Another equivalent axiom only considers collections X that are essentially powersets of other sets:

Another advantage with analog signals is that their processing may be achieved more simply than with the digital equivalent.

Another definition of asymmetric makes asymmetry equivalent to antisymmetry plus irreflexivity.

Another Vala, Aulë, creates the Dwarf race as an act of subcreation that honoured Eru Ilúvatar ( The equivalent of God in Tolkien's writings ), and which Eru accepted and made real, just as Niggle's Tree was made real.

Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa, and Tsuchiya.

Another equivalent definition of the rank of a matrix is the greatest order of any non-zero minor in the matrix ( the order of a minor being the size of the square sub-matrix of which it is the determinant ).

Another feature is the NET ( Null End Tag ) construction:, which is structurally equivalent to.

Another formalism mathematically equivalent to regular expressions, Finite automata are used in circuit design and in some kinds of problem-solving.

Another equivalent definition is

Another prominent opponent of Bligh, Macarthur's ally Thomas Jamison, was made the colony's Naval Officer ( the equivalent of Collector of Customs and Excise ).

Another report suggested that in 1669, Tavernier sold this large blue diamond along with approximately one thousand other diamonds to King Louis XIV of France for 220, 000 livres, the equivalent of 147 kilograms of pure gold.

Another example is al-Tusi's son, Sadr al-Din ( sometimes known as " Pseudo-Tusi "), who wrote a book on the subject in 1298, based on al-Tusi's later thoughts, which presented another hypothesis equivalent to the parallel postulate.

Another place is called the typical thirteenth Pratum magnum, a large open area destined to the market ( equivalent to today's Piazza Trento e Trieste ).

Another equivalent measure of proximity to instability is the phase margin.

Another roughly equivalent title and area in medieval Eastern Europe were those of ban ( bojan, vojin or bayan ) and banate.

* Another variation includes being sent to procure a " long weight " or " long stand ," the idea being that the dupe will reach the shop ( or equivalent source of the mythical object ) and place the request.

Another divide and conquer algorithm with a single subproblem is the Euclidean algorithm to compute the greatest common divisor of two numbers ( by reducing the numbers to smaller and smaller equivalent subproblems ), which dates to several centuries BC.

Another equivalent formula for the area, which more closely resembles Heron's formula, is

Another language game, " Fannee Doolee ," centers around a character who likes any person, place, thing or concept with double letters in it but hates its non-double-lettered equivalent, e. g., " Fannee Doolee likes sweets but hates candy.

Another, equivalent way to describe the same is that the distribution figure of each candidate is the votes for his party divided by his rank within his party ; the candidates with highest distribution figures are elected.

Another equivalent definition with the advantage of brevity is

Another way of putting this is that a phase angle of, say, 5 ° is considered to be completely equivalent to an angle of 365 °.

Another rearrangement shows that the Jacobi identity is equivalent to the following identity between the operators of the adjoint representation:

Another consideration is that due to the fact that territory controlled by Tang central authority was diminished by the equivalent of several of the northern provinces, something like a quarter of the remaining population no longer remained within the imperial revenue system.

Another version of the standardised imperial portrait ; from the house of Jason Magnus at Cyrene, Libya | Cyrene, North Africa ( British Museum ).

Another version describes it to have been really the goat's skin used as a belt to support the shield.

Another version says he was Co-Pontiff with Zadok during King David.

Another version ends with " Now I know my ZYXs, let's all go and walk to Texas.

Another production of the original version, some rehearsals of which Ibsen attended, opened on 3 March 1880 at the Residenz Theatre in Munich.

Another version is that the laws were first bound in books with blue covers.

Another difficulty is that manuscripts of early writers were often incomplete: it is apparent that Bede had access to Pliny's Encyclopedia, for example, but it seems that the version he had was missing book xviii, as he would almost certainly have quoted from it in his De temporum ratione.

Another of his tunes, " Matchbox Blues ", was recorded more than 30 years later by The Beatles, albeit in a rockabilly version credited to Carl Perkins, who himself did not credit Jefferson on his 1955 recording.

Another homebrew version was released in 2011 for the Amstrad CPC home computer.

Another consequentialist version is motive consequentialism which looks if the state of affairs that results from the motive to choose an action is better or at least as good as each of the alternative state of affairs that would have resulted from alternative actions.

Another class of carbine is a semi-automatic version of a submachine gun, with an extended barrel, usually just over 406 mm ( 16 inches ) long, which will escape ban by some " assault weapon " legislation.

Another version of the cyborg Jaime Sommers is featured in a remake series, Bionic Woman, broadcast in 2007.

Another version, however, makes them children of a certain Centaurus, who mated with the Magnesian mares.

Another version of the song was recorded by Chris Kline in August 2005.

: Another version, The Scarecrow of Romney Marsh, was produced as a three-part television miniseries in color by Walt Disney in 1963.

Another example is Francis Ford Coppola's Apocalypse Now Redux, which, like the original film, polarized the audience, with some fans considering the original version to be the definitive cut.

Another version of the story is that he canvassed with Nancy, Lady Astor, MP for Plymouth Sutton, and received an embarrassingly friendly welcome at boarding houses who were used to renting rooms by the hour to sailors and their lady companions.

Another version is the Collector's Edition, a two-disc set featuring a remastered transfer with a 5. 1 audio track, two commentaries ( one by John Carpenter and Kurt Russell, another by producer Debra Hill and Joe Alves ), a making-of featurette, the first issue of a comic book series titled John Carpenter's Snake Plissken Chronicles, and a ten-minute deleted opening sequence.

Another unreleased recording, " Latitude 88 North ", was released as the third bonus track on the 2007 remastered version of their 1977 album Out of the Blue.

Another version of what Álvares wrote was included in an anthology of travel narratives, Navigationi et Viaggi assembled and published by Giovanni Battista Ramusio, and published in 1550.

Another version, slightly different from Scott's, was found in his papers.

Another version of " O Canada " in rock format was recorded by Lee and Lifeson on the accompanying soundtrack CD for the Trey Parker and Matt Stone film South Park: Bigger, Longer, and Uncut released in 1999.

Another theory, considered by New Cambridge editor Kathleen Irace, holds that Q1 is an abridged version intended especially for travelling productions.

" Another version of Hahn – Banach theorem is known as Hahn – Banach separation theorem or the separating hyperplane theorem, and has numerous uses in convex geometry.

Another version of Hahn – Banach theorem states that if V is a vector space over the scalar field K ( either the real numbers R or the complex numbers C ), if is a seminorm, and is a K-linear functional on a K-linear subspace U of V which is dominated by on U in absolute value,