Since Parts 1, and 2, were prepared independently, the abbreviation schemes and the chemical symbols used differ in the two parts.

Since n grows faster than log < sub > 2 </ sub >( n ), there must exist a value n < sub > 0 </ sub > such that

Since 1995 the UK government has advised that regular consumption of 3 – 4 units a day for men, or 2 – 3 units a day for women, would not pose significant health risks, but that consistently drinking four or more units a day ( men ), or three or more units a day ( women ), is not advisable.

Since the Bishop of London refused to ordain ministers in the British American colonies, this constituted an emergency, and as a result, on 2 September 1784, Rev.

Since the 1990s, SO < sub > 2 </ sub > emissions have dropped 40 %, and according to the Pacific Research Institute, acid rain levels have dropped 65 % since 1976.

* Since Big Brother 2, the UK series always opens with a twist which have included the public being able to choose the final housemate out of three possibilities ( Big Brother 2 ), the public voting for a housemate to leave during the first week and then the housemates choosing between the two housemates with the least number of votes ( Big Brother 3 ), First Night Nominations ( Big Brother 4 ), Suitcase Nominations ( Big Brother 5 ), Unlucky Housemate 13 ( Big Brother 6 ), Big Brother Hood ( Big Brother 7 ), an all-female House and the first inclusion of twins as contestants ( Big Brother 8 ), the first couple to enter as housemates and set a secret task to hide their real relationship ( Big Brother 9 ), all " housemates " really being " non-housemates " who had to earn their housemate status ( Big Brother 10 ), a mole entering the House with an " Impossible Task " ( Big Brother 11 ), Jackie Stallone entering a house containing her son's ex-wife ( Celebrity Big Brother 3 ), the entrance of a non-celebrity in a celebrity edition ( Celebrity Big Brother 4 ) and Jade Goody's family announced to be visiting.

Since then, the " great fish " in Jonah 2 has most often been translated as " whale ".

Since these stock additions retain the short pistol barrel ( as short as 100 mm ( 4 inches )) they are highly restricted under the NFA unless the shoulder stocks are of original manufacture for the gun and the gun has been " delisted " as outlined in links 1 & 2 in the paragraph above, as is the case with so-equipped " Broomhandle " Mausers and Lugers.

Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

Since mid-1982, United States pennies are made of 97. 5 % zinc, coated with 2. 5 % copper.

Since the design of such high-end chips nominally takes about five years to complete, to stay competitive a company has to fund at least two of these large design teams to release products at the rate of 2. 5 years per product generation.

Since a comic book shop in his area traded 2 old comics for 1 new, he only had 2 Duck comics left from his sister's collection by the 70s, one of them being The Golden Helmet.

Since being able to choose any resource type allows more building power, gold rivers are either marked with number token of only 2 or 3 dots and / or are far away from starting positions to offset this.

Since the Second World War, they have been attended by an average of over 2, 000 and up to 6, 000 people.

A right to education has been created and recognized by some jurisdictions: Since 1952, Article 2 of the first Protocol to the European Convention on Human Rights obliges all signatory parties to guarantee the right to education.

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

Since the algorithm ensures that the remainders decrease steadily with every step, r < sub > k − 1 </ sub > is less than its predecessor r < sub > k − 2 </ sub >.

Since the proving of the theorem, efficient algorithms have been found for 4-coloring maps requiring only O ( n < sup > 2 </ sup >) time, where n is the number of vertices.

Since Darwin's time, the fossil record has been pushed back to between 2. 3 and 3. 5 billion years before the present.

Since 1989, Brooks has released 19 records in all, which include ; 9 studio albums, 1 live album, 4 compilation albums, 3 Christmas albums and 2 box sets, along with 77 singles.

Since all GWP calculations are a comparison to CO < sub > 2 </ sub > which is non-linear, all GWP values are affected.

2: Since 1855.

This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of K < sup > sep </ sup >, of degree > 1.

Since B < sub > n </ sub >= 0 for all odd n > 1, and many formulas only involve even-index Bernoulli numbers, some authors write B < sub > n </ sub > instead of B < sub > 2n </ sub >.

Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.

Since at this stress the slope of the material's stress-strain curve, E < sub > t </ sub > ( called the tangent modulus ), is smaller than that below the proportional limit, the critical load at inelastic buckling is reduced.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since < tt > ns1 </ tt > is contained in < tt > example. org </ tt >, this requires resolving < tt > example. org </ tt > first, which presents a circular dependency.

