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 equivalent version is

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 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 derivation of the formula, based on a physical reflectance / transmittance model, can be found in a 1981 paper by Bruce A. Wallace.

Another way to define the Bessel functions is the Poisson representation formula and the Mehler-Sonine formula:

Another method of estimating E < sub > o </ sub > in an overloaded system is to measure the busy-hour call arrival rate, λ ( counting successful calls and blocked calls ), and the average call-holding time ( for successful calls ), h, and then estimate E < sub > o </ sub > using the formula E

Another cyclic ketone is Cyclobutanone, having the formula C < sub > 4 </ sub > H < sub > 6 </ sub > O.

Another reason can be seen by looking at the formula for the kurtosis of the sum of random variables.

Another of Gell-Mann's ideas is the Gell-Mann-Okubo formula, which was, initially, a formula based on empirical results, but was later explained by the quark model.

Another way of saying this < u > same </ u > formula is the following:

Another open wheeled stock car formula that races in the UK are Spedeworth Superstox.

Another open wheeled stock car formula that races in the UK are Spedeworth V8 Stock Cars.

Another, easier equation that can be applied to get the correct molecular formula of the CFC / R / Freon class compounds is this to take the numbering and add 90 to it.

Another situation for which this formula is not exact is with alternating current ( AC ), because the skin effect inhibits current flow near the center of the conductor.

* Another area formula, for two sides B and C and angle θ, is

* Another way to deal with it is to allow that experiments with processes of heat transfer to or from the system may be used to justify the formula just above.

Another relationship is given by the Gödel – Gentzen negative translation, which provides an embedding of classical first-order logic into intuitionistic logic: a first-order formula is provable in classical logic if and only if its Gödel – Gentzen translation is provable intuitionistically.

Another way of mathematically constructing a helix is to plot a complex valued exponential function ( e < sup > xi </ sup >) taking imaginary arguments ( see Euler's formula ).

Another formula for the centroid is

Another reason was through an act of industrial espionage in 1709 by a weaver known as James Blake who gained access to the workshops of a damask linen factory in Edinburgh by pretending to act like a simpleton in order to find out and memorise the formula.

Another generalization of Heron's formula to pentagons and hexagons inscribed in a circle was discovered by David P. Robbins.

Another formula is

Up to now, the group's biggest success had been as a five-piece harmony, but it was around this time that they began to favour lead singers for their songs with title credits given to Marty Kristian for " Come Softly to Me " and Eve Graham for " Nevertheless ", but it was in late 1973 that this formula found its biggest success when Lyn Paul took the lead on the new single, " You Won't Find Another Fool Like Me ".

Another factor may have been the company's very conservative ( and possibly dull ) nature and that, with a new decade just dawned, the south of England would be a radically different area ; it was felt that Southern's application was, understandably, more of the same tried and tested formula, which in time would not have reflected the possibilities for the area.