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

Note that with this definition, unlike SNR, a SINAD reading can never be less than 1 ( i. e. it is always positive when quoted in dB ).

Note that unlike in the picture, the triangular setup in the cue game of eight-ball corresponds to an arithmetic progression 1 + 2 + 3 + 4 + 5 = 15.

Note that unlike the other two formulae ( the Euler product and the divisor sum ) this one does not require knowing the factors of n.

( Note: " plebeian secession " was a tactic used by the Roman plebs of vacating a city entirely and leaving its ruling elite to fend for itself, thus an even more radical action than a " general strike ", yet unlike the latter term, it does not pertain to withholding labor within a wage-system.

Note that unlike Cat 4 and Cat 5 cables, Cat 3 is still recognized by TIA / EIA-568-B, its defining standard.

Note that unlike the liar paradox or Russell's paradox, this paradox does not depend on what model of negation is used, as it is completely negation-free.

Note that unlike Judeo-Christian religions Shinto due to its nature does not require the same admission of faith, instead merely participating in certain aspects of Shinto is generally considered enough for association.

Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit — the use of Newton's Second Law, F

Note that, unlike many other computer-related units, 1 kbit / s is traditionally defined as 1, 000-bit / s, not 1, 024-bit / s, etc., also before 1999 when SI prefixes were introduced for units of information in the standard IEC 60027-2.

Note that unlike the word émigré, Emigre is officially spelled without accents.

Note that unlike Greece and Turkey, there are suites of four karsilama dances, different for men and women, some of them other than the standard 9 / 8 tempo.

) Note also that unlike the Say's law story above, there are interactions between different markets ( and their gluts and shortages ) that go beyond the simple price mechanism, to limit the quantity of jobs supplied and the quantity of products demanded.

Note that unlike the general linear group, which is generally defined axiomatically as " invertible functions preserving the linear ( vector space ) structure ", the projective linear group is defined constructively, as a quotient of the general linear group of the associated vector space, rather than axiomatically as " invertible functions preserving the projective linear structure ".

Note that, unlike fresh water, seawater does not have a density maximum at 4 ° C but gets denser as it cools all the way to its freezing point of approximately − 1. 8 ° C.

Note that the British 405-line system A, unlike all the other systems, suppressed the upper sideband rather than the lower — befitting its status as the oldest operating television system to survive into the color era ( although was never officially broadcast with color encoding ).

In March 1862, the first $ 2 bill was issued as a Legal Tender Note ( United States Note ) with a portrait of Alexander Hamilton ; the portrait of Hamilton used was a profile view and is unlike the portrait used currently for the $ 10 bill.

Note the projecting keyboard, unlike the inset Flemish examples.

Note that in First-Person Shooters, unlike the children's game, players can be harmed irrespective of whether they are in their own base.

Note that it is only " possible " that high order polynomials will be lumpy ; they could also be smooth, but there is no guarantee of this, unlike with low order polynomial curves.

Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons.

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, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.

** Note: Marker did the textual adaptation ( Film Comment.

Note that the synchronization of the chronometer on GMT did not affect shipboard time itself, which was still solar time.

The Preliminary Note of Explanation did not in fact alter the value of the statement on collegiality in the text of Lumen Gentium: it " strengthened the adherence to the doctrine of the First Vatican Council on the primacy, but it did not subsequently strike out anything from the direct divine origin of the episcopal office and its function, and the responsibility of the College of Bishops for the Universal Church.

The Chinese did not respond to the Note, and the British took that as Chinese acquiescence.

Note: Dream does not appear in every issue of The Sandman, nor did he appear in the first DC Comics The Sandman series, although several supporting characters in the Vertigo series did.

Note well that if a culture did include one's clan name in one's name and routinely handed it down to all children in the descent group then it would automatically be the family name or surname for one's descent group ( as well as for all other descent groups in one's clan ).

The Chinese did not respond to the Note, and the British took that as acquiescence.

The Editor's Note to The Complete Yes Prime Minister ( supposedly published in 2024 after Hacker's death but actually published by the BBC in 1989 ), thanks " Sir Bernard Woolley GCB " for his help and confirms that he did indeed make it to the position of Head of the Civil Service.

Monk's recordings for Blue Note between 1947 and 1952 did not sell well, but have since come to be regarded as amongst the most important of the bebop era.

Though these avant-garde records did not sell as well as some other Blue Note releases, Lion thought it was important to document new developments in jazz.

( Note: The CIA did not include the Baltic states in its statistic calculations.

Note that the sequence of lower lows and lower highs did not begin until August.

( Note: The United States did not recognize Haiti diplomatically until 1867, so this is not accurate.

Note: Ultra Seven, Ultraman Leo, Ultraman 80 and Ultraman Mebius used their powers to create human forms for their use and did not share their existences with any human host.

** Note: In the early years of the Junior tournament, Canada did not send a true National Junior team to the event.

Note that the number one film in this list premiered in mid-December, and it certainly did not take in $ 400, 000, 000 in December 1939.

*-Massie ( Governor ) ( Note: this candidate did not receive the endorsement of the state party, but was a registered Green ) Received. 25 % of the votes cast for governor

Note that cardinality does NOT imply direct measurability, in which Jevons did not believe.

Note that at the time, Laos was allied with the United States, as the Communist Pathet Lao did not take over the country until later.

* Note: Southern's coverage area coincided only partly with that of the present-day South East England government region, as it did not include the Oxford transmitter region ( Oxfordshire and Buckinghamshire ), which was instead covered by the ITV Midlands licensee.