Here the expression has the value 1 if m = 0 and 0 otherwise ( Iverson bracket ).

Here, we have < tt >( λx. xx )( λx. xx ) → ( xx ):= λx. xx = ( x := λx. xx )( x := λx. xx ) = ( λx. xx )( λx. xx )</ tt >.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

( Here β < sub > N </ sub > = β /( I / aB ) is the normalized beta.

Here Mavrodes ' worry about X = " to make something its maker cannot lift " will no longer be a problem because " God does X " is not logically consistent.

< center >< span style = " font-variant: small-caps "> Here were buried the remains of

Here for real a, b and c, if Δ > 0, the polynomial has two real roots, if Δ = 0, the polynomial has one real root, and if Δ < 0, the polynomial has no real roots.

Here are the concrete instances of these equations for n = 2 and n = 3:

Here only the digit 9 is replaced by the digit 0, such that identities like 1. 000 ... = 0. 999 ... can spoil the result.

Here orthogonality is important not only for reducing A < sup > T </ sup > A = ( R < sup > T </ sup > Q < sup > T </ sup >) QR to R < sup > T </ sup > R, but also for allowing solution without magnifying numerical problems.

Here a and l denote radius and length of the wire, and Y is a constant that depends on the distribution of the current in the wire: Y =

Here F = J + I, where I is the nuclear spin.

Here the substitution function ( v < sub > 1 </ sub >,..., v < sub > n </ sub >) =

Here the solution was assumed to have the special form Y ( θ, φ ) = Θ ( θ ) Φ ( φ ).

Here the polynomial z < sup > 2 </ sup > − 1 vanishes when z =

Here the sets A and B that contain a and b are calculated recursively, with n = 1 and n = 2 being the base case.

Here H = Hubble constant, ρ

: Here AB = 0, BA = B.

Here, g and g ′ are SU ( 2 ) and U ( 1 ) gauge couplings and tanθ < sub > W </ sub > =

Here the sign of the distances is taken negative if and only if the line segment DX ( X = F, G, H ) lies completely outside the triangle.

for any torsion sheaf F. Here j is any open immersion of X into a scheme Y with a proper morphism g to S ( with f = gj ), and as before the definition does not depend on the choice of j and Y. Cohomology with compact support is the special case of this with S a point.

Here the pulmonary vein, as in type 2,, is noted to draw away from the bronchus, and to follow a more direct, independent course to the hilum ( figs. 23, 24 ).

Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Here Acts 12: 21-23 is largely parallel to Antiquities 19. 8. 2 ; ( 2 ) the cause of the Egyptian pseudo-prophet in Acts 21: 37f and in Josephus ( War 2. 13. 5 ; Antiquities 20. 8. 6 ); ( 3 ) the curious resemblance as to the order in which Theudas and Judas of Galilee are referred to in both ( Acts 5: 36f ; Antiquities 20. 5. 1 ).

Here I < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.

Here he defines his genre against a ( probably fictional ) critic ( in the latter half of 2. 77 ):

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Here, according to an allegorical parable, " The Choice of Heracles ", invented by the sophist Prodicus ( c. 400 BC ) and reported in Xenophon's Memorabilia 2. 1. 21-34, he was visited by two nymphs — Pleasure and Virtue — who offered him a choice between a pleasant and easy life or a severe but glorious life: he chose the latter.

Here we have the composite number 90 made up of one atom of the prime number 2, two atoms of the prime number 3 and one atom of the prime number 5.

# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.

br: 2 Here

Here, there are four energy levels, energies E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, E < sub > 4 </ sub >, and populations N < sub > 1 </ sub >, N < sub > 2 </ sub >, N < sub > 3 </ sub >, N < sub > 4 </ sub >, respectively.

Here ends what Wittgenstein deems to be the relevant points of his metaphysical view and he begins in 2. 1 to use said view to support his Picture Theory of Language.

Here the notion of convergence corresponds to the norm on L < sup > 2 </ sup >.

Here, the gain and effective area of antenna 2 are fixed, because the orientation of this antenna is fixed with respect to the first.

With a gross of $ 30. 5 million equating to earnings of $ 12. 2 million, From Here to Eternity was not only one of the top grossing films of 1953, but one of the ten highest-grossing films of the decade.

Here are the remains of a Roman town, belonging to the 1st and 2nd centuries, extending over an area of some 600 by 500 meters (( 2, 000 by 1, 600 ft ), and consisting of fine buildings along the lagoons, including a large open piscina or basin, surrounded by a double portico, while farther inland are several very large and well-preserved water-reservoirs, supplied by an aqueduct of which traces may still be seen.

Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

"( Here They Come ) From All Over the World " b / w " Freeway Flyer " ( Liberty 55766 )-BB No. 56, CB No. 50-( JB )

Here C < sub > b </ sub >( X ) denotes the C *- algebra of all continuous bounded functions on X with sup-norm.

*" I Can't Take It " b / w " Here in the Night ( live )" ( 7 " single ) ( 1985 )

Here, α, β, and γ are the angles at the center of the sphere subtended by the three arcs of the spherical surface triangle a, b, and c, respectively.

Here he met William Tyndale, under whose influence he abandoned the Roman Catholic faith, and married Antwerp native Adriana de Weyden ( b. 1522, anglicised to Adrana Pratt in 1552 ) in 1537.

Here we have another unwanted error ε < sub > b </ sub > with value:

Here by an arc from x to y we mean the image in M of a topological embedding f from an interval to M such that f ( a )= x and f ( b )= y.

The axiom can be stated as follows: For any nonempty set X and any entire binary relation R on X, there is a sequence ( x < sub > n </ sub >) in X such that x < sub > n </ sub > R < nowiki ></ nowiki > x < sub > n + 1 </ sub > for each n in N. ( Here an entire binary relation on X is one such that for each a in X there is a b in X such that aRb.

Here i is the van't Hoff factor as above, K < sub > b </ sub > is the ebullioscopic constant of the solvent ( equal to 0. 512 ° C kg / mol for water ), and m is the molality of the solution.

Here at + b is the trend line, so the sum of squared deviations from the trend line is what is being minimised.

* Bingham fluid model ( for τ ≥ b ) where Here " a " and " b " are constants, with " b " being the minimum shear stress needed to cause flow, known as yield stress.

Here denotes the norm on L < sup > 1 </ sup >( a, b ).

Here, a, b, and c are the angles at the centre of the sphere subtended by the three sides of the triangle, and α, β, and γ are the angles between the sides, where angle α is opposite the side which subtends angle a, and so forth.

Here the initial letter q-represents the PIE labiovelar consonant */ gʷ /, transformed in later Greek into / b /.

* " Weirdo Libido " b / w " Here With My Love "-Virgin Records ( 1986 )

* " Here Comes the Night " ( edit ) b / w " Baby Blue " ( Brother / Caribou ZS9 9026 ), February 19, 1979 US # 44 ; UK # 37

Here, is the similarity of characters a and b. It uses a linear gap penalty, here called d.

Here v ( the number of elements of X, called points ), b ( the number of blocks ), k, r, and λ are the parameters of the design.

* " Leaving Here " ( Holland – Dozier – Holland ) b / w " Next in Line " ( Ronnie Wood ) ( April 1965, Decca F 12140 ) ( Producer: Franklyn Boyd )-UK No. 45