:"< sup > 8 </ sup > and Aaron shall cast lots upon the two goats, one lot for the Lord and the other lot for Azazel.

The translators of the Greek Septuagint understood the Hebrew term as meaning the sent away, and read :"< sup > 8 </ sup > and Aaron shall cast lots upon the two goats, one lot for the Lord and the other lot for the scapegoat ( Greek apompaios dat.

:"< tt > Built to the precise specifications of Lord Dimwit Flathead, its excessive structure holds 69, 105 seats, …</ tt >"

" You name :"< BR >

" The words that brought you here :"< BR >

" The words that will release you :"< BR >

Just as kets and bras can be transformed into each other ( making into ) the element from the dual space corresponding with is where A < sup >†</ sup > denotes the Hermitian conjugate ( or adjoint ) of the operator A.

If A is expressed as an N × N matrix, then A < sup >†</ sup > is its conjugate transpose.

Self-adjoint operators, where A = A < sup >†</ sup >, play an important role in quantum mechanics ; for example, an observable is always described by a self-adjoint operator.

The development ... leads to ... an identification of computability < sup >†</ sup > with effective calculability.

The first collisional family — a group of objects thought to be remnants from the breakup of a single body — is the Haumea family It includes Haumea, its moons, and seven smaller bodies .< sup >†</ sup > The objects not only follow similar orbits but also share similar physical characteristics.

< sup >†</ sup >

The following demographic statistics are from the CIA World Factbook ().< ref name =" CIA_20110303 ">< sup >†</ sup > note: estimates for this country explicitly take into account the effects of excess mortality due to AIDS ; this can result in lower life expectancy, higher infant mortality and death rates, lower population and growth rates, and changes in the distribution of population by age and sex than would otherwise be expected < sup >‡</ sup > note: the preliminary 2011 numbers differ significantly from those of 2010, which were strongly influenced by the demographic effect of the January 2010 earthquake ; the latest figures more closely correspond to those of 2009 </ ref >

)< sup >†</ sup >

⟨ X | R ⟩ of a group H, one can recursively enumerate all homomorphisms h: H → G by first enumerating all mappings h < sup >†</ sup >: X → G. Not all of these mappings extend to homomorphisms, but, since h < sup >†</ sup >( R ), is finite, it is possible to distinguish between homomorphism and non-homomorphisms by using the solution to the word problem in G. " Weeding out " non-homomorphisms gives the required recursive enumeration: h < sub > 1 </ sub >, h < sub > 2 </ sub >, ..., h < sub > n </ sub >, ....

Algeria has always been a source of inspiration for different painters who tried to immortalize the prodigious diversity of the sites it offers and the profusion of the facets that passes its population, which offers for Orientalists between the 19 < sup > th </ sup > century and the 20 < sup > th </ sup > century, a striking inspiration for a very rich artistic creation like Eugène Delacroix with his famous painting women of Algiers in their apartment or Etienne Dinet or other painters of world fame like Pablo Picasso with his painting women of Algiers, or painters issued from the Algiers school.

A number of non-Greek etymologies have been suggested for the name, The form Apaliunas (< sup > d </ sup >) is attested as a god of Wilusa in a treaty between Alaksandu of Wilusa and the Hittite great king Muwatalli II ca 1280 BCE.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

We use the stronger statement that every odd ( antipode-preserving ) mapping h: S < sup > n-1 </ sup > → S < sup > n-1 </ sup > has odd degree.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

We must also prevent the decoder from using the last code in the upper block, 2 < sup > n + 1 </ sup > − 1, because when the decoder fills that slot, it will increase the code width.

A subgroup, N, of a group, G, is called a normal subgroup if it is invariant under conjugation ; that is, for each element n in N and each g in G, the element gng < sup >− 1 </ sup > is still in N. We write

We find the value of 2 < sup > 2 </ sup >, which is 4.

We may calculate the ratio of the populations of the two states at room temperature ( T ≈ 300 K ) for an energy difference ΔE that corresponds to light of a frequency corresponding to visible light ( ν ≈ 5 × 10 < sup > 14 </ sup > Hz ).

We see that p times the integer quantity in parentheses equals − a < sub > 0 </ sub > q < sup > n </ sup >, so p divides a < sub > 0 </ sub > q < sup > n </ sup >.

