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Here and X
Here we define the distance in B ( X, M ) in terms of the distance in M as
Here, X is a set, and Σ is a sigma-algebra on X, so that the pair ( X, Σ ) is a measurable space.
Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.
Here X represents the space of messages transmitted, and Y the space of messages received during a unit time over our channel.
Notable story arcs of this decade are " Revolution " ( 2000 ), " Eve of Destruction ," " E Is For Extinction " ( 2001 ), " Planet X ," " Here Comes Tomorrow ," " Gifted ," ( 2004 ) X-Men: Phoenix-Endsong, " House of M ," " Decimation " ( 2005 ), Deadly Genesis ( 2005 – 2006 ), " Endangered Species " ( 2007 ), " Messiah Complex " ( 2007 – 2008 ), " Divided We Stand " ( 2008 ), " Manifest Destiny " ( 2008 – 2009 ), X-Infernus, " Messiah War ," " Utopia ," " Nation X " and " Necrosha " ( 2009 ).
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.
Here C < sub > b </ sub >( X ) denotes the C *- algebra of all continuous bounded functions on X with sup-norm.
(" Here lies very high and powerful excellent prince Charles X by name king, by the grace of God, of France and of Navarre ")
The American Journal of Human Genetics released an article in 2007 stating " Here we show, by using 86 complete mitochondrial genomes, that all Indigenous American haplogroups, including Haplogroup X ( mtDNA ), were part of a single founding population.
Here A < sub > n </ sub > is the free abelian group or module whose generators are the n-dimensional oriented simplexes of X.
Here one starts with some covariant additive functor F and some module X.
In 1999, DMX released his best-selling album ... And Then There Was X, which featured the hit single " Party Up ( Up in Here )".
Here Q < sub > Y | X </ sub >( y | x ), sometimes called a test channel, is the conditional probability density function ( PDF ) of the communication channel output ( compressed signal ) Y for a given input ( original signal ) X, and I < sub > Q </ sub >( Y ; X ) is the mutual information between Y and X defined as
Here, each vector Y < sub > j </ sub > of the f ' basis is a linear combination of the vectors X < sub > i </ sub > of the f basis, so that
Here Var ( X ) is the variance of X, defined as:

Here and <
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 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 k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.
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 >.
The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:
Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion
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 the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.
Here, R < sub > ij </ sub > is the Ricci tensor.
# 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.

Here and i
In December 2004 Joe Pasquale, winner of the fourth series of ITV's I'm a Celebrity ... Get Me Out of Here !, became well known for his frequent use of the term " Jacobs ", for Jacob's Crackers, a rhyming slang term for knackers i. e. testicles.
Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).
Here, indexes i, j are related to the various components and not to the space coordinates.
Here, sgn ( p ) is the signature of each permutation ( i. e. + 1 if p is composed of an even number of transpositions, and − 1 if odd.
Here the most regular of irregularities, i. e., archaisms, will be delineated:
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, an " event " is a set of zero or more outcomes, i. e., a subset of the sample space.
( Here, e is the base of the natural logarithm, about 2. 71828 ..., and i is the imaginary unit, a square root of − 1.
Here the generalized coordinates q < sub > i </ sub > for i
A decade-and-a-half later, the reggae-rock band 311's hit single " I'll Be Here Awhile " " borrowed " several lines from " The Lust ..." ( i. e., " And if a person, place, or thing can deliver / I will quiver with delight ").
Here and are the i < sup > th </ sup > columns of the corresponding SVD matrices, are the ordered singular values, and each is separable.
Here Saadia controverts the Mutakallamin, who considered the soul an " accident " arad ( compare Guide for the Perplexed i. 74 ), and employs the following one of their premises to justify his position: " Only a substance can be the substratum of an accident " ( that is, of a non-essential property of things ).
Here, is density, u, v, and are the components of wind velocity, and is the 2-dimensional ( i. e. horizontal-component-only ) del.
Here Saadia controverts the Mutakallamin, who considered the soul an " accident " arad ( compare Guide for the Perplexed i. 74 ), and employs the following one of their premises to justify his position: " Only a substance can be the substratum of an accident " ( that is, of a non-essential property of things ).
Here there is the idea that God's heritage ( the created world ) is largely under the dominion of evil – i. e., it is " shared with Azazel " ( Abr.
Here is a known vector, and is an unknown vector of numbers x < sub > i </ sub > yet to be determined.
Here if the null hypothesis weren't rejected ( i. e. there is no reason to reject the hypothesis that A is at least as good as B ), the conclusion would be that treatment A should continue to be used.
( Here< sub > i </ sub > means ℵ < sub > i </ sub > in the full universe, not the constructible universe.
( Here α and β are real and i represents the imaginary unit.

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