In particular, given a point p in a Riemannian manifold, it is always possible to find metrics conformal to the given metric g for which the Ricci tensor vanishes at p. Note, however, that this is only pointwise assertion ; it is usually impossible to make the Ricci curvature vanish identically on the entire manifold by a conformal rescaling.

It is then a theorem that there are in fact infinitely many such lines through P. Note that this axiom still does not uniquely characterize the hyperbolic plane uniquely up to isometry ; there is an extra constant, the curvature K < 0, which must be specified.

Note the first row of this equation already holds, by definition of the normal N and curvature κ.

Note the " breakpoint " at the saturation pressure and the curvature at higher pressures as the Poynting correction factor comes into play

Note that the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied ( this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any ).

Note that the presence of the solute decreases the potential due to being smaller than 1.

Note that the escape velocity from a celestial body decreases with altitude above that body.

In addition to the commerce-decreasing corruption, Civilization III includes waste ( Note: Civ II includes waste as well, but it is considerably less severe ), which decreases a city's productivity.

Note that when a transformation decreases symmetry, a transformation of the same kind ( the inverse ) obviously for some patterns increases the symmetry.

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

Note that " sociocultural evolution " is not an equivalent of " sociocultural development " ( unified processes of differentiation and integration involving increases in sociocultural complexity ), as sociocultural evolution also encompasses sociocultural transformations accompanied by decreases of complexity ( degeneration ) as well as ones not accompanied by any significant changes of sociocultural complexity ( cladogenesis ).

Quite other feelings are evidenced by this style: Af Note the drop to pitch 1 ( the lowest ) on mother with no rise at the end of the sentence ; ;

Note that by Western standards this plan was `` upside down '', as it put North at the bottom and South at the top, with the other directions correspondingly altered ; ;

Note that strengthened negations may be compatible with weakened forms of AC.

Note that the 64x16 TRS-80 mode screen uses only a small part of the monitor screen, because the letters are the same size as the 80 × 25 CP / M screen, this was one of the things that was soon after fixed with the redesign to a commercial product

Note that wav files can also be encoded with the gsm codec.

In 2004, she accorded three stars to chef Jean-Georges Vongerichten ’ s Spice Market restaurant after Vongerichten gave her book Cooking for Mr. Latte a positive blurb ; the Times spotlighted the incident with an Editor ’ s Note.

Note that the constituency boundaries do not align exactly with those of the district of the same name.

Note however that Korean is nearly universally transcribed as vs., with the details of voice onset time given numerically.

( Note that " offshoring " is not synonymous with " outsourcing ", which means " to subcontract from an outside supplier or source ", such as when a business outsources its bookkeeping to an accounting firm.

Note that, although rarely occurring, if a runner tags and advances from second base ( or, theoretically, from first base ) all the way to home and scores ( without an intervening error ) the batter is credited with a sacrifice fly.

( Note that K is the SI unit for temperature ( kelvin ) and should not be confused with k, the SI prefix for kilo.

( Note, however, that a GC stacking interaction with the next base pair is geometrically different from a CG interaction.

" ( KJV ) The Watchtower states: " Note that Jesus first got baptized with water.

Note that this approach falters, in part, with the verb " to appear ".

Note: it is reported in the scientific literature that some " shock " features, such as small shatter cones, which are often reported as being associated only with impact events, have been found in terrestrial volcanic ejecta.

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.

Years are usually counted from a particular starting point, usually called the epoch, with era referring to the particular period of time ( Note the different use of the terms in geology ).

Note that this brain-in-a-vat argument conflates cyberspace with reality, while the more common descriptions of cyberspace contrast it with the " real world ".

Note that unlike Hypatia he did not study ' mathematics, philosophy and astronomy ', thus he and his followers came into conflict with the ancient University of Alexandria which pursued all forms of knowledge including science and human anatomy, politics and history according to the model inaugurated by Alexander the Great, the founder of Alexandria.

Note: Version 1. 6 effectively coincided with the release of Valve Software's Steam content delivery system on September 12, 2003.

Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number ( as with " 2 " and " 2. 0 ", or when scientific notation is used, " 2e3 " and " 2000 ").

Note that a mixture with a given composition has one boiling point at a given pressure, when the components are mutually soluble.

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 that non-elliptic orbits also exist ; If the eccentricity is greater than one, the orbit is a hyperbola.

Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero.

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

Note: For circular orbits apse line is not defined, because eccentricity is equal to zero.

Note: The all or none principle is met when all patients died before the Rx became available, but some now survive on it ; or when some patients died before the Rx became available, but none now die on it.

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

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 none of these listed characteristics are a requirement, as seen in shōnen manga like Yotsuba &!, which features a female lead, and almost no fan service or action, and that what most defines whether or not a series is shōnen are things like the magazine ( see Weekly Shōnen Jump ) it is serialized in or the time slot it airs on T. V.

( Note that there are freeware and shareware TM packages available, but none of these has yet gained a large market share.

Note that none of these titles except Against the Mathematicians and Outlines of Pyrrhonism, are found in the manuscripts.

Note that not every relation which is not reflexive is irreflexive ; it is possible to define relations where some elements are related to themselves but others are not related to themselves ( i. e., neither all nor none ).

Note that none of the Latin allies revolted, remaining loyal to Rome, with the one exception of Venusia.

Note: Recurrent infections alone in a patient who has none of the CRAB features is not sufficient to make the diagnosis of myeloma.

Note that the very rough images drawn up originally to illustrate this article show none of the extremely ornate decorations frequently applied to the front and sides of such a bureau.

Note that none of the opposing planes touch one another, as they cancel each other out violently, particularly in the case of Positive and Negative Energy.

Note that if 2 or more players were to tie with the most of a particular figurine, none of those players would receive the majority for that figurine.

Note that some federal subjects have multiple second-level domains, and others ( not listed below ) have none.

Note that Maimonides ' approach is also widely held amongst the non-rationalistic, mystical streams of Judaism — thus, for example, Rabbi Isaiah Horowitz, the Shlah HaKodosh holds that " none of these sometimes mind-boggling ' stories ' are devoid of profound meaning ; if anyone is devoid of understanding, it is the reader " ( Shnei Luchos HaBris, introduction ).

Note that while these drugs preferentially inhibit PDE5, none of them is truly selective, especially at high doses.

Note that none of the divinatory practices denoted by rhabdomancy in English are documented from ancient Greece sources.

Twenty-eight poems make up The Making of Collateral Beauty beginning with the introductory “ A Note on the Notes ” where promises are made that none of this “ is necessary in order to be entertained, instructed, or mauled by the apodictic poems in Mr. Yakich ’ s book.

Note too that there were no British Troops in Coast Province and certainly none at Hola at the time of this incident.

Note that none of these " schools " seem to have existed in ancient India, but were created after the fact by Tibetan doxographers.