A notable example of an agreement between the Sinaiticus and Vaticanus texts is that they both omit the word εικη (' without cause ', ' without reason ', ' in vain ') from Matthew 5: 22 " But I say unto you, That whosoever is angry with his brother without a cause shall be in danger of the judgement ".< ref group =" n "> The same variant present manuscripts: P < sup > 67 </ sup >, 2174, in manuscripts of Vulgate, and in manuscripts of Ethiopic version .</ ref >

In choosing the means to those ends, they shall follow their accustomed associations of ideas .< sup > d </ sup > Hume has contended and defended the notion that " reason alone is merely the ' slave of the passions '.

< sup > 9 </ sup > And Aaron shall present the goat on which the lot fell for the Lord, and offer it as a sin offering ; < sup > 10 </ sup > while the goat designated by lot for Azazel shall be left standing alive before the Lord, to make expiation with it and to send it off to the wilderness for Azazel.

:< sup > 9 </ sup > And Aaron shall present the goat on which the lot fell for the Lord, and offer it as a sin offering ; < sup > 10 </ sup > but the goat on which the lot of the sent away one fell shall be presented alive before the Lord to make atonement over it, that it may be sent away ( Greek eis ten apompen acc.

APCs then present the fragments to T helper cells ( CD4 < sup >+</ sup >) by the use of class II histocompatibility molecules on their surface.

While K-Ar dating has been used extensively in the geological sciences, the prevalence of < sup > 40 </ sup > Ca in nature has impeded its use in dating.

An alternate form of ( 2 ) – the machine successively prints all n of the digits on its tape, halting after printing the n < sup > th </ sup > – emphasizes Minsky's observation: ( 3 ) That by use of a Turing machine, a finite definition – in the form of the machine's table – is being used to define what is a potentially-infinite string of decimal digits.

The algebra M < sub > n </ sub >( C ) of n-by-n matrices over C becomes a C *- algebra if we consider matrices as operators on the Euclidean space, C < sup > n </ sup >, and use the operator norm ||.|| on matrices.

Character-naming in Don Quixote makes ample figural use of contradiction, inversion, and irony, such as the names Rocinante ( a reversal ) and Dulcinea ( an allusion to illusion ), and the word itself, possibly a pun on ( jaw ) but certainly ( Catalan: thighs ), a reference to a horse's rump .< ref > quijote < sup > 1. 2 </ sup >: rump or haunch.

Although its use has been mainly associated within the high-vacuum range ( down to 10 < sup >− 9 </ sup > mbar ), diffusion pumps today can produce pressures approaching 10 < sup >− 10 </ sup > mbar when properly used with modern fluids and accessories.

Several are known to have occurred in Indo-European languages, including the presumed original Proto-Indo-European words for bear (* rkso ), wolf (* wlk < sup > w </ sup > o ), and deer ( originally, hart — although the word hart remained commonplace in parts of England until the 20th century as is witnessed by the widespread use of the pub sign The White Hart ).

The variance of the estimate X < sub > 1 </ sub > of θ < sub > 1 </ sub > is σ < sup > 2 </ sup > if we use the first experiment.

The expression 0 < sup > 0 </ sup > has to be interpreted as 1.

( 43 )</ sup > gives the following expression, based on the equation of state for an ideal Fermi gas:

The expression a < sup > x </ sup > denotes the conjugate of a by x, defined as x < sup >− 1 </ sup > a x.

Being healed has been described as a privilege of accepting Christ's redemption on the cross .< sup > p </ sup > Pentecostal writer Wilfred Graves, Jr. views the healing of the body as a physical expression of salvation.

In this period the correct expression for kinetic energy, ½mv < sup > 2 </ sup >, and its relation to mechanical work became established.

However, the expression sin < sup >− 1 </ sup > x usually does not represent the multiplicative inverse to sin x, but the inverse of the sine function applied to x ( actually a partial inverse ; see below ).

In algebra, a number that is the multiplier of a variable or expression ( e. g. the 3 in 3xy < sup > 2 </ sup >) is called a coefficient.

Within the parenthesis itself is found the expression 2 < sup > 2 </ sup >.

The first ( and only ) expression we come across that is expressed with an exponent is 2 < sup > 2 </ sup >.

So the correct value for our original expression, 4 × 2 < sup > 2 </ sup > − ( 2 + 2 < sup > 2 </ sup >), is 10.