Since every equivalence relation over X corresponds to a partition of X, and vice versa, the number of possible equivalence relations on X equals the number of distinct partitions of X, which is the nth Bell number B < sub > n </ sub >:

Since 6 has 2 factors ( 2 and 3 ) it should have 2 < sup > 2 </ sup > idempotents.

Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ( other than 1 ) or other function of a variable, equations involving terms such as xy, x < sup > 2 </ sup >, y < sup > 1 / 3 </ sup >, and sin ( x ) are nonlinear.

Since p is prime q − 1 must be a multiple of p. Of course, if the number m = < sup >( q − 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.

Since < ƒ, ƒ > ≥ 0, φ ( f * f ) ≥ 0 for all ƒ in L < sup > 2 </ sup >( m ), where ƒ * is pointwise conjugate of ƒ.

Since any vector v is a linear combination ∑ v < sup > j </ sup > e < sub > j </ sub > of its components, df is uniquely determined by df < sub > p </ sub >( e < sub > j </ sub >) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x < sup > 1 </ sup >, x < sup > 2 </ sup >,... x < sup > n </ sup > are themselves functions on U, and so define differential 1-forms dx < sup > 1 </ sup >, dx < sup > 2 </ sup >, ..., dx < sup > n </ sup >.

Since the heights of all the y < sub > i </ sub > are strictly less than that of x, we can apply the inductive hypothesis to them to get size ( y < sub > i </ sub >) ≥ F < sub > c < sub > i </ sub >+ 2 </ sub > ≥ F < sub >( i − 2 )+ 2 </ sub > = F < sub > i </ sub >.

Since the analysis must typically go beyond two-loop perturbation theory, the definition of the running coupling α < sub > TC </ sub >( μ ), it ’ s fixed point value α < sub > IR </ sub >, and the strength α < sub > χ SB </ sub > necessary for chiral symmetry breaking depend on the particular renormalization scheme adopted.

Since the images φ < sub > n </ sub >( e < sub > k </ sub >( X < sub > 1 </ sub >,…, X < sub > n </ sub >)) = e < sub > k </ sub >( X < sub > 1 </ sub >,…, X < sub > n + 1 </ sub >) for k = 1 ,…, n are still algebraically independent over R, the homomorphism φ < sub > n </ sub > is injective and can be viewed as a ( somewhat unusual ) inclusion of rings.

Since ω and g are nondegenerate, each induces a bundle isomorphism TM → T * M, where the first map, denoted φ < sub > ω </ sub >, is given by the interior product φ < sub > ω </ sub >( u ) = < sub > u </ sub > ω = ω ( u, •) and the other, denoted φ < sub > g </ sub >, is given by the analogous operation for g. With this understood, the three structures ( g, ω, J ) form a compatible triple when each structure can be specified by the two others as follows:

Since the set of complex numbers λ with | λ |< sup > 2 </ sup > = 1 form the unit circle in the complex plane, it follows that for each point m in S < sup > 2 </ sup >, the inverse image p < sup >− 1 </ sup >( m ) is a circle, i. e., p < sup >− 1 </ sup > m ≅ S < sup > 1 </ sup >.

Since BGL ( R )< sup >+</ sup > is path connected and K < sub > 0 </ sub >( R ) discrete, this definition doesn't differ in higher degrees and also holds for n = 0.

Since Out ( N ) = 1 and N has trivial center the homomorphism φ is surjective and has an obvious section given by the inclusion of N in G. The kernel of φ is the centralizer C < sub > G </ sub >( N ) of N in G, and so G is at least a semidirect product C < sub > G </ sub >( N ) ⋊ N, but the action of N on C < sub > G </ sub >( N ) is trivial, and so the product is direct.

Since charge parity is preserved, annihilation of these states in photons ( η < sub > C </ sub >( γ ) = − 1 ) must be:

#" Since U Been Gone " < small >( Enhanced CD video )-3: 10

Since ƒ < sup >′</ sup >( x ) ≠ 0 for x ≠ 0, the only critical point of ƒ is x = 0.

Since universal codes are simpler and faster to encode and decode than Huffman codes ( which is, in turn, simpler and faster than arithmetic encoding ), the universal code would be preferable in cases where D < sub > KL </ sub >( q || p ) is sufficiently small.