Italy and Tuscany but also in Asturias.

Note that this definition of the negative binomial distribution does not easily generalize to a positive, real parameter r.

Wages paid to labor are denoted by w and the rate of profit or the real interest rate is denoted by r. Note that the assumption of perfect competition enables us to take prices as given.

Note that the quantities V, the volume, and r the radius are expressed as single letters.

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

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 )

Note that dv / dr and du / dr approach 0 and ± 2 at large r, not ± 1 as one might expect.

Note the oral tentacles ( ot ), foot tentacles ( ft ), eye ( e ), rhinophore s ( r ), cerata ( c ).

Note that using r = 6, 371, 009 metres is appropriate for calculating great-circle distances between points on the Earth's surface, in which case the result d will also be in metres.

for some polynomials f and g. This congruence can be checked in polynomial time with respect to the number of digits in n, because it is provable that r needs be logarithmic with respect to n. Note that all primes satisfy this relation ( choosing g = 0 in ( 3 ) gives ( 1 ), which holds for n prime ).

Note however, that any Yukawa potential or Coulomb potential are non-zero for any large r.

Note that the r in car would usually be pronounced in this case, because the following word begins with a vowel ( see linking R below ).

Note that the modified duration D differs from the regular duration by the factor one over 1 + r ( shown above ), which also decreases as r is increased.

Note that the formula can be applied for, and gives 0 due to a factor in the numerator, in accordance with the second clause ( for even larger r the factor 0 remains present in the numerator, but its further factors would involve negative powers of q, whence explicitly stating the second clause is preferable ).

Note that the direction of the field points from the position r to the position of the masses r < sub > i </ sub >; this is ensured by the minus sign.

Note that r < sub > k </ sub > is the negative gradient of f at x = x < sub > k </ sub >, so the gradient descent method would be to move in the direction r < sub > k </ sub >.

( 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 from the perspective of the smaller-mass object — from the moon, in the preceding example — a spacecraft might appear to orbit in an irregular path about the or point, but from the perspective above the orbital plane, it becomes clear that both the smaller mass and the spacecraft are orbiting the larger mass ( or more precisely, all of the objects are in orbit around the barycenter of the system ); they simply have overlapping orbital paths.

Note that all materials undergo this orbital response.

Note that the following is a classical ( Newtonian ) analysis of orbital mechanics, which assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible.

Note the extremely strong dependence on orbital radius a.

Note that in turbulent motion, where is the velocity of turbulent cells relative to the mean gas motion, and is the size of the largest turbulent cells, which is estimated as and, where is the Keplerian orbital angular velocity, is the radial distance from the central object of mass.

Note also that the minimum speed achieved during Saturnian orbit is more or less equal to Saturn's own orbital velocity, which is the ~ 5 km / s velocity which Cassini matched to enter orbit.

Note that there is a 3d orbital, but it is not filled until Period 4, such giving the period table its characteristic shape of " two rows at a time ".

Note that the re-emission of photons, which is isotropic in the frame of the grain ( a ), does not affect the dust particle's orbital motion.

Note that, since the kinetic energy is, C < sub > 3 </ sub > is in fact equal to twice the magnitude of the specific orbital energy () of the escaping object.

Note that the strong gravitational interactions between the planets causes rapid orbital precession, so this diagram is only valid at the stated epoch.

Note that the angular momentum L in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum.

Note that, since the kinetic energy is one half m C < sub > 3 </ sub > is in fact equal to twice the magnitude of the specific orbital energy () of the escaping object.